012167150 x Physics Auro

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Rayed auroral band photographed at College, Alaska. Courtesy Prof. V. P. Hessler.

Physics of the

Aurora and Airglow

Interndional Geophysics Series

Edited by

J. VAN MIEGHEM Royal Belgian Meteorological Institute

Uccle, Belgium

Volume 1 . BENO GUTENBERG. Physics of the Earth’s Interior. 1959

JOSEPH W. CHAMBERLAIN. Physics of the Aurora and Airglow. 1961

Volume 2.

Physics of the

Aurora and AirgIow

Joseph W. Chamberlain Yerkes Observafory

University of Chicago Williams Bay, Wisconsin

@ Academic Press New York and London 1961

COPYRIGHT 0 1961, BY ACADEMIC PRESS INC.

ALL RIGHTS RESERVED

NO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM BY PHOTOSTAT, MICROFILM, OR ANY OTHER MEANS,

WITHOUT WRITTEN PERMISSION FROM T H E PUBLISHERS.

ACADEMIC PRESS INC. 111 FIFTH AVENUE

NEW YORK 3, N. Y.

United Kingdom Edition

Published by ACADEMIC PRESS INC. (LONDON) LTD.

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Library of Congress Catalog Card Number 61-14136

PRINTED IN T H E UNITED STATES O F AMERICA

To

J O Y , DAVID, and JEFFREY

and the

future they represent


Preface

Physics of the aurora and airglow is a diversified subject, and this characteristic is, I think, the secret of its charm. But it is growing up in an age when physicists must necessarily specialize in narrow fields of interest. The advantage gained by a scientist applying his particular competence to the aurora or airglow is then partly offset by his lack of familiarity with other areas of the topic. The field is so broad that it is most difficult for him to learn the whole subject while still pursuing and keeping abreast in his own specialty.

Now you know my main incentive for writing this book: I wanted to have some familiarity with all aspects of aurora and airglow, and I felt that many others must find themselves in a similar situation.

The bibliography, containing over 1600 references cited in the text,* is intended to be an exhaustive list of contributions that are currently significant and readily accessible; it contains as well the principal historical works. With very few exceptions, I have been reluctant to reference abstracts of papers presented at meetings, articles in obscure journals, and those printed privately, such as theses and the technical reports of industrial firms, universities, and government laboratories. Almost all the listed papers and books will be available at a good university library. I have tried to make the referencing complete up to January 1960. A few later articles are included. These are mostly ones that I had seen in manuscript, although a handful of others that seemed especially pertinent were added in the final stages of revision.

I have elaborated or abbreviated the discussion of some topics according to whether they had already been treated adequately in other books. This explains, for example, my extensive treatment of the analysis of twilight observations for emission heights, but the absence of a detailed account on the reduction of auroral parallactic observations.

Although I hope I have not overemphasized my own special research interests, I have used the book to develop several topics in a fairly complete manner and to synthesize a number of more fragmentary investigations that I had published previously with various associates. These topics include the theory of hydrogen emission in aurora, reso-

* Since the references are cited by author and date, the longer lists of citations have been relegated to footnotes, where they lie glaring at the discussion above.

ix

X PREFACE

nance scattering by atmospheric sodium, the excitation of the oxygen red lines in the airglow, and an atlas of the auroral spectrum. The latter was compiled with the collaboration of Dr. Lloyd Wallace. Incidentally, a special effort was made to summarize the radio work on the aurora so that it would be intelligible to one who, like myself, has had little training in radio physics or engineering and who often has difficulty reading the original papers.

I have not assumed any particular familiarity on the part of the reader with problems of the upper atmosphere ; however, I have supposed throughout that he is acquainted with the elementary aspects of atomic and molecular structure and with the principles of electromagnetic theory. In the hope that the book may be useful in graduate courses, I have appended a few problems, some practical and some theoretical, after each chapter.

J. W. C.

Williams Bay, Wisconsin April 1960

xi

Acknowledgments

Several of my colleagues have been generous in devoting their time to critical readings of parts of the first draft. Their suggestions were most helpful. My thanks to Professor D. R. Bates, F. R. S., Queens University of Belfast; Prof. P. A. Forsyth and Prof. D. M. Hunten, University of Saskatchewan ; Prof. B. Nichols, Cornell University; Dr. F. E. Roach, National Bureau of Standards, Boulder; and especially Dr. L. Wallace, Yerkes Observatory, who read and constructively criticized the entire volume with Jobian patience. Professor V. P. Hessler, University of Alaska, graciously allowed me the privilege of publishing some of his artistic auroral photographs.

The preparation of some of the material in this book was supported in part by the Geophysics Research Directorate of the Air Force Cambridge Research Laboratories, Air Force Research Division, under Contract AF 19(604)-3044 with the University of Chicago.

For assistance with calculations and the preparation of tables and figures I am indebted to Dr. J. C. Brandt, Mr. A. M. Heiser, Mrs. Beverly Negaard, Mrs. Vidya Pesch, Mr. T. H. Rau, Miss Elaine Sandberg, Mr. C. A. Smith, Mrs. Pamela Stuefen, Mr. J. W. Tapscott, and Mrs. Frances Vandervoort.

Finally, I express sincerest appreciation to my able secretary, Miss Helene Thorson, who has suffered with my handwriting and a thousand other difficulties through nearly three years. Without her conscientious dedication to the whole project, I fear it would never have seen the light of day.


Contents

Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 1

Radiation in Spectral Lines

1.1. Temperature and Thermal Equilibrium . . . . . . . . . . . . 1.1.1. Maxwellian Distribution of Velocities. 1.1.2. Spectroscopic Nomencla- ture. 1.1.3. Boltzmann Excitation Equation. 1.1.4. Doppler Line Broadening

1.2. The Classical Theory of Spectral Lines . . . . . . . . . . . . I:2.1. Classical Theory of Line Emission. 1.2.2. Classical Theory of Line Absorption.

1.3. Quantum Concepts of Spectral Lines . . . . . . . . . . . . . 1.3.1. Transition Probabilities. 1.3.2. Line Strengths. 1.3.3. f-values. 1.3.4. Line Profiles.

1.4. Molecular Bands . . . . . . . . . . . . . . . . . . . . . . 1.4.1. Intensities of Electronic and Vibrational Bands. 1.4.2. Intensities of Rotational Lines.

1.5. Excitation and Ionization Processes . . . . . . . . . . . . . . I .5.1. Radiative Excitation, Ionization, and Recombination. 1.5.2. Particle Collisions and Photochemical Reactions.

Chapter 2

Scattering of Radiation in Finite Atmospheres

2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1. Transfer Problems in the Physics of the Atmosphere. 2.1.2. Definitions and Terminology.

2.2. Equation of Radiative Transfer . . . . . . . . . . . . . . . . 2.3. Applications of the Transfer Equation to Photometry . . . . . .

2.3.1. Photometric Observations of Aurorae. 2.3.2. Photometric Observa- tions of the Airglow.

The X - and Y-Functions in Problems of Radiative Transfer . . . 2.4.1. Formulation of the Transfer Problem with the Principles of Invariance. 2.4.2. Solution for the S- and T-functions.

2.4.

... x111

ix xi

13

20

27

34

38

41

49

xiv CONTENTS

2.5. Correction of Photometric Observations of the Airglow for Tropo-

2.5.2. Exact Solution for a Plane-Parallel Emitting Layer and Isotropic Scattering. 2.5.2. Solution with Rayleigh Scattering.

spheric Scattering. . . . . . . . . . . . . . . . . . . . 55

Chapter 3

Magnetic Fields, Charged Particles, and the Upper Atmosphere

3.1.

3.2.

3.3.

3.4.

3.5.

4.1.

4.2.

4.3.

5.1.

The Geomagnetic Field . . . . . . . . . . . . . . . . . . . 3.1.1. The Main Field. 3.1.2. Magnetic Variations.

Motions of Charged Particles in Electric and Magnetic Fields . . 3.2.2. Uniform Magnetic Field. 3.2.2. Uniform Electric and Magnetic Fields. 3.2.3. Inhomogeneous Magnetic Field. 3.2.4. Constancy of the Magnetic Moment: Adiabatic Invariance.

Propagation of Electromagnetic Waves in an Ionized Atmosphere . 3.3.1. Maxwell’s Equations. 3.3.2. Propagation in the Absence of a Magnetic Field.

The Ionosphere . . . . . . . . . . . . . . . . . . . . . . 3.4.1. A Chapman Layer. 3.4.2. Recombination Processes and Ion Forma- tion in the Atmosphere.

Model Atmospheres . . . . . . . . . . . . . . . . . . . . 3.5.1. Basic Theory of Atmospheric Structure. 3.5.2. Relative Abundances of the Major Constituents. 3.5.3. Temperature Structure of the Atmosphere.

Chapter 4

Occurrence of Aurorae in Space and Time

Geographic Distribution and Periodic Variations

Characteristics of Auroral Displays . . . . . . . . . . . . . .

. . . . . . . . 4.1.1. Recording Auroral Occurrence and Appearance. 4.1.2. Dependence on Geomagnetic Latitude: The Auroral Zones. 4.1.3. Periodic Variations.

4.2.2. Appearance. 4.2.2. Height and Vertical Extent. 4.2.3. Orientations in Space. 4.2.4. Auroral Activity. 4.2.5. Synoptic View of Aurora.

Aurorae and Related Phenomena . . . . . . . . . . . . . . . 4.3.1. Geomagnetic Activity and Earth Currents. 4.3.2. Auroral Proton Bombardment. 4.3.3. X-Radiation. 4.3.4. Ionospheric Disturbances. 4.3.5. Radio Emission. 4.3.6. Cosmic Rays. 4.3.7. Miscellaneous Terrestrial Effects Related to Aurora. 4.3.8. Solar Phenomena.

Chapter 5

Auroral Spectroscopy and Photometry

Spectral Identifications . . . . . . . . . . . . . . . . . . . 5.1.1. An Atlas of the Auroral Spectrum. 5.2.2. Forbidden Atomic Lines. 5.2.3. Permitted Atomic Lines. 5.1.4. Molecular Band Systems.

63

73

80

84

89

100

116

138

151

CONTENTS xv

5.2.

6.1.

6.2.

7.1.

7.2.

7.3.

7.4.

8.1.

Spectral Photometry of Aurora . . . . . . . . . . . . . . . . 5.2.1. Absolute Brightness of Spectral Features. 5.2.2. Latitude and Height Variations in the Composition of the Spectrum. 5.2.3. Spectral Variations with Type of Aurora; Variations in the Hydrogen Emission. 5.2.4. Rapid Fluctuations and Intensity Correlations. 5.2.5. Polarization of Spectral Lines. 5.2.6. Hydrogen-Line Profiles. 5.2.7. Rotational and Doppler Tem- peratures. 5.2.8. Vibrational Distributions.

Chapter 6

The Radio-Aurora

Observed Characteristics . . . . . . . . . . . . . . . . . . 6.1.1. Introduction: The Distinction between Aurora and Radio-Aurora. 6.1.2. Types of Radar and Bistatic Echoes. 6.1.3. Location of Radio-Aurorae. 6.1.4. Periodic Variations. 6.1.5. Apparent Motions of Auroral Ionization. 6.1.6. Polarization. 6.1.7. Aspect Sensitivity and Echo Strength. 6.1.8. Rela- tion to Other Phenomena.

Theory of Auroral Reflections . . . . . . . . . . . . . . . . 6.2.1. Geometry of Reflections. 6.2.2. Critical and Partial Reflections from a Large Surface. 6.2.3. Scattering by Small-Scale Inhomogeneities in the Ionization. 6.2.4. Comparison of Reflection Mechanisms.

Chapter 7

Physical Processes in the Auroral Atmosphere

Proton Bombardment . . . . . . . . . . . . . . . 7.1.1. Statistical Equilibrium for Hydrogen. 7.1.2. The Role of Protons in Producing Aurora. 7.1.3. Hydrogen-Line Profiles and the Spectrum of Proton Energies.

Electron Bombardment . . . . . . . . . . . . . . . 7.2.1. BremsstrahlungX-Rays: Detection ofprimary Electrons. 7.2.2. Cerenkov Radiation at Radio Frequencies. 7.2.3. Gyro Radiation. 7.2.4. Properties of Primary Electrons and Their Energy Deposition in the Atmosphere.

Atmospheric Electrons . . . . . . . . . . . . . . . . . 7.3.1. Secondary Electrons from Particle Bombardment. 7.3.2. Other Mechanisms for Producing Energetic Atmospheric Electrons. 7.3.3. Radio Emission.

Theory of the Auroral Spectrum . . . . . . . . . . . . . . 7.4.1. Fast Particle Impact. 7.4.2. Thermal Collisions. 7.4.3. Radiative Excitation.

Chapter 8

Auroral Particles in Space

Interplanetary Space . . . . . . . . . . . . . . . . . . . . 8.1.1. Properties of the Interplanetary Gas. 8.1.2. Transmission of Geo- physical Disturbances and their Interaction with the Terrestrial Field.

196

217

232

244

269

292

308

321

xvi CONTENTS

8.2. Auroral Particles in the Geomagnetic Field . . . . . . . . . . 8.2.1. Detection and Artificial Production of Charged Particles. 8.2.2. Ques- tions Concerning the Geographic Location of Particle Bombardment. 8.2.3. Questions Concerning the Energy Spectra and Angular Distribution of Auroral Particles.

Chapter 9

The Airglow Spectrum

9.1. Nightglow . . . . . . . . . . . . . . . . . . . . . . . . 9.1.1. On the Distinction Between the Airglow and Aurora. 9.1.2. Historical Summary of Early Work. 9.1.3. The Ultraviolet and Blue Spectrum. 9.1.4. The Green, Red, and Infrared Spectrum.

9.2. Twilight and Day Airglow . . . . . . . . . . . . . . . . . 9.2.1. N,+ First Negative Bands. 9.2.2. Na D Lines. 9.2.3. [OI],, Red Lines. 9.2.4. Other Twilight Emissions. 9.2.5. The Dayglow.

Chapter 10

Analysis of Twilight Observations for Emission Heights

10.1. Apparent Heights z,: The Shadow of the Solid Earth . . . . . . 10.1.1. General Solutions for the Apparent Height. 10.1.2. Solutions for the Vertical Plane Through the Sun. 10.1.3. Approximate Solution for Horizon Observations. 10.1.4. Computation of the Angle of Solar Depression and Solar Azimuth. 10.1.5. Time of Sunset at a Particular Height and Direction from the Observer.

10.2. Height Measurements with Atmospheric Screening . . . . . . . 10.2.1. Actual Shadow Height z,,, for a Known Screening Height ho. 10.2.2. The Zenith-Horizon Method of Height Determinations. 10.2.3. Cal- culation of Transmission Function and Screening Height.

10.3. Height and Vertical Distribution of Observed Emissions . . . . . 10.3.1. Ionized Nitrogen Bands. 10.3.2. Sodium D Lines. 10.3.3. Oxygen Red Lines.

Chapter 11

Theory of the Twilight and Day Airglow

1 1.1. Resonance Scattering and Fluorescence for an Optically Thin Layer 11.1.1. Scattered Intensity with Allowance for Deactivation. 11.1.2. Polar- ization of Resonance Radiation.

11.2. Excitation of Nz+ First Negative Bands . . . . . . . . . . . . 11.2.1. Excitation Mechanism. 11.2.2. The Production of N,+ in the Ionosphere. 11.2.3. Rotational Structure.

326

345

376

394

404

41 3

422

437

CONTENTS xvii

11.3. Photon Scattering by Atmospheric Sodium . . . . . . . . . . . 11.3.1. Introduction: The Physical Theory and Approximations. 11.3.2. Scat- tered Intensity of a Resonance Line from the Theory of Radiative Transfer for a Plane-Parallel Atmosphere. 11.3.3. Twilight Airglow: The Na Abun- dance and Seasonal Variation. 11.3.4. Day Airglow.

11.4. Photochemistry and Ionization of Atmospheric Sodium . . . . . 11.4.1. Photochemistry. 11.4.2. Ionization. 11.4.3. Sodium Ejected from Rockets.

11.5. Theory of the Oxygen Red Lines . . . . . . . . . . . . . . . 11.5.1. Resonance Scattering and Ultraviolet Dissociation. 11.5.2. Collisional Deactivation. 11.5.3. Dissociative Recombination. 11.5.4. Dayglow in the Red Lines.

11.6. Excitation of Other Emissions . . . . . . . . . . 11.6.1. The [NI],, Lines. 11.6.2. 0, Infrared Atmospheric Band. 11.6.3. Ca I1 H and K Lines. 11.6.4. Li I Resonance Lines. 11.6.5. Additional Emissions to be Expected.

Chapter 12

Spectral Photometry of the Nightglow

12.1. Methods of Height Determinations . . . . . . . . . . . . . . 12.1.1. Fundamentals of the van Rhijn Method. 12.1.2. Results of the van Rhijn Method. 12.1.3. Difficulties with the van Rhijn Method. 12.1.4. Height Measurements by Triangulation. 12.1.5. Height Measure- ments by Rockets. 12.1.6. Indirect Means of Deriving Heights.

12.2. Spectroscopic Temperatures . . . . . . . . . . . . . . . . .

12.3. Intensities, Polarization, and Geographic and Time Variations . . 12.3.1. Absolute Intensities and Polarization. 12.3.2. Geographic and Periodic Variations of the Intensities. 12.3.3. Spectral Correlations. 12.3.4. Structure and Motion of Excitation Patterns.

12.2.1. Rotational Temperatures. 12.2.2. Doppler Temperatures.

Chapter 13

Excitation of the Nightglow

13.1. Introduction: Mechanisms of Nightglow Excitation . . . 13.2. Excitation by Recombination in the Ionosphere . . . . . . . . .

13.2. I . Review of Red-Line Excitation. 13.2.2. Recombination and Diffu- sion of Ions in the Nighttime F Layer. 13.2.3. Time Variations in the Red Lines Arising from Dissociative Recombination. 13.2.4. Excitation of the [NI],, Lines.

13.3. Excitation by Particle Collisions . . . . . . . . . . . . . . . 13.3.1. Thermal Electrons. 13.3.2. Extraterrestrial Particles and Other Nonthermal Collisions. 13.3.3. Atomic and Molecular Thermal Collisions.

444

467

473

479

486

498

503

521

523

533

xviii CONTENTS

13.4. Photochemical Reactions in an Oxygen-Nitrogen Atmosphere . . . 13.4. I . Excitation of 0, Band Systems. 13.4.2. Photochemical Excitation of [OI]. 13.4.3. The Continuum and Unidentified Blue-Green Bands. 13.4.4. Artificially Induced Airglow. 13.4.5. Regular Variations in Intensity. 13.4.6. Turbulence and Green-Line Patchiness.

13.5. Excitation of Emissions from Minor Constituents . . . . . . . . 13.5.1. Photochemical Origin of the Meinel OH Bands. 13.5.2. Hydrogen Lines in the Night-Sky Spectrum. 13.5.3. Photochemical Excitation of Sodium D Lines.

Appendixes

APPENDIX I. A Table of Physical Constants . . . . APPENDIX 11. The Rayleigh: A Photometric Unit for the Aurora and

Airglow . . . . . . . . . . . . . . . . . . . . . . . . APPENDIX 111. A Short List of Airglow-Aurora Observing Stations . . .

APPENDIX IV. Temperature, Density, and Composition of the Upper Atmosphere . . . . . . . . . . . . . . . . . . . . . .

APPENDIX V. The Ionosphere . . . . . . . . . . . . . . . . . . . APPENDIX VI. Forbidden Atomic Oxygen and Nitrogen Lines . . . . . APPENDIX VII. Glossary of Symbols . . . . . . . . . . . . . . . .

APPENDIX VIII. A List of Books and Review Articles on the Aurora and Airglow . . . . . . . . . . . . . . . . . . . . . .

BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . AUTHOR INDEX . . . . . . . . . . . . . . . . . . . . . . . . .

537

553

567

569

572

574

577

579

582

590

593

67 1

SUBJECT INDEX . . . . . . . . . . . . . . . . . . . . . . . . . 684

Chapter 1. Radiation in Spectral Lines

The material presented in this chapter is fundamental to spectroscopic and photometric analyses of radiation from the upper atmosphere, and formulae given here will be referred to frequently in later chapters. We assume a basic knowledge of atomic and molecular structure.

While some derivations are presented and others are indicated, many results and equations are simply quoted without proof. Hence the chapter is primarily a summary of the pertinent aspects of spectral emission and absorption.

1.1. Temperature and Thermal Equilibrium

Many of the mathematical relations used in the theory of excitation and line radiation are derived on the basis of thermal equilibrium, for which the temperature is everywhere constant, there are no mass motions, and substances are mixed in such a way that there is no tendency for diffusion or other mass motions to arise [Slater, 1939~1. Some of these formulae, such as the relations between the Einstein coefficients (cf. Section 1.3) are valid under any conditions, even though the derivation assumes thermal equilibrium for simplicity. In other cases, such as the Maxwell-Boltzmann distribution law and its applications, departures in a real system from thermal equilibrium can alter the results profoundly.

Certainly the upper atmosphere is far from thermal equilibrium. Not only is there a large variation of temperature with height, but the atmosphere receives sunlight characteristic of some temperature (depending considerably on the spectral range in question) that is drastically different from the temperature in the atmosphere.

In any particular problem we must decide whether these departures from idealized conditions are likely to be significant for our purposes. That any radiation can escape from the upper atmosphere is a direct consequence of the departures from thermal equilibrium. Hence, in discussing the populations of atomic and molecular levels, it is always necessary to examine the physical processes that are primarily responsible for the distribution of populations over the various levels in question. Erroneous interpretations of airglow and auroral spectra can result when conditions of thermal equilibrium are improperly assumed.

1

2 1. RADIATION I N SPECTRAL LINES

The conditions for statistical equilibrium (wherein the population of particles in a particular level remains constant) are not as stringent as those for thermal equilibrium (in which detailed balancing exists- cf. Section 1.3.1). When the lifetimes of the excited levels are short compared with the duration of the excitation, then these levels may be treated through considerations of statistical equilibrium. On the other hand, if the excitation rate changes during the lifetime of the excited state (as with the forbidden lines of oxygen in active aurorae or the “I] line in twilight) one must consider in detail the time dependence.

1 .I .I. Maxwellian Distribution of Velocities

According to the Maxwell-Boltzmann law (cf. Slater [1939a]) describing the distribution of particles over states with energy E < , the probability of a particle being in the ith state is

i

Considering fox the moment only the translational energy of an atom or molecule, we may replace the summation with an integral and write

ecMvzlzkT dv, dv, dv, .fx,, dvx dv, dvz = sss e-MuzlZkT dv, dv, dv, ’

which is the fraction of particles of mass M with velocity components between v x and v x + dv,, v, and v, + dv,, and v, and v, + dv,. Writing Eq. (1.2) in polar coordinates and integrating over the angular components, we find the fraction of particles with scalar velocities between v and v + dv:

M 312

f(v)dv = 477 ~ v2e-Mva12kTdv. (1.3) ( 2rkT

This is Maxwell’s distribution law; it is illustrated in Fig. 1.1 for atomic oxygen for three values of T.

From the derivative of Eq. (1.3) it follows that the most probable velocity is

u=( ,z , j 2kT lI2 .

The mean and root-mean-square velocities are

and

- v = - U = 1.128 U 6

112 (2y2 = (;) u = 1.22 u

1.1. TEMPERATURE AND THERMAL EQUILIBRIUM 3

v (velocity) (km/rad

FIG. I . I , hlaxwellian distribution of velocities for atomic oxygen.

Table 1 . 1 gives values of these velocities for different temperatures and particles encountered in the upper atmosphere.

TABLE 1 . 1

THERMAL VELOCITIES OF ATMOSPHERIC PARTICLES (KM/SEC)

Particle T (OK) V (i7)lP -

U (most probable (mean velocity) (root-mean-

velocity) square velocity)

Atomic oxygen 200 400 800

Atomic 200 hydrogen 400

800 Electron 200

400 800

0.454 0.642 0.908 1.81 2.57 3.63

77.8 110 156

0 . 5 1 3 0.726 1.026 2.05 2.90 4.11

87.9 124 176

0.556 0.787 1 . 1 1 3 2 .22 3.15 4.45

95.3 135 191

4 1 . RADIATION IN SPECTRAL LINES

Although we speak of the kinetic temperature of the upper atmosphere, it should not be assumed that the velocities of electrons and heavier particles always follow a Maxwellian distribution. On the contrary, ionization by sunlight or fast collisions, exothermic photochemical reactions, and electromagnetic forces in the atmosphere may produce appreciable distortions in the distribution of energies.

Even with distortions in the Maxwellian curve, one might still define a temperature through Eq. (1.6). But in considering the effects of a certain distribution of velocities, we must bear in mind the specific energy range in which we are interested and ask whether it is possible that appreciable distortions in the distribution might appear at these energies without materially affecting the mean energy.

An example lies in the excitation of auroral emissions by atmospheric electrons. While there may be a few electrons present with energies of 20 ev or so, which could produce excitation and ionization, the majority of the electrons may still approximate a Maxwellian curve for normal atmospheric temperatures ; on the other hand, the curve may deviate by great amounts, as in a discharge tube. The result depends on the conditions producing and accelerating the electrons and, for any particular case, the conditions must be considered in detail. Even if the electron distribution is noticeably nonthermal, the kinetic energies of heavy particles may remain virtually unchanged from their distribution outside the aurora; in this case, spectroscopic data may be interpreted in terms of the kinetic temperature of the gas, on the assumption that the populations in the ground vibrational level of a molecule are con- trolled by collisions with other heavy particles.

Oxygen atoms excited in the airglow provide a second important example of possible divergence from a thermal distribution. If excitation is by a photochemical process, the excited atom may have, on the average, more kinetic energy than is given by Eq. (1.6) ; if this is the case, atmospheric temperatures based on the Doppler width (Section 1.1.4) of the green [OI] line become suspect.

1 .I .2. Spectroscopic Nomenclature

Most of the nomenclature for atomic spectra used in this book follows that of Condon and Shortley [1951a]. Although these definitions are generally accepted by spectroscopists, the subject is often confused unnecessarily by some laxity in precise usage of the words.

A transition array consists of all jumps between two configurations: e.g., 3s - 4p. A multzplet includes all transitions between two terms: 3s 2P - 4p zSo. A line arises from a transition between two levels: 3s 2P3,2 -

1.1. TEMPERATURE AND THERMAL EQUILIBRIUM 5

4p2S0,,, . The levels are subdivided into 2 1 + 1 Zeeman states, which give rise to Zeeman components. However, in atmospheric spectra, splitting by a magnetic field may generally be neglected and the levels may be considered degenerate, except when one is considering the polarization of forbidden radiations.

In molecular spectra we consider a band system as consisting of all the transitions between two molecular states: e.g., B 3Ll + A 3Z. A band arises from the transitions between two particular vibrational levels : B 317(v’ = 4 ) + A 3Z(v” = 2 ) . A progression consists of all the bands arising in one system from a particular vibrational level. An example of a c’’ progression (for v’ = const.) is B317(v’ = 4 ) + A ,Z; Similarly, the v’ progressions have v” = const. A sequence is composed of all bands in a system in which A v = v’ - v” is a constant. For example, the LIZ; = + 2 sequence is composed of the bands in B3n(v’) -+

A 3.Z(v” = v’ - 2 ) . A band system may be considered as the totality of either (1) all the v’ progressions, (2) all the v” progressions, or ( 3 ) all the sequences in that system.

Rotational lines appear as a result of transitions between particular rotational levels within a given vibrational level: B ,17(v’ = 4 ; J‘ = 3 ) -+

A 3Z(v‘1 = 2 ; J“ = 4). The totality of lines with a constant d J within a band form a branch. When A J = J’ - J” = + 1 , it is an R branch; AJ = - 1 gives a P branch. An R branch always starts developing toward shorter wavelengths from the band origin: a P branch develops toward longer wavelengths. One of the branches usually doubles back toward the origin, forming an R - or P-head. When transitions with d J = 0 are allowed, a Q branch is formed. Other types of band structure appear in the aurora and airglow spectra (see Chapters 5 and 9). When writing formulae for the .wave numbers of rotational lines, etc., or in specifying a particular transition, we usually use only the rotational quantum number of the lower level ( J ” ) and write simply J for 1”.

In the above examples we have followed the convention of always writing the lower level first, when atomic transitions are specified, although for molecular transitions, it is usual to write the upper level first.

The forbidden atomic lines of 01 and NI and to some extent those of 011 and NII play an important role in atmospheric spectra. The ground configurations of these atoms and ions is either p 2 , p 3 , or p 4 , all of which consist of three terms (see the energy-level diagrams of Appendix VI). It is usual to write forbidden transitions with a bracket: [ 1. In addition, we shall find it easier in many instances to keep the transitions straight if we use the following extension of this notation:

[ I,, indicates a transition between the upper and middle terms; e.g., lD - ‘5’ produces A5577 [OI],,. These transitions are often called


auroral transitions, since [OI],, produces the strongest feature in the visible auroral spectrum.

Iz1 indicates a transition between the middle and lower terms; e.g., 3P - lD producing AA6300 and 6364 [OI],,. In gaseous nebulae [

indicates a transition between the upper and lower terms; e.g., , P - I S producing A2972 [OI.]31. By analogy with the foregoing cases, [ ]31 is called a transauroral transition.

[

Iz1 transitions predominate ; hence the term nebular transitions. [

1 .I .3. Boltzrnann Excitation Equation

Equation (1.1) may also be applied to a computation of the fraction of atoms or molecules in any particular energy state of excitation, for conditions of thermal equilibrium. We must, however, allow for degeneracy of these states. In general, if there are L5ji states within the ith level, and all these states have the same energy E* above the ground state, the total population N i of the ith level is given by

where N is the total number of particles of the same species per unit volume. The factor G% is the statistical weight of the level, and the denominator on the right of Eq. (1.7) is the partition function. The equation also gives the total populations of an atomic term (or even of a configuration) that is not strictly degenerate, provided that the energy differences between the fine-structure levels in the term (or configuration) are small compared with kT.

For low temperatures (viz., where kT is small compared with E ,

for the first excited term), the partition function may be approximated by the statistical weight of the ground term. The relative populations of two levels, a and b, in thermal equilibrium are

where E , ~ = E , - E ~ .

Although these equations are derived for thermal equilibrium, they have some application in the upper atmosphere. In particular, thermal distributions may exist over levels where thermal collisions dominate over radiation; e.g., for the relative populations in levels within the ground term of an atom or for vibrational levels within the ground electronic state of homonuclear molecules (0, and Nz), and for rotational levels within metastable electronic states.

1.2. THE CLASSICAL THEORY OF SPECTRAL LINES 7

1 .I .4. Doppler Line Broadening

Suppose an atom viewed in the same inertial frame of coordinates as the observer emits a frequency v,. When this frequency is emitted by an atom with velocity v r relative to the observer, the observed frequency v is given for nonrelativistic velocities by (v - vo)/vo = - vJc.

From the Maxwell-Boltzmann law (1. l ) , the distribution of particles with different velocities in one direction is

where U is defined by Eq. (1.4). The relative number of atoms emitting in interval dv at v and thus the relative intensity versus v is then

(1.10)

where 9 = Jl, dv is the integrated intensity of the line. Clearly the central intensity of the line is I. =3c/Uvol / ; ; .

The intensity drops to I,/2 at v - vo = & ( Uvo/c) (In 2)1/2; thus the total line width at half intensity is 2(ln 2)1/2 U v o / c in frequency units. In wavelength units this width is

2 I h - A, 1 = 2 (In 2)lI2 Uh,/c = 7.16 x

where p is the molecular weight of the atom. The absorption coefficient has the same shape as that given by

Eq. (1.10). I t will be shown below (Section 1.3.3) that the integrated absorption coefficient per atom is frez/mc, where f is the oscillator strength. Thus for Doppler broadening alone, the absorption coefficient per atom, sometimes called the absorption cross section, is

Ao(T/p)lI2, (1.11)

1.2. The Classical Theory of Spectral Lines

(1.12)

There are a number of ways in which the amount of energy emitted or absorbed in spectral lines might be expressed. In view of the importance of this topic to auroral and airglow spectral studies, it appears advisable to collect the basic relations among absorption coefficients, transition probabilities, f-values, strengths, etc., with some indication as to how

8 1. RADIATION IN SPECTRAL LINES

they enter the theory. We shall do this in Section 1.3, after first reviewing the classical theory, which bears many resemblances to the quantum- mechanical concepts.

1.2.1. Classical Theory of Line Emission

An electron in an orbit around a positively charged nucleus is constantly under acceleration, and consequently radiates energy. This energy must be balanced by a loss of kinetic energy of the electron, as a result of reaction from the emission of radiation. For an oscillating electric dipole the instantaneous rate of energy loss by the eIectron (Panofsky and Phillips [1955a, p. 3011) is

dE - 2 e2 (x), dt 3 6 '

(1.13)

where e is the charge on the electron in electrostatic units and x is the acceleration.

Suppose at a particular instant the reaction force on the electron is Frad. Then to conserve energy this force must satisfy

(1.14)

where zl = 3. When there is radiation damping, the relation between u and zi is not known at this point. We may, however, find an average force for an entire cycle. Integrating the right side by parts, we find

(1.15)

If t , and t , are chosen as times when the electron is at the same point in its oscillation, the right side vanishes. Hence, for the average over a cycle, we have

(1.16) 2 e2 .. 3 c3

Frad = - -U.

The equation of motion for an oscillating dipole that has been displaced and then released is thus

2 e2 ... m j E = - K x + - - x ,

3 c3 (1.17)

where m is the electronic mass and - Kx is the restoring force on the oscillator. T h e reaction force may be assumed small compared with

1.2. THE CLASSICAL THEORY OF SPECTRAL LINES 9

the restoring force. Then approximately x xo exp (- h o t ) , where wo = ( K / v ~ ) l / ~ , and 2 e - w$t. Substituting this expression for 'i into Eq. (1.17), we find

x + yk + w: = 0, (1.18)

where the classical damping constant is

(1.19)

Here vo is the natural frequency of oscillation and A,, in the right term, is the wavelength (expressed in cm).

For small y the solution to Eq. (1.18) is

= x e - Y 1 / 2 e-ioo (1.20)

The amplitude of oscillation at a particular instant is thus xI = xoe-Y1/2. T o examine the decay of radiation, we note that the energy in the dipole is equivalent to the potential energy at maximum dispIacement:

Then the mean rate of energy loss [since Eq. (1.16) is averaged over a cycle] is, by direct differentiation,

(1.22)

This rate may be verified by averaging Eq. (1.13) over one cycle. Thus the intensity of radiation is proportional to the square of the dipole moment ( ex l ) and has a lifetime of l/y. In quantum mechanics also the excited level has a finite lifetime between excitation and emission, but for quite a different physical reason.

If the dipole radiation is observed with a spectrograph, then the radiation recorded is the family of Fourier components. We can think of a spectrograph as a mechanical device for performing a Fourier analysis on a beam of radiation, since it sorts monochromatic waves that are of constant amplitude over a long distance. Thus, because of the damping term in Eq. (l.lS), the radiation is not strictly monochromatic.

The displacement of the electric (and magnetic) oscillations in the wave is proportional to x as given by Eq. (1.20). Hence we may derive


the Fourier components in x to obtain the spectral energy distribution of the radiation. Thus

x = s x, e-iot dw, (1.23)

where x, is the (complex) amplitude of the component waves. Applying a Fourier transform to Eqs. (1.20) and (1.23) we have

W

-W

Thus the intensity is

(1.25)

where I,, is the intensity at the line center. The intensity of the line falls to one half the central intensity when 1 u - vo 1 = y / 4 ~ ; hence the width at half intensity is A u = ~ 1 2 ~ .

1.2.2. Classical Theory of Line Absorption

T o generalize the above treatment to the case of absorption of an incident plane wave, we merely add to the right side of Eq. (1.17) the external disturbing force eE(t) , where the electric field from a plane wave is E(t ) = E, exp (- i d ) .

The equation of motion (1.18) then becomes

( I .26)

Neglecting solutions to this equation that would represent only momen- tary effects, we assume a periodic solution, x ( t ) = x, exp (- i d ) . Sub- stituting this expression into Eq. (1.26), we obtain a time-independent equation for x,:

- eE,/m x, =

(OJt - d) - iyw * (1.27)

As in Eq. (1.24), the complex form of x,, which arises from the damping term, demonstrates that the displacement of the electron is not in phase with the radiation.

The most convenient way of computing the absorption is by means of the complex index of refraction, n’. We shall show how this quantity is introduced through the electromagnetic wave equation as derived from Maxwell’s equations.

1.2. THE CLASSICAL THEORY OF SPECTRAL LINES 1 1

Ampiire's law in Gaussian units, when the conduction-current density, J , is zero, may be written (see Section 3.3.1)

(1.28)

where aP/at gives the current density (in e.s.u.) due to changing polarization. The polarization of a unit volume is

P = - N e x , (1.29)

where N is the density of electrons with displacements x governed by the incoming radiation. Combining Eq. ( I .28) with V x E = - (l/c) aB/at gives

(1.30)

and a similar equation for B. These are the well-known wave equations for electromagnetic radiation, in which

477 Ne2/m - 4TrP E

n ' 2 - K = 1 + - - + (w; - w') - i y w

Ne' (v; - v') . Ne2 ( Y V i W (1.31) = 1 +- + 1 -

xm ( v i - 9)' + ( y v / 2 ~ ) ~ ma (v," - v ' ) ~ + ( y v / 2 ~ ) ~ '

where the third equality follows from Eqs. (1.29) and (1.27). Here K is the complex dielectric constant.

Writing n' = n f ig, we may expand the right side of Eq. (1.31) by the binomial series, when I d2 I * 1, and find the real and imaginary parts of n'. With the additional approximation, in the neighborhood of v,,, that vo + v m 2v, we obtain

Ne2 Y o - v

4 ~ m v ( v - + (y/4n)' n = l + -

and (1.32)

(1.33)

T o interpret n and g, we note that Eq. (1.30) yields the solution

n' E ( t , = E , exp [ - iw ( t - - 41

C

= E , exp 1- iw ( t - n -z) -

C ! e l .

C (1.34)


Hence c/n is the phase velocity and n may be identified with the ordinary index of refraction. From Eq. (1.32) we see that when v > v0 (that is, on the short wavelength side of the absorption line), n < 1. The phase velocity is thus greater than c, but the velocity with which the energy is transported is always less than c (e.g., see Panofsky and Phillips [1955a, p. 3301).

Equation (1.34) also illustrates the role played by g in the absorption (or scattering) of energy within the line. Since the intensity varies as the square of the amplitude of E, the absorption coefficient for a unit volume, defined by

dIv = - I , k, d z , (1.35)

is, by Eqs. (1.34) and (1.33),

(1.36)

In the above treatment N is the number of oscillators with natural frequency v,, per unit volume. Thus if there is a thermal dispersion of

FIG. 1.2. The variation of n-1 and K, near the line cenrer. The curves-were computed for one of the hyperfine components of the D lines of sodium. No

Doppler broadening is included. After Aller [ 19534; courtesy Ronald Press.

1.3. QUANTUM CONCEPTS OF SPECTRAL LINES 13

velocities, there will be a corresponding dispersion in vo, which is the frequency most strongly absorbed by a particular atom. This velocity dispersion not only broadens the absorption line but also dilutes the effect of anomalous dispersion (rapid change of the index of refraction) near the center of the line (cf. Fig. 1.2).

A second correction to Eq. (1.36) stems from quantum mechanics: the capacity of an atom to absorb depends on the particular transition involved. T o allow for this, we insert a factor f (which may be of order unity for strong lines), called the oscillator strength or f-value, in Eq. (1.36). Finally, the classical damping constant y , which, by Eq. (1.22), represents the reciprocal lifetime of the transition, must be replaced by the analogous quantum-mechanical quantity, Tab. These additions will be made in the next section, after we review some of the basic quantum concepts in line emission and absorption.

1.3. Quantum Concepts of Spectral Lines

1.3.1. Transition Probabilities

The concept of transition probabilities was first introduced phenomono- logically by Einstein [1917a] (see also Condon and Shortley [1951a, p. 791). Consider the transitions between two levels, a and b, where a is the higher of the two (see Fig. 1.3). Upward transitions require the absorption of energy by the atom and therefore occur only as a result of incident radiation. Downward jumps occur both spontaneously and by being induced by the external radiation field. The latter process has no analogue in the classical theory of lines, but may be understood quantum mechanically as a result of interaction of the atom with incoming photons.

The number of spontaneous emissions from a unit volume in time interval dt is N,A,,dt, where A n b is the Einstein coeficient of spontaneous emission. I t is a measure of the probability that an atom in state a will cascade to b in one second. When radiation that is continuous near vo with specific intensity1 I, (erg/cm2 sec sterad sec-l) falls on the unit volume from a small solid angle dQ, the number of absorptions during dt will be N , B,,, I , , dt dQ14rr. Similarly, the number of induced emissions

Aob + Bob To b

FIG. I .3. Transitions between levels a and b.

' Specific intensity is defined and discussed more thoroughly in Section 2.1.2.


is N , B,, I , dt dQ/4n. The factors Bba and B, , are the Einstein coeficients of absorption and induced emission, respectively.

Einstein postulates that these three coefficients are definite properties of the atom and are independent of any external conditions. This being so, a relation established between the coefficients for any set of physical conditions must be universally valid. Thermal equilibrium provides three conditions which are sufficient for obtaining unique relations between A,,, Bba, and Bab. First, in thermal equilibrium we have a detailed balancing between atomic states. That is to say, the number of transitions from a to b is precisely the same as the number from b to a . (This condition is much more rigid than ordinary statistical equilibrium, which requires simply that the number of atoms entering a particular state a is equal to the number leaving the same state in the same time interval. In later discussions of the upper atmosphere, we shall invoke statistical equilibrium for many processes, but detailed balancing cannot in general be assumed and its use must always be carefully justified.) In thermal equilibrium every volume element in the system must contain black-body radiation characteristic of the temperature of the system. Hence by definition there can be no loss or gain of radiation at any frequency. For this condition to be true, every upward jump must be balanced by a re-emission. Hence detailed balancing reQuires

(1.37) sphere sphere

Second, in thermal equilibrium the radiation field is isotropic and is given by Planck’s law:

(1.38)

Finally, the relative populations of a and b are given by Boltzmann’s equation (1.8). Substituting Eqs. (1.38) and (1.8), for hv = &a,, into Eq. (1.37), we have

By our basic postulate of the nature of the A’s and B’s, these cannot depend on the temperature of the gas. Therefore, we must have

and (1.40)

(1.41)


If any one of the three basic quantities (say, A ) can be obtained, the others can be derived by these equations. Bohr’s correspondence principle suggested, and Dirac’s theory of radiation confirmed, a relation for A in terms of the dipole moment p = ex. The matrix element for a dipole transition between states a and b is written

where d r is a volume element, 1,4 is Schrodinger’s wave function, and the integration is performed\over all space. Then the transition probability is

(1.43)

On the average the rate at which energy is transformed to radiation by an atom is

(1.44)

This rate may be compared with Eq. (1.22), which gives the rate at which energy is lost from a single dipole. Thus the two expressions are equivalent when the amplitude of the classical dipole moment, ex,, is equivalent to 2 1 Rkb 1.

Also from Eq. (1 22) we found that the lifetime of a classical oscillator is I /y . Quantum mechanically, the lifetime is given in terms of the probability of an atom’s escaping from a particular state. For dilute radiation fields, we may neglect escape from an excited level by absorption or induced emission. Then the lifetime, T,, is given by

( 1.45)

The summation is performed over all states below a. By analogy with the classical y , we call r, the quantum-mechanical damping constant.

1.3.2. Line Strengths

Condon and Shortley [1951a, p. 981 introduced a useful quantity called the strength, which is the square of the matrix element for a transition between states:

S(a, b) = I Rnb 1’- (1.46)


Now consider the level a , composed of 6, = 2J, + 1 states (a ) and, similarly, a lower level /3 that contains 2J, + 1 states (b). If the upper states a have equal populations then the energy emitted by a unit volume in the line a -/3 is

(1.47)

where we write z a b for z a z b . Defining the strength of a line as the sum of the strengths of the individual components, we may also write the energy emitted as

(1.48)

(1.49)

But since N , = G, N , the relation between the transition probability and strength is, from Eq. (1.48)

64r4v3 S(a, /3) 3hc3 6,

A,, = --. (1 S O )

In many ways the strength is more fundamental than the A. Com- ponent strengths can be added to get the strength of a line or multiplet, whereas transition probabilities cannot be simply added. The strength is also independent of whether absorption or emission is considered, as S(a, p) = S(p, a ) ; Einstein coefficients have the disadvantage of not being symmetrical in the initial and final states, as shown by Eq. (1.50).

When the relative populations in the upper levels are proportional to the statistical weights (which may be the case for a group of closely spaced levels), the relative (integrated) intensities of emission are, from Eq. (1.50),

(1.51)

Hence the relative intensities are identical to the relative strengths, except for the so-called Einstein v4 correction.

In LS coupling relative strengths may be readily obtained from tables published by White [1934a] (for lines within a multiplet and for hyperfine structure) and Goldberg [1935a, 1936~1 (for multiplets within a


transition array). These tables were prepared by evaluating the angular component of the matrix element [cf. Eq. (1.42)], which depends on the quantum numbers L, S, J , and the 1 for the jumping electron. For relative strengths within a single transition array it is not necessary to know the radial component of the matrix element, which involves a knowledge of the radial wave function and is more difficult to evaluate. Of course, in any evaluation of absolute transition probabilities the entire wave function must be considered. Aller [1953a, p. 1341 gives samples of the White and Goldberg tables, with examples on their use for particular problems.

Transition probabilities for the forbidden atomic lines of atmospheric interest are collected in Appendix VI. For permitted atomic lines, see the compilation by Allen [1955a].

1.3.3. f-values

Let us now return to the line profile for natural broadening, given in classical theory by Eq. (1.25) for emission and Eq. (1.36) for absorption. In either case the line has the same dependence on v (i.e., the profile has the same shape).

With the corrections mentioned after Eq. (1.36), we have k, = Nor, where the absorption coefficient per atom is

where r,, = r, + r,

(1.52)

(1.53)

and I', and r, are given by Eq. (1.45). I t is intuitively clear why the damping constant must now involve both states, when we recall the physical origin of natural line broadening in quantum theory. In classical theory the finite line width results from radiation reaction on the accelerated electron, which effectively prohibits the electron from radiating indefinitely at the resonance frequency vo. But in quantum mechanics the upper level emits according to a probability A,,, although the exact lifetime of this state for any particular photon is indeterminate. The origin of this uncertainty lies in Heisenberg's uncertainty principle, which may be expressed as d ~ d t - h, or dvdt - 1. The uncertainty of the time, A t , is the order of the lifetime T, of the state. Unless the lower level is in the ground term, it also may have a short lifetime and hence an appreciable uncertainty in the energy. Thus the quantum states cannot be regarded as perfectly sharp energy levels, but rather


they have a finite width of A v , N r,. I t will be clear from Eq. (1.52) or Eq. (1.25), that the width of a line at half intensity is Ta,/2rr.

Forbidden lines, which have a long lifetime for both upper and lower levels, have natural widths that are consequently extremely sharp compared with those, of ordinary permitted transitions.

Integrating Eq. (1.52), we find

(1.54)

By definition of the absorption coefficient, the specific intensity decreases according to dI , = - N a,, I , dx. A beam of unit cross section and subtending a solid angle dQ thus loses an amount of energy, in passing through a I-cm path length, equivalent to

B

(1.55)

where we assume that the loss of intensity in the unit path length is small, so that I , , is essentially independent of u throughout the path.2

In the quantum-mechanical picture the same energy loss is given by N , B,, I , , hv dQ/4rr. Thus

where the second equality involves Eq. (1.41) and y is the classical damping constant of Eq. (1.19). This relation is valid for lines, multiplets, etc., as well as for Zeeman components.

With the dependence of A,, on the strength of a line from Eq. (1 SO), we have for thef-value of a line or multiplet,

8rr2 mv S(a, /I) fPr = -jpr ~ *

GB (1.57)

Thus, as for Einstein A's, thef-value of a multiplet, say, is not thesum of the f-values of the individual lines or Zeeman components. However the relation

C p f p a = 2 & b f b n (1 S7a) ab

is valid when the density N p is taken as the total population of the ground level or term, as the case may be.

When there is strong absorption of the incident beam, the line profile, I,, us. v , is no longer the same shape as a,,; one must then consider curve-of-growth effects, to derive the total loss of energy in the line (see Aller [1953a]). This consideration does not affect the generality of the relation between fpa and A,b derived here, however.


The loss of energy in an absorption line is usually expressed in terms of its equivalent width. From Eq. (1.35) the diminished intensity of a beam after it passes through a uniform absorbing slab of atoms, is

If I f " is a continuous spectrum (independent of v in the neighborhood of the absorption line) the equivalent width is defined as

(1.59)

The equimlent width is the width of a black rectangular line whose area is equal to that of the real line. If k,x is small (i.e., for weak lines), we have

(1.60)

When equivalent width is measured in wavelength units, we have

With f expressed in terms of S by Eq. (1.57), we see that for weak w p = u;c;c) x;jc.

lines

(1.61)

where we have assumed that the lower levels have about the same energy and are populated in proportion to their statistical weights. Equation (1.61) is analogous to Eq. (1.51) for relative emission intensities; hence, relative strengths can be directly applied to equivalent widths as well as to emission lines.

Our discussion here has been confined to the ordinary, permitted electric-dipole transitions. The general relations between f, A, S, etc., apply equally well, however, to electric-quadrupole and magnetic- dipole transitions that give the important airglow and aurora forbidden lines, except that the matrix element of Eq. (1.42) is defined differently for each type of transition.

1.3.4. Line Profiles

A projile-the variation of intensity with frequency-is given by Eq. ( I . lo) for emission lines with Doppler broadening, and for natural broadening we may use Eq. (1.25), with y replaced by Tab.


Absorption profiles for weak lines may be obtained directly from a , as given by Eqs. (1.12) (Doppler) and (1.52) (natural). In the more general case of strong absorption, it is necessary to use the expression (1.58) to find I , relative to the continuum. However, (1.58) neglects any re-emission by the absorbing atoms; if the absorption process is actually line scattering, as in the case of the Na D resonance lines, it may be necessary to consider the scattered photons through radiative- transfer theory (Chapter 2).

In the upper atmosphere, the Doppler effect is invariably the dominant process whereby lines are broadened. In the lower atmosphere collisions may become so important that they affect the widths of telluric absorption lines. The profile for collisional broadening has an identical form to that for natural broadening, except that r must be appropriately modified (cf. Aller [1953a]).

It is necessary to consider Doppler plus collisional (or perhaps natural) broadening when the two processes are of about the same importance. The combined profile may be obtained by considering a Maxwell- Boltzmann distribution of velocities for the emitting atoms, each of which has a profile characteristic of a damped oscillator. The combined profile for any particular set of parameters is most easily computed with the aid of special tables prepared by D. L. Harris, I11 (cf. Aller [1953a, p. 2511).

1.4. Molecular Bands

The transition probabilities and intensities are directly related to the matrix element of the dipole moment, as defined by Eq. (1.42), through Eq. (1.43). T o a first approximation (Herzberg [1950u, p. 1491) we may write the total amplitude wave function as

(1.62)

where is the electronic wave function, the vibrational wave function for an anharmonic oscillator, and $r the rotational wave function. Hence the matrix element becomes

(1.63)

(Since fiV is a real function, we omit writing $$ for its complex conjugate.)

1.4. MOLECULAR BANDS 21

1.4.1. Intensities of Electronic and Vibrational Bands

For purposes of discussing the intensity of an entire band, we may ignore the integrated rotational wave functions, which depend only on the angular coordinates. By resolving the dipole moment into an electronic component, pe, and a nuclear component, pn, and writing dr = dTe r2 sin 0 d+ dll dr, where dre is the volume element for the electronic wave function, we have (Herzberg [1950a, p. 2031) for the electronic-vibrational matrix element

To a first approximation the electronic wave functions do not depend on the internuclear distance, nor do the vibrational functions depend on electron space ; hence Eq. (1.64) becomes

If the upper and lower levels are in the same electronic state, then $&by *dTe = 1 ; but since $; and I&' are evolved from the same potential

function, they are orthogonal. Hence the first term in Eq. (1.65) vanishes and we have

R"'"" = J" $; pn $:,I dr (1.66)

as the matrix element for pure vibrational transitions. In homonuclear molecules (02, N,, etc.), pn = 0 and vibrational transitions are forbidden.

When v' and v" belong to different electronic states, $; and I&' are no longer orthogonal functions, but the second term in Eq. (1.65) vanishes because of the orthogonality of I,& and $:. Thus for transitions involving two electronic states, we may write

R;"" = Re $; 4;' dr, (1.67)

where

Re = J $2 Pe#L' dTe, (1.68)

and the integral in Eq. (1.67) is called the overlap integral. This formulation assumes the complete separation of electronic and

nuclear space in the integrations over the wave functions. Actually there is some dependence of the electronic wave functions (and hence of Re) on the internuclear distance r , as may be demonstrated from the


wave equations that are appropriate when a solution of the form (1.62) is assumed (Herzberg [1950a, p. 1481). Therefore, for more accurate theoretical intensities of bands, Eq. (1.67) should be evaluated with R e under the integral.

As with the line strength S in atomic spectra, defined by Eq. (1.46), we write

(1.69)

where S(V‘V‘‘) is the band ~trength.~

considered, we may write If Re has nearly the same dependence on Y for all the bands being

S(”v”) = R; q(v‘v’’), (1.70)

where q(e)’d’) is the square of the overlap integral:

q(v’v‘‘) = 1 +{ I,!(’ dr 1 2 , (1.71)

The sum of the p’s over all lower or all upper vibrational levels is unity. Bates [1952a] has labelled ~ ( V ’ V ” ) the Franck-Condon f a ~ t o r , ~ since the quantum-mechanical formulation of the Franck-Condon principle is based on Eq. (1.70). In the limit of this approximation the relative intensities of different bands in a system depend simply on how well the wave functions of the upper and lower levels “overlap” to provide a large positive or negative integral.

The energy emitted in all directions by an assembly of N,. molecules in the upper level is then, by Eq. (1.50),

64 v4v4

3c3 Nv, Av,u‘,hv = NV‘ - S(V’V”), (1.72)

where the upper vibrational levels are considered to have unit statistical weight.

Some authors use the term band strength to denote S(o’w“) times certain constants that appear in the expression relating S(v’w”) to the Einstein A. Here we shall keep the notation as consistent as possible with that used in atomic spectra.

In the literature the Franck-Condon factor is often written as p . I have used q here to avoid possible confusion with the dipole moment.

This equation also may be derived by summing the more general equation (1.80) (for the transition probability of rotational lines) over all lower ( J ’ ) rotational levels. The summation gives the probability of a transition from J’ w’ to o”, and as this probability is the same for all J’, it is written A,,,,..


In auroral and airglow spectra the relative intensities are often of interest. Equation (1.72) gives

(1.73)

Similarly, absorption by a band is found from thef-value and its relation to strength by Eq. (1.57).

Various attempts have been made to improve computed band strengths over those derived from the overlap integral and Eq. (1.70). Fraser [ 1954~1 writes

S(V'V") = R;(fv,v,,) q("v"), (1.74)

where f ,~ , , , , is the mean internuclear distance involved in a particular transition and may be computed from

(1.75)

Fraser, Jarmain, and Nicholls (cf. the review by Nicholls [1956a]) have computed f,,,,,, for bands in several systems and have used empirical intensities from the whole band system to derive an average curve of R;(P,,,,<,) from Eqs. (1.73) and (1.74). Then the smoothed RZe(Pvtvt,) curve is used to derive improved strengths for individual bands.

Most of the available calculations give only relative values of band strengths within the same band system-or so-called vibrational transition probabilities. There is considerable need for absolute (electronic) transition probabilities for a number of band systems.

One of the basic difficulties in computing even relative strengths lies in representing the potential with an analytic function that is conveniently handled. The most popular means of representing the potential is the Morse [1929a] function:

V(r) = D, [I - e--80(+7.3]2. (1.76)

Here D, is the dissociation energy and Po is a constant to be fitted empirically to the energy levels.

Writing the vibrational energy G(v) (in cm-I = u/c ) in the usual power series (Herzberg [1950a, p. 92]),

G(v) = we(. + 3) - w , x,(v + $)2 + weye(v + $)3 - ..., ( I .77)


we may express w , in terms of the constants Po and D,, in Eq. (1.76) and w , x, in terms of (Herzberg [1950a, p. loll). If the series (1.77), when carried only to w , x,, does not give a good fit to the energy levels, the Morse function may become less satisfactory as a means of computing transition probabilities.

The notes to Table 5.5 list a number of calculations of vibrational transition probabilities that have been made for band systems of interest in the aurora.

If the intensities of bands arising from different upper vibrational levels can be measured and if the relative strengths are known, we may compute from Eq. (1.73) the relative populations, N,r. In the special case when these populations are governed entirely by collisions with gas molecules in a Maxwellian velocity distribution, they will become distributed according to the Boltzmann equation (1.7) appropriate for thermal equilibrium:

(1.78)

Here N is the total population of the electronic state and G(v) = E / ~ C

is the energy (in cm-l) above zero energy for the electronic state. (Alternatively, Eq. (1.78) may be written with Go(v)-the energy above the ground vibrational level-since this change merely involves multi- plication by a constant factor in numerator and denominator.)

Temperatures derived by Eq. (1.78) are called vibrational temperatures. It is important to note that the conditions for this distribution to be valid are rather stringent. For an excited electronic level the populations might even increase over a range of v’, as is probably the case for the levels emitting the 0, Herzberg bands in the airglow. Even the ground electronic state is not necessarily in equilibrium with slow molecular collisions, as is evidenced by OH in the airglow.

When there is no known reason for doubting that Eq. (1.78) is valid in the ground state, the predicted populations can be used, along with an assumed excitation mechanism (say, collisions with fast electrons), to predict the relative populations in an excited state as a function of temperature. Measurements of the populations in the excited state by Eq. (1.73) may then be compared with the calculations to deduce a temperature. Vibrational temperatures derived in this fashion (and which shall be denoted vibrational temperatures of the ground state) are normally much more realistic than those based on the assumption that the excited state obeys Eq. ( I .78).


1.4.2. Intensities of Rotational Lines

For negligible interaction between electronic and rotational motion, the total matrix element given by Eq. (1.63) may be separated into a product of electronic-vibrational and rotational components (Herzberg [1950a, p. 3821):

> (1.79) R = RZ’U” R J ’ J “

where R;’“’’ is given by Eq. (1.64). From the general relation (1.50) between transition probabilities and strengths, and with S(v‘v“) defined by Eq. (1.69), we have, for the total energy emitted by NJtvI molecules in the levels J’ and v ’ ,

where S(J’J”) = I RJ”“ 1 2 . Applying the rotational sum rule (Herzberg [1950a, p. 208]),

2 S(J’J”) = GJI = 2J’ + 1, J’ ’

(1.81)

we obtain relation (1.72) between the strength and transition probability of an entire band.

Consider now the relative intensities of lines within the same band. Since v changes slowly over a single electronic band, we may ordinarily neglect the v4 factor and write

NJ S(/’J”> G J‘

-9(J’/’’) = const (1.82)

From the sum rule (1.81) we see that the total strength of all lines (that is, the lines in all branches) originating from J‘ is proportional to GJt. To a first approximation we may also suppose that the strength of any individual line is proportional to the statistical weight of the initial level. In this case $(J’ /”) = const N J t , and when the populations are distributed by the Boltzmann equation (1.7), the intensity distribution is

Y(J’J”) = const (21‘ + 1) e-F(J‘ ) hc’kT, (1.83)

where F(J’) is the energy in cm-l given by


and where B and D are the rotational constants. Using only the first term in the series (1.84), we find that the maximum intensity from Eq. (1.83) is at

Approximate rotational temperatures, when the populations N,, are in a thermal distribution, may be found from either Eq. (1.83) or (1.85). However, in many cases it is possible to write formulae more accurate than Eq. (1.83). When the Boltzmann distribution is valid, Eq. (1.82) gives

, Y ( J ’ ~ ” ) = const s(/’J”) ~ - F ( J ’ I h c l k ~ . (1 3 6 )

For singlet bands the strengths are related to J’ and J“ by the Honl- London formulae (Herzberg [1950a, p. 208]), which may also be used as a guide for transitions with higher multiplicity, when spin splitting is not resolved, by replacing J with the quantum numbers K. Theoretical line strengths have also been calculated for the detailed structure of some transitions and for certain forbidden transitions.

Rotational temperatures for forbidden band systems (when the molecules are in the excited level long enough for the relative rotational populations to reach equilibrium with the gas through collisions) may be directly indicative of the kinetic temperature in the upper atmosphere.

Another application of rotational temperatures lies in molecules excited by electron impact. If the angular momentum of the molecule does not change appreciably during excitation, then the distribution over the excited (1’) levels will be the same as over the ground rotational levels. In this situation, Eq. (1.86) may be used provided that F(J’) is replaced withF(J) for the ground electronic state (also see Section 11.2.3). In the case of emission by an ionized molecule, it is generally necessary to decide whether the excitation occurs from the ground state of the neutral or the ionized molecule. (For the particular case of N i bands, the question is of no great importance to the deduced temperature, as the ground states of N, and N;f have similar rotational constants B.)

The quantum number.] gives the total angular momentum of a molecule; K gives its angular momentum apart from electron spin.

1.5. EXCITATION A N D I O N I Z A T I O N PROCESSES 27

1.5. Excitation and Ionization Processes

1.5.1. Radiative Excitation, Ionization, a n d Recombination

Let continuous radiation of intensity I,. at frequency v be incident on a unit volume containing N p atoms or molecules that are capable of absorbing radiation at this frequency. Equation (1.55) gives the energy absorbed for a beam subtending a solid angle dQ. The number of upward radiative transitions by these atoms, F,{?, is equivalent to the number of photons absorbed:

(1.87) sphere sphere

where the relation between BpT.and fpl comes from Eq. (1.56). For the important case of solar radiation, it is more convenient to use the incident flux. When the incident radiation is in a parallel beam, the flux 7r.E per unit area normal to the beam’ is equivalent to the integrals in Eq. (1.87). Hence, for a parallel beam of incident radiation,

(1.88)

For absorption caused by ionization (or molecular dissociation), rather than by excitation of discrete levels, the number of photons captured is equivalent to the number of ionizations:

(1.89)

sphere

where p denotes a bound level, K the continuum, and v B the minimum frequency capable of ionizing the atom from level p.

Captures of free electrons by atomic ions depend on the cross section for radiatioe recombination, OK@. Consider the ions as fixed in space and the electrons as moving with a relative speed u. A single electron would thus have capture collisions at the rate NtQMpv sec-’. For a group of electrons the total number of captures into level p per cm3 per sec is thus

’See Section 2.1.2 for definitions of and relations between the basic quantities in radiative transfer.

28 1 . RADIATION I N SPECTRAL LINES

wheref(v) is the electron velocity distribution relative to the ions. For a strong radiation field there may also be induced captures, analogous to induced line emission.

The Milne relation between QKp and aY(P) may be found by applying an argument based on thermal equilibrium. With detailed balancing between ionizations and recombinations at a particular frequency, we have, for isotropic radiation,

echvlkT) dv = Ni NeQKg(v) v f ( v ) dv, (1.91)

where the exponential on the left allows for induced captures in thermal equilibrium.

For f(v) we take the Maxwellian distribution (1.3); for I,, the Planck law (1.38); and the abundances of ionized atoms and neutral atoms in level p are related by the Boltzmann excitation equation (1.7) combined with the Saha ionization equation. This combined Boltzmann-Saha equation (Aller [1953a]) is

(1.92)

The velocity and frequency in Eq. (1.91) are related by hv = mv2 + (&ion - ca). Here &ion is the ionization potential of the ground state of the neutral atom and E~ is the excitation energy. Hence &ion - E, is the ionization potential for an atom in level p. Putting all these relations into Eq. (1.91), we finally obtain

(1.93)

1.5.2. Particle Collisions and Photochemical Reactions

In the general sense, excitation or ionization by collisions involves all types of encounters between two or more particles that result in a change (increase or decrease) of internal energy for any of the partici- pants. Thus ordinary radiative recombination for an arbitrary element X,

X + + e - + X + h v , (1.94)

as discussed above, results from an electron-ion collision. Any collisional process may be described in terms of its cross section QaS, or by a rate coefficient which is in turn defined in terms of the cross section:

(1.95)

1.5. EXCITATION AND IONIZATION PROCESSES 29

where v,, is the minimum velocity capable of producing the reaction

When QZs does not vary too much over the velocity range of importance, we may approximate Eq. (1.95) by sap - d Qxp(5), where d is the mean velocity of the exciting particles.

For two-body collisions the number of reactions per unit volume and unit time is then

Fa, = Nm Nj (1.96)

where N , is the number of particles colliding with the particle in state 01

and inducing the reaction. For three-body collisions, the reaction rate can be expressed in the same fashion as in Eqs. (1.96) and (1.95), provided that Qail (and consequently sap) take account of the number density of the third body. For example, an eflective recombination coefficient may be defined by Eq. (1.96), even though the actual process may be a three-body collision. It is usually more convenient, however, to use a rate coefficient that is independent of density. Thus the reaction rate for three-body collisions is expressed as

Fa, = N , N , N j s,,. (1.97)

An important mechanism in auroral excitation and ionization consists

a - p .

of inelastic electron collisions:

and X + e + X* + e

X + e + X + * +2e ,

(1.98a)

(1.98b)

where the asterisk (*) will denote an excited atom or molecule. The cross section may be expressed in terms of a quantity SZ(a,B), introduced by Hebb and Menzel [1940a] and aptly called the collision strength by Seaton [1953a]. It is related to the cross section in much the same way that line strength is related to transition probability [cf. Eq. (1.50)]:

(1.99)

In many cases the collision strength is nearly constant over the electron velocity range of interest. With f(v) a Maxwellian distribution characteristic of an electron temperature T e , Eq. (1.95) then gives,

h2R(a/l) - 4.17Q(a/l) - Q ~ s = 4= ,,,zn2 GX V*&-)? .

(1.100)


where level /3 lies at energy ,srrP = & rn .u& above level a. The exponential factor arises from the limit vqij. in Eq. (1.95). For deactivation this limit is zero; the collision strength is symmetric in a and p, so

(1.101)

Direct collisional excitation or ionization through encounters of heavy particles can also be important in the aurora; for example,

or H + X-+H* + X*

H + X -+H* + X+* + e.

(1.102a)

( 1.102b)

A fast collision is necessary for this mechanism to be effective. The fast particle might be a proton or neutral hydrogen atom (which resulted from a previous collision wherein a fast proton captured an electron). If the fast particle is H, as in Eq. (1.102a), the excited atom may be either H or the target atom (or molecule) or both.

Simultaneous excitation and ionization of atmospheric gases can occur through (1.102b) and also by charge transfer:

H+ + X + H * + X+*. ( 1.103)

Charge transfer can also be important in slow collisions (from ordinary thermal motions) in some instances. Bates [19546] pointed out, for example, that

H+ + 0 s H + 0' (1.104)

is in near resonance and might have a high rate coefficient; at present however a large coefficient is quite doubtful. Bates [1955b] suggests that

Of + o,-b0,+ + 0 ( 1.105)

may have a rate coefficient as high as 10-lo cm3/sec, since it can proceed through atom-ion interchange. This type of mechanism is probably important in the formation of the F layers and production of the red lines of [OI] in the airglow.

Radiative recombination (1.94) has a low rate coefficient and proceeds slowly. A more important recombination process for the upper atmosphere is dissociative recombination for molecular ions:

X Y + + e + X * + Y * . (1.106)


Also, mutual neutralization,

X - + Y Z + 4 X * + Y Z * , ( 1.107)

usually has a high rate coefficient. Various possible ionization and recombination processes for the upper atmosphere have previously been summarized by Bates [1952b].

In addition to the ionic excitation mechanisms, chemical reactions may provide excitation of atoms or molecules. Bates and Nicolet [1950b] have discussed, for example, the multitude of reactions that might occur in a hydrogen-oxygen atmosphere.

Radiative dissociation of a molecule may leave one or more of the atoms in an excited state:

X Y + h v + X * + Y*. (1.108)

This mechanism can produce, for example, 0 atoms in the 'D term through dissociation in the Schumann-Runge continuum.

Atom exchange,

x + Y Z-+XY* + z*,

may be an effective means of deactivating metastable molecular states, with the reaction then going to the left.

( 1.109)

Radiative association,

x + Y + X Y * + hv, (1.110)

and three-body association,

x + Y + Z * X Y * +z*, (1.1 11)

can also produce excited molecules. In reaction (1.1 1 1) the third body (2) may pick up some of the energy released by association and enter an excited level.

The rate coefficient for a bimolecular reaction of the type (1.109) is given by the Arrhenius equation (see Glasstone, Laidler, and Eyring [1941a]), which may be written in the form

s , , , ~ = 7PecEalRT. (1.112)

Here is the activation energy per mole, 7 is the classical collision frequency for a density of one molecule/cm3 of the reacting substances, and P is the steric or probability factor that measures the deviation of a particular reaction from ideal behavior. Normally P is of the order


of unity, although in the case of certain “slow” collisions it may become as small as

The kinetic theory expression for may be obtained from Eq. (1.95) written for heavy-particle collisions:

(1.113)

Here M is the reduced mass of the colliding particles and p is the collision diameter or distance between the centers of the molecules upon collision. Bates and Nicolet [1950b] suggest that for atomic systems relevant to atmospheric problems one might take 7 w 1.5 x 10-l1 x TII2 cm3/sec.

The activation energy is unfortunately unknown or known only very poorly in most cases. It is the energy, physical‘or chemical, that the reacting particles must possess before entering the reaction. In the collision of the atom X and the molecule YZ, the potential energy will go through a maximum before it drops toward the value describing the end products XY and Z.

A rule of thumb for estimating crudely the activation energy has been offered by Hirschfelder [1941a] on the basis of a semiempirical relation (originally developed by Eyring et al.) between &a and the binding energy of the original molecule YZ. For reactions of the type (1.109), one may write ea w 0.055 D,(YZ), where D, is the energy required to dissociate YZ. At T = 500 “K and &a = 5 kcal/mole (a typical value), we have &a/RT = 5 and the exponential factor is of the order of lov2.

Radiative association (1.110) and three-body collisions of the type (1.1 1 1) are not nearly so temperature sensitive. For radiative association the rate coefficient may be the order of lO-l5 cm3/sec under ideal conditions (e.g., when a suitable potential energy curve exists for the approach of two atoms). A typical three-body reaction coefficient would be about

cm6/sec. The competition between two- and three-body collisions is governed by the particle density on the one hand and by the activation energy for the two-body process on the other. A knowledge of these two items is necessary to decide which reaction is more efficient.

PROBLEMS

1. Compare the total widths at half intensity of the Na D, line, A5890 for (a) pure natural broadening and (b) pure Doppler broadening a1 220 O K , with each other and with the hyperfine splitting, which ic 0.06 cm-l for the two components with the widest separation.


2. Assume that continuous radiation with monochromatic flux x.?

normal to the beam (where T.? = constant with v over the frequency range of interest) falls on an assembly of N oxygen atoms in the ground term. What is the number of upward transitions to the l D term (in the ground configuration) if the atoms are distributed over the various levels of the 3P term according to the statistical weights? How much is this calculation in error if the atoms are actually distributed according to thermal equilibrium at 200 "K ? (See Bates and Dalgarno [1954a].)

Chapter 2. Scattering of Radiation in Finite Atmospheres

2.1. Introduction

The transfer of radiation through an atmosphere by means of successive scatterings finds application in airglow and auroral photometry, where it is often necessary to correct observed intensities for atmospheric scattering in order to find the intensity outside the scattering atmosphere (i.e., the troposphere). Further, certain airglow emissions, such as the resonance D lines of sodium, may involve appreciable multiple scatterings before the light leaves the emitting layers.

Much of the basic theory given here follows Chandrasekhar’s [1950a] treatise on Radiative Transfer. The reader is referred to that work for more details; our present development is necessarily brief and designed to serve as a summary and as a reference to which we may refer later in developing the applications. We shall be concerned largely with an idealized plane-parallel atmosphere-i.e., one in which the upper and lower boundaries are infinite horizontal planes, parallel to one another. The thickness of the atmosphere will be taken as finite, however.

We shall find it convenient to distinguish between scattering (in which the intensity and frequency of the light leaving a particle is identical to that incident on the same particle) and absorption (in which the incident light is lost to the radiation field, or transformed to a different frequency). An intermediate case exists, however, when there is a probability Go, between 0 and 1, that a given photon will be scattered rather than absorbed; we shall call this scattering with an albedo Go.

Often it is difficult to distinguish between scattering and absorption. The apparent brightness of a star decreases as its zenith distance increases because of absorption as well as scattering. We shall call this net loss of intensity extinction. Whereas the diminished intensity of a point source, such as a star, depends only on the total extinction, an extended source, such as the airglow or aurora, may be significantly affected by scattering back into the line of sight. Hence for an accurate intensity determination of a source with a finite angular extent, we must correct the observations for the scattering of light into the beam as well as the extinction or loss of light between the observer and the source.

34

2.1. INTRODUCTION 35

2.1.1. Transfer Problems in the Physics of the Atmosphere

Radiation associated with the upper atmosphere presents a variety of problems that can be investigated with the techniques of radiative transfer. In this chapter we shall examine not only the basic theory but one application: T h e correction of photometric observations for scattering by the lower atmosphere.

Other problems deal directly with the transfer of radiation in the high atmosphere. In Chapter 1 1 we shall discuss scattering of the Na D resonance lines in the sodium layer in the twilight and day airglow. Similar problems are encountered in the nightglow Na emission.

Rocket experiments also offer problems of radiative transfer. I t is often assumed that rocket measurements of the intensity of airglow radiation versus height give directly the emitting heights. But in the case of a resonance transition (such as Na D), the airglow emission may be scattered by Na atoms at a different height from the excitation and hence make the excitation appear to be located over a thicker region than it actually is.

Another example is offered by the 0-1 band (origin at 8645 A) of the Atmospheric system of 0,. Bates [I95461 first pointed out that emission in the 0-0 band (the Fraunhofer A-band at 7619 A) could be reabsorbed by other 0, molecules, which might then emit the0-1 band. This fluorescence mechanism has been treated by transfer techniques by Chamberlain [1954u] for the airglow. In this example, that part of the 0-1 band resulting from fluorescence would appear (in the absence of deactivation) in the 30-70 km region, while direct excitation of the 0, Atmospheric system would, of course, give 0-1 emission at the height of excitation. Rocket measurements of the height profile of the 0-1 band could thus give valuable information on the deactivation of the b l,Z; state of 0,. As the aurora and airglow spectra in the ultraviolet, where resonance and fluorescence emissions are likely to be important, begin to be explored by rockets, a number of new applications of the transfer equations may present themselves.

An entirely different type of radiative-transfer problem deals with the heat balance and temperature profile of the atmosphere. A large effort has been devoted to planetary problems of this nature by Elsasser [1942u], King [1955a, 1956~1, Plass [1952a, 1956a, b, c], Goody [1958a], Strong and Plass [1950a], and others. We shall not be concerned directly with these problems in this book, but will merely point out that auroral and airglow radiation may have an important bearing on the temperature structure of the atmosphere. Airglow radiation may be an important means of dissipating energy from some atmospheric levels; and if

36 2. SCATTERING OF RADIATION I N FINITE ATMOSPHERES

auroral radiation in the ultraviolet appreciably affects atmospheric ozone, as suggested by Murcray's [1957a] data, it may affect the heat balance in the lower atmosphere. In the Arctic a modification in the ozone abundance by aurorae may have important effects on tropospheric weather.

2.1.2. Definitions and Terminology

I, is the specific intensity. I, dv is the energy between v and v + dv transported across a unit area that is aligned perpendicular to the beam, in a unit solid angle per unit time (see Fig. 2.1). The units of I , are erg/cm2 sec sterad sec-l, or photon/cm2 sec sterad sec-l. I n general, the intensity at any point depends on the directions 0 (polar angle) and #I (azimuthal angle). If, however, I , (cos f?,#I) is independent of both angles, the radiation is isotropic.

I dw

FIG. 2.1. Definition of specific intensity. The energy transported per second across the unit area normal to 8,+ and into a cone of solid angle d w is d&,, = I,, dv d w .

9 = J I , dv is the integrated intensity. When the beam emerges from an atmosphere, 9 is measured by the observer and called the surfact brightness. The units are erg (or photon)/cm2 sec sterad, where it mus' be borne in mind that 9, as well as I , , refers to the energy transportec across a square centimeter taken normal to the beam.

The surface brightness of an extended source is independent of thc distance of the observer from that source, provided that there is nc extinction between source and observer. Imagine a photometer tha measures the radiation from a small solid angle falling on a given are per second. Suppose the source is of uniform brightness over an angula extent large compared with the field of view. Then as the photomete is moved to twice its original distance, the measured radiation is un changed: Although each square centimeter at the source now contribute only one fourth the radiation to the photometer that it formerly con

2.1. INTRODUCTION 37

tributed, the instrument now sees four times the original area. In each case the photometer is measuring what we have defined as surface brightness, which is therefore a property of the source and does not depend on the location of the observer. Similarly, the use of a telescope cannot increase the surface brightness, since the optics serve the same purpose, effectively placing the observer closer to the source. The telescope is nevertheless useful, of course, for observing extended objects that are not otherwise large enough to fill the field of view.'

7 r q is the net monochromatic j lux crossing a specified unit area per second and per unit frequency interval. (It is usual in radiative transfer theory to write the flux as n z instead of simply e, as the factor T cancels out in many applications.) If the intensity toward direction 0, r$ is I,, (cos 0,+) the net flux toward direction 0 = 0 (along the z axis in Fig. 2.1) is

= J I , (cos e, 4) cos e dw, (2.1) sphere

where dw is a differential solid angle: dw = sin 6 d+ do. Let us consider a specific example. Assume the intensity of radiation

emerging from a surface to be independent of 0 and+, as with a diffusely reflecting surface that scatters light according to Lambert's law. Then the net outwardflux (where we integrate Eq. (2.1) only over the outward hemisphere) is

x 2 p " t J = 2T ~ ~ ' 2 1 v cos 0 sin 8 d6 = XI,,. (2.2)

In this example, then, e = I,. and e is thus called the equivalent mean intensity.

J y is the mean intensity defined by

I"(& 4) dw. 4x sphere

For isotropic radiation, J y = I,,. Consider another example wherein radiation enters from only a very small solid angle, e.g., radiation from the sun. If we agree to measure the incident flux TE across a unit area normal to the beam, then in Eq. (2.1), cos 8 = 1 over the finite portion of the integrand and we see from Eqs. (2.3) and (2.1) that

I,, = %/4. (2.4)

Some authors call 4x J v the ommidirectionalflux.

See Appendix I1 for further discussion.


a, is the extinction coefficient per particle, in units of cmz. I t determines the probability that an incident photon is either scattered or absorbed.

t , is the vertical optical thickness at depth (or height) z in the atmosphere, given by

t , = 01, N(z ' ) dz', (2.5) 0

where N is the number density of particles capable of scattering frequency Y. The optical thickness will always be measured from the side of the atmosphere on which the radiation is incident. Usually this will be the top side, although in twilight problems direct sunlight enters i particular layer from below, on its way out of the atmosphere. Thc slant optical thickness will always be given in terms of the vertica thickness and is written t,./p, where p = cos 8. The angle 0 will alway! be measured from the normal to the atmosphere on the side of thc incident radiation (see Fig. 2.2).

T,, is the total optical thickness of the atmosphere. Go is the albedo for a single scattering. ho is the albedo for reflection by the ground.

normal to incident beom the atmosphere V3v[%09 40) I

FIG. 2.2. A scattering atmosphere illuminated by a parallel beam of light flux vg, , ( - po, &), where p = cos 8.

2.2. Equation of Radiative Transfer

The problem of atmospheric scattering that concerns us in this bo is as follows: Monochromatic light with a specified directional dependen is incident on the top or bottom of a scattering atmosphere with optic

2.2. EQUATION OF RADIATIVE TRANSFER 39

thickness 7, (see Fig. 2.2). An observer at the bottom of the atmosphere measures the intensity in different directions. We wish to relate the measured intensity to the incident intensity. The equations will also be developed for the case of incident radiation in a parallel beam (sunlight). It is important to understand that the transfer equation is formulated only for specific intensity I,. and not for the integrated intensity 9. For the case of radiation in a spectral line, it is usually necessary to integrate the emergent specific intensities over frequency to find the total surface brightness.

In this section we shall ignore complications introduced by polarization of the scattered light and suppose that individual scatterings follow a scattering phase function, p ( O ) , where 0 is the angle between the incident and emergent beams at a scattering particle. For isotropic scattering with an albedo 6, for each scattering, p = 3,. For conservative Rayleigh scattering the phase function is p ( 0 ) = $ (1 + cos2 0). So long as the incident beam is unpolarized and single scattering dominates, this phase function should give satisfactory results. But if secondary and higher-order scatterings are important, it is necessary to treat each polarized component separately.

When the incident radiation is from an extended source, as in the problems of tropospheric scattering of night-sky and auroral light, the symbol Iv( tv I p, 4 ) will refer to the entire radiation field (scattered plus direct radiation) at a specific optical depth and in a particular direction. However, in problems involving an incident parallel beam of light, such as the scattering of sunlight by sodium atoms in the upper atmosphere in twilight, it is convenient to use I v ( t u I p, 4) to represent only the diffuse part of the radiation field: that part that has undergone at least one scattering. Then l v ( t v I p, 9) will still, of course, be the total intensity except in the particular direction of the external radiation source.

T o formulate the equation of transfer for an extended source outside the atmosphere, consider the radiation lost and gained by a beam in a small cylinder, as shown in Fig. 2.3. The net change of intensity over distance ds is

where l v ( t v 1 p, 4 ) is the specific intensity at depth t , and toward direction p = cos 0 and 4. The integral term, called the source function, gives the intensity scattered into a unit solid angle in direction p,+.

40 2. SCATTERING OF RADIATION I N F I N I T E ATMOSPHERES

Writing d t , = Na,, dz and2 dz = - cos €' ds = - pds, we have for a radiation field],, that is symmetric about an axis normal to the atmosphere,

Here

and for the Rayleigh phase function it may be shown (see Problem 2) that

(2.9) 3

P(O) (p; p') = g [3 - p2 + (3p2 - 1) p'21.

normol to \ the atmosphere

\ incident rodiotion field

FIG. 2.3. Formulation of the equation of radiative transfer.

Equation (2.7) may be applied to the problem of scattering of airglow emission by the lower atmosphere. This problem has been investigated by Fesenkov [1935a, 1947~1, Barbier [I9444 1949u, 1952u, 1953~1, Piotrowski [ 1947~1, Guirguis and Hammad [1954a], and Constantine and Hammad [1956a, b] on the basis of the transfer equation. The problem is of importance both in deducing the actual amount of airglow emission (with corrections applied for background starlight and zodiacal light and light scattered in the atmosphere) and in finding the true

The minus sign in dz = - pds is introduced through our choice of signs in Figure 2.3: Specifically, z and t , are measured from the side of the atmosphere facing the external source and 8 is measured from the outward normal on the same side of the atmosphere. However, ds is always a positive differential.

2.3. APPLICATIONS OF THE TRANSFER EQUATION TO PHOTOMETRY 41

zenith-horizon variation in intensity (for the purpose of deducing heights -see Chapter 12). Barbier considered both Rayleigh’s phase function and isotropic scattering. For an accurate treatment Rayleigh’s phase function must be replaced with a phase matrix to take account of polarization. The best means of solving the problem of airglow photometry today involves the use of the X - and Y-functions obtained from the principles of invariance; we shall discuss this problem in Section 2.3. In practice the problem of tropospheric scattering is complicated by dust particles and water vapor, which have scattering phase functions different from that for molecules (Rayleigh scattering).

When the incident radiation comes from only one direction (pol +o + T), as from the sun during the day (see Fig. 2.2), the transfer equation is

(2.10)

The source function here involves not only the integral term but an additional term3 that gives the direct incident light scattered in direction p,+.

2.3. Applications of the Transfer Equation to Photometry

2.3.1. Photometric Observations of Aurorae

Ordinarily the aurora does not present a simple geometry, approximating neither a plane-parallel emitting layer nor a point source. Conse- quently, highly accurate solutions to the problem of scattered light

That the factor .FJ4 in the last term is correct may be verified by rewriting Eq. (2.6), where now I , represents scattered light only. That equation will then be unchanged except that the source function will clearly include the additional term

where Z,(O 1 - pe,&) is the incident intensity toward direction - ~ , , , 4 ~ . Then when the incident beam subtends only a small solid angle, 4 3” p e--tv‘/lo replaces this integral term, analogously to Eq. (2.4).


from the aurora are not practical. In principle an accurate solution might be obtained from the X - and Y-functions (Section 2.4) for distant point sources; these point sources could be integrated over the field of view of the aurora to give the scattering from the extended source. But the labor required for each correction is forbidding.

Some useful results can nevertheless be obtained from approximate solutions of the transfer equation. The corrections are important for purposes of deducing accurate variations of auroral brightness with height (luminosity curves); for obtaining the contribution to a weak, diffuse, auroral glow from scattered light, so that the importance of an extended but weak source of auroral excitation can be ascertained; and for deriving corrected relative intensities in different wavelengths, as the scattering cross section is sensitive to the color.

For a scattering atmosphere the equation of transfer (2.6) may be written4

dl at p - = I -$-, (2.11)

where the source function is

At the bottom of the atmosphere ( t = T), the formal solution to the differential equation (2.1 1) gives for the inward-directed radiation

Here I(0 1 - p, 4) is the incident radiation field outside the troposphere. -The radiation diffusely reflected at the top of the atmosphere is

where I(T 1 + p,+) is the outward intensity at the ground and is zero if the ground albedo is zero. By always treating the inward and outward fields of radiation separately, we may restrict ourselves to positive values of p and write + p and - p explicitly for outward and inward directions,

For brevity in the following we shall drop the subscripts v and write I for specific intensity, t for optical depth, etc.


respectively. One advantage of this procedure is that t/p in the exponentials always has a positive value.

This formal solution does not, of course, represent a solution of the physical problem so long as 2 is not given explicitly as a function of t , p, and 4. T o facilitate a solution we shall assume with Barbier [1944a] that in any direction / is independent of t. This approximation should not be too bad for optically thin atmospheres, wherein the mean intensity J is nearly the same at t = 0 as at t = 7. Then Eq. (2.13) becomes

In the following we shall assume isotropic scattering rather than the Rayleigh function (2.9) ; this simplification is justified, since the solution given here is only approximate in any case. The source function (2.12) is then equivalent to the mean intensity J of Eq. (2.3) times the albedo for single scattering, Q,, and is independent of p and 4.

If we consider the transfer problem as one of scattering with an albedo Go, the coefficients of scattering and absorption are in the ratio Qo/(l - Go) . The observed intensity is then given by

I(T I - p, 4) = I(0 I - p, 4) ecT/F + Go J ( 1 - r7’~), (2.16)

where r is computed from the total extinction coefficient for the tropo- sphere5. T h e first term on the right gives the contribution of the diminished direct radiation, while the second term is the scattered intensity. In the limit of large ~ / p , only scattered radiation of magnitude 6, J is observed; but it must be remembered that, strictly speaking, the assumption that J is independent of t invalidates the solution for large ~ / p . In the limit of small r /p , where the solution is most appropriate, the scattered intensity becomes Q, J r ip and thus increases toward the horizon as l / p = sec 8, where 0 is equivalent to zenith distance.

We have not yet discussed, however, the evaluation of J in Eq. (2.16). If observations of I(T j - p,$) have been obtained for a large region of sky, it is possible to evaluate J , and thence the scattered component, from these data. Barbier and Pettit [ 1952~1 have discussed two examples of such an analysis.

The ozone layer, which lies above the scattering atmosphere, is an important absorbing region and must be allowed for separately. This correction is applied to the I (0 I - p, 4) term only and can be accomplished by writing Z(0 I - p, 4) = Zinc( - p, 6) exp ( - ~, , /p) ,

where T,, applies to the extinction from ozone absorption and It,, is the incident intensity above the ozone layer. With ozone absorption thus allowed for, Go applies only to absorption in the lower atmosphere. Note that T in all these equations must not include the ozone absorption.


In the first case, if the sky is observed in an area where the auroral emission itself is weak and uniform, then in this region I(0 1 - p, +) is a constant. Writing Eq. (2.16) as

and plotting measured values of ~ ” { ‘ I ( T I - p,+) versus ~ ~ ( e ~ ’ f i - I ) , we shall obtain a straight line, from which I(0 1 - p,+) and J can be deduced. From an aurora observed in Alaska, Barbier and Pettit [1952a] ascertained by this method that the scattered light at A5577 from the southwest (away from the bright aurora) at zenith distance 80°, was nearly nine times brighter than the direct radiation from the same direction. It is evident, then, that scattered emission can be important, especially near the horizon.

Barbier and Pettit’s second example applies to the case where the auroral intensity changes gradually with time or when the aurora moves north or south through a period of several observations. The procedure is to use the observed intensities to evaluate an approximate J , which we shall call Jo, by direct integration of Eq. (2.3). Usually a laborious numerical integration can be shortened by making some simplifica- tions in the geometry of the auroral structure in the sky (cf. an example below). Integrating I only over the downward hemisphere, we can then make a rough allowance for ground reflection by multiplying the integral by an appropriate factor (say, 2 for snow cover). Thus Jo may be only a crude approximation to the true J , but we might expect that for all observations during the night that J/Jo would be a constant, C. Hence we replace J with CJo in Eq. (2.16) and plot I(T 1 - p, #) versus Jo for a particular region of the sky and for observations at several times. If we choose a direction where the direct auroral light is insignificant or at least constant, Eq. (2.16) will give a straight line, from which I(0 1 - p,+) and C can be derived. If the aurora itself becomes important in the observed direction, then the line will start to deviate from linearity.

Once J is derived, the observed intensities in any direction may be corrected by Eq. (2.16). This entire discussion has assumed that the absorption and scattering coefficients (or, equivalently, the extinction coefficient for the troposphere and the albedo of single scattering) are known. Even if the total extinction coefficient (including ozone) is derived from photometric observations of stars several times a night, some assumption must be made regarding the scattering and extinction of the lower atmosphere. The contributions from various types of scattering and absorption are summarized in Section 2.5.2.


The case of a single auroral arc provides a simple example of auroral photometry, and we. shall use it to illustrate Barbier and Pettit’s technique. For an approximate evaluation of J we may consider the arc to be a band of uniform intensity I, subtending at its highest point in the sky (at p = p,) a small angular width, do,,, measured along a vertical circle through the zenith. We further assume that the arc lies approximately along a circle in the sky, with its center on the horizon and in the azimuth, say, of the magnetic pole. We may then find J from an integration over the hemisphere about an axis through magnetic north (rather than through the zenith). Neglecting reflection at the ground, we have for a first approximation to the mean intensity,

O - 4x hemisphere

(2.18)

Writing J = CJo, we obtain from Eq. (2.16),

The constant C allows for the uncertainties involved in lo, including the ground albedo. Changes in the brightness or position of the arc during the period of the observations can be allowed for by obtaining an approximate I,, d6,, and po = cos 6, for each set of observations of I(7 I - p,+) (where + will be a constant for tracings across the auroral arc at its maximum height).

If at some distance from the arc the background intensity from direct auroral activity is low and uniform, then I(0 I - p,+) in this direction and the constant C can be ascertained from a graph as described above. If there is an appreciable background of direct emission from the aurora or airglow, the luminosity curve of the arc must be corrected for this emission as well as for the scattered intensity. However, if the function J is derived from intensity measurements far from the arc, there is the danger that the scattering from the direction of the arc will be underestimated by perhaps a factor of two in some cases: The simple theory given here does not allow for the Rayleigh phase function, which is most important in the forward and backward directions of scattering.

The amount of scattered light from the direction of a single auroral arc will generally be quite small compared with the arc itself. For observations near the horizon, however, scattering from bright auroral forms in other regions of the sky can be important.


2.3.2. Photometric Observations of the Airglow

The most complete solution of this problem on the basis of the transfe equation has been obtained by Barbier [1952a]. Equation (2.13) give! the intensity at the ground in terms of the atmospheric emission anc the scattered radiation. Similarly, the formal solution can be writter down from the transfer equation (2.11) for any height in the atmospherc (Chandrasekhar [1950a, p. 121):

and

We shall obtain a first-order solution for conservative isotropic scattering ( = J ) , following Barbier’s [1952a] development, albei with some modifications. In a first approximation J may be regardec as a constant throughout the atmosphere; we shall evaluate J at t = T,C on the assumption that J has little dependence on t. Putting I fron Eq. (2.20) in Eq. (2.12), we have for an azimuth-independent field o radiation,

Therefore,

where the exponential integral is

(2.23


In Eq. (2.22) I(0 I - p) is the incident intensity on the scattering atmosphere and may be expressed by the van Rhijn relation, eq. ( 12.2),6 with an appropriate modification for ozone absorption. Thus if we let T~ be the vertical optical thickness of the ozone layer,' the first integral term in Eq. (2.22) becomes

1: I(0 1 - p) ecTi2M d p = 1, @o(T/2), (2.24)

where I, represents the zenith intensity above the ozone layer and

(2.25)

Here a is the radius of the earth and z is the height of the airglow excitation. The function 0, may be evaluated with the aid of the Gaussian quadrature formula (Chandrasekhar [ 1950~1).

T o evaluate the outward intensity at ground, I(T I + p), in Eq. (2.22), we must first find the net outward and inward flux at the ground. If the ground reflects according to Lambert's law (diffuse reflection), then I(T I + p) = constant (= Ig) and by Eq. (2.2)

T 9 ( o u t ) (T) = 2n j' Ig p d p = n I,. 0

(2.26)

The inward flux, obtained by putting Eq. (2.13) in Eq. (2.1) and taking Y = J(7/2), is

The reader should note that the meaning of the angle 0 (and p = cos 0) is slightly different in this chapter and in Chapters 11 and 12. Throughout the book 0 is the polar angle in the atmospheric layers where radiation is emitted or scattered. In the present problem, we are concerned with scattering in the troposphere, so that 0 becomes the zenith angle. In Chapters 11 and 12 0 is the polar angle in the emitting layers and hence 1; is used to denote zenith angle for an observer on the ground. This inconsistency in denoting zenith angle is necessary to preserve consistency through the book in the radiative-transfer notation.

'Strictly speaking, there should be a small correction to the factor l ip = sec 0 for the optical path length in the ozone layer, as this layer is also at a finite altitude, but such a refinement is usually neglected in practice.


The reflected intensity Ig is determined by the condition that

where A, is the ground albedo. By Eqs. (2.26) and (2.27), this condition becomes

I g = 2Ao{Io @1(7) t- J (d2) [g - E3(7)1)* (2.29)

From Eqs. (2.22) and (2.24), we have

With I , determined by Eq. (2.29), we obtain, finally,

(2.30)

(2.31)

The observed intensity is then related to the intensity outside the atmosphere by Eq. (2.16), which may be written, to take explicit account of ozone absorption, as

T(T I - p) = line( - p) e-(7+70)’1~ + J (1 - e-7’p), (2.32)

where Iinc (- p) = I(0 I - p) exp (+ ~ ~ / p ) is the intensity above the ozone layer, and where is given by Eq. (2.31). The zenith intensity above the atmosphere, Iinc(- l ) , is equivalent to I, in Eq. (2.31) and may be computed with Eq. (2.32) from the measured zenith intensity.

Barbier [ 1952~1 has obtained an expression for the scattered intensity on the basis of Rayleigh scqttering; further, he has improved on the approximation of taking $(t) as constant with t by dividing the atmosphere into n finite Iayers and letting$(t) vary linearly between these layers. Huruhata and Tohmatsu [1957u] have derived J for isotropic scattering by an alternative technique, based on imposing the condition of a constant net flux.

Merely in order to compare the accuracy of this type of solution with that obtained from the X - and Y-functions in Section 2.5, we shall evaluate the intensity for a simple set of boundary conditions. When the emission height x in Eq. (2.25) is small, the incident intensity is approximately I i n c ( - p) = Io/p. Then from Eqs. (2.25) and (2.23),

2.4. x- AND Y-FUNCTIONS I N PROBLEMS OF RADIATIVE TRANSFER 49

When ozone absorption is neglected (T,, = 0), the observed intensity is related to the incident intensity by

An exact solution to this problem (pure isotropic scattering; incident intensity proportional to sec 8) is obtained in Section 2.5.1, where we shall discuss the accuracy of this equation (see Table 2.1).

2.4. The X- and Y-Functions in Problems of Radiative Transfer

A powerful new technique for treating transfer problems in finite atmospheres was developed by Chandrasekhar [1950a] on the basis of four principles of invariance, some of which were first introduced in transfer theory by Ambarzumian [1942a]. This approach to the problem is quite different from the method of the integro-differential equation of transfer. The invariance technique of solving problems and the use of the X - and Y-functions are not widely understood, even by many who are familiar with the older methods of solving transfer problems.

Here we shall be able to provide only a brief introduction to the topic, but we may hope that students of the upper atmosphere will gain some familiarity with this method of treating radiation problems. It is assumed in the following that the reader is acquainted with the transfer equation as developed and applied in the preceding portion of the chapter. As in the previous sections, the only applied problem specifically discussed below is the correction of photometric observations. Nevertheless, the general theory outlined below will be utilized in discussing airglow problems in later chapters.

2.4.1. Formulation of the Transfer Problem with the Principles of

The problem we consider is the diffuse transmission and reflection by a plane-parallel atmosphere on which a parallel beam is incident in direction - po, +,, with a flux .rrF normal to the beam. The equation of transfer for this problem has already been given [Eq. (2.10)]. As in the preceding sections we shall omit writing subscripts Y, but it must be borne in mind that the entire discussion applies to monochromatic light.

lnvariance

50 2. SCATTERING OF RADIATION IN FINITE ATMOSPHERES

The light diffusely reflected from this atmosphere will now be expressed in terms of a scattering function S , still to be derived, but which is related to the reflected intensity by its defining equation,

That is, the function S is defined as being proportional to pI(0 I p, 4) ; it turns out that then S will be symmetrical in p, 4 and po, do.

Similarly, the light diffusely transmitted at the bottom (t = T ) of the atmosphere defines the transmission function T :

For the moment we shall neglect any ground albedo and consider radiation striking the surface at t = T to be completely absorbed. At a specific optical depth t there are then three distinct fields of radiation: The reduced incident flux of rrF exp ( -tipo) in direction - po, 40, and the diffuse radiation field, I ( t 1 p,$), which we divide into the outward (0 I p I 1) and inward (- 1 I p < 0) directed radiations. These diffuse radiation fields are written I ( t 1 + p,$), (0 I p _< l), and

The principles of invariance state essentially that if we split an atmosphere of thickness T into two layers of thicknesses t and ~ - t , then each portion will in turn have scattering and transmission functions appropriate to atmospheres of the reduced thicknesses*. This statement is regarded as obvious and is asserted without proof. Let us now see how it is applied to obtain a mathematical formulation of the invariance principles. We shall limit the present discussion to the relatively simple case of isotropic scattering with albedo 6,. (More general laws of scattering, including the Rayleigh phase function and phase matrix, are treated by Chandrasekhar.) As the scattered radiation is then azimuth-independent, so also will be the scattering and transmission functions, S and T.

I ( t I - 1.,4), (0 < p I 1).

8 T h e term invariance principle seems to have arisen from the statement of these principles for a semi-infinite atmosphere. In this case, the emergent radiation is invariant to the addition or subtraction of layers of atmosphere of arbitrary thickness. However, for finite atmospheres the principles may be considered as expressing the invariance of the laws of diffuse reflection and transmission to the addition to (or removal from) an atmosphere of a layer of arbitrary thickness at the top, and to the simultaneous removal from (or addition to) the atmosphere of a layer of equal optical thickness at the bottom.


The first invariance principle (see Fig. 2.4) is that the outward intensity at some depth t results from the reflection, by the atmosphere below t , of two incident fields of radiation: ( 1 ) the reduced incident flux nFe-tl l ‘o

and (2) the diffuse radiation I ( t 1 - p’), (0 < p’ 2 l ) , emerging from the top section of thickness t . In mathematical language, with Eq. (2.35), we haveg

t = o

t

FIG. 2.4. Formulation of the first principle of Chandrasekhar [ I95Ou] ; courtesy Oxford

invariance. Adapted from University Press.

Three other principles may be formulated similarly. We refer to Chandrasekhar [1950a, p. 162 et seq.] for further elaboration, and with

That the integral term in Eq. (2.37) is consistent with Eq. (2.35) can be seen when Z(0 I -p’, 4’) subtends only a small solid angle. In that case we may write

Z(0 I - P’,4’) = 79 S(P’ - Po) 8(+, - 40)

(where 8 is the Dirac 8-function), which may be proved by putting this expression in Eq. (2.1) and integrating. Further, with this expression for Z(0 I - p’, +), we write the diffusely reflected radiation as

(2.37a)

Hence the integral term of Eq. (2.37) involves the same S function as that defined by Eq. (2.35).


this brief indication of how the equations are derived, we merely state the remaining three fundamental equations:

2.4.2. Solution for the S- and T-Functions

The solution of these four equations, to find the form of S and T , is rather lengthy and we shall omit most of the details here. The procedure is first to differentiate the four equations with respect to t and then pass to the limit t = 0 in Eqs. (2.37) and (2.40) and to t = T in Eqs. (2.38) and (2.39). In addition, we apply the boundary condition that there is no incident diffuse radiation: I(0 I - p) = I(T I + p) = 0.

For example, Eq. (2.37) becomes

From the equation of transfer (2.10) (where now p = 6, for isotropic scattering) the derivatives of I in Eq. (2.41) and the three similar equations may be expressed in terms of emergent intensities at t = 0 and t = r. Further, these emergent intensities may be written in terms of S and T by means of Eqs. (2.35) and (2.36). Hence one obtains four equations in S(T 1 p ; po), T(T 1 p ; po), as/&, and aT/& and in which I does not appear.


An example of one of these equations (Chandrasekhar [1950a, p. 178, Eq. (62)]) is

T o simplify the form of the four basic equations, of which Eq. (2.42) is one example, we define

and (2.43)

(2.44)

These are the so-called X - and Y-functions; they are functions of T ,

the total thickness of the atmosphere, and the albedo Go, as well as p. With these definitions the equations in the set including Eq. (2.42) become

8s -- aT - Go Y(P) Y(UO),

(2.45)

and

Eliminating as /& from the first and last of these equations, we find

1 1

and the middle two equations give

I t may be well to remind ourselves at this point that we are seeking a solution for S and T as functions of T , p, po, and Go. I t is clear from the above two equations that this objective is accomplished if values of


X ( p ) and Y(p) can be obtained. Substituting these two equations into the defining equations (2.43) and (2.44), we obtain the following integral equations for X and Y

With these integral equations, numerical values of X ( p ) and Y(p) may be computed by an iteration process. T o start the iterations, one may use the asymptotic values for T - 0 , i.e., X ( p ) .+ 1 and Y(p) +

e c T ' P . Numerical values of the X - and Y-functions for isotropic scattering have been published by Chandrasekhar, Elbert, and Franklin [1952a, Paper I] for several values of T between 0.05 and 1.00; for 6, between 0.5 and 1.00; and for p between 0 and 1.00.

For the particular case of 8, = 1 (conservative scattering) there is an ambiguity in the solution, in that if X and Yare solutions of Eqs.(2.48) and (2.49), then so are X' = X + Q p [ X + Y] and Y ' = Y - Qp[X + Y], where Q is an arbitrary constant. To find which member of this one-parameter family corresponds to the physical problem, it is necessary to introduce another equation (the so-called K-integral) that the X - and Y-functions must satisfy. Without delving into the details (see Chandrasekhar [1950a, p. 2121) we may state that the appropriate functions for 5, = 1 have been obtained and tabulated by Chandrasekhar and Elbert [1952a, Paper 111. For 6, = 1, then, one should not use the values listed in Paper I ; rather, the values listed as X* and Y* in Paper I1 should be used, as the ambiguity has been resolved for these values.

The solution of the problem of diffuse reflection and transmission by a finite, plane-parallel atmosphere with isotropic scattering can thus be readily obtained with the tabulated X- a'nd Y-functions and the foregoing equations. From Eqs. (2.35) and (2.46) the diffusely reflected intensity is

and by Eqs. (2.36) and (2.47) the diffusely transmitted intensity is

In the next section we give one example of a problem that can be solved exactly with these X - and Y-functions.

2.5. CORRECTION OF PHOTOMETRIC OBSERVATIONS 55

2.5. Correction of Photometric Observations of the Airglow for Tropospheric Scattering

2.5.1. Exact Solution for a Plane-Parallel Emitting Layer and Iso-

The treatment of transfer problems by the invariance principles made it possible for the first time to solve exactly a number of problems for finite atmospheres. The accuracy of any solution of these problems is limited only by the accuracy to which the X - and Y-functions have been tabulated.

Let us take a problem that has some resemblances to the airglow emission that is scattered in the troposphere. We shall oversimplify the physical problem in the interest of illustrating the transfer theory. Let emission originate in an optically thin, plane-parallel layer, so that the incident intensity is IInc( - p) = Io/p, where I , is the zenith intensity outside the scattering atmosphere.1° The atmosphere scatters light isotropically with an albedo 3, for single scattering. First we solve the problem for no ground reflection and then we shall derive a correction factor for a ground albedo.

The radiation diffusely reflected by the atmosphere is given in terms of the scattering function by the first equality of Eq. (2.37a):

tropic Scattering

Similarly the diffusely transmitted radiation is

(2.52)

(2.53)

Normally the procedure for evaluating the integrals in these equations would involve substituting S and T in terms of X and Y from Eqs. (2.46) and (2.47). For this particular problem, however, we note that the integrals are precisely the same as in Eqs. (2.43) and (2.44) defining X and Y. Hence the total radiation (primary emission plus diffusely reflected light) seen above the Earth is

(2.54) I

P = " X ( p ) .

lo Note that we neglect the van Rhijn correction for a finite emission height and ozone absorption between the emitting layer and the atmosphere.

56 2. SCATTERING OF RADIATION IN FINITE ATMOSPHERES

Similarly, the total radiation observed at the ground is

+ ztrans(T I - p) 1 ( ~ 1 - p) = zinc(- p)

I P

= 0 Y ( p ) . (2.55)

Equation (2.55) thus gives the desired solution for the total intensity of the emitting layer as seen through a scattering atmosphere.

We shall now generalize the solution for the case of a ground albedo A,. First of all, we must obtain an expression for the outward intensity I , at the ground. We shall assume that I , is independent of p (ground reflection by Lambert’s law). Then the inward intensity at the ground is composed of the intensity of Eq. (2.55) for no ground reflection plus the radiation Ipf)( - p) which comes from the reflection of I, by the atmosphere. Thus

where the second equality defines s(p). The total intensity of the sky as seen from the ground will now be

4‘ I - (2.57)

in place of Eq. (2.55).

flux, as in Eq. (2.28), we find Setting the outward flux at the ground equal to A, times the inward

Thus the ground-reflected intensity may be written

where

and

(2.59)

(2.60)

(2.61)


Substituting Eq. (2.59) in Eq. (2.57), we find

(2.62)

Chandrasekhar [1950a, pp. 274-2751 expresses s(p) in terms of X(p) , Y ( p ) , and their moments. The quantities Po, S, and other moments of X and Y have been tabulated versus T by Chandrasekhar and Elbert [ 1952al.

In Table 2.1 we give some values of I ( , I -p)/Iinc( - p) computed from the exact equation (2.62) for Go = I , along with values of the same ratio obtained from the approximate solution (2.34) of the transfer equation, and values based on Rayleigh scattering for an emitting layer at 100 km (obtained in the next section). Although the computations have assumed that the incident intensity is proportional to I/p, we might expect the ratios computed in Table 2.1 to be only mildly sensitive to the precise form of Iinc( - p). Thus if - p) is corrected for the finite emitting height (van Rhijn correction) and ozone absorption, the observed I(7 I - . p ) might still be given fairly accurately by the ratio I(‘ I - p)/ Ifnc(- p) in the table. Another deviation from the physical problem, however, lies in the assumption of isotropic scattering. In the next subsection we discuss some calculations based on Rayleigh scattering.

TABLE 2.1 I ( . 1 - p)/Iinc( - p) IN THREE APPROXIMATIONS*

5 = 0 5 = 750

T Eq. (2.34) Eq. (2.62) Eq. (2.68) Eq. (2.34) Eq. (2.62) Eq. (2.68)

0.05 1.037 1 ,044 1.160 0.903 0.908 0.889 0.10 1.047 1.061 1.263 0.801 0.809 0.790 0.15 1.049 1.070 1.326 0.712 0.721 0.704

* The table gives ratios of the observed intensity to the incident intensity, with ozone absorption neglected. Since the scattering atmosphere is close to the ground, the zenith distance 5 is equivalent to the polar angle 0 used in the text, where p = cos 0. Equation (2.34) is Barbier’s approximate formula with conservative, isotropic scattering and Iinc( - p) = I o /p . Equation (2.62) is the exact solution for the same conditions. Equa- tion (2.68) uses Ashburn’s tables for Rayleigh scattering and an emitting height of 100 km. In using this equation, we have set +o = 0 (no ozone absorption) and computed ImC( - p)/

Iinc( - 1) with the van Rhijn formula (2.66). Note that when T, = 0, I(0 I - p) is the same as Zinc( - p ) . In all examples the ground albedo is ho = 0.


2.5.2. Solution with Rayleigh Scattering

The problem of atmospheric scattering by molecules is considerably more complicated than the problems involving isotropic scattering that we have already discussed. We shall not go through the details here- even in the brief fashion in which we reviewed the isotropic case-but shall merely summarize the calculations that have been made.

First of all, let us imagine an incident parallel beam of light on a plane-parallel atmosphere. This problem has immediate application to the brightness and polarization of the daytime sky,” and later we shall show how its solution may be generalized to the airglow problem.

When natural (unpolarized) light undergoes Rayleigh scattering, it becomes polarized. Each subsequent scattering process therefore involves incident light that is already polarized; hence for an accurate solution, one must treat each polarization component separately. The problem is best treated in the manner of Chandrasekhar [1950a], who considers the intensity as a vector I, composed of Stokes parameters. The scattering and transmission functions become tensors. In place of Eq. (2.36) the diffusely transmitted intensity is now given by

(2.63)

where x F ( - po, #o) is the flux (perpendicular to the beam) of a parallel beam incident in direction - po, do. As with the intensity, the vectorial flux specifies not only the scalar flux but its polarization.

Chandrasekhar [1950a] has presented an exact solution for this problem in terms of X- and Y-functions that are similar (but not identical) to those discussed earlier for the isotropic case.12 Four pairs of X- and Y-functions are necessary to describe Rayleigh scattering

Y,.. Of these functions, X, and Y , belong to the conservative class and in this sense are analogous to the isotropic solution for 6, = 1. The particular XL and Y, functions that have been tabulated are the so-called standard solutions and the solution for the emergent scattered and transmitted intensities has accordingly been expressed in terms of these functions.

and these functions are denoted X(l), Y(l); Xt2), Y@); X,, Y,; and X r ,

l1 For a review on the subject of polarization of the daytime sky see Sekera [1956a]. la In general, the integral equations for X - and Y-functions are identical to Eqs. (2.48)

and (2.49) except that in place of Go (for isotropic scattering), one has a characteristic function Y(p’) under the integral. For Rayleigh scattering these Y-functions are fairly simple, e.g., 4 (1 - P ’ ~ ) , (3/16) (1 -+ P ’ ~ ) ~ , etc.


The X - and Y-functions necessary for numerical solutions to Eq. (2.63) have been tabulated by Chandrasekhar and Elbert [1954a] and by Sekera [1952a] and Sekera and Ashburn [1953a].13

Now let us see how these solutions may be applied to the airglow problem. We wish to find the diffusely transmitted intensity given, in a fashion analogous to the first equality of Eq. (2.37a), by

Also, if we treat TF as photon/cm2 sec per steradian and integrate Eq. (2.63) over the hemisphere, we have

Hence if we replace TF(- p‘, 4’) by I(0 I - p‘, 4’) and integrate the solution for a point source over the whole sky, we have the airglow solution.

Integrations of this nature have been performed by Ashburn [1954a]. The incident intensity was taken to be independent of the azimuth and characteristic of an emitting layer at height z. Hence, according to the van Rhijn function [Eq. (12.3)],

4 0 I - 1 ) { 1 - [a/(a + z)]2 ( 1 - p’”))”2 ’

I (0 I - p’, 4’) = - (2.66)

where I (0 1 ~ 1) is the radiation incident from the zenith and a is the Earth’s radius. Hence Itrans will obviously be azimuth-independent.

The additional intensity of the sky arising from light scattered upward at the ground is obtained analogously to our solution of this problem for isotropic scattering in the preceding section. This additional intensity is called I*(T I - p).

Ashburn’s [1954a] tables give values [in units of I(0 I - l)] of Itran* (T 1 - p) and I*(T I - p) (the latter for albedos of A,, = 0.25, 0.50, and 0.80) for several values of the zenith distance of observation (i.e., p), for a range of T between 0.01 and 1.00, and for u^ = 100 km, 200 km, 300 km, and 03 in Eq. (2.66).

Sekera and Ashburn’s [1953a] tables are computed with an approximation valid for small T , rather than by Chandrasekhar’s process with the defining integral equations. Their numerical values for T = 0.15, and 0.10, and to some extent even for T = 0.05, differ slightly from the tabulations of Chandrasekhar and Elbert [1954a].


These tables are the best means available for making photometric corrections to the airglow, although they should not be considered as providing an exact solution to the problem. The values for small T ,

which is the region of interest for the observable spectrum, are based on the computations of the X - and Y-functions by Sekera and Ashburn [1953a] that we mentioned earlier 13. The airglow radiation is not incident strictly according to the van Rhijn function (2.66). Even in the idealized case of a uniform emitting layer, the ozone absorption modifies the radiation field before it reaches the scattering atmosphere. This modification reduces the incident intensity at large zenith angles (compared with that from the zenith), so that an approximate correction for this effect might be achieved by using the tables for a height somewhat greater than the real emitting height.

Scattering corrections are generally small, however, and these modifications are usually ignored. Moreover, there is a considerable but unavoidable uncertainty in the results arising from uncertainties in the ground albedo, A,, optical thickness of the scattering atmosphere, T ,

ozone absorption, T~ (see below for a discussion of corrections for ozone), non-Rayleigh scattering by dust and haze particles (Ashburn [1955a] and Seaton [195621]), and even atmospheric turbulence (Sekera [1957a]).I4 When all these matters are considered, it becomes clear why observations made very near the horizon (say, at zenith distance 85O), where scattering can become very important, are likely to give unreliable results.

If the intensity above the ozone layer is written Iinc(- p), then the radiation field incident on the scattering atmosphere is I(0 1 - p) = .Zinc( - p)e-TOlp, where T~ is the optical thickness of ozone. The observed radiation at the ground is then

I ( T 1 - p) = Iinc(- p) e-(7+70)lp + Itrsns(T 1 - p) + I*(. I - p) . (2.67)

The tables of Ashburn [1954a] give Itrans and I* in ini ts of the zenith intensity entering the scattering atmosphere, I(0 I - I). Hence we write the solution for a plane-parallel scattering atmosphere,

I(T 1 - p) = Itnc( - p) e-(7+r0)/i4

lP Uncertainties have also been introduced by the irregular distribution of emission over the sky and by extraterrestrial light; but modern machine methods of analysis of a large number of observations and instrumental techniques that exclude continuous radiation now minimize these effects (see Section 12.1.3).


Note that 7 applies to the scattering atmosphere only and 70 to the ozone layer. According to this equation the values obtained from Ashburn's tables should be multiplied by Zinc(- l)e-?O to give the scattered component of the radiation. This incident zenith intensity is related to the observed zenith intensity by setting p = 1 in Eq. (2.68):

(2.69)

Thus Eq. (2.68) may be solved for Ifnc(- p) in terms of the observed intensity, Z(7 I - p), and Ashburn's correction terms. In this manner the distribution of intensity above the atmosphere can be derived (see Table 2.1).

Equation (2.68) may be partially modified for deviations from a plane-parallel atmosphere by replacing the exponential extinction term, e-(T+70)'~t, with e-('+'a)m(p), where m(p) is the atmospheric air mass (relative to the zenith) in direction p. The scattering correction based on a plane-parallel atmosphere may still be retained, however, without appreciable loss of accuracy.

Table 2.2 presents some values of optical thickness of the atmosphere at different wavelengths and from different sources of extinction, collected by Roach and Meinel [1955a].

TABLE 2.2

EXTINCTION COEFFICIENTS (ATM-I)

(REFERRED TO SEA-LEVEL)

T 5300 5577 5893 6300

Molecular (Rayleigh) 0.112 0.090 0.073 0.055 Ozone (0.25 cm) 0.021 0.029 0.034 0.028 Sum 0.133 0.119 0.107 0.083 Observed (Mt. Wilson) 0.164 0.150 0.125 0.103 Difference 0.031 0.031 0.018 0.020


PROBLEMS

1. Derive an expression analogous to Eq. (2.31) for the source function 9 to be used in correcting airglow observations, when the atmosphere scatters isotropically with an albedo for single scattering

2. Given the Rayleigh phase function, p ( 0 ) = $ (1 + cos2 O), show 4 0 < 1.

by solving the spherical triangle that

p ( p , (6; p’, (6’) = s [1 + p2 + (1 - p2) (1 - cos2 ((6 - 4’) + 2 p p‘ (1 - p2)”2 (1 - p’2)1’2 cos (4 - $’)I.

Then use Eq. (2.8) to prove Eq. (2.9).

Chapter 3. Magnetic Fields, Charged Particles, and the Upper Atmosphere’

A mixed assortment is offered in this chapter, including brief discussions of several topics that form a background for the remainder of the book.

3.1. The Geomagnetic Field

3.1.1. The Main Field

Scalar Potential.-In the general case a vector potential can be used to describe a magneticjeld H; and in regions where there are no currents, the field may be represented by a scalar potential Q, such that

H = - VQ. (3.1)

The Earth’s field may be divided into an internal and external part. The external field arises from current systems in the ionosphere and perhaps higher, and although it is important in providing most of the time variations (Section 3.1.2), by far the main part of the field comes from inside the Earth,

The scalar potential for an arbitrary magnetization can be expressed as a series

a = a(o) + a(l) + a(z) + ... Q ( n ) , (3.2)

where Q(j) is the potential of a pole of order 2’ (e.g., see Stratton [1941a, pp. 172-1831). Since magnetic monopoles evidently do not exist (as do single electric charges) the “Coulomb term” f2@ vanishes, and the leading term is that representing a dipole, Qcl). The potential of a dipole field may be derived by adding algebraically the scalar potentials of two single poles, each of which gives an inverse square jield. Thus at a distance Y from the origin,

Gaussian (cgs) units are used in all electromagnetic equations in this book. Specifically the current density J is measured in electromagnetic units (emu), but conductivity u

is in electrostatic units (esu).

63

64 3. FIELDS, PARTICLES AND THE ATMOSPHERE

In the last expression the gradient is taken at the field point (that is, the dipole is held fixed). Here M is the magnetic moment of the dipole, and three quantities are necessary to specify its magnitude and orientation.

It is convenient for some purposes to write the potential in terms of spherical harmonics. If the orientation of the vector M is characterized by direction cosines a, /3, and y , Eq. (3.3) may be written

(3.4) M !W) = [(a cos 4 + /3 sin 4) Pi (cos 0) + y P; (cos O ) ] ,

where P; (cos 0) is the associated Legendre function, and 0 and rj5 are polar and azimuthal angles (see Fig. 3.1). Since a2 + /3' + y2 = 1, the four quantities a, p, y , and M provide three independent parameters. In the same fashion the quadrupole (see Stratton [1941a, p. 1821) and

FIG. 3.1. Position vectors and angles of the coordinate systems as used

throughout the book.

higher-order terms may be expanded in spherical harmonics. If the magnetic field is measured at a sufficient number of points over the Earth's surface, the various constants in the dipole and higher potentials may then be determined through harmonic analysis. A number of such analyses have been carried out since the original work of Gauss in 1838 (see Chap- man and Bartels [1940a, Chap. 181). With the origin taken at the Earth's center, the quadrupole and higher terms contribute much less at the surface (Y = u) than does the dipole. Because the field of a-centered dipole (which is equivalent to that of a uniformly magnetized sphere) repre-

sents the actual field rather well, it is a widely used approximation. The Centered Dipole.-The coordinates of the geomagnetic poles (that is, the axis points of the centered dipole) that are in general use are those quoted by Chapman and Bartels [1940u, Chap. 181. These poles are at latitude A, = 78P5 N, longitude + p = 69" W (near Thule, in northwest Greenland) and at latitude 78P5 S, longitude 11 I" E. The magnetic moment of the dipole is M = 8.1 x loz5 gauss cm3. An analysis for the epoch 1955.0 by Finch and Leaton [1957a] gives A, =

78?3 N, + p = 69PO W. However, since many calculations of geomagnetic

3.1. THE GEOMAGNETIC FIELD 65

positions, etc., have already been made with the older values and since the small error involved is negligible compared with the error of neglecting the higher-order multipoles, there is considerable advantage to these values being universally adopted as standard.

From Eqs. (3.1) and (3.3) we have for the field

r Y6

= 3 ( M * r ) - - (3.5)

By convention, the pole in the northern hemisphere attracts the northern end of a compass needle and hence is itself a pole with southern magnetization. Thus we may picture the lines of force of the dipole as proceeding from south to north outside the Earth and from north to south within the 4‘magnet.” We shall choose the z-axis along the axis of the dipole and positive toward the north. Then the dipole moment M is oriented along the - z direction.

With the axis so chosen, we have in Cartesian coordinates, from Eq. (3.51,

M - - r5 (3z2 - y2)] . (3.6)

From this equation it readily follows that

(3.7) M

H = (H: + H: + H;)Ij2 = (1 + 3 sin2 Am)112,

where A, is the geomagnetic latitude. The value quoted above for M corresponds to HA=, = 0.315 gauss for Y = a at the equator; H is twice as great at the axis point of a dipole as at the equator.

With M oriented along - z, it readily follows from Eq. (3.5) that the field components along r and perpendicular to r in the meridian plane are

At any point the direction of the field H is said to be tangent to the line of force at that point. Thus the equation for a line of force is given by

- 2 tan A,,, -=- - - dr H , r d h H A (3-9)

which integrates to Y = b C O S ~ A,, (3.10)


where b is a constant, different for each line of force. Physically b can be expressed in terms of the equatorial field (HA=,) on that particular line of force or in terms of the latitude where the line of force intersects the Earth (Am's) :

(3.1 1)

Equation (3.9) also relates i , the angle at which the magnetic field at the Earth's surface is inclined to the horizontal, with A,, the geomagnetic latitude (see Fig. 3.2):

tan i = 2 tan I A,, I. z axis

N. Geomagnetic

(3.12)

f Equatorial Plane A r

FIG. 3.2. The Earth's dipole field.

The geomagnetic pole and the meridian plane through the geographic and geomagnetic poles define the geomagnetic coordinate system (see Fig. 3.3). The geographic coordinates (latitude A, longitude 4) are related to the geomagnetic coordinates (A,, 4,) by the following equations obtained from the spherical triangle in Fig. 3.3:

sin A, = sin A, sin h + cos A, cos h cos (4, - 4) (3.13)

and

(3.14)

Here A, (= 7 8 3 ) and 4, (= -69") are the geographic latitude and longitude of the north geomagnetic pole. Alternative formulae involving the use of an auxiliary angle have been quoted by Chapman and Bartels


[1940a, p. 6461. McNish [1936a] has given nomograms for the determination of A,,L and +,,, if great accuracy is not required ; also Hunten's [ 1958al nomogram may be used.

GEOGRAPHIC POLE

FIG. 3 .3 . Spherical triangle relating geographic and geomagnetic coordinates.

The magnetic-dipole declination $ (see Fig. 3.3) is the angular separation of the two poles as seen from a particular point. It is measured positive eastward from geographic north and may be found from

(3.15)

The concept of geomagnetic time is occasionally used in auroral studies (Vegard [1912a]). I t is defined by the angle between the magnetic meridians that pass through the station and through the sun. Specifically, magnetic noon is the time when the sun is on the magnetic meridian of the station ; and magnetic midnight, when it is on the opposite meridian. These times at a station are the times that the sun reaches an azimuth of 180" + $ or 4, as the case may be.

The magnetic zenith and horizon are also useful concepts. The magnetic zenith is defined by the tangent to the field lines at a station. It has an angular altitude i and an azimuth 180" + 4. T o a first approximation it is the direction from which slow charged particles should enter the atmosphere ; converging rays, forming auroral coronas, appear centered near the magnetic zenith. The magnetic horizon is a great circle90 degrees from the magnetic zenith. In the northern hemisphere, in the direction of magnetic north (i.e., along the magnetic meridian) it has an altitude of 90" - i .

Appendix I11 lists A, 4, A,, +,,, $, and i for a number of aurora-airglow observing stations. Chapman and Sugiura [ 1956~1 have published useful tables giving the arc lengths of dipole lines of force outside the Earth,

68 3. FIELDS, PARTICLES AND T H E ATMOSPHERE

and Block and Herlofson [ 19564 have computed geomagnetic field lines numerically, taking account of the quadrupole term as well. Vestine and Sibley [1959a] have computed lines of force from the first nine terms in the Gaussian expansion in spherical harmonics, and Vestine [1959u] has published a table of conjugate points for a number of stations. Figures 3.4 and 3.5 give polar projections of the Earth in geomagnetic coordinates.

FIG. 3.4. The hemisphere centered on the northern geomagnetic pole (at 7 8 O 5 N, 690 W geographic). Geomugnetic meridians and parallels of latitude are shown. The parallels 4 5 O N, 60° N are the boundaries of the northern subauroral belt; the parallel 600 N contains the northern auroral region (Section 4.1.2). The northern half of the minauroral belt is shown. From Chapman [1957f];

courtesy Pergamon Press.


FIG. 3.5. The hemisphere centered on the south&n geomagnetic pole (at 7805 S, 11 l o E geographic). Geomagnetic meridians and parallels of latitude are shown. The parallels 4 5 O S, 600 S are the boundaries of the southern subauroral belt; the parallel 600 S contains the southern auroral region (Section 4.1.2). The southern half of the minauroral belt is shown. From Chapman [1957f];

courtesy Pergamon Press.

Other Magnetic Poles.-The Earth’s field is not precisely symmetric about an axis through its center. Therefore the field can be approximated somewhat better by a dipole that is not restricted to the center of the Earth. The eccentric dipole is thus obtained by displacing (but not tilting) the centered dipole to a point where it gives an optimum representation


of the true field (or, specifically, to a point where certain of the quadrupole terms vanish). Of course, the very lack of symmetry with the Earth makes the use of the eccentric dipole rather awkward, but it nevertheless would be expected to be more relevant to auroral particles than the centered dipole.

Parkinson and Cleary [1958a] have given the data for the eccentric dipole for the epoch 1955.0. I t is displaced 0.0685a (= 436 km) from the center toward X = 15P6 N, 4 = 150P9 E (just east of the Marianas). This is 6% (= 730 km) north of the geomagnetic equator. The axis points of the eccentric dipole are at 81PO N, 84P7 W, and at 75PO S, 120P4 E. Since this axis does not go through the Earth's center, it is not vertical at these axis points, but is inclined to the vertical at 3P9 in the direction of the corresponding geomagnetic pole.

The magnetic (dip) poles are the points where the field is vertical. The positions of these dip poles are probably affected by local anomalies in the polar regions (Hope [1957uJ). However, the eccentric-dipole field is vertical at 82P4 N, 137y3 W and at 67P9 S, 130P6 E. The latter is close to the southern dip pole (in 1945 near Terre Adelie, on the Antarctic coast, about 68" S, 145" E), but the former is some 1200 km from the northern magnetic pole (in 1948 near Prince of Wales Is., 73" N, 100" W). The dip poles may drift 5 or 6 km a year.

For any longitude the cosmic-ray intensity should reach a minimum at the magnetic equator. In this way Simpson, Fenton, Katzman, and Rose [1956a] first demonstrated that the effective geomagnetic equator for cosmic rays is simulated by a westward shift of the centered geomagnetic dipole by about 40"-45", but the inclination of this cosmic-ray dipole is still about 11" or 12" to the rotation axis. These authors suggested that the geomagnetic field lines, rotating in a conducting medium, suffer a certain amount of geometrical torsion, and are dragged behind the normal (meridional) positions of dipole lines of force. Subsequent theoretical studies by Maeda [1958a], Beiser [1958a], and Ingraham [1959a] tended to support this explanation. A moving magnetic field tends to carry an immersed conducting fluid with it, since the field lines are (hydromagnetically speaking) frozen into a good conductor. At several Earth radii the field becomes weak and the rotation velocity becomes large, with the result that the field lines slip through the interplanetary medium but suffer a sort of viscous drag. Because the field lines are then not strictly meridional, the concept of a dipole field begins to lose some significance for cosmic rays. The angular distribution of cosmic rays at any one station is still represented rather well, however, by the centered dipole and the predictions of Stormer's (dipole) theory (Danielson [1959a]). The cosmic-ray dipole determined from equatorial


observations would not, with this interpretation, be the same as an effective dipole field deduced from cosmic-ray isocontours obtained at middle or high latitudes.

While no doubt important to the general problem of auroral theory, any such lag in the rotating lines of force far above the Earth should not directly affect the positions of the auroral zones. Auroral particles, unlike cosmic rays, move sufficiently slowly that they will adjust their orbits to follow the magnetic lines of force as they approach the atmosphere. Hence one expects the auroral zones to be closely governed by the actual field of the Earth, whichmight be approximatedby the eccentric dipole, or, in a slightly cruder fashion, by the centered dipole.

An alternative interpretation of the cosmic-ray anomalies is that a single dipole term is simply inadequate to give a proper representation of the Earth’s field and its effect on the trajectories of charges particles. Quenby and Webber [1959a] have shown that when higher-order terms of the internal field are considered, the cosmic-ray data may be explained rather well without recourse to external distortions. Considering the total field at high latitudes, they have shown that Vestine’s [1944a] locus for the auroral zone fits an “effective geomagnetic latitude” (which includes the effects of higher-order terms) better than the geomagnetic latitude for the centered dipole (also see Section 8.2.2).

3.1.2. Magnetic Variations

Variations of Internal Origin.-A secular change in the Earth’s field was first noted by Henry Gellibrand in 1634, from slight changes over several years‘ in the declination (east or west deflection from geographic north) of the compass at London. Additional data extending back some 3000 years have been obtained from fired pottery and brick. As the pottery was heated during its manufacture, magnetic particles would align themselves along the geomagnetic field, and retain that orientation as the material cooled. Similarly fossil magnetism appears in ancient lava beds, and fine magnetic particles, weathered from rocks of various kinds, may be reformed in sedimentary rocks, with their orientation providing a clue to the prehistoric field. Also, discrepancies between archaeological ages and radiocarbon dates for the same fossil may arise from changes in cosmic-ray intensity due to variations in the strength of the Earth’s field.

There are numerous difficulties and uncertainties involved in the interpretation of fossil magnetism, but it appears that there have been major changes in the main field. In fact, there is considerable evidence that the field has even reversed its polarity several times in the past


300 million years. I t is also contended that many of the observed field changes at a particular place are actually due to large-scale continental drifts.

Over-all changes in the magnetic field presumably arise from changes in the currents in the Earth’s core. I n addition, some of the short- period variations described below may arise from earth currents, which flow horizontally in the crust. The relation of earth currents to geomagnetic variations is not completely resolved, there being some uncertainty on the one hand as to how much current arises from magnetic variations and on the other, to what degree the varying field is due to changes in the currents. At any rate, harmonic analyses show that the primary cause of daily magnetic variations is above the Earth, with only a small part due to currents within the crust.

Variations of External Origin.-Transient changes of the field fall into three classifications: S, L, and D (solar, lunar, and disturbed). The variations are smooth and regular on so-called magnetically quiet days ; large disturbances are called magnetic storms.

The lunar variation has a semidiurnal period and evidently arises entirely from the dynamo action of gravitational tides. The motion of the ionosphere across the lines of force of the main field induce ionospheric currents of sufficient strength to modify the field at the surface by a few gammas (100,000 gammas = 1 gauss). There seem to be some discrepancies, not yet fully explained, among the ionospheric tidal actions (1) as deduced from L, (2) as observed by radio reflections, in semi-diurnal lunar oscillations of the E layer, and (3) in the resonance theory of tides (see Section 13.4.5).

The quiet day solar variation, S,, may have an amplitude of 25 gammas or more, depending on latitude, time of year, and solar activity. Although the solar gravitational effect is less than the lunar, the sun induces atmospheric winds and oscillations through heating as well.

On magnetically active days there is another component of the field, which also varies with solar time, but whose behavior is quite different from S,. I t is part of the disturbancefield D and is labeled S,, the disturbance daiZy variation. In an analysis of the progress of magnetic storms, Chapman [1918a] showed that in addition to the periodic S, component, there is a systematic dependence on the time interval from the onset of the storm, the so-called storm time. This component of the D field averaged over a parallel of latitude, is written D,,, the storm-time variation of the disturbance field.

* See, for example, Runcorn [1959a] and references to earlier work cited there.

3.2. MOTIONS OF CHARGED PARTICLES 1 3

Normally a magnetic observatory measures the horizontal and vertical components of the field and the angle of declination (displacement of the vector field from the geographic meridian). Storms that occur with sudden commencements (S.C.) begin with an increase in the field that is most noticeable in the horizontal component. At middle or low latitudes its rise may be 25 or 50 gammas and, after an hour or so, a fall occurs to perhaps 100 gammas below normal field strength, the minimum being reached after half a day or so. The brief increase is called the first phase, and the diminished field comes during the main phase and may require one or several days to recover to normal. Great magnetic storms will occasionally exceed 1000 gammas. At high auroral latitudes the daily variation is much more dominant, with the storm as a whole more severe.

The disturbed (D) field may appear as a magnetic bay, which is a gradual change in the field over an hour or so of perhaps 50 to 400gammas at auroral latitudes followed by a similar return to normal. The name bay comes from its appearance on the magnetograph record; it may involve either an increase or decrease in the field.

Micropulsations occur during storms and on quiet days as well, with periods of a few seconds to a few minutes and amplitudes up to several gammas.

Magnetic disturbances are closely associated with solar activity and, in higher latitudes, with aurorae (Section 4.3.1). The frequency distribution of magnetic storms follows an eleven-year cycle and displays a strong seasonal dependence, with maxima in the spring and fall. Weak and moderate storms have a 27-day recurrence tendency, generally found lacking in great storms. The great storms seem closely associated with solar flares, and Bartels has suggested that the weaker storms are related to “magnetically active” M-regions on the sun. These hypothetical M-regions have not been identified with certainty with any optical features, but may be associated with coronal streamers (Sec- tion 4.3.8).

Other aspects of the behavior of magnetic disturbances, and especially their relationship to the aurora, are discussed in Section 4.3.1.

3.2. Motions of Charged Particles in Electric and Magnetic Fields

The basic equation of motion of a charged particle in an electric field E and magnetic field B is

“ 1 dt ( c dv

m - = + . e E + - x B , (3.16)


where v is the velocity, m the mass, and e the absolute value of the charge on the p a r t i ~ l e . ~ The plus sign applies to positive ions, the minus sign to electrons. The vector [e /c ) v x B is the Lorentz force.

If there is no electric field, the energy of the particle remains constant. To show this we take the scalar product of the velocity times Eq. (3.16):

(3.17)

where4 v = I v 1 . Thus, as the acceleration is always perpendicular to the velocity, the scalar speed does not change.

3.2.1. Uniform Magnetic Field

In a uniform magnetic field a particle orbit consists of uniform motion along the field lines plus a circular motion in a plane perpendicular to the field. In a right-handed system of coordinates (see Fig. 3.1) with the magnetic field along the z axis, a positive particle gyrates in the - 4 direction, a negative particle in the opposite direction. That is, a particle tends to circle an external field in the direction such that the small magnetic field produced by the particle is in the direction opposite to the external field. Equating centrifugal force to the Lorentz force, we find for the angular velocity,

(3.18)

Here vL is the absolute value of the velocity component perpendicular to the field, wc is the gyrofrequency or cyclotron frequency, and p is the radius of gyration. For a proton in the Earth’s field near the surface (about 0.5 gauss), wC m 5 x lo3 radian/sec. If vl = lo9 cm/sec, the radius is p e 2 km. For an electron with a comparable velocity the orbital radius is much smaller. The product Bp (= mv,c /e) is often designated the magnetic rigidity.

The symbol B (strictly, the magnetic induction) is used here rather than H (magnetic field strength). Because we are concerned here with the interactions of charged particles and magnetic fields, the induction is the physical quantity we are usually interested in. However, when we deal with currents we shall agree to consider the magnetization current J’ as incorporated in the (total) current J. Ordinarily V x B = 4a(J + J’) and V x H =

4nJ; but with our convention of considering magnetization current as a conventional current, B and H are equivalent, and they may be interchanged as the reader desires.

We shall write A for 1 A 1, where A is any vector quantity.

3.2. MOTIONS OF CHARGED PARTICLES 75

3.2.2. Uniform Electric and Magnetic Fields

If a particle is under the influence of crossed electric and magnetic fields, its orbit consists of a velocity v‘, which is composed of circular motion about the lines of force and the velocity along B, plus a uniform drift velocity given by

(3.19)

T o prove this we write v = v‘ + Vd, where vd is given by Eq. (3.19). Then it readily follows from Eq. (3.16) that

(3.20) E . B B + T I ’ dv’

dt m - = & e

which shows that v‘ involves only the velocity components stipulated above. The drift motion is in the direction E x B regardless of the sign of the charge, and the velocity is independent of the particle mass.

We may interpret the drift motion in the following way: an observer moving with the X‘Y’Z’ axes with velocity vd relative to a coordinate system X Y Z will experience electric and magnetic fields given by the Lorentz transformation (for field components perpendicular to Vd),

and

(3.21)

(3.22)

The approximate equalities are valid for nonrelativistic velocities and for ionized gases, where E is usually small because of the high conductivity.

The magnetic field observed in the X’Y’Z’ system is essentially the same as in the “stationary” coordinates. If vd is given by Eq. (3.19), and if E is perpendicular to B, then from Eq. (3.21) we have E’ = 0; the electric field thus vanishes in the moving system and only the gyrational motion remains. An observer in the XY’Z’ system experiences no electric field perpendicular to the magnetic field, and he consequently observes no drift. (When E and B are not perpendicular, the particle will also be accelerated parallel to B.)


3.2.3. lnhornogeneous Magnetic Field

If the magnetic field is not uniform in space, a charged particle may drift for two reasons, which we shall treat separately. First, suppose that the field lines are straight and everywhere parallel to the y axis, but that B increases (that is, the lines crowd closer together) as the x coordinate increases. Then a particle gyrating around the lines of force will experience a stronger magnetic field on some parts of its orbit than on other parts, with the result that the orbit is no longer circular but contains a drift as well as gyrational motion. The drift is in the - x direction in our coordinate system or, in general, in the direction B x V B for a positive particle. A minus-sign particle drifts on precisely the same path, but in the opposite direction. Alfv6n has shown that the ratio of drift to the gyrational speed is

(3.23)

where V1 B is the gradient of the scalar field B in the plane perpendicular to B.

Let us now consider the special case where there are no currents in the region considered, the currents producing the magnetic field being external to this region. Then from Maxwell’s equations [cf. Eq. (3.38), Section 3.3.11, v x B = 0. In general, the lines of force will not now be straight, as postulated above, but Eq. (3.23) will be valid so long as the radius of curvature B of the lines of force is large compared with the distance the particle moves along the field during one gyration. For simplicity, we choose a magnetic field with B = B,i, and B, = B, = 0 in cylindrical coordinates. Since the curl of the field vanishes, we have aB,/ax = 0 and

(3.24)

Substituting this into Eq. (3.23) and eliminating p with Eq. (3.18), we have

(3.25)

If B is in the + 4 direction, then the drift of a positively charged particle is toward + x. Notice that there is no drift if the lines are straight (9 4 00); this is a consequence of the fact that if there are no currents and the lines of force are straight, they must also be uniformly distributed in space.


Equation (3.25) gives the drift caused by the divergence or convergence of the field in a direction perpendicular to the field. In addition, a particle moving along a curved line of force with speed ol, will experience an outward (centrifugal) force rnvFl/W tending to pull the particle off its curved trajectory. As in the case of an electric force perpendicular to the magnetic field, the net effect is not an acceleration in the direction of the centrifugal force but rather a uniform drift at right angles. In general, the drift for a positive particle is in the direction W x B and has a magnitude v:,/wcW.

The total drift in an inhomogeneous field, due to nonuniformity of the lines of force and the centrifugal force on the particle, is then

(3.26)

3.2.4. Constancy of the Magnetic Moment: Adiabatic lnvariance

Thus far in considering magnetic fields we have restricted ourselves to lines of force that are always parallel to one another, whether they be curved or straight. But a most interesting effect appears when we follow a charged particle in a field where the lines of force converge toward one another.

Picture a particle with a spiral path symmetric about a line of force on the x-axis. This spiral trajectory is composed of a gyrational velocity v, and a motion of the guiding center along the field with velocity vz. Off the x-axis the magnetic field has a small component BR measured positive away from the x-axis. The field is azimuth-independent and B, ;IZ 0.

Since the lines of force must be continuous, V * B = 0 or

(3.27)

The convergence is assumed to be gradual, so that during the time required for the particle to make a single gyration it has experienced little change in the field. Then we may set aB,/az = aB/az. Integrating Eq. (3.27), we have

R2 aB R B R = ---.

2 az

At the position of the particle (I? = p) , we have

(3.28)

(3.29)


If we consider the possibility of a uniform electric field E, accelerating the particle along the magnetic field, the equation of motion (3.16) is

dv 1 p ~ 4 aB m L = & e E , + - -

dt i 2 c d '

Employing Eq. (3.18) to eliminate p , we have

(3.30)

(3.31)

where the minus sign is inserted in the second term on the right because the sense of gyration of a positive particle is in the - 4 direction with our convention for the direction of the field (i.e., v4 = vL) , The equation is valid for particles of either sign.

If the lines of force are converging in the direction of motion (aB/dz > 0), the magnetic field tends to decelerate the forward motion of the particle. But as we have shown in Eq. (3.17), the magnetic field alone cannot change the total speed of a particle. Hence, it is clear that the loss of velocity along the field must reappear as an increase in the absolute value of the v4 component. We shall investigate this point further.

It is convenient to write the equation of motion (3.31) in terms of the magnetic moment of the particle, p, which is defined as the product of the current produced by the particle times the area encircled by this current. Thus

(3.32)

where the second equality follows directly from Eq. (3.18).

from Eq. (3.32), we obtain Multiplying the equation of motion (3.31) by v , and substituting p

d B dt

= f eE, v, - p -. (3.33)

Here d/dt indicates the substantial derivative, which is taken along the path of the particle. (For a stationary observer, we would have

Another relation between v, and p (or v4) can be found from energy considerations. Since the total kinetic and potential energy of the system is a constant,

a q a t = 0.)

(3.34) d z dt

= & eE, - = f eE, v,.


Using Eq. (3.32) we then obtain

(3.35)

A comparison of Eq. (3.33) and (3.35) illustrates that, in the limit of our approximation of a slowly converging field, p is a constant.

Let 8 be the pitch angle between the total velocity vector v and the magnetic field. Then vb = v sin 0. Further, let E = *m(vf + v i ) =

4 mv2, the kinetic energy of the particle. The constancy of the magnetic moment may then be expressed as

(3.36) mv$ mv2 sin2 e E sin2 e 2B

- = ~ = const. p = - - 2B B

If there is no electric field acting on the particle, so that E = constant, and at a given point on the trajectory the field and angle of pitch are B, and 0,, respectively, then the particle will be magnetically reflected when the field seen by the particle increases to the value

B B, = -.-L- sin2 O, ’ (3.37)

where B,,, defines a magnetic mirror point. At this point all the kinetic energy has been transformed into the

gyration of the particle. But it is clear from Eq. (3.31) that so long as aB,Iaz > 0, there will be a force on the particle in the - z direction so that the particle recedes, gaining speed parallel to the field as I wd I decreases.

If there is an electric field involved, the last equation in the set (3.36) should be used, rather than the more familiar relation (3.37). Again we must caution that these relations are not exact and do not apply strictly, for example, to the motion of particles over large distances in the field of a dipole. Nevertheless, AlfvCn [1950a] has successfully applied Eq. (3.36), along with Eq. (3.26) for the perpendicular drift of the guiding center, to an approximate treatment of the Stormer problem -the motion of a charged particle in the field of a dipole.

Equation (3.36) is sometimes called the jirst or transverse adiabatic inaariant and was first developed and applied in the general case by AlfvCn [1950a] (also see Landau and Lifshitz [1951a]). T h e second or 1on.gitudinal invariant is treated in Section 8.2.2.


3.3 Propagation of Electromagnetic Waves in an Ionized Atmosphere

The general problem of interpreting radio reflections from the ionosphere requires a consideration of the Earth’s magnetic field ; this problem has been treated by Appleton [1927u, 1932~1, Goldstein [1928u], and Hartree [1929u] and is summarized in Mitra’s [1952u] and Stratton’s [1941a] books. Here we shall be content with a brief introduction in which the magnetic field is ignored.

3.3.1. Maxwell’s Equations

Any discussion of electromagnetic radiation must start with the complete set of Maxwell’s equations. Ampthe’s law is

(3.38)

where p is the permeability and K the dielectric constant (= permittivity of the medium). Faraday’s law is

1 aB c at V x E = - - - - . (3.39)

The magnetic lines of force are continuous, or

V . B = O , (3.40)

and electrostatic lines of force start and stop on charges:

V - ( KE) = e44Ni - Ne), (3.41)

where Ni and Ne are number densities of ions and electrons. In a stationary atmosphere where there is no magnetic field we may use the ordinary Ohm’s law

(3.42) uE J = - , C

where J is current density (emu) and u the conductivity (esu). We derive a differential equation for the electric vector when there

is no net charge in the region (Ni = Ne) and when p and K are independent of time and position. Taking the curl of Eq. (3.39) and eliminating V .E by Eq. (3.41), B by Eq. (3.38), and J by Eq. (3.42)’ we have

(3.43) ~ L K a2E 4rap aE v 2 E = O m c2 at2 c2 at

3.3. PROPAGATION OF ELECTROMAGNETIC WAVES 81

In a similar fashion we can show that H satisfies the same equation (see Problem 2). When the conductivity is sufficiently large the second term in the equation may be neglected and E is governed by a heat-conduction or diffusion equation. In the event u = 0 and p~ has no imaginary component, Eq. (3.43) becomes the ordinary wave equation, where the phase velocity of the wave is c/n, and n = ( ~ p ) " ~ is the ordinary index of refraction of the medium.

3.3.2. Propagation in the Absence of a Magnetic Field

Propagation in an ionized medium without a magnetic field was treated originally by Eccles [1912a] and Larmor [1924a]. We are here concerned with a plane wave propagating through a dielectric with p = 1, and we shall suppose that any departures from homogeneity in the medium are on a scale that is large compared with the wavelength. The wave equation (3.43) is

(3.44)

where nI2 = K. At aqy point the changing electric field from this wave causes electrons to oscillate back and forth. If the electron suffers collisions with the gas at a collision frequency vc, its kinetic energy is dissipated and the amount of energy re-emitted as electromagnetic radiation is diminished. In addition, frequent collisions, by inhibiting the free motion of electrons, cause their oscillations to lag behind the phase of the incident wave. A convenient way of treating the phase is by the use of imaginary exponentials. A phase lag will then lead to a real exponential in the plane-wave expression for the electric vector, and this factor may be related to the absorption coefficient.

Let the electric vector of the plane wave be E = E, e-i"', where w = 27rv and v is the radiation frequency. The equation of motion of an electron is then

d"X dx dt2 + myc - = - eE, e-iw',

dt m - (3.45)

where x is the displacement of an electron from its neutral position and m is the electronic mass. The equation is based on the supposition that in a collision the electron loses all its momentum, m dxldt. A steady- state solution of this equation (Stratton [1941a, p. 3261) gives

- i e v C - z w wm

x = - E, eciot. (3.46)


For a dielectric impressed with an external field the polarization per unit volume, P, is related to the dielectric constant, K, by

(3.47) P E

K = 1 + 4 ' 7 - .

Here the polarization is P = - N e ex, so that the complex dielectric constant may be written

where Ne ez(v, + iw)

a = m(w'L + v;) *

(3.48)

(3.49)

That the quantity given here as u is equivalent to a complex conductivity can be seen from Ohm's law (3.42), where the conduction current J is replaced by the polarization current, dP/dtc = - ( N e e/c) dx/dt, and x i s given by Eq. (3.46).5

Equation (3.44) has a plane-wave solution

where z is distance along the direction of propagation. The real component of n' is the ordinary index of refraction, which governs the reflection of a wave, and the imaginary component of n' governs the absorption of energy by the medium. Thus we write n' = n + ig. Then since nt2 = K , we have from Eq. (3.48) that the real index of refraction n is given by

(3.51)

In writing the more general equation (3.43) in the form (3.44) applicable to a dielectric, we assumed that there was no conduction current or that u = 0. The u used above is formally a different quantity in that it is introduced through the polarization current. However, the entire derivation here could proceed from the standpoint that the atmosphere is a conductor. We would then use Eq. (3.43) with K = 1 (for the neutral component of the atmosphere) and consider the electron oscillations as contributing to the current J. The conductivity would be given by Eq. (3.49) and later results would be unchanged. Note that at low circular wave frequency w , the real component of the conductivity given by Eq. (3.52) becomes the familiar expression from kinetic theory, proportional to l / v c . Incidentally, the problem developed here is quite similar to the treatment of spectral line absotption in Section 1.2.2.

3.3. PROPAGATION OF ELECTROMAGNETIC

where oo is the real component of the conductivity

N , ex v P uo f

m(w2 + vf) *

WAVES 83

from Eq. (3.49):

(3.52)

Also in Eq. (3.51) K~ is the real component of the dielectric constant,

where the plasma frequency is

w," w2 + vf '

(3.53)

(3.54)

The absorption coefficient is derived by considering the attenuation with distance of the mean intensity (averaged over an oscillation). We have I = $ E .E* = I, exp (- 2wgz/c), so that the votume absorption coeficient is k = 2wg/c or, from the imaginary component of Eq. (3.48),

k = 4xoO/cn cm-I. (3.55)

For the case of a low collision frequency, vc << w , the real index of refraction becomes n = ( 1 - w i / ~ ~ ) l / ~ . Waves with a circular frequency w < w0 cannot exist in the medium; in the ionosphere they will be prohibited from entering the region where wo 2 w by refraction or reflection.

The refraction of a wave by the ionosphere can be computed with Snell's law: If the incident angle, measured from the normal, is O,, the wave will be turned back a t an electron density corresponding to n = sin Bo. For the particular case of vertical incidence (0, = 0), reflection occurs when w0 = w . Thus the electron density required to reflect a wave with frequency v = w/27r is, by Eq. (3.54),

T m v2 e2

N e z - - - 1.24 x 104 v2, (3.56)

where the numerical value applies to v in Mc/sec and Ne in electron/cm3. The absorption coefficient for the case vc << w is

47r Ne eB vC m c w(w2 - ~ i ) ~ / ~ '

k = (3.57)

At w a wo the coefficient is large, the attenuation being associated with a low index of refraction. At the frequencies well above the local plasma frequency the absorption varies as w - ~ ; hence low-frequency waves


may become quite susceptible to absorption in the ionosphere below the altitude at which they would be reflected (i.e., in the region where w, < w ) .

3.4. The Ionospheres

3.4.1. A Chapman Layer

An idealized case of atmospheric ionization by sunlight was first treated in detail by Chapman [1931b, c, 195363. In spite of several simplifying assumptions introduced, the theory contains the essential features that we might expect for an ionized atmosphere in which ions and electrons recombine directly with one another. For more complicated means of recombination, the Chapman theory requires appropriate modification.

We consider an incident parallel beam of nearly monochromatic radiation with a total photon flux n9, measured normal to the beam. The radiation strikes the atmosphere at a zenith angle O,, and we shall write, consistent with the radiative-transfer notation used throughout this book, po =cos 8,. For an isothermal atmosphere the number density at any height is N ( x ) = No exp (- z /H) , where No is the density at height z = 0 and H (= kT/Mg) is the scale height. If a, is the mean absorption coefficient per particle (or absorption cross section) at the frequency of the incident radiation, the photon flux at a particular height will be ~9 exp [- a" N(z)H/p,], provided that the angle B0 is less than about 85", so that the approximation of a plane-parallel atmosphere is not vitiated.

Let /3, be the absorption coefficient for ionization alone. (If photoionization is the only process responsible for attenuating the solar flux, then a , = f l y . ) The number of ionizations produced per cm3 per sec at a height z and for a solar zenith angle B0 is

d z I Po) = / B Y N ( 4 7r 9 exp [- 01" N ( 4 HiPo1

Differentiation of this expression gives the height, xmBx, at which Q is a maximum:

this height varies, of course, through the day, depending on p,.

(3.59)

For a general review, see Ratcliffe and Weekes [1960u].

3.4. THE IONOSPHERE 85

The maximum rate of ion production is then

(3.60)

It is convenient to express q in terms of the maximum q (= qM) for an oyerhead sun. We shall write zM for the value of z m a x when po = 1 and qhf = q(zhI 1 po = I ) is then the maximum rate of ionization when po = I . Using qh,, and zM as found from Eqs. (3.60) and (3.59), we obtain from Eq. (3.58) the rate of ionization

(3.61)

In a so-called Chapman layer recombination is taken proportional to N,2. Also, we shall suppose that the ionization is in a state of quasi equilibrium ; that is, while the ionization is constantly changing because of the rising or setting sun, the atmosphere is assumed to adjust rapidly, so that the electron density at any instant is given by the equilibrium expression

q = arec N,“ (3.62)

where Urec is the recombination coefficient. Then with q given by Eq. (3.61), we have the Chapman layer

where N:’) = (qh.JcYrec)”2 is the maximum electron density for an overhead sun. When the sun is near the zenith, so that pa sz 1, the electron density close to the height zM is

(3.64)

In the region near the peak, then, Ne approximates a parabolic distribution; the approximation is very good within the region zM & H , but clearly becomes worthless as z approaches zM f 2H.

Two additional items based on these considerations are of some interest. From Eqs. (3.60) and (3.62) it is readily seen that

which shows the dependence of the m-imum electron density in a layer on the solar zenith angle, and therefore indicates the daily, seasonal,


and latitude variations to be expected. Finally, by means of Eq. (3.59) the air density (or more correctly, the density of the absorbing substance) at the layer maximum is N(zmax) = po/myH. If the theory correctly describes a particular layer, then observation of the variation of Zmax during the day gives a means of finding the air density distribution in the ionosphere. (For the technique to be useful, vertical movements of a layer due to tidal oscillations or other systematic motions would have to be negligible.)

The Chapman layer has also been treated for times near sunrise and sunset and without the assumption of quasi equilibrium for the ionization (that is, time lags may be treated explicitly). Other departures from the idealized conditions that have been considered are a variation of H with height, ionization by continuous (rather than nearly monochromatic) radiation, diffusion of the electron-ion gas, and departures from the recombination law dN,/dt = ~r,,,Ni (see Mitra [1952a]).

3.4.2. Recombination Processes and ion Formation in the Atmosphere

In the Chapman theory we have considered the rate of recombination to be arec N;. This recombination law is valid when, for example, all the heavy ions are singly charged and positive and belong to the same atomic or molecular species. When negative ions become abundant or when it is likely that in a collision an ion will yield its charge to an atom or molecule of a different species, then the recombination law may not be so simple. However, it is still convenient to write the rate of change of electron density as

where q is the rate of ionization and where m e i f , the effective recombination coefficient, may now vary with Ne and with the atmospheric density.

Bradbury [1938a] and Mohler [ 1940~1 first considered the modifications in the Chapman theory required by an alternative recombination law, such that

dNeldt = q - fi Ne, (3.67)

where f l may depend on the atmospheric, but not the electron, density. If electrons disappear from the gas by attachment to neutral atoms, then Eq. (3.67) will be the appropriate equation, provided, of course, that the negative ions are disposed of by mutual neutralization (1.107) before the captured electrons are again detached.

3.4. T H E IONOSPHERE 87

Bates and Massey [1946a] pointed out that Eq. (3.67) would also apply in a case where most of the positive ions are atomic but where the atomic charge can be transferred to a molecule in a collision of the type (1.105). Thus if the molecule, once it becomes charged, recombines rapidly by (1.106), the rate of electron removal from the gas is determined effectively by the rate of charge transfer. In the case of reaction (1.105), the coefficient p in Eq. (3.67) would be proportional to the density of the molecule.

I t appears that in the E and Fl layers recombination may occur as N & so that these layers are approximately of the Chapman form. In the D region electron attachment becomes important, and in the F, region charge transfer seems to be a dominant process, so that the Chapman distribution is not valid. Indeed, it is likely that both Fl and F, arise from a common ionization process, with the bifurcation into two layers due to the change in the recombination law with height, as first advocated by Bradbury [1938a].

We shall have occasion to discuss the problem of F-layer recombination in connection with the formation of the airglow [OI],, red lines, and in Section 13.2.2 we shall treat the nighttime N , distribution with allowance for vertical diffusion of ions.

Most of the ions in the F region are probably the result of photoionization of 0 by the solar Lyman continuum or by helium emission lines. In the F, region the ionization remains predominantly in the form of O+, but recombination occurs with the aid of the intermediate process of charge transfer to 0; or, more likely, to NO+ followed by dissociative recombination. In most of the Fl region, dissociative recombination is itself the limiting process, which means that the O+ ions are readily destroyed by charge transfer, and the most abundant ions are molecular. Direct measurement of ions by mass spectrometers by Johnson, Meadows, and Holmes [1958a] in the Arctic shows the presence of O:, NO+, and 0+, with the relative concentrations of molecular and atomic ions versus height in qualitative agreement with expectations. For applications of ion recombination to the airglow and further discussion, see Sections 1 1.5.3 and 13.2.2.

T h e possibility cannot be excluded that there is a source of ionization in F, in addition to that producing both Fl and a low-attenuation F, layer as described above. There is also probably a considerable amount of N: formed during the day, but observations of the twilight airglow show that very little of the twilight and nighttime ionization is of this species. Any daytime N: evidently recombines rapidly after sunset. These matters are treated in Sections 11.2.2 and 13.2.4.

In the E layer 0: is presumably the dominant ion, being produced


possibly by absorption in the first ionization continuum (hv > 12.0 ev). Pre-ionization (band absorption at hv > 12.0 ev followed by a spontaneous, radiationless transition that dissociates the molecule) was formerly advocated by Nicolet [1949a] but does not now seem necessary, as the absorption coefficients for direct photoionization are sufficiently large (see Nicolet and Mange [1954a]). Ultraviolet radiation with h v > 13.6 ev is absorbed in the F region and cannot contribute to the E layer. Hoyle and Bates [1948a] have, however, considered solar x-rays as a possible ionizing agent. A final decision should become possible as better information on the atmospheric densities and solar radiation becomes available.

The persistence of a nighttime E layer and the sporadic E (= E,) are not adequately explained.' The E , radio reflections are difficult to interpret. Evidently they do not arise from critical reflection ; thin patches of ionization produce only a partial reflection. Perhaps meteoric dust or charged atomic particles bombard the atmosphere with sufficient intensity to cause the required ionization. The long persistence of E , clouds and of the normal nighttime layer may be due in part to ionization of metallic atoms such as Na+ (see Section 11.4.2). However, a rocket flight at middle latitudes (Johnson, Heppner, Holmes, and Meadows [1958a]) showed a sporadic E region to be composed primarily of N l ions.

Above the D region ultraviolet radiation with h v > 12.0 ev has been filtered out, so there are not many substances available with a sufficiently low ionization potential. Bates and Seaton [1950a] concluded that Na, which has an ionization potential of 5.1 ev, would be ineffective because of its rarity, as deduced from the twilight airglow. One possible source of D-layer ions is photoionization of NO (Nicolet [1949a]), whose threshold is at 9.2 ev. The main ionizing radiation could be the solar emission line Ly a at 1215A (10.2 ev). Perhaps NO is an important constituent in the production of airglow emission (Section 13.4). Solar Ly a also manifests itself in the night sky, where Ly a arises from resonance scattering of sunlight, probably by interplanetary hydrogen (Section 13.5.2).

Following a solar flare there is an increase in the solar x-ray spectrum shortward of 8A, although Ly O( seems to remain at about its normal intensity, according to rocket measurements of Chubb, Friedman, Kreplin, and Kupperian [1957a]. The increased ionization in the lower D region, which is responsible for strong radio absorption and fade- outs, is evidently produced by this x-ray ionization, and there is a

' Reviews of experimental knowledge of the E layer and the sporadic E are given by Robinson [1959a] and Thomas and Smith [1959a], respectively.

3.5. MODEI. ATMOSPHERES 89

possibility that x-rays are predominant in producing the normal D ionization as well.

Thus there appear to be numerous relationships, direct and indirect, between the ionosphere and the optical radiation from the night sky. Appendix V contains a summary of the salient characteristics of the ionized regions and of the processes thought to be primarily responsible for these regions.

3.5. Model Atmospheres

A model atmosphere is a tabulation of pressure, density, temperature, and chemical composition of air as a function of height, based in part on measurements and in part on theoretical analysis. Of course, if all these quantities could be measured, as at the ground, there would be no need for a model. In practice only some of these parameters are known directly, and one then applies theoretical considerations on the structure of atmospheres to these data to derive the other quantities. Clearly the correctness of any model will depend on the accuracy to which the theory describes the behavior of the atmosphere.

3.5.1. Basic Theory of Atmospheric Structure

The basic relations between pressure, density, and temperature in an atmosphere are the equation of hydrostatic equilibrium,

dP = - g p d z ,

and the perfect-gas law, p = NkT.

(3.68)

(3.69)

If the atmosphere has a number density N j of the j t h species, with a particle mass Mj, the total mass density is

(3.70)

which defines M as the mean mass per particle. Combining these relations we obtain, from (3.68), dp/p = - d z / H or

(3.71)

where the local scaie hekht is

(3.72)


The scale height will vary with altitude because of changing temperature, composition, and the decrease of g with distance from the center of the Earth. In the simplified case where the variation of g is neglected, an isothermal atmosphere with complete mixing of the constituents (i.e., when T and M remain constant with height) gives the familiar barometric law,

p(z) = p(zo) e-(z-zo)IH. (3.73)

At some level in the high atmosphere we expect diffusive separation of the various constituents. In diffusive equilibrium Eq. (3.71) holds for the partial pressures pi, expressed in terms of the scale height H j for the j t h species, where now

(3.74)

This is to be contrasted with the case for complete mixing, where every constituent has the same scale height as given by Eq. (3.72). From Eq. (3.70) we see that the atmospheric scale height may be written

I (3.75)

where H j applies to diffusive equilibrium.

height z is The total number of particles in a square-centimeter column above

(3.76)

for diffusive equilibrium and

N(z) = N(z) H (3.77)

for perfect mixing. Occasionally it is convenient to write the integrated density in terms

of the length of a column of air at sea level that contains the same number of particles. This length, which we define as the equivalent depth, is

(3.78)

H e r e 4 and Na represent numbers of atoms, where we take a diatomic molecule as equivalent to two separated atoms. If we are interested in

3.5. MODEL ATMOSPHERES 91

the deceleration of incident auroral particles in passing through the upper atmosphere, this procedure is usually adequate. If we are concerned with the attenuation of sunlight at some particular frequency, it is, of course, quite inappropriate to consider a diatomic molecule and its component, dissociated atoms as equivalent.

If the pressure or density is measured by rockets or satellites at several altitudes, the scale height may be derived from the differences. (Gerson [1951a] has written an extensive review of the methods of determining scale heights and temperatures i n the upper atmosphere prior to the extensive use of rockets and satellites.) A difficulty in interpretation has been the uncertainty in chemical composition and the variation of the molecular weight with altitude. Also, there have been few density measurements at several hundred kilometers, so that it is necessary to attempt some judicious interpolation. For example, at high altitudes diffusive separation dominates over mixing, so one might take the chemical composition to vary as in diffusive equilibrium. Then assuming the scale height to vary linearly with height according to

dH = p d ~ , (3.79)

one can determine the value of ,8 required in order to fit a high-altitude density measurement.

An alternative method used prior to the measurement of densities by satellites was to extrapolate the temperature linearly (from the last known values) to some point, beyond which T is constant with height. Unless there is an inflow of heat from the interplanetary medium to the high atmosphere by conduction, an isothermal region would be expected (see Section 3.5.3). The height at which the atmosphere should become isothermal is not easy to ascertain, depending as it does on the heights at which solar energy is absorbed and reradiated. But the exosphere, the uppermost region of the atmosphere, from which fast atmospheric atoms may escape to interplanetary space, should be included in the isothermal region.8

The temperature of the exosphere is not known precisely, but is thought to be at least 1500" K in order to explain the fact that the amount of He4 in the atmosphere is less than that produced by radioactive rocks in geologic time (see Spitzer [1952a]). Thus there has been considerable uncertainty, in constructing any particular model on this

* The base of the exosphere is called the critical level and is defined as the height at which a fast neutral particle moving upward has a probability of l ie of escaping from the atmosphere without having any collisions. If Q is the cross section for atom-atom collisions, then the critical level has a density N = l/QH (see Problem 4).


basis, not only in the proper temperature gradient but in the height (or temperature) of the isothermal atmosphere.

In extensive discussions of the problem Nicolet [19573] and Bates and McDowell [1957u] have noted, moreover, that there is a paradox between the temperatures required to explain the atmospheric abundances of He4 and He3, if the latter is produced solely as a result of cosmic-ray bombardment. Extending an earlier suggestion of Spitzer’s [1952a], Nicolet suggests that the data can be reconciled by considerations of departures from average conditions, with the temperature of the high atmosphere fluctuating with solar activity; but Bates and McDowell offer criticisms of this solution. They propose instead that helium may not be in equilibrium, with its current generation rate exceeding the escape rate. Shklovskii [1958a, b], on the other hand, suggests that He3 is also provided by meteorites and that an even more important source may be capture of atoms from the interplanetary gas. Unfortunately, too many data are still quite uncertain, including the isotopic ratio of helium in the sun (which presumably regulates the ratio in the interplanetary gas).

Before discussing the temperature and density of the upper atmosphere, we shall examine the height variations to be expected in the chemical composition.

3.5.2. Relative Abundances of the Major Constituents

There are three main competing types of processes that affect the variation of the chemical composition with height: (1) mixing due to convection, turbulence, etc., which tends to homogenize the atmosphere; (2) diffusive separation, due to the differences in molecular weight of the various constituents ; and (3) photochemical alterations in the composition.

Below about 80 km mixing is the dominant process; the atmosphere is-almost completely N, and 0, in a ratio of about 4/1. There is some photodissociation of 0, through absorption in the weak Herzberg continuum, with the maximum dissociation rate occurring near 30 km. These 0 atoms unite with 0, to form the ozone maximum in this region. Other photochemical processes also occur below 80 km,. and the airglow OH and perhaps some other radiations may be produced in the middle atmosphere or mesosphere (see Appendix IV, Fig. IV.1). But these processes are not so important as to diminish appreciably the relative concentrations of 0, and N,, which thereby determine the mean molecular weight, p = M/Mo.

Above 85 km dissociation of 0, in the Schumann-Runge continuum


becomes important and begins to affect the molecular weight of air. Pressure measurements at various heights can yield the scale height, but the molecular weight must be known to derive the temperature. Earlier analyses obtained the abundance ratio O,/O on the basis of local photochemical equilibrium ; that is, the rate of 0, dissociation due to sunlight was set equal to the rate of three-body association (see Bates [ 195463). Nitrogen has generally been assumed to be entirely molecular (N,) at these altitudes. And a common practice was to assume the total oxygen and nitrogen atomic abundances to be in the perfect- mixing ratio, so that

(3.80)

Nicolet [1959a] has emphasized that the assumptions of local photochemical equilibrium and complete mixing for the total abundances should be abandoned. The first assumption gives an 0 concentration peak near 110 km and an 0 production peak between 90 and 95 km. Three-body association,

proceeding with a rate coefficient agl, gives for an average lifetime of an 0 atom (that is, the time for the 0 concentration to drop to one half its initial value),

(3.82)

Nicolet estimates that T~~~ (0) - 3 months at 100 km, and it increases rapidly with height. In a perfectly static atmosphere (that is, one in local photochemical equilibrium), association would alone govern the 0 lifetime with the result that the concentration peak lies considerably higher than the production peak.

There is good reason for believing, however, that 0 atoms are transported downward the order of one scale height in a time considerably less than 3 months. At the top of the atmosphere the lifetime of an 0, molecule before dissociation by absorption in the Schumann-Runge continuum is Td ls (0,) TV 10 days (Nicolet [1954b]). Hence if the characteristic time for vertical transport were much longer than 10 days, the 0, distribution with height would be nearly that expected for local photochemical equilibrium, which would mean that 0, would virtually vanish above 120 km. The rocket observations of Byram, Chubb, and


Friedman [1955a] show that 0, is still in appreciable abundance at much greater heights, so we conclude that mixing by large-scale motions or turbulence or by diffusion occurs in the 100 km region with a characteristic time ~~i~ of a few days or less.

The qualitative picture that emerges, therefore, is that 0 atoms at 100 km will be transported down to 90 km or so before they have a chance to associate into molecules. At the lower altitude association occurs much more rapidly. Quantitatively the O,/O ratio at these heights is still uncertain. Nicolet [1958a, 1959~1 has considered the 0 distribution that would result if 0 recombined entirely in the region 90-95 km, near the production peak. Nicolet’s final model (see Appendix IV) has been slightly altered from this idealized case to allow the concentration peak to be just slightly above the production peak. The numerical computations suggest that N ( 0 ) m +N(N,) at 100 km and Nicolet takes nearly uniform mixing for 0 and N, in this ratio from 100 to 1 10 km.

The model is thus still rather arbitrary, but the association of 0 predominantly below 100 km is suggested by the airglow heights for the [OI],, green line and the 0, bands, which are probably produced by such association. From considerations of the rate of diffusion of a gas in which the constituents are “initially” well mixed (see Mange [1957a]), Nicolet [1958a, 1959~1 has adopted diffusive equilibrium for all constituents above 110 km.

Atomic nitrogen in the upper atmosphere may be produced by predissociation of N,, or by the indirect process of photoionization

N, + hv .+ N,+ + e (3.83)

followed by dissociative recombination

N$ + e -t N + N,

or by atom-ion interchange

o+ + N, -t NO+ + N.

It disappears through association with 0,

N + 0 + X + NO + X

and atom-atom interchange,

(3.84)

(3.85)

(3.86)

(3.87) NO + N - t N, + 0.


At higher altitudes, where the temperature is sufficiently large to overcome an activation energy of 0.25 or 0.30 ev, the reaction

N + 0, --f NO + 0 (3.89)

may also be important. Nicolet concludes that the amount of N available in the upper atmosphere will not be sufficient to lower the molecular weight appreciably. He has made some quantitative estimates of the high-altitude abundances of N and NO. In Appendix IV concentrations of the major constituents and total densities are listed from Nicolet's model.

3.5.3. Temperature Structure of the Atmosphere

Tempera ture Profile.-A temperature profile of the atmosphere is shown in Appendix IV. The various regions of increasing, decreasing, or constant temperature with height also provide a convenient basis for dividing the atmosphere ; we shall follow the nomenclature of Chapman [1950a, b], which is now in general use. These divisions are labeled troposphere, stratosphere, mesosphere, and thermosphere; the upper boundary of a region is given the suffix "pause," as tropopause, strato- pause, etc.

In the troposphere heat is transported largely by convection, with the result that the temperature and density are related approximately as in adiabatic expansion. The temperature gradient is modified, however, by condensation of water vapor, which releases latent heat to the surrounding air. The observed gradient is about 6.5"K/km.

The temperature decrease stops at a (tropopause) height of about 17 km over the tropics, about 10 km in temperate latitudes, and probably even lower in the polar regions. Above this height is a region of more or less constant temperature, the ~tra tosphere .~ This region is heated through absorption of infrared radiation emitted by the Earth's surface and by the atmosphere above and below the stratosphere. Goody [1958a, p. 1741 finds that CO,, H,O, and 0, are important to the radiative equilibrium, and that the stratospheric temperature increases toward the polar regions as a consequence of the latitudinal dependence of water vapor concentration in the stratosphere.

In the mesosphere the temperature rises to a peak, produced by ozone absorption in the ultraviolet. Above that is a region of decreasing temperature, where again the heating is largely by convection. The temperature minimum forming the mesopause is probably as low as 150" K ; there is

@Some authors use the term stratosphere to include as well what we shall call the mesosphere. In that usage, the isothermal region is called the lower stratosphere.


some information available from rocket flights on the latitudinal and seasonal variation of temperature at these heights.

The region above the mesopause is the thermosphere; in its lower part the temperature increases upward with a gradient of about 9"K/km. In the thermosphere there is a downward flow of heat by conduction over the region where there is a positive temperature gradient. Spitzer [1952a] first pointed out the importance of this conduction in cooling the F region and Bates [1951a] (see Section 13.3.3) drew attention to thermal excitations of a forbidden line of [OI] at 62 microns that would radiate large amounts of energy in the F region. The temperature profile in the upper thermosphere is not yet known and depends critically on the manner in which the thermosphere receives its thermal energy.

Radiative Heating of the Thermosphere.-The source of heat for the thermosphere may be simply the solar ionizing radiation producing the F or E layers. One can estimate the ionization rate from radio determinations of the effective recombination coefficient, aeff, and Ne by Eq. (3.66). The heating provided by this ionization is far short of that required to account for a high-temperature F region. Bates [19546] has shown that there is not necessarily any discrepancy, however, as measurements of aeff may be completely unaffected by the rapid formation and destruction of a species of ion that has a small abundance. For example, N, might be ionized by sunlight and disappear by dissociative recombination, thereby providing more heating of the atmosphere than is deduced from the indirect arguments. The question can be checked as quantitative data on the ultraviolet solar spectrum become available.

Below the region where the absorption of solar radiation through photoionization attains a maximum, the temperature decreases downward. There is thus a flow of energy downward by conduction and a dissipation of energy by radiation. Above the absorption region the temperature would decrease again with increasing height if there should be important energy losses by radiation. The thermosphere profile would then resemble qualitatively that in the mesosphere, where the temperature attains a maximum due to ozone absorption.

Above the height where both absorption and emission of radiant energy are important, the atmosphere becomes isothermal, owing to the equalizing tendency of thermal conduction. For the exosphere this result may be demonstrated from Liouville's theorem, which is proved in textbooks on statistical mechanics. The theorem states that the density of particles in phase space does not change as the particles are followed


along a dynamical trajectory (where the total energy of the system remains constant). The number of particles in an element of volume of 6-dimensional phase space is N(x, y, z ) f ( x , y, z, vz , v U , v z ) dv, dv, dv, dx dy dz , where N is the density in real space and f is the distribution function. At height z1 we take Nf from the Maxwell-Boltzmann law, Eq. ( l . l ) , where the total energy, E = &Mvi + Mgzl, includes both kinetic and gravitational energy. Then Liouville’s theorem tells us that Nf is a constant along any orbit followed by a homogeneous group of particles. Suppose that a group at height zl moving in a particular direction with total velocity vl will have a velocity v2 at height z2 ; then for these particles

where No is a constant. At height z2 the particles are still on the same Maxwellian curve (although at a different part of the curve), and the gas temperature is therefore unchanged. Moreover, as particles in every velocity range are affected by the same height factor, the total density decreases with height according to the barometric formula (3.73) (Spitzer [ 1952~1).

Allowing for the variation of gravitational attraction with height, we find that the scale height increases upward although T is constant. For large distances above the Earth, one must consider a spherical atmosphere and allow for the loss of particles exceeding the velocity of escape. The appropriate theory has been developed from Liouville’s theorem by Chamberlain [1960a] and applied to the solar atmosphere (also see Johnson and Fish [1960a]). For hydrogen in the Earth’s atmosphere, the partial truncation of the Maxwellian distribution function at distances exceeding several Earth radii will lower the density only slightly but, more importantly, it lowers the equivalent temperature (defined by the mean energy per particle). There is also some question as to whether satellite particle orbits that do not intersect the critical level are depleted (opik and Singer [1959a]). Sample calculations with these various assumptions have been given by Brandt and Chamberlain [1960a].

The isothermal region would certainly include the exosphere on this model, since little radiant energy can be absorbed there. Spitzer [1952a] has shown that the flight time of an exosphere particle in a nearly parabolic orbit is much less than the average time required for ionization, recombination, or other photochemical processes that would alter the energy content. Thus the exosphere is in diffusive equilibrium and the ratio of ionized to neutral particles can be computed on this basis, provided that it is known at, say, the critical level.


Conductive Heating of the Thermosphere.-An alternative means of heating the thermosphere has been proposed by Chapman [1957a, 195983. If the interplanetary medium at the Earth (and beyond) is heated by conduction from the solar corona and if energy losses by radiation are not important, this gas may be extremely hot(Section 8.1.1). In this event, Chapman suggested, heat may be conducted from the interplanetary gas to the upper atmosphere at a sufficient rate to account for the high temperature of the latter.

If the exosphere were heated by downward conduction, the temperature there would increase with height, in marked contrast to the isothermal situation discussed above. However, Bates [ 1959~1 has maintained that such a situation is not realistic. The exosphere, composed by definition of particles belonging to the atmosphere, possesses energy determined by collisions below the critical level. Any high-energy interplanetary gas will not have collisions in the exosphere with terrestrial atoms, and the exosphere will still be isothermal.

In any event downward conduction is important below the isothermal part of the thermosphere. Nicolet’s [1959a] model thermosphere is based on heat transport from high altitudes entirely by conduction. But the temperature gradient depends on the energy flux from conduction, which is not yet known. Nicolet assumed a variety of values for this flux in the range 0.1 to 1.0 erg/cni2 sec and if the general conduction picture is correct, comparison of the computed densities with satellite data should indicate the best model and the rate of heat influx.

In Section 13.3.1 we discuss excitation of the [OI],, red lines by thermal electrons. For a given density, temperature, and degree of ionization versus height, one can compute the red-line intensity. Larger values of the conduction flux yield greater red-line intensities, because both the temperature and the density are increased. It seems that the highest values of the conduction flux considered by Nicolet can be excluded on the basis of airglow observations.

Mechanical Processes for Heating the Thermosphere.-Other processes might conceivably be important in heating the uppermost atmosphere. Daniels [1952a] proposed that infrasonic waves from the troposphere, produced by agitation of turbulence and winds, could carry energy to the upper atmosphere. Krassovskii [ 1959~1 has suggested that Joule heating from the ionospheric currents responsible for magnetic perturbations would be important. Dessler [ 1958a, b, 1959~1 (see also Lehnert [I 956~1) has estimated that hydromagnetic waves with large amplitude should exist above the ionosphere, being generated by collisions of clouds of ionized gas from the sun with the outer regions


of the geomagnetic field. In the ionosphere, where the amplitude of the wave becomes comparable to the mean free path of an ion, the waves are damped and the energy is transformed into heat (see also Sec- tion 7.3.2).

There is evidence from rocket flights that the temperature in the auroral-zone mesosphere is much higher than at lower latitudes. It might be supposed on this basis that particle bombardment provides additional heating. How important particle bombardment is in this respect, both at high and low latitudes, is still a matter of some speculation, but one on which the aurora and airglow should cast some illumination (see Sections 7.3.1, 1 I .2.2, and 13.3.2).

The heating effect of hydromagnetic waves would also be more important at the higher latitudes. Both processes, supplying heat mainly below the critical level, would cause an isothermal region in the upper thermosphere in the same manner as radiative heating.

PROBLEMS

1 . (a) Show that a magnetic scalar potential is defined only in a

2. Show that H is governed by the same differential equation (3.43)

3. Show that for small pitch angles 0 the angular drift of a particle in

current-free region. (b) Derive the field of a dipole.

as E, under the same assumed conditions.

moving along a dipole line of force from latitude A, to A, is

4. Show that for an isothermal exosphere, the density at the critical level is such that the mean free path for a fast particle in the horizontal direction equals the vertical scale height. How does the critical level for neutral particles compare with that for ions and electrons?

Chapter 4. Occurrence of Aurorae in Space and Time

The geographic distribution of aurorae, their most likely times of occurrence, the development of an auroral display and its appearance over the globe, and the association of aurorae with other phenomena-all these things combined form the subject of auroral morphology, the over- all structure of auroral occurrence.

4.1. Geographic Distribution and Periodic Variations

4.1 .I. Recording Auro ra l Occurrence and Appearance

Most of the analysis of auroral occurrences so far available has been based on visual observations. More extensive and homogeneous observations are necessary, however, and the collection of these data has been a prime objective of the auroral program in the International Geophysical Year (IGY). Systematic observations have been made by a vast number of volunteer observers, whose reports make it possible to draw fairly accurate synoptic maps, showing the geographic coverage of a particular aurora (Chapman [ 1957f1, Gartlein [ 1959~1).

More systematic data than can be obtained visually were secured in the IGY at the higher latitudes through a network of all-sky cameras. For patrol work on auroral occurrences high resolution is not always an important factor. An optically simple design that is quite adequate for many purposes involves a normal motion-picture camera mounted above a convex, spherical mirror. This type of arrangement has been used for years by meteorologists in photographing cloud cover. Gartlein [1947a] pioneered in the use of these all-sky cameras on the aurora.

Stoffregen [1955a] developed an all-sky camera with the normal camera situated below the spherical mirror. Light from the sky is reflected by this primary mirror into a plane, secondary mirror and then downward through a hole in the primary, similar to the optical path in a Cassegrain telescope. A similar camera was developed by T. N. Davis and C. T. Elvey in Alaska and was later modified to include some of Stoffregen’s design. These cameras are described fully by Elvey and Stoffregen [1957a]. The sky is severely distorted in an all-sky photograph, so it

100

4. I . GEOGRAPHIC DISTRIBUTION APiD PERIODIC VARIATIONS 101

is useful to mark altitude intervals by small lights mounted on the framework holding the secondary mirror. The film is advanced auto- matically at intervals of one minute, but the exposure time need not necessarily be that long. A similar camera has been designed by Park [1957a]. Cialdea [1956a] has discussed the aberrations in cameras of this type and ways in which the aberrations may be minimized.

Photography of a large area of the sky with high resolution was initiated by Osterbrock and Sharpless [ 1951~1, who utilized a camera developed by J. L. Greenstein and L. G. Henyey. The new feature of the Green- stein-Henyey camera (see Struve [1951a]) was a lens that made it possible to photograph a spherical, concave mirror (which reflected the sky) without spherical aberration.

Lebedinskii [1955a] also has pioneered in the development of all-sky cameras and their application to auroral studies. The Lebedinskii camera has a spherical, convex primary mirror and a concave secondary. A motion-picture camera, equipped with an ordinary lens, is below the primary and looks upward into the mirror system and sky through a hole in the primary. The correction for spherical aberration is accomplished by means of the corrected secondary, rather than by a special lens as in the Greenstein-Henyey instrument.

Some sequences of all-sky photographs are shown in the accompanying figures. Figure 4.1 gives a sequence taken with the camera used in the U.S.A. program (Davis-Elvey-Stoffregen design) which covers the entire sky. Figure 4.2 shows a series taken with the Greenstein-Henyey camera. This instrument is limited to a field about 140 degrees in diameter because it uses a concave mirror.

For some statistical purposes it is sufficient to measure the total green-line or visible radiation throughout the night. A variety of instruments, both spectrographic and photoelectric, have been developed for this purpose (Vegard [1916a], Harang [1932a, 1946~1, Vallance Jones and Gush [1954a], Hunten [1956d]).

4.1.2. Dependence on Geomagnetic Latitude: The Auroral Zones

We shall follow the terminology on auroral geography suggested by Chapman and widely used during the IGY (see Figs. 3.4 and 3.5). The auroral regions (north and south) extend from geomagnetic latitudes (A,J 60" to the poles; the subauroral belts, between A,, = 45" and 60"; the minauroral belt between A,,, = 45" N and 45" S. The auroral regions include the auroral zones (the regions of maximum occurrence) and the auroral caps (the polar regions within the auroral zones).

Although aurorae occur primarily in the auroral regions, large displays

102

GREAT AURORA SEPTEMBER 22-23, 1957

PART I

FIG. 4.1. All-sky photographs obtained with the Davis-Elvey-Stoffregen camera from the roof of Yerkes Observatory. The sky is oriented as it would be seen by an observer lying on his back with his feet toward the north; that is, geographic north is at the bottom. The dome of the 40-in telescope is in the west; smaller domes are in the northeast and southeast. Since the sky is photographed through two mirror reflections and the clock through only one, the image of the latter, which shows Greenwich Civil Time (local zone time plus 6 hr) is reversed. The matrix of lights on the left indicates the date and IGY station number. Exposure

time for each frame was 20 sec.

103

FIG. 4.1 ( c o n t . )

The aurora is present in the north on frame I (01 15 GCT, 23 Sept. 1957). About an hour later (frame 2 ) it began a southward spread, covering nearly the entire sky at 0400 (frame 8). At 0435 (frame 10) it was concentrated south of the zenith, a most unusual situation at this geomagnetic latitude (530 N). Frames 14 to 22, taken at one-minute intervals, show the eastward motion of structure in the southern sky and of a drapery fold low in the north. The last frame (27)

was made at 0902 GCT.

104 4. OCCURRENCE OF AURORAE I N SPACE AND TIME

may reach quite low latitudes and through the ages these great auroral storms have attracted much attention. Several ancient writers, including Aristotle (“Meteorologica,” Book I, Chap. 5 [ca. 340 B.C.]), Pliny (“Histo- riae Naturalis,” Book 11, Chaps. 27 and 33 [ca. 77]), Seneca (“Quaestiones Naturales,” Book I, Chaps. 14 and 15 [ca. 631) made vivid references to aurorae, indicating their occasional presence in southern Eur0pe.l But aurorae in tropical and even low temperate latitudes occur so rarely, and have been recorded so inconsistently when they did occur, that little is known of the actual frequency of these great storms.

Because of the auroral association with sunspots, ancient records of aurorae are of use in establishing any secular variability in the sunspot cycle. Recent summaries of older observations of aurorae extending into the minauroral region have been made by Schove [1955a], Matsushita [1956a], and Chapman [1957c, el. Several aurorae occurring at very low latitudes have been described rather fully by Chapman [1953a, 1957d], Abbott [1951a], Abbott and Chapman [1959a]; A. and E. Vassy [1953a, 1954~1 have suggested that faint low-latitude aurorae are more prevalent than generally thought, being often detected only through apparent airglow enhancements. This distinction between weak aurorae and bright airglow is not an easy one and we shall discuss the problem at some length in Section 9.1.1.

The frequency of auroral occurrences does not increase continually toward higher latitudes but goes through a maximum some 20” or 25” from the geomagnetic poles. The existence of a belt of maximum occurrence-the auroral zone-seems to have been realized first by Muncke [1837a] and later by Loomis [1860a, 1868~1 and Fritz [1868a]. An extensive list of auroral observations, compiled by Fritz [1873a] from numerous sources, furnished the material for a more complete analysis (Fritz [1874a, 1881~1). The studies for the northern hemisphere were brought up to date by Vestine [1944a], who obtained the isochasmsz- lines of equal auroral frequency, corrected for visibility-given in Fig.4.3.

In the southern hemisphere the data are more spotty. Preliminary studies by Boller [1898a, b], Davies [1931a], and Geddes [1939a], led to a thorough discussion of the available data by White and Geddes [1939a], whose map is reproduced as Fig. 4.4. Vestine and Snyder [1945a] estimated the position of the southern auroral zone by comparing southern geomagnetic disturbances with similar observations in the

For interesting discussions of ancient auroral observations, see the historical books listed in Appendix VIII.

The word isochasm is derived from chasmata (in English, chasms) used by Aristotle in the “Meteorologica.” The name refers to the dark areas of sky bordered by the auroral light (Chapman [1957e]).

4.1. GEOGRAPHIC DISTRIBUTION AND PERIODIC VARIATIONS 105

GREAT AURORA JUNE 29-30, 1952

FIG. 4.2. A sequence of one-minute exposures taken successively from the' roof of Yerkes Observatory, June 29-30, 1952. Magnetic north is at the bottom. The telescope dome is the one seen in the northeast in Fig. 4.1. The shadow in the top center is the camera and its framework. Note the motion of the drapery fold toward the east. Photographs by Meinel and Schulte [1953a] ; courtesy University

of Chicago Press.

106 4. OCCURRENCE OF AURORAE I N SPACE A N D T I M E

northern hemisphere. Programs started during the I GY are producing more thorough results (e.g., Evans and Thomas [1959a]).

The frequency of aurorae observed in any part of the sky from a single station, even when the data can be corrected for visibility conditions, is not quite the information that is desired from the point of view of auroral theory. As Chapman [1953a] has emphasized, instead of

FIG. 4.3. ThF geographic distribution of the frequency of aurorae in the northern hemisphere according to Vestine [1944a]. The isochasms refer to the fraction of nights on which an aurora might be seen at some time during the night and in any part of the sky if clouds and other factors affecting visual detection of aurorae

do not interfere. Courtesy Journal of Geophysical Research.


isochasms one would like isoaurores-lines connecting points with the same frequency of overhead aurorae. We can see in Fig. 4.5 that an aurora with lower border at a height of 100 km can be seen (with clear visibility, of course) 1100 km, or 10" of latitude, away. T o construct a diagram of isoaurores, one must have rather accurate data on the position in the sky of an observed aurora.

FIG. 4.4 Zone of maximum auroral frequency in -the southern hemisphere according to White and Geddes [ 1939~1; courtesy Journal of Geophysical Research.

108 4. OCCURRENCE OF AURORAE I N SPACE AND T I M E

With good isoauroral data it becomes possible to examine questions of the time variations (see Section 4.1.3) in the location of the auroral zone. So far, little has been done in analyses of this sort. Elvey, Leinbach, Hessler, and Noxon [1955a] divided observations near the auroral zone into latitude zones 1" wide, and Gartlein and Moore [1951a]

FIG. 4.5. Geometry of high-altitude observations on the Earth, showing the relation between horizontal and vertical distance and zenith angIe. Diagram courtesy

M. H. Rees.

collected a large number of zenith observations and discussed the southern extent of North American aurorae. In the southern hemisphere Jacka [1953a] used observations of homogeneous arcs from Macquarie Island to locate the position of maximum occurrence of overhead aurorae.

The width of the auroral zone may be defined in terms of the frequency of zenith aurora. A working definition might consider the auroral zone as the area where overhead aurora could, with ideal observing conditions, be seen visually during ten percent of the time at night. Davies [1950a] found that the average width of a zone defined in this manner would be about 2000 km (stretching roughly between 60" and 80" geomagnetic latitude in the western hemisphere, slightly further north in the eastern), but the zone shifts, shrinks, and expands on a regular basis (see Sec- tion 4.1.3). Considering the auroral zone to apply to a rather wide


region may be justified on the basis of disturbed radio communications, magnetic disturbances, etc., which frequently exhibit their auroral-zone characteristics over similarly large areas.

4.1.3. Periodic Variations

Sunspot-Cycle and Yearly Variations in Occurrence of Aurorae.- The variation throughout a year or over a sunspot cycle in the frequency of aurorae at a given location may be influenced by two rather distinct factors: the geographic variation in the distribution of aurorae over the globe and changes in the total number of aurorae. Although some conclusions may be drawn regarding periodic shifts in the auroral zones (see below) it is not possible as yet to ascertain how much the world-wide incidence of aurorae changes with time.

The most striking variations occur well outside the auroral zone. Figure 4.6 shows, as an example, the number of aurorae observed at

80-

FIG. 4.6. Number of aurorae observed visually from Yerkes Observatory ( A , = 53O N), 1897-1951. From Meinel, Negaard, and Chamberlain [1954a];

courtesy Journal of Geophysical Research.

Yerkes Observatory over nearly 5 sunspot cycles. These observations were recorded by E. E. Barnard and F. R. Sullivan. Probably additional faint aurorae could have been detected in this period with continuous patrolling by wide-angle cameras, as was done during the IGY. But these observers have nevertheless provided a valuable and homogeneous record of visual observations.


During the 55 years represented, a total of 1267 nights, or an average of 23 nights per year, had visible aurorae. This is 6.3 percent, and is somewhat higher than the 5 percent estimated by Vestine (see Fig. 4.3) for this location with no interference from clouds and artificial lights.

x

4c

M

M

la

0

gi 1,s

p B .s Q

" I 2 3 4 5 6 7 8 9 D II

P W s E m

FIG. 4.7. Average auroral, sunspot, and magnetic frequency curves for four solar cycles, 1901 - 1944. Aurorae observed at Yerkes Observatory. From Meinel, Negaard, and Chamberlain [ 1954~1; courtesy Jourfial of Geophysical Research.

Figure 4.6 clearly illustrates the 1 1.1 -year period. Previous investigations of the 1 I-year period or the relation between sunspots and auroral occurrences have been made by many p e ~ p l e . ~ In Fig. 4.7 the average

They include Mairan [1733a], Loomis [1873a], Boller [1898a, b], Tromholt [1882a, 1902~1, Egedal [1937a], Stetson [1939a, 1940~1, Clayton [1940a], Stormer [1942a], and Garner [1951a].

4.1. GEOGRAPHIC DISTRIBUTION AND PERIODIC VARIATIONS 1 1 1

curve for the four cycles ending in 1944 is compared with the sunspot area and magnetic activity over the same period. Although the minimum auroral activity seems to coincide with minimum solar activity, the aurorae usually reach a maximum frequency about two years after the sunspot maximum. A similar lag behind sunspots occurs in magnetic activity (Chapman and Bartels [1940a]).

In Fig. 4.8(a) the aurorae observed during the 55-year interval are J*H FEB Lw rpR MAY JUK JUY YIG SEPT OCT H(N Mc

JAN FEB M M AFU M Y JM J U Y &IG SEPT OcT N(N w:

FIG. 4.8. (a) Fraction of all aurorae observed in each calendar month at Yerkes Observatory; (b) monthly frequency distribution corrected for cloudiness and number of dark hours in each month. From Meinel, Negaard, and Chamberlain

[1954a] ; courtesy Journal of Geophysical Research.


plotted by month. An approximate correction was applied to these observations for the relative number of clear, dark hours at Yerkes Observatory during the different months, and the corrected histogram is given in Fig. 4.8(b).

The spring and fall maxima in low-latitude occurrences have been known for many years (Mairan [1733a]). I t was first suggested by Cortie [1912a] that the similar maxima in magnetic disturbances were due to the fact that in the spring and fall the Earth is farthest from the plane of the sun's equator. Activity on the surface of the sun is ordinarily confined to middle latitudes, with the region within 10" or so of the equator kept fairly free of sunspots. The sun's equator is tilted about 7" to the plane of the ecliptic and the Earth reaches its maximum negative and positive heliographic latitudes near the beginning of March and September, respectively. The statistical fluctuations in auroral and geomagnetic data are so great that it has not been possible to ascertain whether the yearly maxima coincide better with the equinoxes or with the Earth's maximum positions in heliographic latitude, the difference between the two being only about two weeks.

An alternate way of ascertaining whether Cortie's explanation might be correct lies in comparing the spring and fall amplitudes with the preponderance of sunspots in the southern or northern solar hemisphere during a given year. Cortie himself found some support for his hypothesis when he divided magnetic storms by this criterion. For aurorae the cloudiness and moonlight exert such a strong effect on the observations of a given year that it is difficult to establish any conclusion from the data taken at a single station.

If the yearly variation is due to this Cortie efJect, the angular diameters of the streams or clouds of solar particles believed to produce magnetic storms and aurorae could not usually exceed about 5 degrees, as seen from the sun. For larger streams the heliographic latitude could scarcely play so sensitive a role. Further, it would appear on this basis that the streams normally tend to be ejected from the sun with little north-south variation from the radial direction. The time lag of a day or so between the passage of an active area across the solar meridian and the onset of geomagnetic disturbance is usually interpreted as indicating little departure in longitude from radial ejection, and the delay is ascribed to the travel time from sun to Earth. Storms associated with major events on the sun seem to be less restricted in their direction (see Section 4.3.8).

Shifts in the Auroral Zone.-In the previous section we have quoted data that show the auroral zones to be located on the average around


20" or 25" from the poles. The zones have been determined with all the available observations, irrespective of the time. But there is evidence that the auroral zones vary with time.

Here, incidentally, we shall use the term auroral zone to refer to the region where an aurora is. statistically most likely to appear at a particular time. I t is often (but not in this book) used in the sense of defining the most active auroral region or the region of precipitation of extraterrestrial particles at a given instant. Thus one often reads statements that, for example, the auroral zone moves toward the equator with increasing magnetic activity (as indicated, say, by the planetary magnetic index, Kn). Actually the aurora itself may move out of the auroral zone, while the latter, by our definition, varies only in a periodic fashion.

The first suggestion of a shift in the auroral zone with sunspot cycle seems to have been made by Tromholt [1882a] in a paper analyzing observations by K. Kleinschmidt at high latitude from 1865 to 1882. The data indicated that within the auroral cap the sunspot minimum corresponded to an auroral maximum, and vice versa.

Davies [1950a], defining the width of the-zone in terms of the frequency of zenithal aurorae, found that both the center of the zone and its southern edge (in the northern hemisphere) move southward during times of high sunspot activity. It seems that the zone may shift some 3" between sunspot maximum and minimum.

There also seems to be a seasonal shift in the auroral zone. At low latitudes there are pronounced maxima of occurrences in the spring and in the fall (see above), whereas within the zone and the auroral cap, a yearly maximum occurs in the winter, according to observations by K. Kleinschmidt (see Tromholt [1882a]) and data collected by Davies [ 19504. Summer observations in high latitudes are halted by perpetual sunlight. But data at hand suggest an expansion of the zone near the equinoxes, a contraction near the solstices.

27-Day Recurrence Tendency.-A harmonic analysis of the time interval between a given aurora and succeeding aurorae up to 400 days later was performed on the Yerkes Observatory data by Meinel, Negaard, and Chamberlain [1954a] for 1200 aurorae from 1904 to 1949, inclusive. The most striking recurrence tendency that appears in such an analysis is at multiples of 29.5 days, the synodic lunar period. The recurrence tendency does not diminish with successive cycles (see also an analysis by Dixon [1939a]); and were it a true indication of auroral occurrences, it might be interpreted to imply the existence of one or a few permanent, active regions on the sun, rotating with this synodic period.

The lunar period is, however, undoubtedly due to observational

114 4. OCCURRENCE OF AURORAE IN SPACE AND TIME

selection, showing simply that aurorae are not easily detected near full moon. When the analysis is corrected for this effect, a small but definite indication of a recurrence maximum around 26 and 27 days remains, which is evidently due to rotation of the sun. By the second and third solar rotation, no enhanced recurrence tendency remains. When only a short region on either side of 27 days is examined for a recurrence tendency, a more striking effect is found (e.g., Sverdrup [1927a]); but many of these recurrences are due to the observational selectivity imposed by moonlight.

Daily Variat i~ns.~-A large number of studies have been devoted to daily variations of auroral activity. But the behavior is evidently dependent upon geographic location, and perhaps even on the time of year and phase of the sunspot cycle, and probably on the type of auroral display. Consequently the daily variationis still rather clouded in mystery.

Outside the auroral zone the daily variation may be studied by counting the frequency of auroral occurrences between specific time intervals of, say, every half hour. A disadvantage is that strong and weak aurorae count equally, and in the auroral zone some auroral activity may be present a high percentage of the time, so that the amplitude of any daily variation is less pronounced than it might be if total luminosity is measured by continuously recording apparatus (Section 4. I . 1).

A better understanding of daily variations is likely to be one of the more important results of the IGY effort. However, there are indications in earlier data of a maximum probability of occurrence near magnetic midnight [defined in Section 3.1.1, following Eq. (3.15)]. Vegard [1912a] found such a maximum for bright-rayed aurorae in analyzing observations from the First Polar Year, 1882-83. There are suggestions of a less pronounced, secondary maximum in the early morning hours at some stations but not at others (Hulburt [1931a]). A dependence on geomagnetic time for various auroral forms has also been found by Fuller5 [1933a, 1935~1.

Stormer’s auroral theory explained the auroral zone in terms of the spiral precipitation curve (Fig. 8.3) for monoenergetic particles entering the Earth from a specific longitude (but from a wide range of latitudes). The curve shows that the charged particles will not strike the atmosphere

We shall here use the word “daily” to characterize variations occurring in 24-hr intervals and shall reserve “diurnal” (often used in this connection) for sinusoidul daily variations.

Also see Fuller and Bramhall [1937a], Currie and Edwards [1934a], Davies [1935a, 1950~1, Jacka [1953a], Elvey, Leinbach, Hessler, and Noxon [1955a], Murcray [1959a], Malville [1959a], Hale [1959a], Chamberlain and Thorson [1960a].

4.1. GEOGRAPHIC DISTRIBUTION A N D PERIODIC VARIATIONS 1 15

beyond a certain polar angle (which depends on the energy), thereby setting the outer radius to the auroral zone. The inner boundary exists because particles that enter near the pole also enter on the daytime longitudes. There are difficulties to accepting Stormer’s theory in original form, but there have nevertheless been some attempts at interpretations of auroral and magnetic activity in terms of Stormer’s particle-precipitation curves.

Nikolskii [1957a] has maintained, for example, that there wilI be four main regions on the curve where the precipitation or bombardment of particles will be at a maximum. Starting closest to the pole and moving outward, we find these regions for positive particles at geomagnetic times of 8 hr, 2 hr, 20 hr, and 14 hr. Nikolskii has attempted to locate the geomagnetic latitudes of these subzones-that is, the scale of Stormer’s curve-by analyzing geomagnetic activity and especially the daily variations. He concludes that the ordinary auroral zone corresponds to the summed effect of the subzones at 2 and 20 hr, an inner zone exists with maximum activity at 8 hr, and a zone at somewhat lower latitude has a maximum probability for proton bombardment around 14 hr geomagnetic time.

Meek [1955a] similarly analyzed magnetic data from the Second Polar Year, 1932-33, and showed that stations with the same geomagnetic latitude had about the same daily variation in geomagnetic time. Plotting (in polar coordinates) the polar distance of the stations against time of maximum decrease in H , for stations north of 40” N, he found a precipitation spiral corresponding to positive particles (unwinding clockwise); a plot against time of maximum increase in H gave a spiral in the opposite direction.

An interpretation of these variations in terms of Stormer spirals is rather questionable, regardless of the correctness of Stormer’s theory of aurora. Contrary to what is often implied, the Stormer spiral is not an instantaneous precipitation curve. Instead, only small portions of the theoretical spiral are applicable at any one time. Stormer applied the entire curve to give the latitude boundaries of auroral bombardment as the sun moves through its yearly range of geomagnetic latitude; and he suggested that small segments of the curve explain the dimensions and orientations of auroral forms. On a long-term statistical basis there may therefore be a relationship between the geomagnetic latitude and geomagnetic time for bombardment of monoenergetic solar particles. But the Stormer spiral seems inappropriate as a basis for discussing regularly recurring (daily) variations (also. see Agy [ 1960~1).

Auroral light has not been detected in the day and the question naturally arises whether the aurora is strictly a nighttime event or whether

116 4. OCCURRENCE OF AURORAE IN SPACE A N D TIME

it could be detected if the background brightness of the sky were less. Radar reflections of the types associated with aurorae are observed occasionally in the daytime, but as there is not a one-to-one correspondence between the visible aurora and the radio aurora, these observations do not completely satisfy one’s curiosity. Daytime aurorae might be detected when the background light is diminished during a total eclipse of the sun, especially if observations are made from very high altitude (Chapman and Stibbs [1953a]).

Another possibility lies in the use of a high-resolution monochromator, to limit the background continuum to about the width of the superimposed emission line from the aurora. Jarrett and Byard [1957a] have estimated that the brightness of the daytime sky near 5577 A gives6 47rI = 5000 kR/A. Over a band width of 0.2 A, the scattered sunlight would have an integrated brightness 9 corresponding to 4719 w lo3 kR. Only an exceptionally bright aurora would have a green-line emission rate of this same order (Appendix 11). But if observations with such a monochromator could be made from a height of 25 km, where the scattered light is diminished by a factor of about 30 according to Jarrett and Byard [1957a], a daytime aurora would probably be just within the realm of detectability.

4.2. Characteristics of Auroral Displays

For the most part we are concerned with visual aurora, that is, an aurora bright enough to be detected by the dark-adapted human eye. In the larger sense we may define aurora to include not only visual displays but other radiation as well. These matters will be dealt with in Section 6.1.1, where the working definition of aurora, for purposes of this book, is given.

Aurorae may be classified or described according to several different criteria, including structure or form, brightness, color, height (and vertical extent), orientation in space, and activity or motions. We shall discuss these items in turn.

4.2.1. Appearance

Auroral Forms.-Vivid descriptions of auroral displays have been written by many authors. Several of the historical references in Appendix VIII and some more recent books such as Chapman and Bartels [1940a,

See Appendix I1 for a discussion of the rayleigh (R) unit.

4.2. CHARACTERISTICS OF AURORAL DISPLAYS 117

Chap. 141 and Stormer [1955a, Chap. 13 contain especially beautiful passages, including some of the descriptions by Aristotle, Pliny, and Seneca.

As an aid to observers during the Second Polar Year, 1932-33, an Atlas of Auroral Forms (Stormer [1930a]) and a Supplement (Stormer [1932a] and La Cour [1932a]) were published by the International Union of Geodesy and Geophysics. Stormer’s [ 1930a, 1955~1 classification scheme of 12 basic forms is rather widely used and accepted and is a convenient basis for distinguishing aurorae of different types. Brief descriptions follow ; for more extensive discussions, see Stormer’s book [1955a].

I. Forms without ray structure

Homogeneous’ arc. A luminous arch usually stretching from magnetic east to west (approximately: see Section 4.2.3) with its highest point near the magnetic meridian. The lower edge of an arc appears rather sharp; the top portion fades more gradually with height.

Similar to an arc, its shape is less uniform and it generally shows active apparent motion along its length. The band may have one or more “horseshoe” turns.

Pulsating arc. Part or all of an arc may pulsate in brightness with a period of a few seconds to a minute or longer.

Diffuse surfaces are amorphous glows without distinct boundaries or isolated luminous patches resembling clouds.

Pulsating surjaces remain nearly constant in position and shape, but pulsate in brightness irregularly with periods of several seconds.

Feeble glow is a term applied to auroral light seen near the horizon. I t is not a true auroral form, and may arise, for example, from an arc or band whose lower border is below the horizon.

Homogeneous band.

Ii. Forms with ray structure

is broken by numerous vertical striations. Rayed arc.

Rayed band. Drapery is a band composed of very long rays. Often it has a horseshoe

Rays sometimes appear singly or (more often) in isolated bundles or

Corona is a rayed aurora seen near the magnetic zenith. Since rays

Similar to the homogeneous arc except that the luminosity

A band composed of numerous vertical rays.

fold, giving the appearance of a hanging curtain.

more extended groups.

’ The word homogeneous is used in this connection to signify the absence of perceptible ray structure; it must not be taken too literally.


are aligned more or less along the dipole lines of force, they appear to converge toward the magnetic zenith. This railroad-track effect produces the illusion of a dome or, if it is developed on one side only, a fan.

III. Flaming aurora

Waves of light move rapidly (less than a second) upward, one after the other, from the base of the aurora toward the magnetic zenith.

Examples of some of these forms are given in Figs. 4.9-4.14, which show some beautiful photographs taken at College, Alaska by V. P. Hessler. Drawings of Stormer’s 12 forms have been published by Chapman [1957fl.

FIG. 4.9. A remarkable group of auroral arcs; courtesy V. P. Hessler.

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FIG. 4.1 1 . Homogeneous horseshoe band (also see Frontispiece); courtesy V. P. Hessler.


FIG. 4.12. Auroral draperies. The drapery at the left is seen nearly edge-on. Courtesy V. P. Hessler.

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FIG. 4.14. Fan-shaped corona. The structures in silhouette are dipoles of a radio telescope. Courtesy V. P. Hessler.


The salient features of auroral structures may be summarized as follows:

1. Arcs and bands are characterized by extremely narrow (north- south) thickness (of the order of 1 km and frequently less) but great (east-west) dength, perhaps occasionally covering a considerable fraction of a circle of constant magnetic latitude. There may be folds and turns in this structure without destroying the ribbon or curtain appearance.

2. Rayed structure may become exceedingly fine, probably as narrow as 0.1 km and perhaps even less for some of the short-lived (less than one second) structure.

3. It is not necessary that either type of structure appear and, indeed, during a strong aurora, the sky often appears to be just a mess. One type of structure may appear either with or without the other.

The different auroral forms as listed above are characterized not only by their structure but by activity (as in pulsating forms and flaming aurorae). Activity, including brightness fluctuations and motions, is discussed further in Section 4.2.4.

Brightness, Durations, and Color.-It may seem strange at first that there is much less known about the brightness of aurorae than of the much fainter airglow. But in spite of the aurora’s brightness, the fine structure and changing patterns and brightness combine to make photometric observations rather difficult. We shall discuss auroral photometry more thorougly in Chapter 5, and here only summarize the general features that affect visual appearances.

Normally the brightest feature in the visible auroral spectrum is the [OI],, green line at 5577 A, which also dominates the visible airglow. The faintest aurora that can be distinguished against this background is about 3 or 4 times the normal airglow brightness (Roach and Jamnick [1958a]). Visual observers estimate the brightness of an aurora in terms of an international brightness coe3cient (IBC). There are four classes: I, brightness of the Milky Way; 11, brightness of thin moonlit cirrus clouds; 111, brightness of moonlit cumulus clouds; and IV, provides a total illumination (at the ground) equivalent to full moonlight.

These definitions are extremely crude and Seaton [1954a] made a first effort to place the IBC scale on an absolute basis in terms of green- line intensities. Seaton’s results have been slightly modified by Hunten [1955a], who proposed the definitions listed in Appendix 11.

The frequency of occurrence of aurorae decreases rapidly with increasing brightness. There is some uncertainty as to how closely the frequency distribution fits the same curve as airglow brightness in the green line


(see Section 12.3.2; also see Ashburn [1955b], St. Amand and Ashburn [ 1955~1, Roach, McCaulley, and Marovich [ 1959~1).

Short-lived aurorae seem to be much more frequent than long displays. At Yerkes Observatory Chamberlain and Thorson [ 1960~1 found a maximum frequency for aurorae of one hour or less and a rapidly decreasing distribution for longer displays. However, these results refer to aurorae that are visually detectable and may be due simply to the facts that faint aurorae are the most frequent and that any aurora varies in brightness through the night. Thus the apparent durations are undoubtedly affected by the visual threshold for auroral detection and do not necessarily indicate the duration of disturbed conditions.

Aurorae of IBC I or I1 appear, like the airglow, colorless. Brighter aurorae (II+, 111, IV) lie above the color threshold of the eye (Roach and Jamnick [1958a]) and generally appear green. Vegard [1926a, b, 1936a, 1937a, b, 1938al and Vegard and Tonsberg [1937a] have shown that there are two distinct types of red aurorae. At high altitudes the red lines of [OI],, at 6300 and 6364 A may dominate the visible spectrum, even though the eye is less sensitive in the red than the green. These aurorae are of the so-called type A and may merely show red at the upper parts of rays or may consist of a high-altitude red arc or diffuse surfaces. Occasionally auroral displays will appear yellow (or orange) between the lower, green emission and the upper, red parts of the type-A aurora. This yellow evidently arises from a physiological blending of red and green by the observer and does not indicate a true yellow emission.

Quite a different red aurora is the rare type B which is a red lower border to a band or arc. Type-B aurorae are lower than normal arcs and bands and are exceptionally bright and active. The red color arises from an enhancement of the N, First Positive (Vegard and Tonsberg [1937a]) and the 0: First Negative bands (Dahlstrom and Hunten

During the observer’s twilight an aurora may be illuminated by direct sunlight. Such sunlit aurorae are observed occasionally and have been studied particularly by Stormer [1927a, b, c, 1929a, b , c, d , 1930b, c, 1937a, b, 1939~2, 1941a, 1942~1 and also by Vegard [1936a], Vegard and Tonsberg [1940a], Harang [1937a], Geddes [1939b], Barbier and Williams [1950a], and Rees [1959b]. High sunlit rays usually appear violet, owing to a strong enhancement and vibrational development of the N: First Negative bands. The [OI],, red doublet is also enhanced relative to the green [OI],, line and in some cases sunlit rays appear red; more rarely they have been described as blue.

[ 195 l a ] ) .

P

FIG. 4.15. Parallactic photographs of auroral rays. Note the displacement relative to the “Big Dipper” (Ursa Major). The stations were located about 80 km apart.

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4.2.2. Height and Vertical Extent

Heights.-Auroral heights have been estimated with rough precision by visual observers dating back to Mairan [1733a]. The favored opinion prior to 1900 was that the aurora generally occurred above 50 km and perhaps as high as several hundred kilometers above the Earth. There were, however, a sufficient number of reports of very low aurorae to raise doubts as to the correctness of any height and, indeed, precise measurements awaited the inventions of photography8 and the telephone and their application by Stormer [1910a, 1911a, b] and his many dedicated assistants.

For details on parallactic photography and the reduction of a pair of photographs to obtain heights, refer to the excellent accounts in the books by Harang [1951u, Chap. 11 and Stormer [1955a, Chaps. 3-51, who have been instrumental in developing the technique^.^ An example of a pair of parallactic photographs is given in Fig. 4.15.

Measurements of numerous parallactic photographs of aurorae of different forms and at different geographic locations have provided some rather definite information on heights.1°

On auroral arcs and bands the most convenient height to measure is the apparent lower border, which is fairly sharp. An example of a set of such measurements in and near the auroral zone is shown in Fig. 4.16, after Harang [1944a, 1951~1. The total number of measurements shows a concentration between 95 and 110 km, with a double peak, which appears also in the height distributions found by other investigators. Harang’s division of the aurorae into groups of varying intensity suggests that the height depends on the intensity and that the double peak results from the distribution of aurorae in the different intensity classes. This interpretation is also supported by the work of McEwen and Montalbetti [1958a]. A suggestion by Egedal [1929u] that the double maxima appear

The first auroral photographs were evidently taken in 1892.b~ Brendel and reported by Raschin [1900a].

Methods of reducing parallactic photographs have been developed and improved by Stormer [1911b, 1938~1, Vegard and Krogness [1920a], Harang and Tonsberg [1932a], Chapman [1934a, 1953~1, Fuller and Bramhall [1937a], and N. Herlofson (reported by Stormer [1938a]).

lo Extensive measurements in Norway have been reported and analysed by Stormer [1911a, b, 1921a, 1935a, 1936a, 1938a, 1942a, 1948a, 1949~1, Vegard and Krogness [1916a, b, 1920~1, Vegard [1916b], Harang and Bauer [1932a], Harang and Tonsberg [1932a], and Harang [1937a, 1944a, 1945~1. Observations in Canada and Alaska have been reported by McLennan, Wynne-Edwards, and Ireton [193 la], Currie [1934a, 1955~1, Fuller and Bramhall [1937a], and McEwen and Montalbetti [1958a]. Southern hemisphere observations have been published by Geddes [19396].

4.2. CHARACTERISTICS OF AURORAL DISPLAYS I29

because of tidal oscillations of the atmosphere has received little statistical support (however, see Harang [1945a]). Probably the tidal effects have an amplitude smaller than 7 km or so, which is the difference in the two peaks of the height distribution.

I t is not clear how much of the dependence of height on intensity (which appears in a similar fashion for draperies) is real. A strong

Km.

20 20 40 bO 20 20 40 20 40 60 80 100 points measured

FIG. 4.16. Distribution of heights of lower borders of auroral arcs, Tromso, 1929-38. Adapted from Harang [1951a]; courtesy John Wiley & Sons.

aurora that actually fades out gradually with depth, rather than having an abrupt cutoff, would appear on a photograph (which would be judged in terms of the contrast with the background sky) to have a lower height than if it were fainter. The matter is of some importance to the physics of aurorae, as it is related directly to the question of how much auroral brightness depends on the velocity (rather than on just the flux) of incident particles. Stormer [ 1942~1 has also reported a few homogeneous arcs lying in the dark atmosphere near 200 km, about twice the height of most of the arcs.

The lower limits of individual rays appear 10 or 15 km higher than the lower edges of most arcs, bands, and draperies. Sunlit auroral rays appear systematically higher, of course, than displays in the dark atmosphere. Figures 4.17 and 4.18 show the heights of rays over southern Norway, as published by Stormer. A few sunlit rays extend higher than 1000 km.

Red aurorae of type A are also preferentially much higher than “normal” green displays. These include the higher parts of rays and

130 4.

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1 I,I I 1 i n I I I I 1 I II I 0 1918 -201 -26 -28 - 29 -32 -33 -36 - 38 -39 -40 -43

- 21

FIG. 4.18. Length and position in the atmosphere of the vertical projections of rays in sunlight, 1917 to 1943. Compare Fig. 4.17. After Stonner [ 1955~1; courtesy Oxford University Press.

> c 73 0 P * r


red diffuse surfaces (which have been observed as high as 600 km). The rare red arcs also probably lie a t several hundred kilometers (Stormer [1955a, p. 971).

Type-B red aurorae, on the other hand, are exceptionally low. These aurorae are quite bright and active and may simply be extreme cases of the general relationship that brighter arcs and bands appear at lower heights. Harang and Bauer [1932a] made numerous measurements of one such type-B display and obtained some points extending as low as 65 km, whereas the normal arcs, both before and after the type B, seldom dipped below 85 km.

The average height for the lower borders of homogeneous arcs is about the same all during the night and at all locations where extensive measurements have been made. In striking contrast to these aurorae are the rayed bands, whose heights vary both during the night and with geomagnetic latitude. Their daily variation in the auroral zone is quite large: In the first part of the night the lower borders are around 95-1 15 km, i.e., similar to homogeneous arcs. In the early morning hours the heights sink to about the 80- to 95-km region. At lower latitudes Stormer finds this daily height fluctuation to have less amplitude and the mean height to be somewhat lower.

There may also be a greater high-altitude extension for low-latitude aurorae. This conclusion is suggested by the height measurements of Stormer [1948a] and by spectra (Barbier [19496]) which show an enhancement of nebular-type forbidden lines (which are especially susceptible to deactivation).

Vertical Distribution of Intensity.-While the data that have gradually become available on auroral heights are extremely important, they alone are not sufficient for discussions of auroral excitation and the characteristics of the incident particles responsible for such excitation. The height measurements can be greatly supplemented with measurements of the intensity versus height. Most of the information of this sort that is now available has been obtainedphotographically and probably applies mainly to the N l First Negative bands and green [OI],, line. Measurements of the brightness in different emissions and for different auroral forms at various (measured) heights constitute one of the most important, as well as one of the most neglected, of auroral observations.ll

l1 The work of Vegard and Krogness [1920a], Vegard [1921a], Harang [1945c, 1946~1, and Currie and Weaver [1955a] shows that homogeneous arcs generally have an apparent vertical extent in the neighborhood of 15-30 km. When rayed structure is present the vertical extension increases. Draperies may be 50 or 100 km in vertical length and isolated rays or ray bundles occasionally extend for several hundred kilometers.


4.2.3. Orientations in Space

Radiant Point of Rays.-If rays are indeed produced by an influx of charged particles, they should lie almost exactly along the magnetic field.lZ Were the Earth's magnetic field that of the centered dipole, the rays would then be oriented nearly toward the magnetic zenith of the dipole, as given by the declination ~,h and inclination i (Section 3.1.1 and Appendix 111). Since the departures from the centered dipole are generally important, as far as measurements of this type are concerned, one must compare the orientation of rays with the true magnetic zenith derived from actual measurements of I,!I and i at the observatory.

The orientations of rays are most easily and accurately obtained from photographs of coronae (Vegard and Krogness [ 1920a1, Stormer [1938b], Abbott [ I 958a]), but visual observations (see results collected by Vegard and Krogness [1920a]) with a theodolite can give a good position for the point toward which the coronal rays appear to converge-the radiant point or auroral zenith.

Wilcke [ I777aI first noticed that rays are aligned approximately along the Earth'.s field-or in the direction of magnetic dip. Later visual observations and the photographic work of Vegard and Krogness indicated that the auroral zenith is systematically one degree or so lower (that is, displaced toward the south in the northern hemisphere) than the magnetic zenith. This is in the direction in which the auroral zenith should be displaced owing to the curvature of the geomagnetic field, but the rays would have to be at 1000 km or so to produce a one- degree displacement (Problem 4.1). Stormer's analysis did not relate the radiant point to the magnetic zenith but did disclose a small wandering of the auroral zenith on successive photographs, a result previously suspected by Wilcke [1777a] because the direction of magnetic dip was found to fluctuate.

Abbott's three photographs from Alaska fix the radiant point to within lo', and disclose an average rate of motion (in a 21-min period) of at least one degree in five minutes of time. The radiant point was found on either side of the normal (undisturbed) magnetic zenith, but simultaneous measurements of the disturbed field showed that the instantaneous magnetic zenith was lower by 7" or 8" than the radiant point. There seemed to be no relationship between wanderings of the magnetic zenith (as determined from magnetometer readings on the ground) and the auroral zenith (as determined from the radiant point).

Ahnost, because a charged particle moving in a nonuniform magnetic field does not spiral precisely about a fixed line of force. But for particles in the auroral energy range, these deviations are very small. See Problem la, Chapter 8.

134 4. OCCURRENCE OF AURORAE I N SPACE A N D TIME

Extended investigations of this sort have barely scratched the surface of their potentialities and could conceivably yield important clues to the auroral mystery. The orientations of rays, presumably outlining the magnetic field in the upper ionosphere, when compared with ground readings (and perhaps occasional rocket measurements of the field) should indicate the general location of the currents responsible for magnetic disturbances.

Direction of Arcs and Bands.-The orientation of an auroral form in space can be derived from parallactic measurements just as the height is determined. For arcs and bands the heights of the lower borders are so predominantly clustered around 105 km that one may obtain their orientations by assuming the height and measuring the angular elevation of two or more points from a single station. I t will be clear from Fig. 4.5 that the horizontal distance, and hence the orientation, can thus be deduced. Variations on this basic technique have been summarized by Harang [19453, 1951a, p. 351.

T o a first approximation arcs and bands are aligned along circles of constant geomagnetic latitude. If this orientation were precisely correct, their geomagnetic azimuth would be 90". Vegard and Krogness [1920a] (see also Vegard [1921a]) conducted an extensive analysis of data from the First Polar Year 1882-83 and of their own observations from Haldde in northern Norway. They found that the arcs and bands at most of several stations scattered around the Arctic had an average geomagnetic azimuth (measured eastward from geomagnetic north) of about 100". The aurorae were thus aligned not quite west to east but tilted slightly in the sense northwest to southeast (which corresponds to the tilt of a precipitation curve for negative particles in Stormer orbits; cf. Fig. 8.3).

Measurements in Canada during the Second Polar Year (1932-33), analyzed by Currie and Jones [1941a], also showed average orientations of this nature, but aurorae at some stations seem to have average orientations that depart considerably from the 100" azimuth. There is a rather wide dispersion (mean deviations of perhaps f 15") in the distribution of orientations at any one station, and the older data suggest that near the geomagnetic poles the orientations may be completely random.

However, Jensen and Currie [1953a] found evidence of a strong (amplitude 5 15") seasonal variation about the mean azimuth (96") at Saskatoon and a similar variation at Chesterfield. This variation probably has a semiannual oscillation, as in the frequency curve of auroral occurrences, but the number of summer observations is too few to establish this with certainty. It seems likely that for many, if not all, of the stations that seem to show anomalously large or small average


orientations, the discrepancy may be due to a preferential selection of data from certain months.

The orientation of arcs also seems to have a daily variation, which is evidently more pronounced at some stations than at others (Mawson [1925a, pp. 179-1821, Harang [1944a, 1945~1, Jensen and Currie [1953a], Weill [1958u]). The problem of these orientations is one of the most fascinating in auroral morphology. Probably the situation is more complicated than the earlier observations indicated and stands as a challenge to those engaged in analysis of the ICY data.

4.2.4. Auroral Activity

Rapid motions and brightness changes in a brilliant display contribute enormously to the effect of a grandiose spectacle, and even weak displays have motions and brightness fluctuations of various types. But the quick changes cannot be adequately described and occur too rapidly to be photographed.

Two types of activity are used in the classification scheme of auroral forms (Section 4.2.1 ): pulsating aurorae and JEaming aurorae. These forms can be most spectacular. An extreme example of a pulsating aurora is the flashing aurora described by Stormer [1942u], wherein narrow arcs suddenly disappeared and then reappeared near the original position; the time scale of this flickering on and off was a few seconds.

Bright, rayed aurorae, such as the fascinating type-B red bands, often give an appearance of a horizontal wave motion. A region a few degrees wide and including a number of rays may appear much brighter than the rest of the band and this bright patch will move rapidly in either direction, resembling a searchlight sweeping across a gigantic bamboo curtain. These active bands and draperies may give an illusion that the individual rays are moving, whereas only the excitation pattern moves. An individual group of rays will be seen to brighten, then fade, only to reform or brighten again with the next “wave.” When the pattern reaches an S-curve in the band, it follows the detour and does not jump across.

An auroral form may shift its position in the sky rather rapidly. As a display develops, an arc usually moves southward in the northern hemisphere, south of the auroral zone. (Within the auroral cap the tendency seems to be for an arc to move northward-again, away from the zone). A motion of 5” in latitude in half an hour would correspond to a speed of the order of 300 meter/sec, which is typical (Kim and Currie [1958a]), although speeds as high as 2500 meter/sec have been measured (McEwen and Montalbetti [ 1958~1). Stormer [ 1942~1 has


reported on a large cloud-like aurora, several hundred kilometers in diameter and with a height near 100 km, that moved westward with a speed of about 700 meter/sec, but a more typical speed is 100 to 200 meter/sec (Krogness and Tonsberg [ 19364).

Sometimes the aurora may develop, change its appearance, or move across the sky with astounding rapidity. The series of photographs in Fig. 4.19 was taken within 4 min, while the aurora appeared in the west and moved high into the sky, developing into a bright drapery. It is particularly exciting to watch a drapery or band change its shape, like a curtain blown by a celestial breeze.

Motions of individual rays or other structure in an aurora can be studied to advantage with time-lapse photography by motion-picture wide-angle cameras. Some examples are shown in Figs. 4.1 and 4.2, the latter showing a dramatic example of a drapery moving eastward across the northern sky.

Meinel and Schulte [1953a] (also see Meinel [1955a]) found evidence of a preferential drift toward the west in the evening. After midnight it seems that the motions are less systematic, but toward dawn the direction of drift may become predominantly eastward. The speed of the drifts generally increases for bright displays and strong magnetic activity, and may exceed 1000 meter/sec. There seem, however, to be some differences in the details of the systematic east-west motions as observed at different ~ t a t i0ns . l~ Kim and Currie, for example, find no characteristic daily variations for the east-west motions at Saskatoon. The IGY program, providing nearly homogeneous data from various places, should greatly clarify this exciting aspect of auroral morphology.

4.2.5. Synoptic View of Aurora

For a proper understanding of the auroral phenomenon, one should know how an aurora is distributed over the Earth and how this coverage changes during the development of a display. Onfortunately, we so far have only the scantiest knowledge in this area. Again, the IGY program offers a promise; but there remains the laborious task of measuring and synthesizing data from a large network of stations into a synoptic picture.

The development of a typical auroral display might begin with the formation of a homogeneous arc in or near the auroral zone. The arc can move several degrees toward lower latitudes. At some point the

l3 See Meek [1954a], Bless, Gartlein, and Kimball [1955a], Kim and Currie [1958a], Malville [1959a], Hale [1959a], and Evans [1959a].

137

FIG. 4.19. Motion and development of an auroral drapery. The series of photographs shows the rapid (within 4 min) progression from west to east of an auroral structure. For a few minutes this extremely active display also produced a type-B

red aurora. Photographs by the author at College, Alaska.


arc will often brighten and break into a rayed arc or band. While additional auroral emission may appear, the arc or band will form the low- latitude boundary of the display. Observations within the auroral cap of arcs that move in from lower latitude (e.g., Currie [1955a]) suggest that aurorae may spread in both directions from the zone or from a center of activity.

The latitude coverage of an aurora is probably related to its intensity (Vegard [1912a]). Further, the motion of an auroral arc toward lower latitudes may be indicative of an expansion of the latitude belt affected, and not simply a shift of a belt of constant width. Aurorae that extend well into the subauroral regions are also likely to be exceptionally bright (and therefore colorful) and active ; hence they become known as “great aurorae.’’ Little is known also regarding the extent of an aurora in longitude, although a great aurora is probably observed all around the nighttime longitudes. Such questions as the extent of a single arc and the simultaneity of breakup along the arc are still to be answered.

One of the questions most important to an understanding of the auroral phenomenon is the connection between northern and southern displays -the aurorae borealis and australis. Little and Shrum [1950u] found a statistical relationship between auroral occurrences in New Zealand and in the northern United States. A more exciting possibility, however, is that individual aurorae, or even details of a display, may be duplicated in the two hemispheres.

4.3. Aurorae and Related Phenomena

An aurora is not an isolated phenomenon but is invariably linked to other observable events. I n this section we shall discuss this aspect of auroral morphology. However, a discussion of radio observations of atmospheric ionization intimately associated with visible aurora-the radio-uuroru- will be reserved for Chapter 6.

4.3.1. Geomagnetic Activity and Earth Currents

A relation between aurorae and magnetic disturbance has been known since Halley [1716a] (for other references see Chapman and Bartels [1940a, p. 9231). On a statistical basis magnetic storms, like large auroral storms, show 1 I-year and seasonal variations (Figs. 4.7 and 4.8). Further, there is a good correlation between auroral activity and planetary magnetic activity (e.g., Bartels and Chapman [1958a]). But of more immediate interest is the relation between an aurora and the local

4.3. AURORAE AND RELATED PHENOMENA 139

magnetic activity at a single station. (The world-wide morphology of magnetic storms is reviewed briefly in Section 3.1.2.)

Auroral observers have long used the magnetic compass as a daytime indicator that an aurora would be present at twilight. At Yerkes Observa- tory a flux-gate variometer, of the type devised by Meek and Hector [1955a], has been of great value in predicting when a display will be visible after sunset.

The physical connection between magnetic and auroral activity is not entirely clear. On the one hand, it has been thought that much of the magnetic disturbance arises in extraterrestrial currents generated by auroral particles moving in the geomagnetic field. Alternatively, one can construct hypothetical current systems in the ionosphere that would reproduce a particular magnetic disturbance over the Earth (Chapman [ 19354). If such ionospheric currents are indeed responsible for magnetic storms, perhaps the increased ionization from auroral-particle bombardment affects the conductivity and thence the disturbed magnetic field (Chapman [1951a], Vestine [1953a, b], Fukushima [1953a]).

In the auroral region one may find horizontal voltage differences from place to place of the order of 0.1 to 1 volt/km during magnetically disturbed periods (e.g., Hessler and Wescott [1959a]). These earth potentials and the resulting earth currents are presumably due to induction from changing magnetic fields. However, it is difficult to relate the earth currents to the changing field in individual cases, since the distribution of the field and of the electric conductivity of the ground are not generally known with adequate precision. An earth-current record provides a good index of atmospheric disturbance, however, and may be used in the same manner as a magnetometer to provide an auroral alarm system. Such an alarm used by V. P. Hessler at College, Alaska was instrumental in his obtaining some of the fine photographs shown in Figs. 4.9-4.14.

Detailed comparisons of simultaneous changes in the aurora with magnetic activity have been made by Meek [1953a, 195483, Heppner [1954a, 1955~1, Zaborshchikov and Fediakina [1957u], Fan [1958a], and Bless, Gartlein, KimbaH, and Sprague [ 1 9 5 9 4 The disturbance usually begins with a small increase in the horizontal component ( H I Y ) of the magnetic field. During these positive increments the aurora appears in the form of a homogeneous arc or band. Very bright auroral displays seem to be associated with rapid changes in the magnetic field to a negative AH,,.

Heppner [1954a] finds that the strong decrease usually occurs at College around midnight and the change in AH,, from a positive to a negative value seems almost invariably to be associated with a distinct


change in auroral activity, involving a breakup of homogeneous arcs or bands into rayed or diffuse forms or, alternatively, a northward recession and temporary disappearance of aurora. He finds several fairly general relationships between the sequence of changes in auroral activity and the negative bay: (1) The fairly abrupt decrease in H , (horizontal, northward component), characteristic of the first part of a bay type of disturbance, coincides with a rapid movement southward of the southernmost auroral arc and the appearance of rayed structure north of the arc. (2) Early in the period of large - AH,, the arc breaks either into active rayed forms, followed by diffuse aurora (diffuse surfaces, diffuse draperies, and pulsating diffuse forms), or directly into diffuse aurora. (3) The recovery of the horizontal component takes place during diffuse and pulsating aurorae. (4) In the majority of cases, there is a short period following the negative bay in which the A H , component is positive relative to its average value on very quiet nights. The diffuse and pulsating aurorae usually continue through this + A H , period, but frequently a homogeneous arc will form again over part of the area which was previously covered with diffuse and pulsating aurorae.

4.3.2. Auroral Proton Bombardment Fan [1958a] found during two strong displays seen at Yerkes Observatory that the breakup of a homogeneous arc into rayed aurora coincided not only with the onset of a negative bay but with a decrease in the hydrogen- line emission. His recording apparatus included a wide-angle camera to integrate the H/3 emission over most of the sky. Previous investigations (Dahlstrom and Hunten [1951a], Gartlein [1952a], Meinel [1952a, 1954a1, Fan and Schulte [1954a], Vegard [1955a]) had suggested that hydrogen emission was weaker in rayed aurorae than in homogeneous arcs and characteristic of the early part of a display. Fan’s results imply that there is a marked change in the amount of proton bombardment, and not simply a defocusing action, at or near the time of breakup.

The daily variation of HP has been compared with that of A4709 N,f by Romick and Elvey [1958a]. They find that statistically H,B has its maximum intensity about two hours before N:, appearing strongest in the early, homogeneous phases of the aurora. There is a suggestion of two daily maxima at College, Alaska, occurring about three hours before and after local midnight. For additional discussion see Section 5.2.3.

4.3.3. X-Radiation Rocket flights at high latitudes first disclosed a “soft radiation” in and near the auroral zone (Meridith, Gottlieb, and Van Allen [1955a],

4.3. AURORAE A N D RELATED P H E N O M E N A 141

Van Allen [1957u], Anderson [1960a]). This radiation has been shown to be electromagnetic (i.e., x-radiation) and, because of the pronounced dependence on latitude, was thought to be produced as bremsstrahlung from incident (primary) electrons (Section 7.2.1). At rocket altitudes the radiation seems to be present regularly in the auroral zone.

A direct association between x-rays and visible aurora was established by balloon experiments over Minneapolis (Winckler and Peterson [ 1957~1, Winckler, Peterson, Arnoldy, and Hoffman [ 1958u, 1959~1). There is a suggestion from the limited data available that the x-ray bursts appear when a homogeneous arc breaks up into rayed structure and that they increase with auroral intensity and activity. X-rays during the great red aurora of 1 1 February 1958 were associated with bright, active bands near the zenith. The major x-ray bursts at Minneapolis were coincident with large negative bays in the magnetic records and with cosmic-noise absorption (Section 4.3.4) observed at Boulder.

Anderson [1958u] has found a relation between x-rays at balloon altitudes in the auroral zone (Churchill) and geomagnetic activity. Although there was some variable x-ray emission associated with the first part of the storm, the most spectacular effect was a large increase in intensity coincident with the onset of a large decrease in the local magnetic field. The high x-ray intensity continued for at least 1 $ hr, until the sun set and the balloon began to sink.

4.3.4. Ionospheric Disturbances14

The Rising of the Higher Ionosphere.-A relationship between magnetic activity and the height and density of the F2 layer is well established (see Matsushita [1959u] and references cited there). During a magnetic storm the apparent height of the F , layer increases and at high latitudes its maximum electron density (or critical frequency) decreases. Tandberg- Hanssen [1958u] finds evidence that Fl also rises but that the normal E layer remains fixed. T h e rise in the ionosphere is generally ascribed either to some heating effect, as from particle bombardment or hydromagnetic waves, or alternatively to vertical electron-ion drift. If there is an electric field giving rise to the current systems that in turn produce magnetic perturbations, this same field will produce a vertical drift when crossed with the horizontal component of the magnetic field.

Sporadic-E a n d D-Region Ionization.-A number of early investigations established the existence of abnormally high ionization in the E region and

l4 An extensive review of the relation between geomagnetic storms and ionospheric disturbances has been prepared by Obayashi [I 9 5 9 ~ 1 .

142 4. OCCURRENCE OF AURORAE IN SPACE A N D TIME

below during times of auroral and magnetic activity.15 More recent studied6 at high latitudes have shown that ionospheric reflections resembling those from sporadic-E clouds seen at lower latitudes are often associated with aurora. Zenith aurorae are usually accompanied by Es echoes. Further, the top frequency in the auroral E, echoes increases with the brightness of inactive auroral forms (E, reflections often extend to frequencies high enough to obscure or “blanket” the F region), and the range of oblique Es echoes is related to the distance of the visible aurora. When a bay disturbance occurs at night in the auroral zone, it is frequently accompanied by complete blanketing of F , by E,.

It is not established that auroral Es ionization is identical to the ionization-excitation yielding the visible aurora, and in fact there is some indication that as the aurora moves toward lower latitudes, an advance fringe of Es ionization moves ahead of the aurora.

Stoffregen [1958a] has reported that as an auroral disturbance pro- gresses, frequencies of 0.33 to 1.5 Mc/sec become reflected from low heights, 75-90 km. This low-lying ionization forms in the later stages of aurora, after the auroral E , is developed and often as visible ray structures appear.

Ionospheric Absorption.-Ionospheric reflections usually extend to frequencies of several megacycles per second. The complete absence of ionospheric echoes (blackout), due to absorption of the probing wave, often occurs in the polar regions without being accompanied by aurora. However, exceptionally bright aurora (Harang [ 1936a, 1937b, 1945c, 1946~1, Hakura, Yugoro, and Otsuki [1958a]) and pulsating forms (Heppner, Byrne, and Belon [ 195201, Zaborshchikov and Fediakina [1957a]) are generally accompanied by absorption, as are large magnetic- bay disturbances (Matsushita [19566, 195801).

At frequencies greater than a few megacycles per second the ionosphere is normally transparent (or nearly so) and no information on absorption can be obtained from reflection experiments. Sources of cosmic radio noise, such as the sun, galactic thermal emission, and some discrete sources (for example, certain filamentary gaseous nebulae and colliding galaxies) provide radiation that can be monitored continuously. (For discussion of appropriate instrumental techniques, see Little and Leinbach [1959a].)

Appleton, Naismith, and Builder [1933a], Harang [1936a, 193761, Appleton, Naismith, and Ingram [1937a], Wells [1947a].

l6 Heppner, Byrne, and Belon [1952a], Meek [1953a], Meek and McNamara [1954a], Knecht [1956a], Matsushita [1956a, 1957~7, 1958~1, Zaborshchikov and Fediakina [1957a].


At high latitudes the nighttime absorption of cosmic noise at 30 Mc/sec is related to visual aurora in the same way that polar blackouts and aurora are related (Little and Leinbach [1958a], Reid and Collins [ 1959~1): pulsating and flaming aurorae are usually accompanied by strong and variable amounts of absorption, which occurs below the E region, but other aurorae, even active type-B bands, often occur in a nearly transparent atmosphere.

The great red aurora of 1 1 February 1958 seemingly produced a peculiar effect in the cosmic absorption at 18 Mc/sec at Boulder, Colorado. Warwick [ 1958~1 reported that following intense absorption associated with the aurora, the daytime absorption was greatly reduced for a day or so following the display, as though the aurora had destroyed the ionizable constituent in the L) region and thereby diminished the amount of absorption possible in that region.

Harang and Troim [1959a] have discussed a case of strong absorption in the auroral zone at 40 and 45 Mc/sec in the early morning hours following great solar activity. A large magnetic storm began with a sudden commencement several hours after the absorption started. I t is not clear whether this particular case of absorption should be attributed to electromagnetic radiation or to particle bombardment.

Strong absorption covered the Arctic within one to three hours after the great solar flare of 23 February 1956, although auroral and magnetic activity did not commence for 48 hours. Bailey [1957u, 1959~1 explains this absorption, observed to decay gradually over a period of several days, by the bombardment into the D region of solar electrons and ions trapped in the geomagnetic field.

A similar strong absorption occurring in the 60-70 km region over Alaska was reported by Leinbach and Reid [1959a], following a great flare on 29 July 1958. Hultqvist and Ortner [1959a, b] have observed several cases of strong absorption below 50 km, evidently a result of the bombardment of solar protons from giant (importance 3 or 3 f ) flares. The particle energies are of the order of 100 Mev with a flux of 10 or 100 cm-2 sec-1. (Also see Section 4.3.6.)

Scintillations of Radio Stars.-The scintillation of radio stars is analogous to the twinkling of optical stars, which is produced by the un- steadiness, or the so-called astronomical “seeing” quality, of the atmosphere. For radio sources the scintillation is imposed on the wave as it passes through the ionosphere.

Some scintillation is always present and some observers have related it to the ionospheric phenomenon of “spread F,” wherein the critical frequency and height of the maximum of the nighttime F-layer are


ou longer sharply defined but become spread over large frequency and height ranges. Others do not find a relationship with spread F but with sporadic E instead. Scintillation has been explained in terms of diffraction of the incident waves by irregularities in the ionosphere. These matters are discussed more fully in the review of Little, Rayton, and Roof [ 1956~1.

Little and Maxwell [1952a] find that an auroral disturbance increases the rate of scintillation by about a factor of four, and active (pulsating and flaming) aurora may be accompanied by an increased amplitude in the scintillations. The rate also increases when a weak radio-aurora is observed (Chivers and Greenhow [1959a]) and with increasing magnetic disturbance, although the amplitude does not seem to be correlated closely with magnetic storms (Little, Lovell, and Smith [ 1950~1).

4.3.5. Radio Emission

Emission at Very-High and Ultrahigh Frequencies.-Atmospheric radiation near 3000 Mc/sec was first reported by Covington [1947a, 1950~1, who found it to occur sporadically but associated with certain geomagnetic storms and aurorae. In connection with studies of the reflection of radio waves by the aurora, Forsyth, Petrie, and Currie [1949a, 1950~1 occasionally received radiation at 3000 Mc/sec, even when no signals were being transmitted. Indeed, their equipment did not detect ordinary radar reflections at this frequency. These observations were confirmed by Getmantsev [1956a]. Later R. P. Chapman and Currie [1953a] reported that the microwave “emission” was no longer observable, an effect attributed tentatively to a dependence on the sunspot cycle. Harang and Landmark [1954a] were also unable to detect emission.

Hartz, Reid, and Vogan [1956a] discovered VHF (32, 50, and 53 Mc/ sec) emission as the maximum of another sunspot cycle approached. T o obtain greater directionality, Hartz [1958a] then used a 20-ft parabolic antenna at 500 Mc/sec. Whereas there was no perceptible noise from numerous displays of various types, a type A red, patchy aurora did appear simultaneously with increased noise. In the southern hemisphere Seed [1958a] found auroral emission at 69 Mc/sec.

Radio absorption of a nature similar or related to that discussed in Section 4.3.4 was observed by Chivers and Wells [1959a, b] at Man- Chester. They found, however, that simultaneously with strong absorption in one direction there appeared an increased signal lasting for perhaps an hour, presumably due to ionospheric emission at 80 Mc/sec, from another sector of the sky. In addition, a more sudden and fluctuating

4.3. AURORAE A N D RELATED P H E N O M E N A 145

type of emission, probably auroral in origin, was associated with magnetic disturbance but not with absorption.

Thus the sporadic existence of radio-frequency emission from the upper atmosphere seems to be confirmed but the conditions that must exist for this radiation to be detectable are still obscure. Plasma oscillations and thermal emission(Section7.3.3)seem the most likelymechanisms responsible, but Cerenkov radiation (Section 7.2.2) is also a possibility.

Emission a t Low and Very-Low Frequencies.-In the audio frequency range of, say, 1 to 10 kc/sec, there are two principal types of electromagnetic signals routinely detected. The signals most frequently heard (by amplifying the voltage on an antenna and directing it across a headphone or speaker) are whistlers, which are produced by lightning discharges. The electromagnetic waves are guided by the geomagnetic field, the lines of force resembling a waveguide, so that the signal travels from one hemisphere to the conjugate point in the other. The theory of whistlers was developed by Storey [1953a] (also see Northover [1959a, b]); a general review is given by Helliwell and Morgan [1959a]. The study of whistlers, whose propagation depends on the ionized component of the outer atmosphere, provides a means of studying the characteristics (and their time variations) of the transition region between the ionosphere and the interplanetary gas.

The other principal type is generally called the dawn chorus (Storey [1953a]) or more simply the chorus, since the time of maximum intensity is now known (e.g., Pope [1957a]) to vary from place to place, possibly depending on latitude.

The chorus has not been related specifically to the aurora, but it does appear to result from solar activity and to be associated with magnetic disturbance (Watts [ 1957~1, Allcock [ 1957~1). Besides a daily variation, the chorus may exhibit a weak seasonal effect.

T h e chorus is probably produced by an influx of charged particles into the outer atmosphere (Allcock [1957a]). Fast electrons could initiate Cerenkov radiation, which then propagates into the atmosphere in the same fashion as whistlers (Gallet [1959a], Gallet and Helliwell [1959a]; see Section 7.2.2). Gyro radiation from protons has been proposed as an alternative (MacArthur [1959a]), but this theory is actually more appropriate for proton Cerenkov radiation than for gyro radiation (see Section 7.2.3).

In addition, bursts of low-frequency (5 kc/sec) noise have been found to be associated with magnetic activity and increased brightness of the airglow (or auroral) red lines (Duncan and Ellis [1959a]). Dowden [1959a] has found such signals in the lOO-kc/sec region, and Ellis


[1959a, 1960~1 has observed a strong correlation of auroral and magnetic activity with bursts in the frequency range 2-30 kc/sec. Low-frequency emission, not necessarily propagated in the whistler mode, has been discussed by Ellis 11957~~1 in terms of Cerenkov radiation of particles entering the outer realms of the ionosphere (Section 7.2.2). Electron gyro radiation may also explain some of these bursts (Section 7.2.3).

4.3.6. Cosmic Rays

Atmospheric Bombardment by Low-Energy Cosmic Rays.-Atmos- pheric ionization is undoubtedly a complex phenomenon, arising in part from solar electromagnetic radiation and bombardment by electrons and heavy ions. Protons with initial energies less than 1 Mev will not penetrate below the altitudes of the visible aurora ; their bombardment was discussed in Section 4.3.2. But some of the ionospheric ionization responsible for radio absorption, as discussed in Section 4.3.4, is probably due to protons with considerably higher energies-the very-low-energy cosmic rays of solar origin-so that direct observation of these particles and their correlation with solar and other geophysical events becomes of immediate interest to auroral physics.

I t is well established that occasional solar flares are accompanied and followed by large increases in cosmic radiation, especially in the low-energy region of the spectrum (e.g., Meyer, Parker, and Simpson [1956a]). These increases are detectable from the ground and include particles with energies of lo3 Mev and greater. However, a few observations with balloon-borne equipment have disclosed cosmic rays with even lower energy. For example, Anderson [19588] found an influx of solar protons with energies of the order of 170 Mev associated with solar radio noise, although there was no accompanying aurora or magnetic storm.

Freier, Ney, and Winckler [1959a] found a similar increase at Minnea- polis of 200 Mev protons associated with a magnetic storm and a Forbush decrease (see below) of the background cosmic rays. At the onset of the magnetic storm there was strong cosmic absorption at high latitudes, as measured by Leinbach and Reid [1959a], presumably due to the precipitation of low-energy ionizing particles into the D region. But protons at 200 Mev are normally excluded by the magnetic field from entering the atmosphere at Minneapolis (Avn = 5 5 O ) , and a logical interpretation is that the solar ion cloud modified the field sufficiently for these particles to enter. Similar observations by Anderson, Arnoldy, Hoffman, Peterson, and Winckler [1959a] showed the flare particles to continue for two days, with the particles probably stored and emitted


gradually by the solar atmosphere. A much more spectacular event, with 1000-fold increase over the normal cosmic-ray background, has been reported by Ney, Winckler, and Freier [1959a].

Forbush Decrease.-World-wide decreases in the cosmic-ray intensity were first investigated extensively by Forbush [1938a, 1939al. These decreases, often amounting to several percent at sea level, may be accompanied by a magnetic storm or may follow the onset of a storm by a few hours. The recovery to normal intensity often requires several days and sometimes much longer. Winckler, Peterson, Hoffman, and Arnoldy [ 1959al reported a small precursor accompanying the sudden commencement of the magnetic storm of 11 February 1958 (which was associated with a great red aurora), while the main decrease began an hour later. The Forbush decrease is probably an effect produced by magnetic fields imbedded in a solar ion cloud or stream of particles, which modulates pre-existing cosmic rays. The decreases are probably related physically to the general decrease of cosmic rays near the peak of the sunspot cycle as compared with solar minimum.

4.3.7. Miscellaneous Terrestrial Effects Related to Aurora

The Radio-Aurora.-Radio reflection at frequencies much higher than the normal ionospheric reflections are often observed during aurora. This radio-aurora has been studied rather extensively and related to other observations of aurora and to magnetic activity. Discussion of the observations and their interpretations will consume a complete chapter (Chap. 6).

Ozone Emission.-A preliminary report by Murcray [ 1957al indicates that the 9 . 6 ~ band of O3 may become enhanced by the aurora. If the observation is confirmed it might signify either heating of the ozone layer or an increase in the total ozone content as a result of the aurora.

Auroral Noise.-Reports of sounds accompanying the aurora are frequent, but their reality is still very much in doubt. Chapman [1931d], Stormer [1955a], and Elvey [1957a] have reviewed a number of interesting accounts. If real, the sounds must be produced by some effect at the ground related to the aurora rather than the aurora itself.

4.3.8. Solar Phenomena

Most statistical analyses on solar-terrestrial relationships have dealt with magnetic storms, very few with aurora. In Section 4.1.3 we discussed


the 1 1-year cycle of aurorae at low latitudes and the weak 27-day recurrence tendency.

Greaves and Newton [1928a, 1929~1 and Allen [1944a] have segregated magnetic storms into two basic types. One class, the more intense storms with sudden commencements, are associated with sunspots and flares, and show little or no 27-day recurrence tendency. The weaker storms, which start gradually, are not related to sunspot areas but show a pronounced 27-day recurrence. While this division may be an over- simplification, it does suggest at least two distinct sources of magnetic storms: one is directly associated with sunspots and the other, more evasive source has been labeled, for lack of a more definite name, the “ M region” (for “magnetic”) by Bartels [1932a, 1934~1. The M regions dominate geomagnetic activity during sunspot minimum.

Both types of disturbance are associated with aurorae, but statistics on relative probabilities of occurrence are not available. Aurorae seem to show less 27-day (and subsequent multiples) recurrence tendency than do magnetic storms, but the auroral data are contaminated with moonlight, which requires a large correction to the analysis and might obscure some effects.

Sunspots, Flares, and Radio Bursts.-Sunspots are generally the center of most of the observable activity on the solar disk. Newton [ 1948~1 noted that the correlation between spots and geomagnetic activity is increased if only large spots or only spots with large amounts of flare activity are included. Later work has shown that the low- frequency radio emission from a spot group is also correlated with the geophysical effectiveness of the group (Denise [ 1952~1, Tanberg- Hanssen [1955a]). The most likely time interval between the passage of a spot group across the central meridian of the sun and the onset of a magnetic storm is about 1.5 days.

The most spectacular aurorae and accompanying magnetic storms can usually be associated with the most spectacular of solar events- flares. Often observed simultaneously with radio fade-outs and other ionospheric disturbances caused by ultraviolet light and x-rays, flares are also a source of cosmic rays, at least in some instances (e.g., Meyer, Parker, and Simpson [1956a]). Newton [1943a, 1944~1 found that the largest flares, those of importance 3 + , when they occurred within 45” of the center of the disk, were followed in over 80 percent of the cases by a magnetic storm within a maximum time of three days. The most likely time interval between a great flare and its associated geomagnetic storm is about one day or slightly less (Newton and Jackson [1951a]). However, many storms occur after delay intervals of one to two days,


and in general the delay time preceding a major storm is shorter than that preceding a weaker one.

A study by Dodson and Hedeman [1958a] has shown that a flare is especially effective (92 percent of the cases studied) as the source of sudden-commencement geomagnetic disturbances if it is accompanied by a solar radio burst at frequencies below 200 Mc/sec before the flare reaches maximum brightness. They found for a group of 68 cases where a flare and geomagnetic storm were well associated that occurrence of the flare near the center of the disk and high flare “importance” favored severity in the subsequent storm (see also Warwick and Hansen [ 1959~1, Maxwell, Thompson, and Garmire [1959a]). The average time interval between flare and start of the storm was 2.3 days, with the delay following great flares a little shorter than for flares of importance 1.

Solar radio emission at high frequencies is probably characteristic of the plasma frequency where the emission originates. Thus high radio frequencies provide information about the lower levels of the solar atmosphere and low-frequency emission originates in the upper layers and in the corona. Probably the early radio bursts below 200 Mc/sec indicate the passage of material through relatively high levels of the solar atmosphere and imply the successful escape of fast particles shortly after the flare began. These, at least, were the considerations that led to the fruitful examination of the radio bursts as a criterion for distinguishing flares with important geophysical consequences.

The escaping particles do not necessarily arise from the flare itself, however. Dodson, Hedeman, and Chamberlain [ 1953~1 found material ejected from the sun faster than the velocity of escape (618 km/sec) immediately following solar flares but not always in the flare’s immediate neighborhood.

An outburst observed on different radio frequencies shows a time lag increasing toward lower frequencies. The accepted interpretation is that a disturbance moving outward generates successively lower frequencies at greater heights in the atmosphere. Again, the computed velocities are often in excess of the escape velocity for the sun.

Identification of M Regions.-The M regions on the sun were hypothesized by Bartels [1932a, 1934~1 as the source of magnetic storms with a high 27-day recurrence tendency ( M disturbances), but the relationship of these M regions to other phenomena on the sun was unknown. The M regions cannot be identified with sunspots nor with activity directly associated with spots since they in fact avoid spot groups (Allen [ 1944~1).

Waldmeier [ 1946~1 and Kiepenheuer [ 1947~1 proposed that quiescent


prominences (which appear as dark filaments when seen projected against the solar disk) might be the elusive M regions. But an analysis by Hansen [1959a] failed to support the idea.

Several attempts have been made to find a correlation between coronal structure and the M regions. Allen [1944a] (also see Roberts and Pecker [1955a]) suggested the extended coronal streamers, seen in white light at solar eclipse, as M regions. They usually seem to be formed around quiescent prominences. On the other hand, regions with high intensity of the coronal green line, h5303, evidently tend to coincide with active (sunspot) areas and avoid the M regions (C. Warwick [1959a]).

Magnetic maps of the solar surface have also suggested a possible origin of the M disturbances. Preliminary analysis suggests that the rare but long-lived unipolar magnetic regions-i.e., regions in which the magnetic polarity is of predominantly one sign-are the M regions (Babcock and Babcock [1955a], Simpson, Babcock, and Babcock [1955a]; also see Wood [1956a] and Babcock [1957a]). Presumably the lines of force that emanate from unipolar regions return to the sun, but in areas far removed. I t seems reasonable that charged particles could leave the sun with much greater facility in such a region than in the usual bipolar regions where the field lines never extend far above the solar surface.

PROBLEM

1. Show €or a dipole field that the inclination of the lines of force in the upper atmosphere near the auroral zone changes at a rate of approximately 0.1 '/I00 km altitude.

Chapter 5. Auroral Spectroscopy and Photometry

5.1. Spectral Identifications

Spectroscopic observation of the aurora began with the researches of Angstrom [ 18684 1869~1, but many others soon observed and measured the spectrum and attempted interpretations. The earliest work was done visually, but photographic studies, which opened the violet and ultraviolet regions to exploration, were initiated by E. S. King (see Pickering [1898a]) and Paulsen [1900a]. I n 1912 Vegard began his work in auroral spectroscopy. With his able assistants he obtained numerous photographs of the auroral spectrum and contributed enormously to the advance- ment of a subject that might otherwise have lain dormant for many years. Vegard [19326, c] also succeeded in obtaining the first infrared spectra, which had a dispersion of 1400 A/mm. Each group of identifications has its own history, which will be discussed briefly in the following sections. More general reviews of the early work will be found in the article by Kayser [1910a] and in the older books listed in Appendix VIII.

5.1.1. An Atlas of the Auroral Spectrum’

Photographic spectra of the aurora are illustrated in Figs. 5.1 to 5.7. Figure 5.1 gives a low-dispersion spectrum covering the visible region. Spectra with higher dispersion are shown in the remaining halftone figures. Microphotometer tracings and direct recordings from photoelectric and photoconductive spectrometers are shown in Figures 5.8 to 5.27.

Tables 5.1, 5.2, and 5.3 list by atom and molecule the lines and bands that have been identified in the auroral spectrum. Table 5.4 lists these same features by wavelength. These tables are an extension and modification of similar listings prepared by Chamberlain and Oliver [1953c]. For the revised tables, we have made extensive use of an unpublished atlas of the auroral spectrum prepared by Vallance Jones [1955a] and of spectra obtained at Yerkes Observatory. The atomic multiplet numbers and the wavelengths for atomic lines are from Moore [1945a], except that a few more recent measurements of forbidden lines, quoted in Section 5.1.2, have been included.

of the spectra, tracings, and tables in this atlas.

151

Dr. Lloyd Wallace has kindly collaborated with me in the compilation and preparation

I52 5. AURORAL SPECTROSCOPY AND PHOTOMETRY

All molecular wavelengths refer to band heads. For the N, First Positive bands these wavelengths are quoted from Dieke and Heath [1959a]; for N, Second Positive, from Pearse and Gaydon [195Oa]; for N, Vegard-Kaplan, from Bernard [1935a], Janin [1946a], Herman [1946a], and our own calculations from the energy levels and rotational

FIG. 5.1. Low-dispersion spectrum of a green aurora, obtained with a patrol spectrograph of the type used in the United States and Canada in the IGY. The north horizon is at the top, south at the bottom, with the slit along the geographic meridian at Yerkes Observatory. The horizontal dark lines are at zenith angles of 45". A transmission grating produced a dispersion of about 350 A i m . This frame is a 27-min exposure, with a geometrical camera speed of f/0.625, on the great aurora of 2 March 1957. The N: emissions are from the First Negative system and the Nz bands in the red are First Positive; other N, bands appear

among the First Negative system, but are not labeled here.

constants. All the V-K wavelengths given here, except those for 1-9, 1-10, and 1-1 1 (Janin), are poorly determined. For N l First Negative we used Pearse and Gaydon [1950a] and Herzberg [1928a]; for the N l Meinel bands, the R, (shortward) head given by Douglas [1953a]. The positions of the 0, band origins and heads have been computed from the known molecular constants (Herzberg [1950a]). For several Atmospheric bands these wavelengths have already been tabulated by Chamberlain, Fan, and Meinel [1954a]. The band origins are often used to designate these bands; they are 8645 A for 0-1 and 7708 A for i-1. Similarly, for the I.R. Atmospheric 0-1 band, the origin is at 15,803 A. For the 0; First Negative system, the wavelengths are from Pearse and Gaydon [1950a].

A rough indication of relative intensity is furnished by the spectra and tracings reproduced here ; intensities are discussed further in Section 5.2.1. It should be borne in mind, however, that the high- dispersion spectra are necessarily from bright displays and, with the long exposures required, it is not feasible to keep the spectrograph directed to a particular auroral form or height.

FIG. 5.2. Auroral spectra, 3340-4710 A, obtained with a dispersion of 28 A/mm. Tracings are shown in Figs. 5.8 and 5.9. After Petrie and Small [1952n]; courtesy

University of Chicago Press.

154 5. AURORAL SPECTROSCOPY AND PHOTOMETRY

FIG. 5.3. Auroral spectra, 3700-4750 A. The spectrum 3700-4430 A was obtained with a dispersion of 22A/mm during the great red aurora, I 1 February 1958. The one on the right is from an ordinary green aurora, 10 November 1956; dispersion 33 A/mm. From Yerkes Observatory plates nos. 128 and 77, Tracings

are shown in Figs. 5.11, 5.12, and 5.13.

FIG. 5.4. Auroral spectra, 4620-6370 A, with a plate dispersion of 43 A/mm. Tracings are shown in Figs. 5.14, 5 .15 , and 5.16. After Petrie and Small [1952a];

courtesy University of Chicago Press.


FIG. 5 .5 . Auroral spectra, 6290-6710A, from the aurora of 2 March 1957, with dispersion 33 A/mm. Compare with the low-dispersion spectrum of the same aurora in Fig. 5.1. The upper part of this spectrum was photographed with light from near the north horizon, while the lower part shows the spectrum near the magnetic zenith, which was fainter. The central portion is a mixture. Faint neon lines from advertising signs in a neighboring village contaminate the upper half, but can be identified with the aid of the neon comparison spectrum at the top and bottom edges. Tracings of H a are shown in Fig. 5.19. From Yerkes

Observatory plate no. 92.

L” c

0 a M 0 4 % >

uoo+o~so(; r

saqJak E z 2 3

=!

3

0 > 0

FIG. 5.6. Auroral spectra, 7200-8800 A. Spectrum at the top, Yerkes Observatory plate no. 25, aurora of 12 April 1954, 66 A/mm. Spectrum on the bottom obtained at Saskatoon from the red aurora of I I February 1958, 66 A/mm; after Vallance Jones [ 196Oal; courtesy CanadianJournal of Physics. Note the great enhancement of the [OII],, lines, AX731 9-7330,

in the high-altitude aurora. Tracings are shown in Figs. 5.20, 5.21, 5.22, and 5.23.

158 5. A

UR

OR

AL

SPE

CT

RO

SCO

PY

AN

D P

HO

TO

ME

TR

Y

a 9 FIG. 5.7. Auroral spectra, 7200-1 1,600A, obtained with a grating spectrograph and image converter.

After Bagariatskii and Fedorova [ 19564 ; courtesy Pergamon Press.

5.1. SPE

CT

RA

L ID

EN

TIF

ICA

TIO

NS

1-59

FIG. 5.8. Microphotometer tracings, 3340-3820 A, of spectrum in Fig. 5.2. After Chamberlain and Meinel [ 1954~1; courtesy University of Chicago Press.

1 60 5.

AU

RO

RA

L

SPE

CT

RO

SCO

PY

AN

D P

HO

TO

ME

TR

Y

FIG. 5.9. Microphotometer tracings, 3720-4220 A, of spectrum in Fig. 5.2. After Chamberlain and Meinel [1954a]; courtesy University of Chicago Press.

5.1. SP

EC

TR

AL

IDENTIFICATIONS

161

a

0

m

m

m

a s

m

m

0,

z 8 n

a

W I

f < -0 -N

--(o

-

--P - -5

--N -

-s

- --m - -W -

--P -

--(u

-0

- -

--N

--P

-W

-

FIG. 5.10. The auroral N: 0-0 First Negative band, h3914. Plate dispersion, 7A/mm. From a spectrum obtained by Dr. A. Vallance Jones. The numbers below the tracing are the rotational quantum numbers, K , of the lower level.

162 5. A

UR

OR

AL SPEC

T.RO

SCO

PY A

ND

PHO

TO

ME

TR

Y

FIG. 5.1 I . Microphotometer tracing, 3700-41 10 A, of spectrum in Fig. 5.3. Aft-er Wallace [1959a]; courtesy Pergamon Press.

5.1. SPE

CT

RA

L ID

EN

TIF

ICA

TIO

NS

163

P -- -5

FIG. 5.12. Microphotometer tracing, 4050-4430 A, of spectrum in Fig. 5.3. After Wallace [1959a]; courtesy Pergamon Press.

I 4300 4400

FIG. 5.13. Microphotometer tracing, 4220-4750 A, of spectrum in Fig. 5.3.

I I I 45po 4600 4700

5.1. SP

EC

TR

AL

ID

EN

TIF

ICA

TIO

NS

165

FIG. 5.14. Microphotometer tracings, 4620-5210 A, of spectrum in Fig. 5.4. After Chamberlain and Meinel [ 1954aI; courtesy University of Chicago Press.

166 5.

AU

RO

RA

L

SPE

CT

RO

SCO

PY

A

ND

P

HO

TO

ME

TR

Y

3’P-5’D0 Q

FIG. 5.15. Microphotometer tracings, 5210-5750 A, of spectrum in Fig. 5.4. After Chamberlain and Meinel [ 1954~1; courtesy University of Chicago Press.

5.1 . SPE

CT

RA

L

IDE

NT

IFIC

AT

ION

S 167

FIG. 5.16. Microphotometer tracings, 5550-6240 A, of spectrum in Fig. 5.4. After Chamberlain and Meinel [ 1954aI ; courtesy University of Chicago Press.

?i FIG. 5.17. Microphotometer tracings, 6240-6900 A, of a spectrum published by Petrie and Small [1952a]; plate dispersion, ;i 43 A / m . After Chamberlain and Meinel [ 1954~1; courtesy University of Chicago Press. 4

5.1, SPECTR

AL LD

ENTIFIC

ATIO

NS

8

, ,

, ,

, ;fi d

a

+ FIG. 5.18. Microphotometer tracing, 6100-7700 A , of a spectrum published by Meinel [1951c]; plate dispersion, 250 A/mm. Q\ \o After Meinel ; courtesy University of Chicago Press.

I70 5 . AURORAL SPECTROSCOPY AND PHOTOMETRY

x 6513 6523 6533 6543 6553 6563 6573

I I I I I I I

I..[

80

I I I I I -2500 -2000 -1500 -loo0 - -500 0 +500 -

Velocity (km/sec) Velocity (km/sec)

FIG. 5.19. Profiles of Ha in the zenith and horizon portions of the spectrum in Fig. 5 .5 . Intensity measurements in the faint wings of these lines are likely to have low accuracy, especially for the underexposed zenith portion. After Chamberlain

[ 1958el; courtesy Sky and Telescope.

5.1. SPECTRAL IDENTIFICATIONS 171

4-2 NS I I 5-3 Nz I

I I 1 I I 7200 7600 75100 7600 7700 7800 7900 8000

I

FIG. 5.20. Microphotometer tracing, 7250-8020 A, of the Yerkes spectrum in Fig. 5.6. Airglow OH contamination may contribute a few of the faintest features

on the spectrum.

7300 7400 7500 7 6 b 7fOO 7dOO 7900 800 I I I

FIG. 5.21. Microphotonieter tracing, 7250-8020 A, of Vallance Jones' spectrum in Fig. 5.6, 1 1 February 1958 aurora.

172 5 . AURORAL SPECTROSCOPY AND PHOTOMETRY

8lbo 8200 do0 d o 0 8:OO 8$00 8/00 8sbo 8900 I

I I I I I I I I I

FIG. 5.22. Microphotometer tracing, 8000-8900 A, of the Yerkes spectrum in Fig. 5.6. Auroral features are marked; some of the background is due to OH

airglow (see Fig. 9.11).

I I I d o 0 edoo 8fOO 8100 8200 eioo 8400

FIG. 5.23. Microphotometer tracing, 8000-8700 A, of Vallance Jones’ spectrum in Fig. 5.6, 11 February 1958 aurora.


FIG. 5.24. Auroral spectra, 8400- I 1,000 A, recorded with a photoelectric scanning spectrometer at 20 A resolution. These examples illustrate variations in relative intensity among the more prominent features. After Hunten [ 195833 ; courtesy

Annales de Giophysique.


11.041~ n

atomic lines

I I I 0.9 1.0 1.1 1.2

Wavelength p

FIG. 5.25. Auroral spectrum, 9000-12,OOO A, obtained with a lead-sulphide (PbS) spectrometer; projected slit width, 100 A. This reproduction was obtained by averaging a number of individual spectra. After Harrison and Vallance Jones

[ 1957~1; courtesy Pergamon Press.

-0”

I I I I I I 10,200 10,300 10,400 10,500 10,600 10,700 x),BOO

Wavelength i

FIG. 5.26. Microphotometer tracing, 10,200- 10,8oO A, of auroral and airglow spectra recorded on Eastman IZ(3) emulsion. Plate dispersion, 85 A/mm; projected slit width, 10 A. After Harrison and Vallance Jones [1957a]; courtesy Pergamon

Press.


FIG. 5.27. Auroral spectra, 14,000-16,500 A, obtained with a lead sulphide spectrometer; projected slit width, 200 A. The dotted curve is the airglow spectrum fitted to the auroral spectrum in a region where the auroral emission appeared feeble. Spectra (a), (b), and (c) yere made in consecutive scans, with a total time of 3 min. T h e relative intensities of features on a single scan are not significant, since the aurora fluctuates in brightness during the scanning period. After

Harrison and Vallance Jones [ 1959~1; courtesy Pergamon Press.


TABLE 5.1

FORBIDDEN ATOMIC LINES IN AURORAL SPECTRAe

Multiplet (excitation potential, ev) 1 (A) Transition

[OI],, Auroral

[OI],, Transauroral

[OI],, Nebular

2p4 ID - 2p4 1s

2p4 3P - 2p4 1s (4.1 I)

(4.17)

(1.96) 2p4 'P - 2p4 ' D

2 - 0 5511.345

1-0 2912.325

2- 2 1 - 2

6300.308 6363.190

- 5 1 2 - 5 5 3 2 - z

[011]32 Auroral 2p3 ,DO - 2p3 ,PO (5.00)

7318.6

7319.4

7329.9

7330.7

3726.16

3728.91

$ - # 3 3 z - E [OII],, Nebular 2p3 4so - 2ps ,DO

(3.31) - 3 5 2 - T

- 5 2 - 3 2 -

Auroral

Transauroral

2p3 200 - 2p9 =PO

2p3 4s0 - 2p3 =PO (3.56)

(3.56)

10,395.4

10,404.1

3466.4 - 3 2 -

3 3 z-z 3 5 2 - 2

[NI],, Nebular 2p3 as0 - 2p3 200

(2.37)

5198.5

5200.7

[NIIIS2 Auroral 2p2 ' D - 2p2 'S

(4.04)

2 - 0 5754.8

[NIIlzl Nebular 2p2 3P - 2p2 'D

(1.89)

2 - 2 6583.6b

a See Appendix VI for energy-level diagrams and additional data. b Uncertain; see text, Section 5.1.2.


Multiplet Mult. (excitation 1 4-4) No. potential, ev)

TABLE 5.2 PERMITTED ATOMIC LINES IN AURORAE

An asterisk after the wavelength indicates an identification that is uncertain or questionable because of blending with or obscuration by other features or because there are too few lines in the same transition array to make the identification convincing.

Multiplet Mult. (excitation 1 44 No. potential, ev)

1 3 5 . 9 - 3 5P 2 - 7774. (10.69)

(12.23)

(10.94)

(12.31)

(12.82)

(12.61)

(1 2.70)

3 3 5 S 0 - 4 5 P 2 - 3947.5

4 3 ' S o - 3 ' P 1 - 8446.5

5 3 ' S o - 4 ' P 1 - 4368.30

6 3 ' s ' - 5 'P 1 - 3692.44

9 3 5P- 5 5 s o - 2 6455. *

10 3 ' P - 4 ' D o - 6157.

11 3 6P- 66So - 2 5436. (12.96)

(13.01)

(13.18)

12 3 6 P - 5 s D o - 5330.

14 3 'P- 66D0 - 4968.

19 3 'P- 3s' 'Do 2 - 3 7995.12 (12.49) - 2 7987.

20 3 ' P - 5 ' S O - 1 7254.4* (1 2.64)

(12.98) 22 3 'P- 6 's ' - 1 6046. *

011

1 3s 4P - 3p 'DO 2 i - 3 h (25.54) 1 4 - 2 4

2 1 2 1 4 - 1 4

1 4 - 1 ;

8 - B 2 3s 'P- 3P'PO 2 3 - 2 3

2 - 2

(25.74) 1 3 - 1 3 1 3 - 3 1 i - 2 9

3 3s 'P- 3p ' S O 2 4 - 1 4

t - 1 3

(26.19) 1 '- - 1 2 2

5 3s 'P - 3p 2Do 1 4 - 2 4

4649.139 4641.811 4638.854 4676.234 4661.635 4650.841 4349.426 4336.865 4345.562 4319.63 1 43 17.139 3749.49 3727.331 3712.75* 4414.909

011

6 3s IP - 3p aPo 1 4 - 1 & 3973.263 (26.45) 4 - B 3954.312

11 - L 3982.719

4075.868 (28.58) 2 4 - 3 ; 4072.164

4 - 1 4 3945.048' 10 3p 'Do - 3d 'F 3 4 - 4 3

4069.8 1 4 - 2 3

1 2 - 1 3 3 t - 3 4 1 4 - 1 3

4092.94P 4078.862'

11 3p 'DO - 3d 'P 1 4 - 8 3872.45* (28.71) 1 4 - 1 4 3882.45'

(28.73) 13 3p4DO-3d2F 2 $ - 2 & 3857.18'

(28.74) 3 4 - 2 4 3875.82*

12 3p 'Do - 3d 'D 3 3 - 2 3883.15'

(26.14) - 1 ; 4416.975 15 3s' '0 - 3p' 'Fa2 i - 3 4 4590.971' 1 $ - 1 4 4452.377 (28.24) 1 4 - 2 4 4596.174'


TABLE 5.2 (cont.)

Multiplet Multiplet Mult. (excitation 1 W) 1 Mult. (excitation J W) No. potential, ev) No. potential, ev)

011 I 011

16 3s' 2D - 39' 'Do 2 $ - 2 & 4351.269 (28.39) 1 9 - 1 4 4347.425

3912 .O* I 17 3s' '0 - 3p' 'Po 2 9 - 1 9 (28.71) 1 4- 1 9

1 4 - $ 3919.287' 19 3p 'Po - 3d 4P 2 $ - 2 8 4169.230'

(28.70) 9 - 1 4121.48' 20 3p 4 P o - 3d ' D 2 9 - 4120. *

(28.73)

21 3p 4 P o - 3d 2F 2 4 - 2 4 4112.029* (28.74)

26 3p 'Do - 3d 2D 1 4 - 1 4 4369.28: (28.94)

28 3p 'So - 3d 4P 1 4 - 2 4 4924.60: (28.71) 1 $ - 4 4890.93'

33 3p 'Po - 3d zD 4 - 1 4 4941.12: (28.94)

36 3p'aFo-3d'ZG 3 4 - 4 4 4189.788 (31.18) 2 4 - 3 4 4185.456

NI

1 3s 'P - 3p 'DO 2 4 - 3 4 (11.71) 1 6 - 2 $

1 1 - 1 1 2 9 - 2 4

4-4 2 3s4P- 3P4PO 2 4 - 2 4

1 4 - 2 9 k - 1 4

2 2

(11.79) 2 4 - 1 4 1 1 - 1

2 2

8680.24 8683.38 8718.82 8711.69 8703.24 8216.28 8242.34 8223.07 8184.80 8187.95

NI

5 3 s 4 P - 4 p 4 P o 2 4 - 2 4 4223.04*

6 3 s 4 P - 4 p 4 S o 2 3 - 1 4 4151.46* (13.21)

(13.26)

(12.07) 9 3 s 2 P - 4 p 2 S o 1 4 - 4 4935.03

(13.14) 4-4 4914.90

(12.91)

8 ~ s ' P - ~ P ' P " l a - 1 4 8629.24

15 3P'So- 3d'P 4- 1 8 9060.6'

1 2p3 'DO - 3p 'P (20,32)

(20.57) * 3 3s 'Po - 3p 'D

NII I NII

4 3s'PO - 3 p a s (20.85)

5 3s3PO - 3p 'P (21 -07)

2-1 4895.20'

2-3 5679.56 1-2 5666.64 0-1 5676.02 2-2 5710.76 1-1 5686.21 2-1 5730.67 2-1 5045.098 1-1 5010.620 0-1 5002.692 2-2 4630.537 1-0 4621.392 1-2 4601.478 0-1 4607.153

6 3 ~ ' P o - 3p 'D (21.51)

(20.32)

(20.56)

(21.51)

(23.02)

(23.04)

8 3s'Po - 3p'P

3s ' P O - 3p '0 9

12 3s ' P O - 3p 'D

14 3p 'P - 3d 'F0

19 3p 'D - 3d 'Fa

1-2 3955.851

1-1 6482.07

1-2 5747.29* 1-1 5767.43* 1-2 3994.996

1-2 4564.78'

3-4 5005.140

2-3 5001.3 1-2 3-3 5025.665 2-2 5016.387


20 3p 'D - 3d 3D0 3-2 4810.286'

2-1 4791. * (23.14) 2-2 \

TABLE 5.2 (cont.)

39 3d ' F O - 4f 3G (26.10)

Multiplet Multiplet Mult. (excitation J h(A) I Mult. (excitation J @) No. potential, ev) No. potential, ev)

NII I NII

2-3 ' 4780.5' 1 - 1 !

21 3p 'D - 3d 'Po 2-2 4488.15' 40 3d 'Fo - 4f 'G

(26.10) (23.31) 3-2 4507.559 *

(23.32) 24 3p ' S - 3d 'Pa 1-0 4987.377'

4-5 4041.321 3-4 4043.531 2-3 4035.087 4-4 4057.00' 3-3 4044.751 3-4 4026.080

42 3d IDo - 4f IF (26.05)

(26.05) 43 3d lDo - 4f SF

28 3p 3P - 3d 3Do 2-1 5960.93;

(23.14) 29 3p 'P - 3d 'Po 1-0 5454.26'

47 3d 'Do 4f I F

(26.05)

(26.05) 48 3d 3Da - 4f 3F

(23.32) I

2-3 4176.164

2-3 4171.608

2-3 4241.787

3-4 4241.181 2-3 ' 4237.0* 1-2 j

H He I

I 2 2 P 0 - 3 2Deta l . - 6562.817 1 2 ' s - 2 'Po 1 - 10,830. *

1 2 2 P 0 - 4 2 D e t a l . - 4861.332

1 2 2 P 0 - 5 2 D etal . - 4340.468

(1 2.04) (Ha) (20.87)

(12.69) (HB)

(13.00) (HY)

Na I

1 3 'S - 3 ' P O $ - 1 $ 5889.953 (2.10) =& - 4 5895.923


TABLE 5.3

MOLECULAR BANDS IN AURORAE

An asterisk after the wavelength indicates an identification that is uncertain or questionable because of blending with or obscuration by other features or because there are too few bands in the same progression to make the identification convincing.

N, First Positive (B 317, --f A 3Zi)

0-0 1-0 2-0 2- 1 3-0 3-1 3-2 4-0 4- 1 4-2 5- 1 5-2 5-3 5-4

l0,SlO. 8912.4 7753.7 8723.0 6875.2 7626.8 8542.5 6186.8* 6788.6 7504.7 6127.4 6704.8 7381.2 8205.5*

N, First Positive ( B + A 3Z,3

6-2 6- 3 6-4 6- 5 7-3 7-4 7-5 7-6 8-4 8-5 8-6 8-7 9-4 9-5

6069.7 6623.6 7274.0 8047.9* 6013.6 6544.8 7164.8 7896.9* 5959.0 6468.5 7059.5* 7752.0* 5478.2* 5906.0*

N, Second Positive (C --f B 3Llg)

0-0 0- 1 0-2 0- 3 0-4 1-0 1-1 1-2

3371.3 3576.9 3804.9 4059.4 4343.6* 3159.3 3339. 3536.7

N, Second Positive (C 3Ll,, -+ B 3Lln,)

1-3 1-4 1-6 2- 1 2-2 2-3 2-4 2- 5

3755.4 3998.4 4574.3 3136.0 3309. 3500.5* 3710.5 3943.0

N, First Positive ( B 3Llrr -+ A 3Zi)

9-6 6394.7 9-7 6957.7 9-8 7612.9*

10-6 5854.4 10-7 6322.9* 10-8 6859.3* 10-9 7479 .O* 11-7 5804.3; 11-8 6253.0* 11-9 6764.0* 11-10 7349.8* 12-8 5755.2* 12-9 6185.2*

N, Second Positive (C 317,, -+ B 3Llg)

3-2 3-3 3-4 3-5 3-7 4-4 4- 8

3116.7 3285.3 3469. * 3671.9 4141.8 3268.1 * 4094.8’

5.1, SPECTRAL IDENTIFICATIONS 181

N; Meinel (A + X ,Z;)

N, Vegard-Kaplan (A 3Z: --f X lZ;)

N; Meinel (A ,IT-+ X2Zi)

0-10 3602. 0-12 4218. * 1-9 3198. 1-10 3425. 1-11 3683. 1-12 3978. 1-13 4320. *

N; First Negative (B 2Zi + X ,Z;)

0-0 0- 1 0-2 0- 3 1-0 1-1 1-2 1-3

3914.4 4278.1 4709.2 5228.3 3582.1 3884.3 4236.5 4651.8

N: Meinel (A ,TT-+ X2Zi)

0-0 11,036.2 0- 1 14,523. 1-0 9145.3 1-2 15,114. 2-0 7825.7

0, Atmospheric (b lZ; + X *Z;)

0- 1 8598. 1-1 7684.

TABLE 5.3 (coat.)

N, Vegard-Kaplan (A 3Z; + x 'Z;)

1-16 5752. * 2-10 3268. 2-1 1 3502. * 2-12 3767. 2-13 4072. 2-14 4425. 2-15 4837. *

Nl First Negative (B ,Z; + X ,Z;)

1-4 2- 1 2-2 2- 3 2-4 2-5 3-2 3-3

5148.8 3563.9 3857.9 4199.1 4599.7 5076.6 3548.9 3835.4'

N, Vegard-Kaplan (A 3Z,'( --f X lZ;)

3-14 4169. * 3-15 4534. 3-18 6068. * 4-1 1 3192. * 4-14 3948. * 5-15 4045. * 5-17 4771. *

N; First Negative (B 2Zi + X 2Z;)

3-4 4166.8 3-5 4554.1 4- 6 4515.9* 4-7 4957.9 5-6 4121.3' 5-7 4485.9' 6-7 4110.9' 6- 8 4466.6'

2- 1 9431.2' 2-2 1 1.820.2. 2- 3 15,748. 3-0 6853.0

3-1 8053.6 4- 1 7036.8 4-2 8293.4 5-2 7239.9

0, Infrared Atmospheric alA,+XSZ;

0- 1 14,663. *

0; First Negative (b 4Zj -+ a ' f l u )

0-0 6026.4 0- 1 64 1 8.7' 1-0 5631.9 1-1 5973.41 2-0 5295.7


TABLE 5.4 EMISSIONS IDENTIFIED IN AURORAL SPECTRA

ARRANGED ACCORDING TO WAVELENGTH

An asterisk after the wavelength indicates an identification that is uncertain or questionable because of blending with or obscuration by other features or because there are too few lines or bands in the same transition array or progression to make the identification convincing. Additional features, uxally quite weak, have been observed, but have received no satisfactory identification.

~~~

Atom or Multiplet (A) Molecule or band

2972.325 3116.7 3136.0 3159.3 3192. * 3198. 3268. * 3268.1* 3285.3 3309. 3339. 3371.3 3425. 3466.4 3469. * 3500.5' 3502. * 3536.7 3548.9 3563.9 3576.9 3582.1 3602. 3671.9 3683. 3692.44 3710.5 3712.75' 3726.16 3727.33% 3728.91 3749.49 3755.4 3767. 3804.9 3835.4'

Transauroral 2P( 3-2) 2P(2-1) 2P(1-0)

VK(4-11) VK( 1-9)

VK(2-10) 2P(4-4) 2P( 3-3) 2P(2-2) 2P(1-1) 2P(O-0)

VK( 1-1 0) Transauroral

2P(3-4) 2P(2-3)

VK(2-11) 2P( 1-2) lN(3-2) lN(2-1) 2P(O- 1) 1 N(l-0)

VK(0- 10) 2P(3-5)

VK( 1-1 1) 6

2P(2-4) 3

Nebular 3

Nebular 3

2P(1-3) VK(2- 12)

2P(0-2) 1 N(3- 3)

~~ ~ ~

Atom or Multiplet (A) molecule or band

3857.18' 3857.9 3872.45' 3875.82* 3882.45' 3883.15* 3884.3 3912.0* 3914.4 3919.287* 3943 .o 3945.048* 3947.5 3948. * 3954.372 3955.851 3973.263 3978. 3982.719 3994.996 3998.4 4026.080 4035.087 4041.321 4043.537 4044.75' 4045. * 4057.00' 4059.4 4069.8 4072.164 4072. 4075.868 4018.862' 4092.940" 4094.8.

011

011 011 011 011 N: 011 N: 011 NZ 011 01 NZ 011 NII 011 NZ 011 NII NZ NII NII NII NII NII NZ NII Nz 011 011 N, 011 011 011 N2

N: 13

lN(2-2) 11 13 11 12

1 N( 1 - 1) 17

1 N(0-0) 17

2P(2-5) 6 3

VK(4- 14) 6 6 6

VK(I- 12) 6

12 2P( 1-4)

40 39 39 39 39

VK(5-15) 39

2P(0-3) 10 10

VK(2- 13) 10 10 10

2P(4-8)


TABLE 5.4 (cont.)


4110.9' 41 12.029' 4120. * 4121.3' 4121.48' 4141.8 4151.46* 4166.8 4169. * 4169.230' 4171.608 4176.164 4185.456 4189.788 4199.1 4218. 4223.04* 4236.5 4237. Oc 4241 . I81 4241 . I81 4278.1 4317.139 4319.63 1 4320. * 4336.865 4340.468

4345.562 4347.425 4349.426 4351.269 4368.30 4369.28. 441 4.909 441 6.975 4425. 4452.371 4466.6' 4485.9' 4488.15' 4507.559' 4515.9' 4534.

4343.6'

N; 011 011 N; 0 1 1 N* NI N; NZ 011 NI I NII 011 011 N; Nz NI N; NII NII NII N; 011 011 NZ 011 HY NZ 011 011 011 011 0 1 011 011 0 1 1 Nz 011 N; N; NII NII N; NZ

1 N(6-7) 21 20

lN(5-6) 19

6 2P(3-7)

1 N(3-4) VK( 3- 14)

19 43 42 36 36

1 N(2-3) VK(0- 12)

5 lN(1-2)

48 47 48

lN(0-1) 2 2

VK( 1-1 3) 2 1

2P(0-4) 2

16 2

16 5

26 5 5

VK(2-14) 5

1 N(6-8) lN(5-7)

21 21

lN(4-6) VK(3-15)


4554.1 4564.78' 4574.3 4590.971' 4596.174' 4599.7 4601 ,478 4607.153 4621.392 4630.537 4638.854 4641.811 4649.139 4650.841 4651.8 4661.635 4616.234 4709.2 4711. * 4780.5' 4791. * 4810.286' 4837. * 4861.332 4890.93' 4895.20' 4914.90 4924.60* 4935.03 4941.12' 4957.9 4968. 4981.377* 5001.3 5002.692 5005.140 5010.620 501 6.387 5025.665 5045.098 5076.6 5148.8 5198.5 5200.7

N; NII NZ 011 011 N: NII NII NII NII 011 011 011 011 N; 011 011 N: NZ NII NII NII NZ HkJ 011 NII NI 011 NI 011 N: 01 NII NII NII NII NII NII NII NII N; N;

"I1 "I1

lN(3-5) 14

2P(1-6) 15 15

lN(2-4) 5 5 5 5 1 1 1 1

IN(]-3) 1 1

1 N(0-2) VK(5-17)

20 20 20

VK(2-15) 1

28 1 9

28 9

33 lN(4-7)

14 24 19 4

19 4

19 19 4

I N(2-5) lN(1-4) Nebular Nebular


TABLE 5.4 (cont.)


5228.3 5295.7 5330. 5436. 5454.26* 5478.2* 5577.345 5631.9 5666.64 5676.02 5679.56 5686.21 5710.76 5730.67 5747.29* 5752. * 5754.8 5755.2' 5767.43' 5804.3* 5854.4 5889.953 5895.923 5906.0* 5959.0 5960.93' 5973.4' 6013.6 6026.4 6046. * 6068. * 6069.7 6127.4 6157. 6185.2' 6186.8* 6253.0* 6300.308 6322.9' 6363.790 6394.7 6418.7' 6455. * 6468.5

1 N(0-3) 1 N(2-0)

12 11 29

lP(9-4) Auroral 1 N( 1-0)

3 3 3 3 3 3 9

VK( 1-1 6) Auroral

lP( 12-8) 9

lP(l1-7) lP( 10-6)

1

lP(9-5) lP(8-4)

28 1 N( 1 - 1) lP(7-3) lN(0-0)

22 VK(3-18)

lP(6-2) 1 P(5- 1)

10 lP( 12-9) lP(4-0)

lP( 11-8) Nebular

Nebular lP( 10-7)

lP(9-6) lN(0-1)

9 lP(8-5)


6482.07 6544.8 6562.817 6583.6* 6623.6 6704.8 6764.0' 6788.6 6853.0 6859.3* 6875.2 6957.7 7036.8 7059.Y 7164.8 7239.9 7254.4% 7274.0 7318.6 7319.4 7329.9 7330.7 7349.8' 7387.2 7479.0' 7504.7 7612.9* 7626.8 7684. 7752.0' 7753.7 7774. 7825.7 7896.9' 7987. 7995.12 8047.9* 8053.6 8184.80 8187.95 8205.5' 8216.28 8223.07 8242.34

8 1 P(7-4)

1 Nebular 1 P(6-3) lP(5-2)

lP(11-9) 1 P(4- 1)

Mein.(3-O) lP( 10-8) lP(3-0) lP(9-7)

Mein.(4-l) lP(8-6) lP(7-5)

Mein.(5-2) 20

lP(6-4) Auroral Auroral Auroral Auroral

1 P( 1 1- 10) lP(5-3)

1 P( 10-9) lP(4-2) lP(9-8) lP(3-1)

Atm.(l-1) lP(8-7) lP(2-0)

1 Mein.(2-0)

lP(7-6) 19 19

lP(6-5) Mein.(3- 1)

2 2

lP(5-4) 2 2 2


TABLE 5.4 (cont.)

Atom or molecule

8293.4 8446.5 8542.5 8598. 8629.24 8680.24 8683.38 8703.24 8711.69 871 8.82 8723.0 8912.4 9060.6*

N; 0 1 N* 0 1

NI NI NI NI NI NI N2 N* NI

Multiplet or band

Mein.(4-2) 4

lP(3-2) Atm.(O- 1)

8 1 1 1 1 1

lP(2- 1) 1P( 1-0)

15

9145.3 9431.2* 10,395.4 10,404.1 10,510. 10,830. * 11,036.2 11,820.2’ 14,523. 14,663. * 15,114. 15,748.

Atom or molecule

Multiplet or band

Mein.( 1-0) Mein.(Z-l)

Auroral Auroral

1 Mein.(O-0) Mein.(2-2) Mein.(O- I )

IR Atm.(O-1) Mein.( 1-2) Mein.(2-3)

IP(0-0)

5.1.2. Forbidden Atomic Lines2

Oxygen-The strongest emission in the visible region is ordinarily the [01],, yellowish-green line, first measured by Angstrom [ 1868a, 1869~1 and soon after confirmed by Struve [1869a] and many others. Angstrom and others found the green line to be present even when visible auroral structure was not, but it was many years before the existence of the airglow was firmly established (see Section 9.1.2).

Precise measurement of the green-line wavelength was first accomplished by Babcock [ 1923~1 with an interferometer. Measurements by Cabannes and Dufay [I 955~~2.3 give the wavelength as 5577.345 & 0.003 A. Production of the green line in the laboratory by McLennan and Shrum [1925a] eventually led to the identification of the green line as the [OI],, transition (see the discussion in Section 9. I .2).

The [OI],, line at 2972.325 A (Sayers and Emeleus [1950a]) should have a photon intensity of about one sixteenth that for A5577 [OI],,. Because of ozone absorption it is not observable from the ground.

Zollner [1870a] made the first measurement of the red line of [OI],, at 6300 A. The wavelengths of the two lines given in Table 5.1 are from the interferometer measurements of Cabannes and Dufay [1955a, b, 1956a, b]. The identification was made by Frerichs [1930a], who computed the energy levels from observations of the ultraviolet spectrum

A summary of the transition probabilities, lifetimes, and energy levels associated with oxygen and nitrogen forbidden lines is given in Appendix VI. The spectroscopic nomenclature is discussed in Section 1.1.2.


of oxygen and, incidentally, confirmed the green-line identification previously made by McLennan and his collaborators and by Sommer (Section 9.1.2).

Lines of [OII],, at 7319 and 7330 A were first discovered in low- latitude aurorae by Omholt [1957b] and M. Dufay [1957b, 1959~1. These spectra had low resolution and showed only a single feature near 7325 A. A high-dispersion spectrum obtained by Wallace [1959a] confirmed the identification; it is exceptionally strong in Vallance Jones’ spectrum in Fig. 5.6. Previously it had been thought that the lines were absent (Petrie [1952b]), but two OH lines in the infrared airglow are superimposed on the [OII],, lines, making the latter somewhat difficult to detect unless they are fairly strong.

The [OII],, doublet centered at 3727 A has been reported by several groups3 but appears to be rather variable in its occurrence. The identification of the feature as [OII],, was uncertain until a high-resolution spectrum of the great red aurora of 11 February 1958 obtained at Yerkes Observatory showed the two components (Wallace [ 1959~1; also see Chamberlain [1958d, p. 7161). Nitrogen.-The auroral transition [NI],, produces lines at 10,3954. and 10,404.1 A, which are blended with the 0-0 band of the First Positive system of N,, a rather strong emission. Bagariatskii and Fedorova [1955a, 1956~1 with an image converter and Harrison and Vallance Jones [1957a] (see Fig. 5.26) with infrared photographic plates obtained spectra with a resolution of about 10 A that showed a narrow feature around 10,40OA, superimposed on the N, band. Both groups have interpreted this feature as the unresolved “I],, lines. Similarly, M. Dufay [19576, 1959~1 believed he recorded [NZ],, in bright aurorae at low latitude with a photoelectric monochromator having a resolution of about 20 A.

The presence of A3466 “I],, was firmly established by the auroral measurements of Bernard [1938g, 1939c, 1948~1, the prediction of the wavelength by Nicolet [1938a], and production of the line in an afterglow with the forbidden Vegard-Kaplan N, bands by Kaplan [1938a, b].

The “I],, close doublet, XX5198.5 and 5200.7, often appears as a moderately strong line on spectra obtained at low auroral latitudes and was first identified by Slipher and Sommer [1929a] (also, Gotz [1941a, 1947~1, Dufay and Tcheng [1942a], Vegard [1950b], and Gartlein and Sherman [1952a]). The line is quite variable and may, on exceptional occasions, have an intensity comparable to that of the green [OI],, line

Vegard and Kvifte [1945a], Barbier and Williams [1950a], Petrie and Small [1952a], Oliver, Wolnik, Scanlon, and Chamberlain [ 1953~1.


(M. Dufay [19576]). The A5199 line is of particular interest because of its extremely long radiative lifetime-of the order of a day (Appendix VI).

The [NII],, line, h5755, appeared weakly on moderate-dispersion spectra obtained by Petrie [ 19524, but he noted the nebular transition at 6584 A to be absent. The A5755 line is blended with the 12-8 First Positive band of N, and rather good dispersion is required to show the line superimposed on the band, unless the line is exceptionally strong. M. Dufay [19573] also found the [NII],, line in a low-latitude aurora, and Belon and Clark [ 1959a] have found it on many of the low-dispersion IGY patrol spectra obtained in Alaska. Belon and Clark have also measured a variable emission at 6584 A, which they believe to be the [NII],, line. The other member of the [NII],, doublet, A6548, is only one third as strong and is obscured by the 7-4 First Positive band of N,. Confirmation of this line with higher resolution seems to be in order.

5.1.3. Permitted Atomic Lines

Many incorrect identifications of atomic lines in the auroral spectrum have appeared in the literature. Critical analyses by Nicolet [1938b, 1939aJ and Bates, Massey, and Pearse [1948a] first began to sort and evaluate the identifications from the viewpoint of physical processes. Permitted atomic lines of 01 and NI have become generally accepted since the observation of strong lines in the near infrared by Meinel [1948a, 1950a, 1951~1 and Petrie [1950a, b], which made it plausible that some of the weaker features in the visible, previously attributed to atomic lines (Vegard [1938b], Vegard and Kvifte [1945a], Dufay and Tcheng [1942a]), might indeed be due'to 01 and NI (see Dufay [1949b]). Although numerous lines from ionized atoms have been listed in several publications by Vegard et al., the presence of 011 and NII was not usually recognized until their confirmation by Petrie and Small [ 19524 w&h spectra of moderately high dispersion (43 A/mm in the second- order visible). Other important papers reporting many wavelength measurements and identifications have been published by Barbier and Williams [ 1950~1, Wallace [ 1959a1, and Vegard and his collaborator^.^

Compilations of atomic lines probably in the auroral spectrum have been prepared by Pearse [ 1954~1 and Chamberlain and Oliver [ 1953~1; Table 5.2 is based primarily on the latter paper, with some modifications derived from more recent investigations as discussed below.

In particular, Vegard [1932d, 19500, 1955b], Vegard and Tonsberg [1944u, 1952~1, Vegard, Tonsberg, and Kvifte [1951a], Vegard and Kvifte [1945u, 195101.


Oxygen.-The lines composing an 01 multiplet are usually so close together that they appear as a single line in auroral spectra. However, a number of low-lying multiplets do appear with relative intensities that seem reasonably consistent with expectations from laboratory data, so that there can be no legitimate doubt about the presence of 01 (see Fig. 5.28). The strong infrared lines in the 3s - 3p transition array,

19 2 2 2 p3 ( 2 ~ e )

- - 3- -”%

1 17 I

1 P I I I

9C

3 5 7 0

01 1 FIG. 5.28. Excited configurations and transition arrays of 01 in aurora. Dashed

transitions are uncertain.

A7774 and X8446, are of particular interest; since one “line” is a quintet and the other a triplet, their relative intensities may be sensitive to changes in the excitation mechanism. Multiplet 4 at 8446.5 A is composed of three lines, two of which are extremely close and about 0.4 A from the third. Mularchik [1959a] has resolved the multiplet into two components with an interferometer. Kvifte [ 1959b] reported considerable variation in the intensities of the 01 multiplets.

For most of the observed 01 lines, all the atomic electrons except the “jumping” electron form the parent term 2s2 2 ~ 3 ( ~ S o ) . If, however, the parentage is 2s2 2p3(2Do) or (ZP“), the resulting configurations are denoted by nl’ and nl”, respectively. The 3p - 3s‘ transition is the only


transition from terms with “excited parents” that is suspected in the auroral 01 spectrum, and even it is doubtful.

Since the review by Chamberlain and Oliver [1953c], a high-dispersion spectrum analyzed by Wallace [1959a] have added several 011 lines that supported the identifications of multiplets 5 , 6, 10, and 16 and added multiplets 17 and 36. The transition array 3p’ - 3d‘ is based on only two lines and hence must still be considered doubtful, but the other 011 transitions shown in Fig. 5.29 are well substantiated.

3s

30

In t- 2 2 25

z 0 K t- o w J W

20

I 5

/ /

-4P- / 4s -

3s I

FIG. 5.29. Excited configurations and transition arrays of 011 in aurora. Energy is measured from the ground level of 011. T h e dashed transition is uncertain.

Nitrogen.-The 3s - 3p transition of NI (Fig. 5.30) is quite definite, yielding a number of distinct infrared lines. The transition 3s - 4p is not so readily observed, but the two lines listed for multiplet 10 seem to be strong on Petrie and Small’s [1952a] plate. Chamberlain and Oliver [1953c] listed the 3s - 3p’ transition array as possibly present, primarily on the basis of two lines in the near ultraviolet. But the high resolution of Wallace’s [1959a] plate has shown that these features are


most likely part of the rotational structure in the Vegard-Kaplan bands of N,. Hence the presence of lines with the 'D or ' S (the latter not shown in the figure) parentage is very improbable. Bagariatskii [1957a] has reported a 3p - 3d line at 9060 A.

4P - \ \ \ 4s-3d- \ \ \ \

- \

- 3px 3s \

N I

FIG. 5.30. Excited configurations and transition arrays of NI in aurora. The dashed transition is uncertain.

Wallace's spectrum considerably extended the NII identifications, establishing six multiplets in the 3d - 4f transition array (see Fig. 5.31). One of the most conspicuous lines in the visible region, h5002, arises from NII-primarily from multiplet 19 (Vegard [ 19504, Vallance Jones [1955a]).

Sodium.-The D lines definitely seem to be present at times in the aurora (e.g., Vegard and Kvifte [1945a], Petrie and Small [1952a], Hunten [1955a]), although on many and perhaps most occasions they are not enhanced over the airglow background (Cario and Stille [19546], Mironov and Shefov [1956a]). The lines are probably quite variable, and possibly appear only in low displays, but in view of the rarity of


atmospheric sodium, any noticeable enhancement at all poses an intriguing excitation problem.

30

25 u)

0 w I

I-

A W

3

e s =

15

la

4d- 4f

FIG. 5.31. Excited configurations and transition arrays of NII in aurora. Energy is measured from the ground level of NII.

Hydrogen.-The Balmer lines of hydrogen, Ha and HP, were first identified in auroral spectra obtained near Oslo by Vegard [1939b, 1940bl. The lines were exceptionally strong and the simultaneous enhancement of both lines greatly supported the identification. The observation was soon confirmed by N. Herlofson (see Stormer [1941a]). One spectrum published by Vegard and Tonsberg [1944a] shows a diffuse line peaked about 5 A shortward of the normal position of H/? (this plate was not sensitive to Ha). The observation was tentatively interpreted as indicating a Doppler displacement (Vegard [ 1948b]), but it is lamentable that no information on the orientation of the spectrograph was given and that the observations were not extended and confirmed until much later.

Interest in the topic was stimulated by Swings [1948a] and Wurm [1948a], who emphasized that heavy ions might play an important part in

I92 5. AURORAL SPECTROSCOPY A N D PHOTOMETRY

auroral excitation, and by Gartlein [1950a], who found broad lines at the positions of Ha, HP, and Hy. These lines fluctuated in intensity from one spectrogram to the next, but always showed about the same intensities relative to one another, establishing the identification once again. Vegard [1950a] also reported broadened H lines.

The first definite indication of the entry of fast protons into the atmosphere during an aurora was a spectrogram obtained by Meinel [1950i, j , 1951b1, who pointed his spectrograph toward the magnetic zenith during a great aurora. The Ha profile was not only shifted with its peak at a Doppler velocity of roughly 500 km/sec, but the short wavelength tail of the profile extended to much higher velocities. In the direction of the magnetic horizon (defined in Section 3.1 . I ) the profile was broadened but the peak was not shifted. The Doppler displacement was quickly verified by Gartlein [1951a, b] and Vegard [1952a].

References to more recent measurements of the Doppler displacement and broadening are given in Section 5.2.6. In Section 7.1 we discuss the theory of the profiles in terms of the characteristics of incident protons.

Helium.-The detection of He lines in the auroral spectrum is of considerable interest, as the solar atmosphere is composed of 80 or 90 percent hydrogen and nearly all the rest is helium, but for one percent or so of heavier atoms. A comparison of He and H lines in the aurora might provide critical clues to the origin and acceleration of auroral primaries. Bernard [ 1947a, 194863 interpreted a number of features in the auroral spectrum as lines of He I and He 11, but the identifications are doubtful and unconfirmed. Mironov, Prokudina, and Shefov [1959a] believe that a feature at 10,830 A was superimposed on the 5-2 OH airglow band in the great red aurora of 11 February 1958. This enhancement was thought to be the He I multiplet 2 3S - 2 3Po.

Fan [1956a] has obtained laboratory spectra of air excited with He+ ions in the range 10 to 45 kev. On the basis of this work and considering the regions of the auroral spectrum where He I lines will be relatively unobscured, he suggests that the multiplet at 5876 A, 2 3P0 - 3 3S, might be observable.

5.1.4. Molecular Band Systems Table 5.3 gives a list of molecular bands in the auroral spectrum.

N2 Bands.-The Second Positive system (C 317, -+ B 317,) was definitely identified in the blue and the First Positive system ( B 317, .--f A 32:) correctly suspected in the red by Vegard [1932d]. The Second Positive bands are degraded toward shorter wavelengths and are excited


N: 20 - -

1 8 - 8 - W

- - w s

16 - x’za

14- Nz - 312 - c3n,

- -

in the aurora to z.” = 3 or 4. Their structure is fairly complex, with 6 strong branches, three P and three R.

The First Positive bands are quite complex, and several heads are distinguishable even at the moderate dispersion of auroral spectra. Altogether each band contains 27 branches, all with comparable intensity.

FIG. 5 .32. tion

dashed transi- aurora.

The system is excited to at least v’ = 9 and becomes stronger in the infrared than in the visible region. The 0-0 band, peaked near 10,400 A, was first observed and distinguished from the [NI],, lines by Harrison and Vallance Jones [1957a] (also see Hunten [19583]). The bands are degraded toward the violet.

In seeking to reproduce the auroral green line in the laboratory, Vegard [ 1924~1 tried bombarding solid nitrogen with electrons, and produced some emission bands later established in the aurora (Vegard [ 1933a, b]). Kaplan’s [ 19334 193433 afterglow investigations produced the same bands, which arise from the “forbidden” transition A 3Zi +

X IZ: (Fig. 5.32). Wilkinson [1959a] has obtained two Vegard-Kaplan

1 94 5. AURORAL SPECTROSCOPY A N D PHOTOMETRY

bands in absorption. These bands are degraded toward the red with a head formed by two R-form branches. With low resolution the structure resembles a simple band with single R- and P-form branches. A few V-K bands in the near ultraviolet are well established in the aurora, with v’ = 1 , 2, and 3 ; a number of others are questionably present. The lifetime of the upper level is perhaps 30 sec or longer (Hunten [1955a] ; also see Lichten [ 1957~1 and Wilkinson [1959a]).

N: Bands.-Vegard [1913a] first showed conclusively that the First Negative bands, B 2Z: -+ X zZT, were present in the blue and near ultraviolet (also see Rayleigh [19223]). These bands have sharp P heads and open R branches degraded toward shorter wavelengths, making the bands convenient for temperature measurements. They dominate the blue end of the visible spectrum.

A new system of bands, A 217 -+ X Z Z , was identified in the infrared auroral spectrum by Meinel [1950g, h, 1951dl. The system has since been produced in the laboratory by Dalby and Douglas [1951a], R. Herman [1951a], and Sayers [1952a], and the rotational and vibrational constants have been determined by Douglas [1953a]. Each band has 6 branches (P, Q, and R); the two most prominent heads are formed by the R, and Q1 branches, and the bands are degraded toward long wavelengths. The Meinel bands have been observed in the aurora longward of 9000A with an image converter by Bagariatskii and Fedorova [1955a, 1956~1, with an infrared photomultiplier in a spectrometer by Lytle (Hunten [1958b]), and with a spectrometer equipped with a PbS photoconductive cell by Harrison and Vallance Jones [ 1957a, 1959aI (see Figs. 5.7 and 5.24 to 5.27).

0, Bands.-The forbidden (magnetic dipole) Atmospheric system, b lZ; -+ X 3q, composed of two R- and two‘ P-form branches, shows the 0-1 band whose origin is at 8645 A (Meinel [1951c]) but, as in the airglow, the 0-0 band at 7619 A is reabsorbed by the great mass of 0, in the lower atmosphere. Kvifte [1951b] proposed that the 1-1 band, h7708, might be present, and a high-dispersion spectrum by Chamberlain, Fan, and Meinel [1954a] (reproduced here in Figs. 5.6 and 5.20) resolved it from a neighboring First Positive band.

Harrison and Vallance Jones [ 1959~1 observed an anomalous enhancement in the 2-3 Meinel N,+- band that is probably the 0-1 (magnetic dipole) Infrared Atmospheric (a Id,, -+ X ”;) emission at 1 . 5 8 ~ . As in the Atmospheric system the 0-0 band at 1 . 2 7 ~ would be absorbed below the emitting region. These bands contain the same P- and R-form


branches as the Atmospheric system, and in addition have three Q-form branches and an 0- and an S-form branch.

0: Bands.-For many years one of the most intriguing identification problems in the auroral spectrum was the so-called second green line, a broad, diffuse, and variable feature between 5200 and 5300 A (e.g., see Vegard [1927a]; also see the low-dispersion spectrum in Fig. 5.1).

FIG. 5.33. Electronic states and band systems of 0, and 0:. Only the Infrared Atmospheric, the Atmospheric, and the First Negative systems have been detected

in aurora.

The two strong peaks on the shortward side of the feature are A5199 "I],, and Ni First Negative 0-3. Although the 0: First Negative bands, b 4Z; --f a 417u, were well known from laboratory work, they were thought to be absent in the aurora until Nicolet and Dogniaux


[1950u] constructed synthetic spectra (by numerically smearing each rotational line in the band as it would be smeared by the spectrograph slit-see Section 12.2.1) and found that the peaks of these complex bands should coincide with published lists of auroral “lines.” The second green line thus arises largely from the 2-0 band.

The 0: identification was verified by Vegard [1950u, b, c] and Gartlein and Sherman [ 1952~1. With a low-resolution spectrometer, Dahlstrom and Hunten [1951u] found the bands greatly enhanced in type-B red aurorae.

5.2. Spectral Photometry of Aurora

5.2.1. Absolute Brightness of Spectral Features

The auroral spectrum goes through many changes in relative intensities of its features, some of which (e.g., the H lines) are extremely marked. Hence in prefacing a list of spectral intensities, it is necessary to emphasize the enormous uncertainties involved. Most intensity measurements are made on bright aurorae, so we shall refer everything to the green line of an aurora of brightness I11 (see Appendix 11). Only rarely have reliable measurements been reported for specific auroral forms or heights, so that Table 5.5 refers principally to what is thought to be an average for a bright aurora, except where the notes specifically indicate otherwise.

Some of the quoted intensities are estimated with the aid of relative transition probabilities from measured features. Measured relative intensities in most of the visual region are not strongly affected by atmospheric scattering and absorption, although these estimates do include corrections to outside the lower atmosphere. For features in the ultraviolet and far infrared, the estimates also refer to above the absorbing atmosphere. There are undoubtedly many spectral features in the unobserved region, such as the Lyman-Birge-Hopfield bands of N, and various atomic lines in the ultraviolet, that may contribute significantly to the total and for which we have no valid intensity estimates. Finally, the quoted values of 4n-4 do not necessarily refer to the zenith (as they do usually for the airglow, where the uniformity of the emission makes the zenith a convenient reference direction). The rayleigh unit adopted here is defined in Appendix 11.

5.2. SPECTRAL PHOTOMETRY OF AURORA 197

TABLE 5 .5 ABSOLUTE INTENSITIES IN THE AURORAL SPECTRUM, IBC 111

47r4

Sp’ectral features (A) kR erg/cm’ sec Notes (oblique column)

0 1

011

NI

NII

Na

H

N, (IstPos.) N, (2nd Pos.) N, (V-K)

N: (1st Neg.) N; (Meinel)

0, (Atm.) O2 (Infrared Atm.) 0.; (1st Neg.)

5571 2972 6300-64

7319-30 2410 3727

10,400 3466 5199

Visible

Photog. infrared Far ultraviolet

Visible Far ultraviolet

Photog. infrared Far ultraviolet

Visible Far ultraviolet

5893

Balmer lines Lyman lines

Infrared Ultraviolet Ultraviolet

Blue-ultraviolet Infrared

Infrared Infrared Visible

100 3

50

5 1 0 .5

100 7 1

1

25 25

5 5

5 5

25 20

1

10 100

2000 100 150

165 2500

400 1000

10

0.36 0.02 0.16

0.014 0.008 0.003

0.19 0.04 0.004

0.004

0.06 0.37

0.02 0.18

0.01 0.08

0.10 0.55

0.003

0.03 1.65

4.0 0 . 6 1.2

0.85 5.0

1 .o 1 .3 0.04

1 2 3

4 2 5

6 2, 7 8

9

10 1 1

12 1 1

13 1 1

14 11

15

16 17

18 19 20

21 22

23 24 25

Total (Lower limit) 18.0


NOTES

1. Definition of an aurora of IBC I11 (Appendix 11).

2. From ratio of transition probabilities (Appendix VI).

3. Ratio3(6300)/4(6364) is always 3/1. The value quoted is perhaps typical for long photographic exposures but these lines are extremely sensitive to height. For low type-B aurorae, the red lines may be almost completely suppressed and in high type-A displays, they may completely dominate the green line. See Section 5.2.2.

4. Related to the green line by Omholt [19576] and to the nightglow OH by Wallace [1959a]. Relatively stronger in the upper parts of aurora.

5. Highly variable and probably limited to high altitudes. Quoted estimate is from Wallace’s [1959a] long photographic exposure on a high, brilliant aurora, and was obtained by referring this line to N, bands in its neighborhood.

6. From Harrison and Vallance Jones [1957a] and Hunten [19583]. Some uncertainty due to blend by N,(O-0); this feature may be dominant when averaged over the time of a photographic exposure, although N2 becomes more intense for short periods. This value is one fourth the total intensity for both features.

7. This value also seems consistent with relative intensity of this line and neighboring N, bands on photographic spectra.

8. Highly variable. The quoted value seems appropriate as an average on photographic exposures. Hunten [I95831 notes that for the short periods covered by photoelectric scans, it is less than one tenth this value. Probably the line persists for long time intervals compared with permitted emissions. M. Dufay [I95761 has found the line exceptionally strong on occasion at low latitudes.

9. The main contributor is [NII],, A5755 and this is a rough estimate for the weak First Positive band in this region, which usually obscures this line.

10. The main lines observable from the ground are in the photographic infrared. The intensities of several lines of 01 have been measured relative to A7774 and A8446 by Petrie and Small [1953a]. Of these, A8446 is usually the stronger, sometimes by as much as a factor of 3, but their ratio fluctuates. These lines have been referred to A5577 by Omholt [19573].

11. Each electron cascading down the higher configurations ultimately leads to an ultraviolet quantum. This value is considered a lower limit; there may he appreciable emission that is not preceded by observable cascading.

12. Relative 011 intensities of Petrie and Small [1953a] have been put on a crude absolute scale by taking 011 A4415 to have the same intensity as 01 A4368.

13. Omholt [I95731 has made rough measurements of multiplet 2 (Ah8186 and 8216) on the same scale as the green line and Petrie and Small [1953a] have measured relative NI intensities.

14. Hunten [1955a] has obtained an average ratio A5002/A5577 (multiplet 19) and Petrie and Small [1953a] have measured relative NII intensities.

15. This value is presumed to be an upper limit and applicable only for low-lying displays. It is based on a measurement by Hunten [1955a] for a type-B aurora.

16. This is probably an upper limit and is estimated from H a on photographic exposures of homogeneous arcs. The relative intensities of Balmer lines are taken from theory (Section 7.1.1). Hunten’s [ 1955~1 spectrometer observations indicate large fluctua-


tions, with the Balmer intensity usually lower than the quoted value. Gartlein and Sprague [1957a] and Galperin [1959a] find that Ha rarely exceeds 200 R although it may attain several kR; see also Osterbrock [1960a].

17. Photon intensity of Ly 01, the main contributor, is about 8 times that of Ha, according to the theory in Chapter 7.

18. Based on absolute measurements by Harrison and Vallance Jones [1957a] and

19

20.

Hunten [1958b] and intensities relative to A5577 by Omholt [1957b]. For the high progressions (and weaker bands in the visible), one may relate Petrie and Small’s [1953a] relative intensities to the others. Hunten [1955a] has made some absolute measurements on bands in the risible during a type-B aurora. If at least one band in each a’’ progression is known, the others may be estimated with the Franck- Condon factors (Jarmain, Fraser, and Nicholls [19530], Jarmain and Nicholls [1954a], Turner and Nicholls [1954a]). Probably the bands are enhanced at low altitude (Vegard [1939c, 1940~1). Petrie and Small [1952b] have measured intensities of these bands relative to h3914, N;. Hunten’s [1955n] measurement of the 0-2 band, A3805, in a type-B aurora is about one third Petrie and Small’s value. Franck-Condon factors have been computed by Jarmain, Fraser, and Nicholls [19530]. Also see Wallace and Nicholls [1955a], Jarmain and Nicholls [1954u]. Extremely uncertain. Quoted value is based on rough estimates from photographic exposures of the weak V-K bands in the near ultraviolet, relative to neighboring Second Positive bands. Such estimates are intrinsically uncertain because of the open structure of V-K bands and much blending with other features. Franck-Condon factors of Jarmain, Fraser, and Nicholls [1953a] give an indication of the intensities shortward of 3000 A. Hunten [1955a] finds the bands enhanced relative to Second Positive in the diffuse glow following a bright display, as though the emission persists after particle bombardment subsides, as for “I],, (see note 8).

21. The strongest band, A3914 (0-0), has approximately the same intensity as the green line (e.g., Vegard and Kvifte [1954n], Hunten [1955a], Rees [1959a], Zhuravlev [1955a, b]) and has been taken as 100 kR. Petrie and Small [19530] have measured the other bands relative to this one. Franck-Condon factors are given by Jarmain, Fraser, and Nicholls [1953a] and Wallace and Nicholls [1955a].

22. The strongest bands are 0-0, 0-1, 1-0, 1-2, and 1-3. All these but the latter have been measured by Harrison and Vallance Jones [1957a, 1959~1. Fraser, Jarmain, and Nicholls [1954a] and Nicholls [1958u] have listed Franck-Condon factors, from which the intensities of bands farther in the infrared may be estimated. Other absolute measurements have been reported by Hunten [1958b] and relative intensities of the weaker bands in the photographic region are given by Meinel [1951c] and Omholt [ 1957b1.

23.

24

Omholt [1957b] has measured the 1-1 band. The 0-1 band is about twice as strong (Chamberlain, Fan, and Meinel [1954a]) and the 0-0 band will emit about 20 times as strongly as the 0-1 (Fraser, Jarmain, and Nicholls [1954a]). Harrison and Vallance Jones [1959a] have measured a strong feature overlapping the N; Meinel 2-3 band; this value is obtained by assigning the entire feature to 0, (0-1) and applying a factor of 10 for the 0-0 band.

25. A very rough estimate for a type-B aurora, where these bands are their strongest, based on Hunten’s [1955a] measurement of the 0-0 band. Franck-Condon factors have been computed by Jarmain, Fraser, and Nicholls [1955a].

200 5. AURORAL SPECTROSCOPY A N D PHOTOMETRY

5.2.2. Latitude and Height Variatidns in the Composition of the

Latitude .Variations.-Differences in various features of auroral spectra at high and low latitudes have been discussed by Vegard [1939c, 1940~1, Dufay and Tcheng [1942a], Barbier [1947e, 1949b], M. Dufay [1957b], and Dufay and Moreau [1957a]. The principal differences they report are the following: (a) At lower latitudes the First Negative bands of N: show a greater development, with higher vibrational levels of the upper state appearing relatively more populated. (b) The highly forbidden nebular transitions, [OI],, (hX6300-64) and [NI],, (X5199), are enhanced at low latitudes. The A5199 line especially is characteristic of

Spectrum

N

W

T S

N

W

S

FIG. 5.34. A diffuse red arc observed at Rapid City, 22 October 1958. At the left are sample reproductions of the airglow photometer records, showing spikes in A6300 but not in A5577 in the east and west. The numbers on these records give the zenith angle of the scan. The isophote maps at the right give emission rates in kilorayleighs. In addition to the faint red arc passing overhead, an aurora is developing in the north. After Roach and Marovich [1960a]; courtesy National

Bureau of Standards.


low-latitude spectra. (c) There is also some indication (Vegard [1952b, 1958~1, Vegard and Kvifte [1951u, 1954~1) that the H lines are stronger at lower latitudes.

An interpretation of these, and perhaps other less striking variations, is difficult, partly because the differences may be due largely to altitude rather than strict latitude variations. Many of the aurorae observed at low latitudes are observable because they are exceptionally high. There- fore, an observational selectivity may enter the data. The stronger H lines might be taken as an indication of a greater importance of protons relative to other particles at low latitudes, but caution is necessary in

W E

S 6300

2155 MST

S 5577

2200 MST

FIG. 5.35 Isophote maps showing the red and green emission 2 % hr after those in Fig. 5.34. The aurora in the north is now well developed, but the diffuse red arc has maintained its identity. After Roach and Marovich [1960a]; courtesy

National Bureau of Standards.

drawing any fundamental conclusions of this nature. The relative importance of H lines in the auroral spectrum depends on the initial energy of the protons as well as their flux. Thus once again high aurorae (or a small depth of penetration for the protons) would give H lines enhanced relative to other emissions (see Section 7.1). With regard to the reported vibrational development of N l , see Section 5.2.8.

Photoelectric photometry at low latitudes during the IGY disclosed a type of “aurora” not previously recognized: diffuse red arcs that are generally too faint (a few kR) to be seen with the eye. These arcs have been observed by Barbier [19576, 195861, Duncan [1959a], and Roach and Marovich [1959a, 1960~1 (also see Sandford [1958a]). Figures 5.34 and 5.35 show an example of such an ,arc measured in A6300 [OI],,.


The green oxygen line and the N: bands show no appreciable enhancements. The arcs are much wider and higher than the usual auroral arcs, lying at several hundred kilometers altitude. Other very large enhancements of h6300ih5577 are occasionally seen at low latitudes when a great aurora occurs (see below).

Height Variations.-Reliable quantitative information on height variations is scarce because of the difficulty of guiding a photographic exposure unless the aurora remains stationary, and because of contamination from the diffuse background glow and from scattered light. Some preliminary results have been obtained with fast spectrographs by Vegard [19406], Meinel [1952a], and Omholt [1957b]. Some of these variations are mentioned in the notes to Table 5.5. The most conspicuous altitude effect is in the [OI],, red lines, which show an increased brightness, relative to the green line, with increasing height more than any other strong f e a t ~ r e . ~

Because of the contamination of a ray with, for example, diffuse background emission, spectrographic exposures may give incorrect results. Using a photoelectric photometer, Jorjio [ 1959~1 has measured intensity ratios of h6300/h5577 at Loparskaya (near Murmansk) as high as 5.5 in red, rayed aurorae, with an average value of about 2. Ordinary green aurorae have an average ratio of about 0.2. I t seems likely that the height distribution of X6300/h5577 in a “normal” aurora may be due entirely to collisional deactivation of the red line at lower altitude (Harang [1956a, 1958a]), but it is impossible to be certain when even the deactivating mechanisms are still in doubt.

The great red (high-altitude) aurora of 1 1 February 1958, on the other hand, showed a ratio X6300/h5577 of about 2.5 x lo3, at low latitudes (AnL = 44” N), according to Manring and Pettit [1959a]. While the aurora seldom exceeded 10 kR in the green line, it attained at one t ime lo5 kR in the red line.6 Duncan [1959b] found a redlgreen ratio of 60 for an aurora at Sydney = 43” S). T h e red enhancement at low latitudes may thus be far greater than is ordinarily seen in the upper parts of aurorae in the auroral zone, and suggests a marked change from

In the extreme case of the aurora appearing red to the eye because of h6300, it becomes known as type A . Similarly, in low, type B aurorae, the enhanced N, First Positive and 0; bands are evidently altitude effects. These cases, as well as sunlit aurorae, are discussed further in Section 4.2. I .

Other large enhancements of X6300ih5577 have been reported for this aurora from low latitudes by Huruhata [1958a], Hikosaka [1958a], and Fishkova and Markova [1958a]. As usual, it is not possible to say whether these enhancements should be classified purely as latitude or altitude effects.


the excitation process usually encountered for the forbidden lines (Sections 7.3.1 and 7.3.2).

Other forbidden radiations, such as A3727 [OII],, and A5199 [NI],,, as well as the N, Vegard-Kaplan bands (Bernard [1939d]) are probably high-altitude features also. The height variation of the ratio A3914/A5577 is discussed in Section 5.2.4.

5.2.3. Spectral Variations with Type of Aurora; Variations i n the

Spectral characteristics of the different auroral forms are not as easy to establish as one might imagine. Long photographic exposures often cover a conglomeration of different types and in any event it is difficult to sort out type effects from pure altitude variations. Such variations may be studied with fast spectrographs, but a better technique is to use all-sky cameras equipped with different filters. The light may be recorded photographically (L. Herman and Leinbach [1951u]) or photoelectrically (Fan [ 1958~1). Also, scanning spectrometers (Hunten [1953u]) and photoelectric photometers (Omholt [ 19574) have been used advan- tageously.

‘The most important change found in the auroral spectrum is the variation of the hydrogen lines. Several attempts have been made to find a systematic behavior in the hydrogen variations and perhaps the truth is divided among several effects. Early investigations (Dahlstrom and Hunten [1951a], Gartlein [1952a], Meinel [1952a, 1954~1, Fan and Schulte [ 19544, Vegard [ 1955~1) suggested that H lines were characteristic of homogeneous arcs and weaker in rayed aurorae and that H appeared at the earlier stages of an aurora. Fan [1958u] found H/3 to decrease over the entire sky after the breakup of homogeneous aurora into rayed forms and as a negative magnetic bay began.

The hydrogen lines do not disappear immediately with breakup, however. Omholt [1957c] found the ratio H&’A4709 (N:) to be about 0.25 in the diffuse background immediately after breakup at Yerkes Observatory. This ratio diminished to about 0.10 in about one-half hour. The rayed structure itself did not show any noticeable H emission. Omholt estimates that an arc, by comparison, may have a ratio of 0.2 to 0.7. Veller [1958u] has also found H emission rather strong in diffuse auroral glows in the auroral zone. Osterbrock [1960u] observed the H/3 intensity to decrease by a factor of 5 within 10 min after breakup, and Bless and Liller [1957u] observed an aurora in which the ratio HpjA4709 gradually increased, both before and after breakup.

Romick and Elvey [1958u], Galperin [1959u], and Malville [1959a] have noted a tendency for hydrogen emission to precede the full develop-

Hydrogen Emission


ment of auroral intensity by one or two hours. Galperin finds in the northern auroral zone that the H emission moves from north to south at the beginning of a display and may occasionally reverse the motion toward the end of the night. Montalbetti and Vallance Jones [1957a] observed Ha from Saskatoon and Churchill and concluded that hydrogen precipitation is strongest on the southern fringe of activity and that this fringe moves southward with increasing magnetic activity. Spectra obtained at Oslo and Tromso suggest that H is enhanced at low latitudes (Vegard [ 19523, 1958~1, Vegard and Kvifte [ 195 1 a, 1954~1).

Galperin [1958a, 1959a, 31 has also divided auroral spectra into two main, extreme types. Spectra of type I are produced by high, red aurorae (Vegard’s auroral type A). They have permitted atomic lines that are relatively strong, and enhanced [OI],, red lines. Type I1 is characterized by relatively strong molecular bands of N, and 0:. Galperin reports that H emission is more closely associated with type I. (Vegard [1955a] also noted strong H associated with type A displays.) If true in general, this conclusion may simply indicate strong H ’in high aurorae and low-latitude displays, which are often of this spectral type. Great caution is necessary in drawing fundamental conclusions about auroral excitation from qualitative results of this sort, since an enhancement of H with height may arise simply from the fact that low- energy protons give a large Ha/ionization ratio (see Section 7.1.1). The appearance of H lines in low, homogeneous arcs indicates that protons do at times penetrate deeply. But Vegard [1952c, 195533 has also found H to be enhanced near the upper parts of rayed aurorae, although it does not seem likely, on the basis of Omholt’s [1957c] measurements, that H lines are emitted by the rays themselves. Galperin notes, further that there appears to be a correlation between the appearance of H emission and radio reflections from the auroral ionization (Section 6.1 A).

The relationship between proton bombardment and aurora is further complicated by the fact that bright H lines may occur in the auroral zone without visible aurora. Montalbetti [1959a], observing with a scanning spectrometer, found HP to decrease from 500 R to less than 100 R over several hours, during which the airglow green and red [OI] lines were slightly enhanced but no other auroral emissions were observed. The HP profile indicated smaller than usual proton velocities, but the proton flux appeared to be of the order of lo* cm-2sec-1, of the same order as the flux of the faster protons commonly found in bright aurorae. (There may, however, be a large flux of auroral protons at velocities so low they have little effect on the profile; see Section 7.1.3.)

Montalbetti finds in the auroral zone that there is no marked preference for H lines to occur in aurorae of any particular form. I t is


particularly interesting that H lines are not always detectable in even very bright displays. At Saskatoon Hunten [1955a] finds that H lines can appear sporadically with almost any auroral form (see below). The hydrogen-line character of an auroral display may change significantly in a few minutes time.

5.2.4. Rapid Fluctuations and Intensity Correlations

The use of a scanning spectrometer allowed Dahlstrom and Hunten [1951a] and Hunten [1955a] to detect large fluctuations in the H lines, relative to other emissions that remained about constant, over successive scans of 10-sec duration. Thus, proton bombardment is possibly a sporadic, rather than a continuous, event during active aurorae. Correla- tion of brightness fluctuations of other features with H lines may afford a means of determining what portion of the auroral excitation is derived from protons.

Comparisons of the intensity fluctuations of the strong N: (0-0) band, A3914, and [OI],,, A5577, have been made photoelectrically by Omholt and Harang [1955a], Omholt [1956a, 195933, Ashburn [1955c], and Jorjio [1959a]. The upper term for [OI],, has a radiative lifetime of about 314 sec (Appendix VI), whereas the N: bands are permitted and have a lifetime of the order of lo-’ or sec. Consequently there is a noticeable sluggishness of the green line in following the rapid fluctuations of A39 14. Through detailed measurements, Omholt and Harang found that the delay of A5577 was apparently never greater than what would be expected from the radiative lifetime. I t could, they thought, be rather less, indicating some deactivation of the green line with a lifetime between collisions of a few tenths of a second (see Section 7.4.2 for discussion of deactivation).

For the larger and slower fluctuations there is a remarkable correlation between A5577 and A3914. The ratio of the photon intensities for A55771 A3914 is about 1 or 2 (Vegard and Kvifte [1945a], Hunten [1955a], Zhuravlev [ 1955a, b]) and is nearly constant over a wide range of auroral intensities (Kees [ 1959~1, Omholt [ 1959b]), for various auroral forms (Omholt [1957c, 1959b], Jorjio [1959a], Frishman [1959a]), and probably over a wide height interval (Frishman [1959a], Omholt [19593]). This fact has considerable importance to theories of auroral excitation (Sec- tion 7.3).

5.2.5. Polarization of Spectral Lines

Ginzburg [ 1943~1 drew attention to the possibility that permitted auroral radiations might be polarized, owing to a preferential direction


of motion of the exciting particles. With regard to forbidden lines he noted specifically that the green [OI],, line should not appear polarized, but the red [OI],, lines might show a small effect. Dollfus [1957a] has constructed a polarizing filter for observing aurorae and the birefringent photometer of Dunn and Manring [1955a], widely used in the IGY, is a polarizing device.

Using the latter instrument, Duncan [1959b] found a red, low- latitude aurora to be 30 percent polarized. Such strong polarization of radiation that was generally thought to be excited by rather low-energy electrons (which would presumably be nearly isotropic) is quite surprising (Chamberlain [ 195961). Ginzburg had suggested that molecular nitrogen bands be examined, since they are perhaps excited by primary incident particles, but no theoretical calculations have been made for impact excitation of molecules. Harang [ 1933~1 looked for polarization in the blue and violet by photographic photometry, but found none.

A quantitative theory of the red-line polarization for impact excitation is also lacking. (The theory of polarization for resonance scattering and fluorescence is treated in Section 11.1.2.) Any polarization is a direct consequence of the Zeeman effect and consequently depends on the relative transition probabilities for different Zeeman components in the downward transition. Also, i t depends on the relative probability of excitation of the different Zeeman states of the upper level and hence may be a function of the velocity of the exciting particles. The separation of Zeeman states of O(l0) in the Earth’s field greatly exceeds the natural width of these metastable states. Thus degeneracy is completely removed by the field, which then depolarizes radiation emitted parallel to the field. This magnetic depolarization may be understood from the consideration that the angular-momentum vector of the atom gyrates about the field many times during the lifetime of the excited state. Hence, when one looks along the field, he finds complete azimuthal symmetry in the orientation of the excited atoms, regardless of the direction of motion of the exciting particles. Perpendicular to the field, there may well be an asymmetry, but the resulting polarization might be either positive or negative (see Chamberlain [ 195963).

5.2.6. Hydrogen-Line Profiles

The discovery of broadened H lines in the auroral spectrum was reviewed in Section 5.1.3. The profiles in different directions from the observer depend on the characteristics of the protons bombarding the atmosphere and provide clues for a theory of the origin of auroral particles.


A typical pair of Ha profiles is shown in Fig. 5.19. The peak intensity of the zenith profile occurs at a Doppler displacement of 300 or 400 km/ sec; its high-velocity tail on the short wavelength side may be detectable to 2000 km/sec. The profile on the longward side of the neutral position (the red shif2) is visible to several hundred kmlsec, which probably arises in part from light scattered from other parts of the sky and in part from Doppler motions away from the observer. Some upward-directed protons could be produced by a number of small-angle scatterings of protons that initially were moving nearly perpendicular to the magnetic field.

The horizon projile is symmetrical about the neutral position and extends to about 500 km/sec on either side of the center.

The profiles do not usually show much variation among different aurorae. Galperin [1957a, 195833 has measured a number of Ha profiles with a dispersion of 83.5 A/mm; there seem to be no important differences from the profile in Fig. 5.19, except that at high velocities of approach the line may not be as strong as in the figure. Generally, good profiles are obtained only from fairly bright aurorae, and photographic exposures integrate the profile over a considerable time, perhaps several hours. Therefore, it may well be that the instantaneous profiles or the profiles in faint aurorae differ from these results and fluctuate markedly with time.

Montalbetti’s [ 1959~1 observations of HP emission in the absence of visible aurora (Section 5.2.3) disclosed a Doppler shift much smaller than is ordinarily found. The shortward wing of the profile did not extend beyond 1200 kmjsec. The displacement of the peak was less than 100 km/sec, but since the hydrogen emission probably covered most of the sky, Rayleigh scattering may have seriously distorted the zenith profile and disguised a larger shift in the peak.

Malville [1960a] also obtained a very narrow Ha line in the southern auroral zone. The line indicated a flux of about 108 proton/cm2 sec with velocities below 500 km/sec. We shall see in Section 7.1.3 that even the usual, broadened profiles require a large fraction of the protons to have such low velocities. Perhaps the broad and narrow profiles differ only in that with the latter, the high-energy tail of the proton spectrum is absent.

5.2.7. Rotational and Doppler Temperatures

Interpretation of Rotational Temperatures.-There are two principal difficulties to be overcome in deriving information about the temperature of the ionosphere from the rotational distribution within a molecular band. The first is the observational problem of recording only light


that is emitted from a definite and known height. The other problem is the proper interpretation of the rotational intensity distribution in terms of the local temperature (see Section 1.4.2). As the first problem is more directly concerned with the specific observational attempts that have been made, we shall first review the second or interpretational problem.

If the upper state has a long lifetime compared with the time between gas-kinetic collisions, then a Boltzmann distribution becomes re- established in the upper state and one uses the rotational constant of that state to derive the gas temperature. But for permitted band systems, where the rotational distribution is not altered within the upper state, one must inquire as to the excitation process.

Electron impact probably produces little or no change in the rotation of a molecule, especially if the molecule is not ionized by the impact. Then the rotational temperature should correspond to the gas temperature, provided that the rotational constant of the ground state is used in the temperature formula. There is evidence that the N i First Negative bands in ordinary aurorae are excited from the ground state of N,. In sunlit aurorae the excitation is probably from the ground state of NZ. In practice both these states and the upper state of the First Negative system have very nearly the same rotational constant, Be, so it matters little which constant is used in the reductions. In the case of sunlit aurorae there is the added complication of the Fraunhofer absorption lines in the exciting radiation, which is the same problem encountered in twilight- airglow studies and treated in detail in Section 11.2.3.

Laboratory studies of impact excitation have tried to establish the equivalence or differences between N: First Negative temperatures and the gas temperature. Duffendack, Revans, and Roy [1934a] concluded that there was a relationship between the energy of the exciting electrons and T,,t(N:), and they suggested that with simultaneous ionization and excitation, a small portion of the electron energy could go toward increasing the molecular rotation. Vegard [1932d] found, however, that for electron impact the rotation was an accurate measurement of the gas temperature.

Recent measurements with proton excitation have disclosed no temperature differences for particle energies around 3 kev and in the range 10-30 kev (Carleton [1957a], Roesler, Fan, and Chamberlain [ 1 9 5 8 4 , although earlier experiments by Vegard [1934a] with canal rays suggested that such low-energy, heavy particles do raise the rotational temperature. Branscomb, ShaIek, and Bonner [ 1954~1 estimated rotational temperatures between 700 and 1000" K for proton impact at 100 kev at room temperature. There is always a difficulty in being


certain that an enhanced rotational temperature is due to the excitational collision and not to Joule heating by the electric currents passed through the gas. Experiments in which some of the excitation is by secondary electrons may show less enhancement than would be the case for proton impact alone.

There is no direct information available on the temperature effect produced by a fast collision with a neutral H atom. While there may, therefore, be some enhancement of Trot(Nz+) as a result of the exciting collision, laboratory experiments have not yet established such an effect. Quite possibly the rotational temperatures do not depart significantly from the kinetic, and this is generally the assumption that has been made in interpreting measurements on aurorae that are not sunlit. (For the case of sunlit aurora, see below.)

Rotational Temperatures of First Negative Bands.-Rotational temperatures were obtained in 1932 from the A4278 N,f First Negative band by Vegard who, with his collaborators, subsequently made many temperature measurements from this system.' Their temperatures were invariably low (- 225" K) and nearly constant for all types and heights of aurorae. On the other hand, various observations in Canadas have generally indicated a temperature variation with height that is reasonably consistent with that derived from rocket investigations. Vegard [ 1955b] has maintained that there is a real difference between the two sets of results, the higher temperatures found in Canada being due to proton excitation and not indicative of a real variation with height in the kinetic temperature.

I t is difficult to accept this view. The agreement of Montalbetti's results at Churchill with those from Saskatoon cast doubt on any dependence of rotational temperature on the latitude or amount of proton influx. I t seems more likely that the Canadian work has been rather more successful in recording spectra (sometimes with a scanning spectrometer) of auroral radiation from great heights. The spectra of Vegard et al. that presumably pertain to the upper parts of long rays were often obtained by long exposures with the spectrograph directed toward the magnetic zenith. Perhaps these spectra were severely contaminated by scattered light from neighboring, low-lying aurora and by the diffuse glow that usually forms a substantial background to the rayed structure. Most of the Canadian spectra have been obtained

' Vegard [3932d, e, 1934a, 1937c, 395563, Vegard and Tonsberg [1935a, 19380, 1940a,

LI Petrie [1953a], Vallance Jones, Hunten, and Shepherd [1953a], Vallance Jones and 1941a, 1944~1, Vegard and Dorum [19360], Vegard, Tonsberg, and Kvifte [19510].

Harrison [1955a], Shepherd and Hunten [1955a], Montalbetti [1957a].


from bright forms, with careful pointing of the instruments throughout the observations.

Vallance Jones and Harrison [ 1955aI and Wallace [ 1959al found that the N l bands could not be represented by a single temperature. On Wallace's plate the lines with low rotational quantum numbers, K , gave Trot of the order of 225" K, but at large K the value increased to 575" K. Probably the auroral emission came from a large range of heights; the temperature variation with height in the atmosphere would then cause the total number of excited molecules along the line of sight to deviate from a simple Boltzmann distribution.

Sunlit Aurora.-Vallance Jones and Hunten [ 1960~1 (also see Hunten, Koenig, and Vallance Jones [ 1959~1) measured the rotational distribution in a sunlit aurora in the 300- to 600-km region. They have derived a rotational temperature for the ground state of N: of about 2200" K, on the basis of resonance scattering of sunlight (Section 11.2.3). Lytle and Hunten [1960u] similarly found Trot = 1060" K for the 200- to 300-km region. Clark and Belon [1959a] have reported values of Trot as high as 2500" K ; their temperatures may also refer to sunlit aurora, but were not computed with allowance for the Fraunhofer absorptions.

One must examine whether these temperatures are indicative of the kinetic temperature, since frequent absorptions and re-emissions could distort the rotational populations from the distribution that would be established by thermal collisions. In the limiting case where an NZ molecule scatters a photon much more frequently than it suffers a collision or captures an electron, the rotational distribution would be in radiative equilibriums and therefore approach a rotational temperature of about 7000" K if there were no Fraunhofer absorptions. Vallance Jones and Hunten found, however, that for A3914 these lines actually reduce Trot in radiative equilibrium to about 1200" K, which is lower than the observed value at extreme heights.

The rotational temperature could also conceivably deviate from the kinetic if the N: ions have short lifetimes. In the process of ionizing the N, molecule, protons and H atoms might alter the rotational distribution in N: (X22: ) from that in collisional equilibrium (i.e., the equi-

If the gas were completely surrounded by a black-body source, the molecules would be in strict thermal equilibrium (Section 1.1). But as long as collisions are very rare, the rotational distribution is unchanged if the intensity of the incident radiation is diminished. If the radiation is not so dilute that collisions compete with radiative processes, radiative equilibrium governs the populations, which are then described by the "color temperature" of the radiation-Le., by the black-body temperature that gives the same slope as the actual radiation curve in the spectral region envolved.

5.2. SPECTRAL PHOTOMETRY OF AURORA 21 1

librium established by frequent thermal collisions). Should recombination occur before either radiative or collisional equilibrium is established, the scattered radiation will give a temperature governed by the excitation process. However, secondary electrons are probably at least as important in ionizing N, as primary collisions (Section 7.3.1), and even proton impact may produce little change in the rotational distribution.

Vallance Jones and Hunten thus suggest that 2200" K is close to the kinetic temperature in the 500-km region during intense auroral bombardment.

Other Rotational Temperatures.-The Vegard-Kaplan bands arise from a forbidden transition involving a change of multiplicity, and hence the upper state might achieve an equilibrium with the gas temperature. Hunten [1955a] estimated the lifetime for the upper state to be the order of half a minute from the rate of decay of these bands in active aurorae (also see Wilkinson [ 19594). If collisions involving rotational change proceed at about the rate of a gas-kinetic collision, or a rate coefficient of about 3 x 10-lo cm3/sec, the mean time between collisions will be 7 - 3 x 109/N sec, where N is the density. Thus the Vegard- Kaplan bands would be expected to indicate kinetic temperatures for total gas densities above 108 particles/cm3 or heights below 400 km. The lifetime derived by Hunten could, however, be considerably in error, if the excitation at high altitudes persists much longer than in the lower, brighter regions. The laboratory measurements suggest a shorter lifetime.

Petrie [1952a, 1953~1 estimated temperatures around 850" K for one strong aurora from 5 V-K bands in the ultraviolet. These bands are seriously blended with other features and accurate measurements of Trot are difficult. Petrie's results were obtained from the wavelength difference between the band origin and the maximum of the P-form branches.

Wallace [1959a] has analyzed a plate with rather high dispersion (22 A/mm) that showed well-exposed 2-12 and 1-12 V-K bands in the great red aurora of 11 February 1958. The overlapping of other emissions made precise conclusions impossible, but Wallace was able to assign a lower limit of 800" K. Probably the bands are emitted at significantly greater heights than the permitted N: system and therefore have higher temperatures. I t has not been shown that the line intensities follow a Boltzmann distribution over the entire band.

Petrie [1953a] made a rough estimate of 350" K for the First Positive bands of N, but emphasized that the accuracy was low because of the extremely complex structure of these bands. For reliable values of Trot


it is necessary to construct theoretical profiles of a band, with allowance for instrumental broadening, whenever the rotational structure is not resolved, and this is especially true for the First Positive system. Gartlein and Sprague [1952a] reported that the peaks of these bands appear to be shifted toward higher rotational temperatures during times of intense Ha. However, noticeable changes in the relative intensities of these peaks would be expected with a change in temperature before any appreciable wavelength shift occurs. Consequently, the effect is questionable.

Mathews and Wallace [1961a] have computed model profiles of two N,+ Meinel bands. Comparisons with spectra of three aurorae gave Trot M 350" K, with an estimated uncertainty of 75" K. This temperature is higher than the average for the N; First Negative bands, but in no case were the two band systems recorded with high dispersion from the same aurora.

Wallace and Chamberlain [1959a] have measured the forbidden 0, Atmospheric bands 0-1 and 1-1 in several aurorae. The former gives TrOt(0-1) M 200" K (referred to equilibrium in the upper state) and is probably indicative of the kinetic temperature in the low auroral region. But the other band gives a much higher value, Trot(l-l) - 700" K. The bands have not been resolved into their rotational structure and so it is not absolutely certain that the discrepancy is real and not an illusion caused by underlying blends. However, it appears that a high rotational temperature, for vibrational levels above v' = 0, may be reconciled with the excitation mechanism of energy transfer from O(l0) (see Section 7.4.2).

Doppler Temperatures.-With the high resolution afforded by an interferometer, it is possible to measure the width of strong atomic lines and derive the Doppler temperature defined by Eq. (1.1 1). Armstrong [1956b, 1959~1 has obtained temperatures from A5577 [OI],, of 310" to 540" K above faint auroral arcs. Mularchik [1959a, b] obtained similar results for A5577, but for the red line A6300 [OI],, he found T D o p N 1000" K. The great red aurora of 1 1 February 1958 showed an extremely wide red line, corresponding to TDop > 2500" K. Wark [1960a] found for A6300 TDop in the range 700" to 800" K for two aurorae.

As in the case of rotational temperatures, one must be cautious in interpreting Doppler temperatures. In many instances they may give directly the kinetic temperature of the gas, but it is not difficult to imagine situations where the emitting atoms would have a greater mean velocity than unexcited atoms. For example, atomic forbidden lines from low-lying levels might be excited by dissociative recombination of


a molecule [Eq. (1.106)] and receive an excess of kinetic energy. For the particular case of h6300, gas-kinetic collisions may not be able to absorb this excess motion during the lifetime of the excited level at heights above 400 km or so.

Excitation of permitted lines and bands by impact with fast, neutral hydrogen atoms [Eq. ( I . 102)] or excitation-ionization through charge transfer [Eq. (1.103)] may impart an appreciable momentum to the target atom, so that its lines would show excess broadening and perhaps even a very small Doppler shift. Another such possibility for permitted atomic lines is molecular dissociation by particle impact, with an atom left in an excited level (see also Section 7.4.1).

5.2.8. Vibrational Distributions

Vibrational Temperatures for Excited States.-The relative populations of vibrational levels within an electronic state may be used to define a vibrational temperature Tvlb through Eq. (1.78), provided that the populations approximate a Boltzmann distribution. It is generally very difficult to relate such a Tvlb to the kinetic temperature, however, because populations in the upper state of a transition depend on the excitation process and will not usually reach thermal equilibrium befQre radiating (Oldenberg [ 1934~1).

Of course, a molecule in a highly metastable state may suffer collisions involving an interchange of vibrational energy, and could approach equilibrium. The main candidates for thermal equilibrium among the upper vibrational states in auroral spectra are the Atmospheric 0, and the Vegard-Kaplan N, bands.

For 0, the relative populations of u' = 0 and 1 (Chamberlain, Fan, and Meinel [ 1954~1, Wallace and Chamberlain [ 1959~1) usually correspond to Tvfb in the range 500-700" K. A study of the excitation mechanism (Section 7.4.2) suggests that there is considerable vibrational deactivation of levels with u' > 0, but probably not enough to make the populations approach thermal equilibrium. A temperature estimate from the N, V-K bands would be quite uncertain because of the low accuracy of relative-intensity estimates and of the Franck-Condon factors for the few useable bands.

Vibrational Distributions to Obtain Excitation Mechanisms or Tvll, in the Ground State.-If the excitation occurs directly from the ground state and the details of the mechanism are understood, the distribution of populations over the excited vibrational levels may be used to derive the vibrational temperature of the ground state. For


temperatures of only a few hundred degrees, the populations of the excited levels, and consequently the relative band intensities, are quite insensitive to temperature, since the level V" = 0 contains virtually the entire population of the ground state.

Bates [ 1949~1 has developed the theory for the vibrational distribution of the N: First Negative bands excited by electron impact from the ground state of N,. The relative rates of population of the upper levels were taken to be proportional to the Franck-Condon factor for a transition between the two levels concerned. The population rates for v' = 0 and V' = 1 should be in the ratio of about lO/l at low temperatures.

Since Bates' paper appeared, measurements have been made by Petrie and Small [1953a] and Hunten [1955a], which seem to be in good agreement with expectations. The main value of this work is not in deriving kinetic temperatures, but rather in showing that, with the temperature found for the auroral region by other means, the intensities are consistent with electron impact being the excitation mechanism. For collisions by heavy particles, the population rates would not follow the Franck-Condon factors so well (see below).

In sunlit aurorae the vibrational distribution is more highly developed, with higher vibrational levels relatively more populated than in ordinary aurorae. Stormer [1939a] first observed this effect and an explanation was offered by Bates [1949a] in terms of resonance scattering and fluorescence of the First Negative bands as in the twilight airglow. The primary auroral particles evidently produce N,+ ions through collisions, and most of the emission arises from scattering of sunlight by these ions rather than by simultaneous excitation-ionization. The N i ions in their ground state have too few collisions at the great altitudes of Stormer's sunlit rays to achieve vibrational equilibrium with the gas temperature. Instead, successive absorptions and re-emissions may establish a vibrational radiative equilibrium with sunlight, and Tvib for the ground state of N,+ would then be about 4500" K.

The establishment of radiative equilibrium may be inhibited, however, more by recombination of N: ions than by vibrational collisions. A newly formed N$ ion will have Tvib somewhat in excess of the kinetic temperature, by about 10 percent for electron impact at temperatures around 2000" K and somewhat more for heavy-particle ionization (see below). The value of Tvib would thus lie somewhere between the kinetic temperature and the 4500" K applicable to radiative equilibrium. Vallance Jones and Hunten [1960a] have obtained Tvib = 2050" K for sunlit aurora in the 300-600 km region and have concluded that it is not greatly different from the kinetic temperature during aurora.

When the rotational structure is also highly developed, as in these


high aurorae, the apparent relative intensities of band heads within a sequence may also be affected by the underlying rotational structure of neighboring bands. Clark and Belon [1959a] have made some illustrative calculations of the effect for a particular spectrographic resolution. Vallance Jones and Hunten [1960a] point out that when spectra are corrected for this effect, the vibrational temperature is lowered to the point that the previously accepted radiative equilibrium is no longer plausible.

There are cases of high vibrational development that possibly are not due to resonance scattering (see Section 5.2.2 and Rayleigh [1922b, c] and Clark and Belon [1959a]). An alternative explanation might be excitation by heavy-particle (e.g., protons, H atoms) collisions. Laboratory experiments by several groups1° show that such collisions populate the higher vibrational levels more than do electrons, especially at low particle energies where charge transfer (1.103) becomes more important than simple ionizing collisions (wherein a free electron is produced). (Fan has also noted that the ratio of the Meinel N: to the First Negative system seems to be different for excitation by low-energy heavy particles and by electrons. At higher energies a proton ionizes in the same way as an electron of the same speed, and in addition, when secondary electrons are produced, they can in turn produce the majority of the total ionization.) There is some question, however, as to whether the spectra showing high vibrational development may not invariably have been obtained from high sunlit aurorae (Seaton [1956a], Vallance Jones and Hunten [1960a]).

Bates [1949a] has computed the relative intensities of the Second Positive N, bands for electron impact. The problem is more difficult for these bands in that the intensity measurements are more vulnerable to errors due to scattered light and overlapping emissions. The predicted intensities are not very sensitive to the temperature. Omholt [1954a, 1955~1 concluded that Tvib in the ground state of several thousand degrees was required to explain the observed intensities, and hence it seemed that electron impact was not the only excitation mechanism. However, small errors in the measurements would reconcile the result with electron impact at TVll, < 1000" K. Indeed, Hunten and Shepherd [1955a] have emphasized that a number of their own measurements as well as those of Petrie and Small [19523] are consistent with electron impact, so that additional mechanisms are not necessarily indicated by presently available data. Neither, however, are they necessarily excluded and

"Smyth and Arnott [1930a], Vegard and Raastad [1950a], Fan and Meinel [1953a], Branscomb, Shalek, and Bonner [1954a], Fan [1956a, b ] .


Nicholls [ 1948~1 has proposed that in some laboratory sources an indirect excitation mechanism may be more important than direct excitation.

PROBLEMS

1. Assume that the Second Positive N, bands are excited by electron irhpact at a kinetic temperature of a few hundred degrees. With the relative intensities given by Bates [1949a] and the total absolute intensity of Table 5.5, compute the intensities of the First Positive bands that result from Second Positive cascading. Compare this prediction with the observations.

2. With the observed intensities of the First Positive system, extrapolated to unobserved bands by means of Franck-Condon factors, compute the intensities of the Vegard-Kaplan system without any correction for vibrational or electronic deactivation. Compare with observations.

Chapter 6. The Radio-Aurora

6.1. Observed Characteristics

6.1 .I. Introduction: The Distinction Between Aurora and Radio-Aurora

The term radio-aurora, introduced by Collins and Forsyth [1959a], signifies the ionization, associated with aurora, that gives rise to certain characteristic types of radio reflections in the very-high (30-300 Mc/sec) and ultrahigh (300-3000 Mc/sec) frequencies.l The key phrase in the definition is “associated with aurora”; it is not always obvious whether a particular signal is reflected by radio-aurora. Usually when we speak of the aurora we refer to the visual atmospheric radiation that shows the various characteristics described in Section 4.2. T o the physicist, however, a definition of a natural phenomenon, based on the characteristics of the human eye, seems most artificial. It would be better to define aurora with physical processes or prime causes in mind. Although these matters are still inadequately understood, we do find it convenient at times to use the term subvisual aurora, which is actually self-contradictory if the aurora must have the properties described in Section 4.2, but which implies that the physical processes essential to visual aurora may occur on a reduced scale. The auroral spectrum supplies a more direct link to physical processes and has the practical advantage of possessing features not present in the airglow spectrum (see, however, Section 9.1.1).

As a working definition, let us now consider aurora to be the sporadic electromagnetic radiation that is emitted from the atmosphere and induced by extra-atmospheric atomic or subatomic particles.2 By

At these frequencies the radio-aurora is an extremely poor reflector. Little, Rayton, and Roof [1956a] estimate that at 100 Mc/sec the energy reflected is never more than lo-‘ of what would be returned by a perfect reflector having the same dimensions as the associated visible structure.

* The qualifying adjective “sporadic” provides some desirable looseness to the definition, but still places emphasis on the aurora as arising from disturbed conditions. Radiation produced by the bombardment of background cosmic rays, for example, is more appropriately assigned to the airglow. But radio waves emitted (as distinct from reflected) by the auroral atmosphere would be part of the aurora (Section 4.3.5). Note that the definition as worded does not necessarily require particle bombardment, but would include an aurora excited by electric discharges or hydromagnetic waves, provided that these mechanisms were induced by extra-atmospheric particles.

217

218 6. THE RADIO-AURORA

definition the aurora does not include the radio-aurora ; they are separate phenomena with the same basic origin. Aurora is basically emitted radiation ; radio-aurora is basically ionization that reflects radiation. Emission of radiation requires active atomic processes, one of the most important of which is ionization. Freed electrons, when they give rise to the characteristic radio reflections, form the radio-aurora. Of course, the radio-aurora depends not only on the presence of ionization but on the geometry of the observation, and its detection may also be hindered by radio absorption.

Therefore, i t is plausible (and seems to be the case, in fact) that aurora is not always accompanied by observable radio-aurora and that radio-aurora may occur without visible aurora. The precise relationship between the two phenomena is still a little vague (see also Section 6.1 .S). The morphology and reflection mechanisms for the radio-aurora are gradually becoming understood. Perhaps simultaneous radio and spectrophotometric observations will open new frontiers of understanding.

Discovery of the scattering of VHF radio waves by auroral ionization was made by Harang and Stoffregen [1938u, 1940~1 and later with radar techniques by Lovell, Clegg, and Ellyett [1947u]. Observers had previously noted auroral effects on the lower frequencies used for conventional ionospheric soundings (Appleton,. Naismith, and Ingram [ 1937~1). Radio amateurs have also noticed peculiar propagation conditions associated with aurora (Moore [1951a]). Summaries of the early work on the radio-aurora and brief reviews of the status of research have been given by Kaiser [1956a], Little, Rayton, and Roof [1956u], and Nichols [1959u]. An extensive review of the subject has been written by Booker [1960a].

6.1.2. Types of Radar and Bistatic Echoes

Most of the work on radio-aurora has utilized the principles and equipment of radar. A signal is emitted in pulses, or sometimes a pair of closely spaced pulses, and the echo is received at the same station. The time lapse gives the range of the reflection point.

Aspinall and Hawkins [ 1950~1 and several subsequent observers have distinguished two basic types of radar reflection (Fig. 6.1). Diffuse echoes show a wide spread in range (perhaps several hundred kilometers), whereas discrete echoes indicate a reflection occurring over a fairly small range (within a few kilometers). Several discrete reflecting centers may exist on the line of sight, then suddenly coalesce into a diffuse structure, and after a time become resolved again into a series of discrete echoes (Bullough and Kaiser [1955a]).

6;l . OBSERVED CHARACTERISTICS 219

FIG. 6.1. Characteristic echoes at 72 Mc/sec. Diffuse echoes are shown in (a) and (b); discrete ones in (c). Meteor echoes appear at 2323.8 and 2327.6 U.T. Note that the structure appears in double images, since the pulses were transmitted in closely spaced pairs, which give a spread in apparent range of 50 km. After

Bullough and Kaiser [ 1955~1; courtesy Pergamon Press.


Birfeld [ 1957~1 uses a more elaborate classification scheme for echoes. He assigns three letters to a given observation, classifying the echo separately according to structure, lifetime, and radial motion of the reflector.

A second method for probing the radio-aurora involves the use of at least two stations forming a circuit. A signal (which may be a continuous wave) transmitted from one station is scattered or reflected in the ionosphere and received at the second station, possibly as much as several hundred kilometers from the t r an~mi t t e r .~

This so-called bistatic method has been developed over an extensive network of stations operating on several frequencies between 30 and 50 Mc/sec by Collins and Forsyth [1959u]. These authors classify the auroral reflections obtained in this way and recorded on an amplitude- time trace, into three types, A,, A,, and A,. The A, signal is often quite large and its most distinctive characteristic is a high rate of fading (Section 6.1.5), too rapid for the recording pen to follow. The A, signal is large and subject to deep irregular fading at a much slower rate. T h e A , signal rises slowly and smoothly, exhibits much fading at a rate not too rapid for the recording pen to follow, and may persist for several hours. Reflections that do not seem to be associated with aurora are called type E, which seems to arise from sporadic-E clouds, and type S (for solar control), which is similar to type A , except that S is not accompanied by magnetic disturbance in contrast to A,. T h e distinction between S and A , is therefore not well defined and may be unrealistic, although the two types do show quite a different daily variation. But perhaps even the S events should be classed as a form of radio-aurora.

The A, and A, events seem to be associated with the early and later stages, respectively, of auroral displays. The A , reflections, which occur most frequently and usually with less amplitude than the others, are often the third phase of the radio-aurora and do not seem to have an analogue in the visual aurora.

6.1.3. Location of Radio-Aurorae

Although radio-aurorae exist in the same geographic and height regions that contain the aurora,4 there are some important differences

Collins [ 1958~1 has conducted experiments with a continuous-wave, frequency- modulated radar. This technique combines some of the advantages of the other two systems, providing both range information and Doppler motions.

See, for example, Currie, Forsyth, and Vawter [1953a], Unwin and Gadsden [1957a], Unwin [19596], Fricker, Ingalls, Stone, and Wang [1957a], Martvel and Pogorelov [1958a], Harang and Troim [ 1959b], Presnell, Leadabrand, Peterson, Dyce, Schlobohm, and Berg [1959a].

6.1. OBSERVED CHARACTERISTICS 22 1

between them. Of particular interest are radio-aurorae occurring at heights much higher or lower than ordinarily found for aurorae, and radio- aurorae at low latitudes.

At least some of the auroral reflections have a pronounced aspect sensitivity, that is, reflections occur predominantly from certain directions (see Section 6.1.7). T o a first approximation the preferred direction is the same as for specular reflection from columns of ionization aligned along the magnetic field. Thus radar reflections occur preferentially at the range where the line of sight is perpendicular to the magnetic field. In the subauroral regions and near the auroral zones, the range for a reflection from the lower auroral heights is of the order of 500 or 1000 km.

T o obtain reflections with a high degree of aspect sensitivity from great altitudes, it is necessary to place the radar at low latitudes. Peterson and Leadabrand [ 1954al first observed such long-range (1 600-4700 km) echoes on high frequencies (between 6 and 18 Mc/sec) at Stanford (A,,, = 44” N), although these echoes were evidently propagated from the auroral zone by way of F-layer reflection. Later Peterson, Villard, Leadabrand, and Gallagher [1955u] detected direct auroral reflections in the same frequency range from F-region heights, with ranges up to 1700 km. Nakata [1958u], working with frequencies 2 to 17 Mc/sec in Japan (A, = 25” N), also found occasional auroral echoes from the F region.

Weak reflections at frequencies less than 30 Mc/sec were also found to originate in the E region, with ranges of approximately 220 km from Stanford. I t occurs nearly every night, with a maximum probability around midnight. The characteristics of the echoes are suggestive of auroral origin and, therefore, of frequent but weak particle bombardment at middle latitudes.

At higher frequencies (VHF and UHF) auroral reflections occur a t middle latitudes less often, but Seed and Ellyett [1958u] and Seed [1958a] observed a number of “minor” radio-aurorae at 69 Mc/sec on magnetically calm days, as well as a few “major” disturbances. These events gave discrete reflections from about 120 km height. And at A , = 43” N the Stanford group (Schlobohm, Leadabrand, Dyce, Dolphin, and Berg [ 1959~1) obtained 106-Mc/sec reflections from radio-aurorae as high as 300 km. Echoes resembling those associated with aurora have been found at A,,, = 30” N on 32 and 140 Mc/sec by Dyce, Dolphin, Leada- brand, and Long [1959a].

Within the northern auroral cap most of the aurorae are south of the observer, but at Pt. Barrow (A, = 68” N) Dyce [1955u] found most of the radar echoes to the north on 52 Mc/sec, in accord with the aspect sensitivity. Harrison and Watkins [ 195841 have compared echoes from


northern and southern hemisphere stations and find that at least the stronger auroral disturbances occur simultaneously in both hemispheres.

6.1.4. Periodic Variations

Daily Variations.-Auroral radar reflections usually exhibit a marked decrease during the daytime hours, but otherwise show little over-all similarity with the visual a u r ~ r a . ~ The difficulty in understanding the

0 3 w

I-

s * W V

1200 I do0 0400 I $00 C.S.T

FIG. 6.2. Daily variation of bistatic radio-aurora. T h e histograms show the relative contributions of A, events (shaded), A, events (dash line), and A3 events (solid line). T h e results are plotted against the local zone time (6 hours west) and the arrows indicate the range of occurrence times for magnetic midnight.

After Collins and Forsyth [ 1959~1; courtesy Pergamon Press.

behavior is compounded by variations with latitude, type of visual display or radio-aurora, and the radio frequency of observation. Usually the peak activity comes in the evening hours, before the statistical

The daily variation has been studied at 30 Mc/sec by Hellgren and Meos [1952a]; at 56 and 106 Mc/sec by Currie, Forsyth, and Vawter [1953a]; at 72 Mc/sec by Bullough and Kaiser [1955a] (also see Kaiser [1956a]); a t 50 Mc/sec by Dyce (reported by Booker, Gartlein, and Nichols [19550]); between 30 and 50 Mc/sec by Collins and Forsyth [1959a]; at 216, 398, and 780 Mc/sec by Presnell, Leadabrand, Peterson, Dyce,Schlobohm, and Berg [1959a]; and at 55 Mc/sec by Unwin [19593]. Broadcast records (30-150 Mc/sec) of radio amateurs have been analyzed by Gerson [1955a].

6.1. OBSERVED CHARACTERISTICS 223

visual maximum, and may have a secondary maximum near the middle of the night or in the early morning. Different sets of data show quite different behavior. That there is a physical distinction between the two maxima is suggested by the finding of Bullough and Kaiser that discrete echoes occurred predominantly in the midnight and morning hours and avoided the early evening. Presnell et al. found a broad maximum around midnight for discrete echoes, and morning and evening peaks and midnight and noon minima for diffuse echoes.

Collins and Forsyth found a maximum shortly after magnetic midnight for all auroral echoes together. But their type A, shows a deep minimum around midnight, with evening and morning maxima (Fig. 6.2). The A, and A , signals have maxima after magnetic midnight. Also, A, events occur frequently on low-latitude paths but less often at high latitudes, a result, probably associated with the aspect sensitivity. At any rate, some understanding of the different daily variations at different stations seems about to emerge, as the different types of radio-aurora are analyzed separately.

Yearly a n d 1 I-Year Variations.-The strong maxima found for aurorae in March-April and September-October are not so clearly established for radio-aurorae.6 There may well be different behavior for echoes of different types. Relatively few data have been analyzed from this point of view, however, and any conclusions drawn now would be premature. One would not be likely to construct a good yearly curve for visual aurorae from one or two years’ observations, as have been utilized so far with the radio-aurora.

An 11-year variation somewhat similar to that of the visual aurora (Section 4.1.3) has been anticipated on the basis of a decrease in echoes from 1950 through 1954 found by Bullough and Kaiser [1955a]. A more complete picture should soon be available.

6.1.5. Apparent Motions of Auroral Ionization

The radio-aurora is characterized by apparent motions similar to those of the visual auroral forms (Section 4.2.4) and an order of magnitude faster than normal ionospheric motions and nightglow patterns (Sec- tions 11.4.3 and 12.3.4). These motions have been investigated in several ways.

li See the yearly variations plotted by Bullough and Kaiser [1955a], Booker, Gartlein, and Nichols [1955a], and Collins and Forsyth [1959a].


Shifts in Range.-Bullough and Kaiser [1955u] have measured the movements in range of individual echo features and derived the corresponding velocities.' Their observations at Jordell Bank (A, = 56" N) were made at an azimuth 50" W of the geomagnetic meridian. Almost invariably in the evening the echoes were receding and in the morning, approaching.

They considered the motions to be principally along parallels of magnetic latitude, rather than north-south. The motion is thus toward the sunlit hemisphere: westward in the evening and eastward in the morning with reversal occurring around 2200 local time. Typical apparent speeds are around 1000 meter/sec, but they often become 2 or 3 times as fast. Weiss and Smith [1958u] report similar behavior for motions a t subauroral latitudes in the southern hemisphere.

I t is not likely that velocities deduced in this way represent true systematic motions of atmospheric electrons. These apparent drifts, as well as those of visible structure, could arise from a motion, above the atmosphere and along parallels of magnetic latitude, of the primary auroral particles that produce the luminosity and ionization (see Section 6.1.8).

Fading.-A distinctive feature of the radio-aurora is the rapidly varying amplitude of the returned signal, with an unsteady "beat" frequency of the order of a few milliseconds. This effect, calledfuding, is best observed with a continuous wave, but it can be seen on pulsed radar if the pulses are more frequent than the beat frequency. Otherwise, the amplitudes of successive echoes are completely uncorrelated with one another.

Moore [1951u] called attention to the rapid fading and interpreted it qualitatively in terms of moving patches of ionization. This is a common interpretation of fading, but in the case of the radio-aurora the fading is so rapid that the velocities implied are an order of magnitude higher than those found in the normal ionosphere. A brief explanation may be of interest.

The basic point is that at a fixed position in space a passing wave train may be described mathematically or observed physically in two distinct ways. The oscillations of the electric vector in the wave are a function of time, E( t ) , which can in general be represented by a family of monochromatic, sinusoidal waves of infinite extent. If the monochromatic wave of frequency v = w/27r has an amplitude E,, then E(t ) and the family E, are related by Eq. ( 1 . 2 3 ) . (Note that the amplitude

' Also see Kaiser and Bullough [1955a], Aspinall and Hawkins [1950a], McKinley and Millman [1953a], Harang and Landmark [1954a], Lyon and Kavadas [1958a], and Unwin [1959a, b ] .

6.1. OBSERVED CHARACTERISTICS 225

of the electric vector of the wave is proportional to the amplitude x of an oscillating electron.)

In Section 1.2.1 we treated the particular case where E( t ) had an exponential decay superimposed on a sinusoidal oscillation of frequency v0, as given by Eq. (1.20). This wave was shown to be equivalent to a very long wave train with a frequency spectrum representing the natural broadening of a spectral line. In the same manner a reflected radio signal that has Doppler broadening (see Section 1.1.4) will fluctuate rapidly in total intensity, since E ( t ) and E, are Fourier transforms of one another. Physically, we may think of the intensity fluctuations as due to statistical fluctuations in the interference among the various monochromatic waves (Fourier components) contributing to the total.

If the wave train is dispersed in frequency, one may record the line broadening. Alternatively, if the intensity of the wave is recorded with high time resolution, one measures the rapid oscillations or fading. But the two observations are equivalent and with precise measurements of one type, the other can be predicted. A very sharp line is equivalent to a very long interval between beats; and as the line is broadened, the fading oscillations become more rapid.

The frequency spectrum found by Bowles [1952a] at 50 Mc/sec extends to 200 cyc1e;sec or more corresponding to more-or-less random radial velocitiesE for the reflecting centers of f. 600 meter/sec. At other frequencies the width of the spectrum, dv, as deduced from the fading, seems to be proportional to v , as would be expected if fading is due to Doppler broadening of the signal (Booker, Gartlein, and Nichols [ 1955al).

Frequency Spectrum of Returned Signal.-A number of direct investigations of spectral broadening and shift of the signal have been made with electronic spectrum analyzer^.^ The frequency width of the

For a radar reflection, with transmitter and receiver located together, the Doppler relation is A v / v = - 2nv/c, where v is the radial velocity, positive outward, and n is the mean index of refraction of the medium containing the reflector. The factor 2 enters because the total path length changes at a rate 2w, rather than just v , as in the case of an emitting source. Incidentally, it is not always appreciated that since the Doppler shift merely indicates a changing path length between the source and receiver, it does not necessarily measure real speeds of atmospheric electrons. Just as with the motions derived from range shifts, these velocities could apply to advancing or receding sources of ionization, which would give the reflecting surfaces or volumes an apparent motion. I t is not necessarily true, however, that the motion of the reflector is also the motion of the component electrons.

@ Bowles [1954a], McNamara [1955a], Nichols [1957a, 1959~1, Blevis [1958a], and Leadabrand, Presnell, Berg, and Dyce [1959a].


signal again corresponds to mean Doppler speeds of the order of 500 meter/sec. In addition, the peak of the returned signal is often shifted several hundred or a thousand meters per second. The signal is thus not only broadened, evidently owing to random motions of reflecting centers within the observed volume of radio-aurora, but it is displaced as a whole, indicating a superimposed systematic motion of the radio-aurora.

Some observers found a tendency for the directions of motion to be westward in the evening and eastward in the morning, in agreement with the velocity pattern derived from range shifts by Bullough and Kaiser [1954a] and Unwin [1959a]. If the Doppler velocities were to correspond to real electron motions, thkre is a possibility that they would be associated with electric currents responsible for magnetic bays. As Meinel and Schulte [1953a] pointed out in connection with their photographic studies of auroral motions, a reversal near the middle of the night is reminiscent of the reversal of ionospheric current systems hypothesized to explain magnetic variations. The electrons carry negative current, so their tendency to move toward the sunlit hemisphere is consistent with the direction in the auroral zone of positive current toward the midnight meridian (roughly speaking) and thence over the polar cap (e.g., Silsbee and Vestine [1942a]).

This orderly picture has become somewhat clouded by the failure of Leadabrand et al. to detect any dependence of direction on local time at 400 Mc/sec and with good (3") resolution at Co!lege, Alaska. The situation is thus as confused as the analogous problem of systematic motions of the visual aurora (Section 4.2.4). Moreover, there is a strong theoretical argument against the principal Doppler motions representing real electron drifts (see Section 6.1.8).

6.1.6. Polarization

If the transmitting antenna emits a pIane polarized wave, which is specularly reflected by a uniform conducting sheet, the returned wave will still have the same polarization. Several investigations have established, however, that actually the returned signal may be partially or completely depolarized.1° At the higher frequencies, and particularly in the UHF range, there is very little depolarization, but the extensive studies in the neighborhood of 50 Mc/sec show a strong depolarizing

lo Harang and Landmark [1953a, 1954~1 at 35 and 74 Mc/sec; McNamara and Currie [19546] at 56 and 106 Mc/sec; Fricker, Ingalls, Stone, and Wang [1957a] at 413 Mc/sec; Presnell, Leadabrand, Peterson, Dyce, Schlobohm, and Berg [1959a] at 398 and 780 Mc/sec; Collins and Forsyth [1959a] at 39 and 49 Mc/sec; Kavadas and Glass [1959a]at 48 Mc/sec.


effect. The amount of depolarization seems to be a function of range (McNamara and Currie), and is less if the radar wave and the magnetic field are nearly perpendicular in the E region. Kavadas and Glass believe that the reflected wave contains a component polarized parallel to the field, regardless of the azimuth of observation.

The phenomenon is still not completely understood. Two mechanisms have been proposed for destroying the polarization.

If the direction of wave propagation has a component parallel to the Earth’s field, the plane of polarization will be rotated. The oscillations of electrons, as imposed by the passing wave, are partly perpendicular to the field, but the electrons also tend to revolve in Larmor orbits and alter the polarization of the wave. The mathematical treatment by the magneto-ionic theory is rather involved (Mitra [1952a], p. 194), but the effect is essentially a Faraday rotation, discussed in most texts on physical optics. A plane-polarized wave may be represented by the sum of two (ordinary and extraordinary) components, circularly polarized in the opposite sense from another, but with the same frequency. Since these waves move through the medium with different velocities, their phase relationship changes with distance along the path. The combined waves then give a linear polarization whose orientation continually changes with position along the wave.

The second possibility is multiple scattering by an assembly of electron clouds. A combination of the two effects may also be effective. An alignment of scattering centers along the magnetic field, Kavadas and Glass suggested, is probably responsible for the polarization component parallel to the field.

6.1.7. Aspect Sensitivity and Echo Strength

Both the aspect sensitivity and the strength of the reflected signal vary with the frequency. The precise relationships are difficult to establish, because different radars usually have different beam widths and other performance characteristics. Investigations of this sort generally involve simultaneous observations with two or more frequencies, but some qualitative conclusions may also be drawn from isolated experiments at a variety of 1atitudes.ll

l1 The principal investigations with two or more frequencies have been made by Harang and Landmark [1953a, 1954~1 at Oslo and Tromso on 35 and 74 Mc/sec; Currie, Forsyth, and Vawter [1953a], Forsyth [1953a], and McNamara and Currie [1954u] at Saskatoon on 56 and 106 Mc/sec; Forsyth and Vogan [1957u] and Collins and Forsyth [1959a] between Nova Scotia and Ottawa on 32, 39, and 49 Mcjsec; Presnell, Leadabrand, Peterson, Dyce, Schlobohm, and Berg [1959a] at College on 216, 398, and 780 Mcisec.


Aspect Sensitivity.-Herlofson [ 1947a1, in proposing the mechanism of partial reflections to explain auroral echoes, suggested that the reflection would be specular from a plane surface. The surface would presumably be defined by arcs, draperies, etc., and would lie along the Earth's magnetic field and along a parallel of geomagnetic latitude. Alternatively, one might imagine with Aspinall and Hawkins [ 1950al and Booker, Gartlein, and Nichols [1955a] that the reflecting surface is cylindrical and formed by ionization aligned along lines of force and delineated by individual auroral rays. This condition is much less restrictive, allowing reflections from azimuths other than geomagnetic north (or south). Because there is considerable deviation from aspect sensitivity in either event (demonstrated, for example, by the occurrence of echoes in the auroral cap), it has not been a simple manner to ascertain which type of reflecting surface is the best approximation.

Bullough and Kaiser [1954a] and Kaiser [1957a] studied the geographic location of echoes at Manchester and Stanford and concluded that they were clustered about a parallel of geomagnetic latitude and that echoes were reflected from an arc of auroral ionization. The occurrence of echoes from azimuths some 50" from magnetic north was taken as evidence of large deviations from specular reflection from a sheet. These echoes did not fit the locus of reflecting centers to be expected for specular reflection from lines of force of the dipole field(Section 6.2.1).

However, Unwin [1958a] and Pogorelov [1958a] have shown that the reflecting centers do agree with expectations for aspect-sensitive columns if the local field at the Earth's surface, rather than the centered- dipole approximation, is used. Thus it appears that, as a first approximation, aspect sensitivity refers to columns along the magnetic field. Also, specular reflection provides for other echoes a useful reference direction ; for single-station radars the off-perpendicular angle indicates the departure from cylindrical specularity.

There is evidence that toward higher frequencies the aspect sensitivity becomes increasingly more rigid. For example, at 780 Mc/sec the maximum off-perpendicular angle observed at College (where, incidentally, strict perpendicularity may be impossible) was 6", whereas at 216 Mc/sec it was 12". A frequency dependence also seems to manifest itself in the range of azimuths that give echoes. Booker [1956a] reports that at College, echoes at 100 Mc/sec are obtained over azimuths of approximately f 45"; at 30 Mc/sec, around 3 90".

On the other hand, Forsyth [1960a] has emphasized that the range of azimuths giving strong reflections depends in a critical way on the characteristics of the equipment, even if there were no preference for perpendicular reflection. It may be unrealistic to make comparisons of

6.1, OBSERVED CHARACTERISTICS 229

the relative limits of echo directions without allowing for the radar characteristics.

Collins and Forsyth found considerable differences in the aspect sensitivity for the three types of echo found with their bistatic arrangement. They concluded that A, events were highly aspect sensitive; A, events were moderately so, although deviations as high as 30” or 40” from specularitp might occur; and A , events, like the similar, non- auroral S type, showed no aspect sensitivity. These results serve as clues to the reflection mechanisms, which will be discussed in Section 6.2.

Echo Strength.-Toward higher frequencies the echo generally becomes weaker. In their early investigation, Lovell, Clegg, and Ellyett [1947a] found echoes at 46 Mc/sec but none at 72 Mc/sec, and the subsequent work referenced abovell has substantiated this qualitative frequency behavior. For example, 56-Mc/sec echoes were observed at Saskatoon, Forsyth reported, about 4 times as often as those on a similar radar at 106 Mc/sec. The main questions are, “What is the precise frequency dependence of echo strength ?” and “How does the echo strength depend on the angular deviation from cylindrical specularity ? ”

The relative amplitudes of simultaneous signals on 3 frequencies over a bistatic path have been studied by Forsyth and Vogan [1957a] and Collins and Forsyth [1959a]. The amplitudes are not always in the same ratio. For A, and A, events the amplitude of the lowest frequency may show much larger variations than the other two signals. This behavior suggests that a contributing mechanism is critical reflection, with an electron density sometimes just above the critical value for the lowest frequency. The amplitudes of A , events, on the other hand, always have about the same ratio, even though the amplitudes themselves change over large factors. This steady frequency dependence suggests scattering by small volumes (Section 6.2.3) or surfaces (Section 6.2.2) with Ne well below the critical value. Absorption may also play an important role in determining the frequency dependence of the returned signal strength.

6.1.8. Relat ion to O t h e r Phenomena

Virtually all the papers reporting studies of radio-aurora have com- mented on their relation to visual aurora, a relation that is still not entirely clear. Some of the differences can be attributed to extraneous factors affecting the observability of one or the other: aurora is not observable during daytime; radio-aurora is more probable if the condition of aspect sensitivity (i.e., perpendicularity, for single-station radar)


is met; and the radio waves may be attenuated by ionospheric absorption. Allowing for these factors, we still do not know exactly how the two

phenomena are associated. That their relationship is not as simple as we might have anticipated is shown by the differences in daily variations -at least, for all aurorae and all types of radio echoes combined. As radar sensitivities are increased, a larger number of echoes are found that cannot be related to visible forms. Collins and Forsyth’s A, events, especially, occurred more frequently than could be explained by visible aurora. On the other hand, it seems that every visible form does not serve as a good reflector, even when the aspect condition is fulfilled. Gadsden [ 19594 has emphasized that the correspondence between echoes and visible structure is often very poor.

Perhaps there are some criteria, such as the type of optical display or the occurrence of related events, whereby we might distinguish aurorae that are associated with strong radio-aurorae. Currie, Forsyth, and Vawter [1953a] found that radar echoes were usually observed with moderately bright aurorae that showed some structure, with the ray structure a more important criterion than the brightness. Booker, Gartlein, and Nichols [1955a] also found ray structure to be important at Ithaca, but Bowles [ 1954~1 frequently obtained echoes at College from homogeneous as well as rayed forms.

Galperin [1959a] has found a good correlation between the appearance of H emission in the spectrum and the occurrence of radar reflections observed by Birfeld [1957u] at 72 Mc/sec. The main exceptions seem to occur for very high aurorae or when the magnetic field is especially quiet. Otherwise the radio-aurora seemed to indicate proton bombardment. In view of the negative correlation, obtained by several (but not all) workers (Sections 4.3.2 and 5.2.3), between proton bombardment and visible ray structure, a dependence of radio-aurora on both H emission and structure seems paradoxical. The behavior of proton bombardment, including its relation to the display as a whole, is still a rather confused topic, however. An explanation may also lie in the observability of different types of radio-aurora. Collins and Forsyth [1959a] associate A, events with the early stages of a display (homogeneous forms) and A, events with the later stages having fine structure. The early radar systems of low sensitivity might have detected A, events preferentially and thereby greatly overemphasized the correlation with ray structure.

Kaiser [1956a] has noted a similarity between radio-aurora and the ionospheric irregularities responsible for radio-star scintillations (Sec- tion 4.3.4).

Magentic disturbances also show some relationships to the radio-


aurora.12 Near Manchester the daily variation of occurrences of radio- aurora is similar to the mean daily variation in magnetic disturbance. In the first part of the night a disturbance, A H , is normally positive, and is believed to be associated with westwaFd motions of the auroral electrons and with diffuse echoes. Later (between 2100 and 2200 local time at Manchester) the magnetic disturbance becomes negative as the motions tend eastward and as the discrete echoes make their appearance.

Radio echoes are more likely to occur with positive magnetic bays than negative ones. And a close correspondence exists, Bullough et al. reported, between the occurrence of radio-aurora and individual features in the magnetic disturbance.

The association of apparent motions of radio-aurora, as well as its occurrence, with magnetic disturbance supports the hypothesis that the derived velocities represent real motions of electrons. The direction (eastward or westward) seems to be generally the same as the flow direction of negative current to explain the magnetic variations. And the required absolute value of this current could be delivered by electron densities of lo6- 1 O7 cm-3 distributed over volumes consistent with those of the radio-aurora and having drift velocities (relative to the positive ions) about the same as the observed drifts of reflecting regions.

A difficulty with this interpretation of apparent motions is that the expected lifetimes for free electrons are quite short. The lifetime for direct recombination with positive ions is 7 - l /Ni arec, where Ni, the density of ions, would be about the same as the electron density at E-region heights, and arec is the rate coefficient for recombination (see Section 1.5.2 for a discussion of recombination processes). If a significant portion of the ions are molecular (e.g., N;), areC may be the order of lo-' cm3/sec or larger. Hence we expect electron lifetimes of only a few seconds in the lower auroral region.

The persistence of reflecting regions must therefore be due to a continuous creation of new ionization. As the radio-aurora moves, it thus traces the locus of the source of ionization-presumably particle bombardment. In this view, the drift of radio-aurora is not necessarily

"The simultaneity of the two phenomena is discussed by Bullough, Davidson, Kaiser, and Watkins [1957a]; also see Meek and McNarnara [1954a] and Gadsden [1959a]. Further, Bullough et al., Bullough and Kaiser [1955a], Nichols [1957a], and Unwin [1959a, b] have related apparent motions to the magnitude of magnetic disturbance. Reviews and general discussions on the physical relationship between the two are given by Kaiser [1956a, 1958~1 and Nichols [1959a]. The relation between aurora and magnetic activity is discussed in Section 4.3.1. Motions of the radio-aurora, which have a close bearing on the current systems, are treated in Section 6.1.5.


the same as the real motions of ionization clouds. I t may very well develop, however, that the ionospheric currents are directly related in magnitude and direction to the longitude drifts of the auroral primaries in the space outside the atmosphere (see Section 8.2.2). Possibly both kinds of motion are governed by the same forces.

6.2. Theory of Auroral Reflections

In the following sections we shall be concerned with the manner in which VHF and U H F signals are reflected, and the interpretation of the observations in terms of structure and electron density of the radio- aurora.

6.2.1. Geometry of Reflections

Aspect sensitivity and its variation with frequency provide clues to the geometry of the reflections and therefore to the structure of reflecting centers. (Not all echoes are strongly aspect-sensitive; see Section 6.1.7.) There are conflicting opinions, however, as to the explanation of aspect sensitivity. Although deviations from specular reflection from cylindrical columns of ionization are quite important, cylindrical specularity does indicate the direction which is likely to be most productive of echoes.

Consider first of all single-station observations toward magnetic north (in the northern hemisphere). An observation at a particular angular elevation will intersect the magnetic field perpendicularly (see Fig. 3.2 for illustration of the dipole field) at a determined range and height. Chapman [1952a] has derived an expression for the locus of echo points-the meridian echo curve-for a magnetic dipole:

(6.1) r 1 - = cos (a - 0) + - tan O sin (a - O), a 2

where r is radial distance from the center of the Earth, a is the Earth’s radius, 8 is the colatitude (geomagnetic), and CL is the colatitude of the observer. Chapman’s paper contains the equation in Cartesian coordinates, as well. An example is shown in Fig. 6.3. Chapman has also plotted height of the echo point as a function of angular elevation of the radio beam for various colatitudes, as shown in Fig. 6.4; plots of constant 8 and distance d of the echo points are given on the same diagram.

If reflections occur from columns of ionization analogous to auroral rays, the geometrical problem is one of reflections from cylindrical

6.2. THEORY OF AURORAL REFLECTIONS 233

surfaces centered on magnetic lines of force. Reflections are then allowed from a range of azimuths and are not confined to the meridian plane. Chapman [1952a] has also made calculations for this geometry and a dipole field for geomagnetic colatitudes of 30”, 45”, and 60” and Cain [ 1953~1 has published calculations for 34”.

f ARTH’S MAGNETIC

A X I S

FIG. 6.3. Section of the Earth (semicircle BEA) in a plane through the geomagnetic axis BOA ( B is the boreal axis-pole, A the austral), and the meridian echo curve for a radio station Q(P, 0 P,VQ 0) in geomagnetic colatitude a. The “real” parts of the curve are drawn more heavily than the part (PNQ Ps) below the horizon of Q. The curve approaches the asymptote on the far right and left.

In this diagram a is 450. After Chapman [1952a]; courtesy Pergamon Press.

For a fixed elevation of the radar beam, there is a definite relation between the range and azimuth of allowed echos. Observed echoes do not seem to emanate precisely from the regions predicted by the Chapman dipole theory (Kaiser [1957a]), but Unwin [1958a] has shown that the local field at the ground gives much better agreement between the observed and predicted regions. On the other hand, Forsyth [1960u] has suggested that the range-azimuth dependence may be due mainly to the variation of the volume of radio-aurora, within a fixed increment in range, as seen by the radar in different directions. Thus the aspect sensitivity as observed along the magnetic meridian may be distinct from the variation of the range of echoes with azimuth, although with the Chapman model the two phenomena have the same basic explanation.


An explanation of the departures from strict specularity depends on the mechanism for producing the echo. Kaiser [1956a] and Forsyth and Vogan [1957a] think of the reflecting clouds as being approximately ellipsoidal (rather than cylindrical), elongated along the magnetic field.

FIG. 6.4. Each full curve refers to a radio station in the geomagnetic colatitude a marked thereon, and gives the height h (km) of the echo point for a radio beam from Qto the reflecting aurora, at beam elevation e. By interpolation between these curves h can be inferred for a beam of elevation e from a station in any intermediate colatitude. The broken curves (- -) similarly show (if necessary, by interpolation) the geomagnetic colatitude 6 of the echo point P at a chosen height h for a beam of elevation e , or alternatively for an echo point P corresponding to a beam of elevation e from a radio station in geomagnetic colatitude a. The chain curves (---) similarly give the distance of the echo point P from Q. After Chapman

[ 1952~1; courtesy Pergamon Press.

Some of the wave would be reflected specularly from the surface of such a cloud for any incident direction, but the specularly reflected intensity is greatest for incidence normal to the long axis. The observed degree of aspect sensitivity would require a ratio of length to diameter of the order of 4 or 5.

There is still some question as to whether absorption of radio waves


in the D region has an important effect on the reflected intensity and specifically on the aspect sensitivity. Currie, Forsyth, and Vawter [1953a] first made the proposal that a highIy absorbing region lay directly below the radio-aurora. For observations at long range, the radar wave passed through the D region sufficiently far from the absorbing locale that reflections could be observed. For a radio-aurora close to the observer, requiring high angles of radar elevation, the signal was seriously attenuated. Aspect sensitivity is probably a result of the orientations of the reflecting centers, but absorption may nevertheless play a small role, especially at the lower frequencies.

Departures from cylindrical specularity may also result from scattering by small-scale inhomogeneities in the ionization, even if their shape is cylindrical. The angular dependence of the scattering depends on the size and orientation of these irregularities (Section 6.2.3).

It should perhaps be emphasized, in concluding the discussion of geometry and before approaching the reflection mechanisms, that the radio reflections we are concerned with are genuine auroral echoes. This rather essential question was in doubt for a time when Harang and Landmark [ 19544 interpreted their observations as (backscatter) echoes from the rough surface of the Earth, mirrored in the auroral E region both on the outward and return path. Such an effect is known at lower frequencies. But subsequent analyses and criticisms13 have shown this process is actually unimportant for the VHF and UHF auroral signals.

6.2.2. Critical and Partial Reflections from a Large Surface14

Critical reflection, the mechanism responsible for returning radio waves in the high-frequency range from the ionosphere, was thought by Lovell, Clegg, and Ellyett [1947a] also to be the source of the echoes found in their pioneering radar study. The basic idea, developed in Section 3.3.2, is that the index of refraction at a given wave frequency v depends on the electron density Ne. For normal incidence, reflection occurs when the index is zero or when the plasma frequency w,, is

l9 For example, McNamara and Currie [1954a], Booker, Gartlein, and Nichols [1955a], Meos and Olving [1958a].

l4 Actually, a discontinuity in the ionization is not necessary for the mechanisms discussed here, but it is convenient to speak of the reflection as occurring from a surface nevertheless. The important points are that small-scale irregularities in the electron density are neglected, and that the “surface” dimensions must be large compared with the wavelength. Otherwise diffraction effects, which are treated in Section 6.2.3, become important.


equal to 2 ~ v . Since w, depends on N e , we obtained Eq. (3.56) giving the electron density for critical reflection:

where v is in Mc/sec. Critical reflections at 400 Mc/sec would require N e = 2 x lo9 ~ m - ~ .

If critical reflection does produce auroral echoes these densities would not occupy large volumes. The radio-aurora as a whole has a low reflect- ivity, which could mean that very large areas (comparable to the area covered by the radio beam) reflect with low efficiency or that relatively small areas reflect very efficiently. In either case the radio-aurora is mostly transparent and returns only a small fraction of the incident intensity.

If the electron density at the surface is not sufficient for total or critical reflection, the wave is still partially reflected. The situation is quite analogous to optical reflection at a glass-air interface or a water-air surface. The only important difference is that in the present problem the index of refraction at the reflecting surface may drop to zero, allowing total reflection even for normal incidence. In the water-to-air optical experiment, total reflection is possible only for oblique incidence.

The laws of electromagnetic reflection and refraction are derived from the condition that the tangential components of E and H must be continuous across the boundary. Let E, be the amplitude of the incident plane wave, as defined by Eq. (3.50). Similarly, EA and E,” are the amplitudes of the refracted and reflected waves, respectively. For the particular case of normal incidence the boundary condition on E gives

and the one on H gives15

Here n, is the refractive index in the medium containing the incident and reflected wave, n2 that in the medium carrying the refracted wave.

l5 In general, H = n k x E, where k is a unit vector in the direction of propagation and n is the index of refraction of the medium. This condition follows from the fact that bothE and H have plane-wave solutions and are related by Faraday’s law, Eq. (3.39). For a general derivation for any angle of incidence, see Panofsky and Phillips [1955a, p. 1761.


For normal incidence the fraction of the intensity that is reflected-the reflection coeficient- is (see Problem 6.1)

When n2 = 0, the boundary is totally reflecting. For negligible collisions we have the relation from Section 3.3.2, n = ( I - Let us take n, = 1 corresponding to very low Ne, and 1 - nz << 1 (but not quite zero) corresponding to density N,, as determined by Eq. (3.54) giving w,, in terms of Ne. The reflection coefficient from a sharp surface is then

- 4 x 10-10N: - e4 N,“ R = 16d m2 v4 v4 ,

where the numerical value is for v in Mc/sec and Ne in electron/cm3. (Herlofson’s [1947a] equation contains an error of a factor of 4.) As illustration, for Ne = 5 x lo6 ~ m - ~ and v = 100 Mc/sec, we obtain R = and R decreases rapidly toward higher frequency.

Let us now consider the additional reduction in R for a boundary that is not sharp, but diffuse. So long as there are no irregularities in the electron density in a plane perpendicular to the direction of wave propagation, the wave equation (3.44) is valid. Writing E = El(z) exp (- i d ) , we obtain for the amplitude equation, when there is no absorption,

a2 E , a22 + ($ - 4TmN:2e2 ) El = 0.

By employing a Green’s function, we may write El as an integral equation (Morse and Feshbach [1953a, p. 10711):

The first term on the right represents the plane wave incident from z = - 00. In the limit of z + - Eq. (6.8) gives both the incident and reflected wave. When the reflecting region perturbs the incident wave only slightly, the amplitude El(z,) is approximately E, exp (iwz,/c).


This is the Born approximation often used in scattering problems in quantum mechanics. The reflection coefficient is then

which is valid when Ne is well below the value for critical reflection.16 Unless the boundary is much sharper than a wavelength, interference

between waves reflected at different distances into the boundary drastically reduces the reflected amplitude (Herlofson [ 19474 ; see Problem 6.2). For “surfaces” more diffuse than a few tenths of a meter the reflection is seriously diminished. With this mechanism any one reflecting center might have a very short lifetime because of rapid outward diffusion. And if the incident ionizing particles are not in a sharply focused beam, it appears that partial reflection is extremely inefficient.

6.2.3. Scattering by Small-Scale Inhomogeneities in the Ionization

If the auroral ionization is characterized by irregularities of the order of the radio wavelength or smaller, reflection occurs in a manner somewhat different from that from a large surface. The basic mechanism of reflection is always the same, of course: An incident plane wave sets electrons in motion and their oscillation in turn reradiates the electromagnetic wave. If the medium is perfectly uniform, interference destroys the scattered amplitude in all directions but directly forward. When there is an abrupt change in the index of refraction, n, in the direction of propagation, a portion (determined by the boundary conditions, as shown in the previous section) is reflected and the remainder transmitted. For a more gradual change in n, interference between the reflected amplitudes from varying depths into the “surface” reduces the reflected component.

Now we wish to consider the wave that is reradiated by a single small volume of ionization, Again, interference between amplitudes reflected from different parts of the small volume will determine the net amount of radiation that is scattered in all directions. Scattering by a multitude of irregularities (as distinct from reflection by a surface) has an analogy in the optical region in the scattering by water droplets in a fog or in Rayleigh scattering by molecules.

lo If Y is near the critical frequency for the maximum N , in the reflecting volume, the Born approximation is not valid. One may then use, however, the so-called W.K.B. method, provided that N , changes gradually compared with the wavelength. This problem has practical importance in partial reflection by relatively thin ionospheric layers, such as sporadic E (see Mitra [1952a, p. 2181).


Scattering by small-scale irregularities in the radio-aurora was considered by Forsyth [1953a] on the basis of a scattering theory, developed for another purpose, by Booker and Gordon [1950a]. Later Booker [1956a] extended the theory and applied it specifically to auroral scattering.

Booker considers the irregularities to be aligned along the magnetic field and to be cylindrical in shape. The departures from perpendicular reflection from lines of force are then explained in terms of the scattering phase function of these cylinders. I t is clear that if this is the geometry, the cylinders cannot be much larger than a few wavelengths, or else they would appear as large surfaces and reflections would be strictly specular. Booker thus uses the observed degree of aspect sensitivity to derive a mean size for the reflecting volumes. But the basic assumption of cylindrical structures may be incorrect.

We shall present here a simplified version of scattering by irregularities in the refractive index. The Booker theory takes the electron density to vary according to an assumed (Gaussian) autocorrelation functi0n.l’ That is, statistically over a large volume, the density in the irregularities decreases away from the peaks (and increases from the valleys) in a specified manner, merging smoothly into the background electron density. The scale size of the fluctuations is determined by the observed aspect sensitivity. But here we shall consider small, homogeneous cylinders with sharp boundaries distributed randomly through the medium. We shall investigate the scattering from a single cylinder, assuming (with Booker) that there is no correlation between the location of neighboring cylinders and that therefore only random interference effects between their waves occur, so that the total intensity is the sum of the individual intensities.18 Thus we shall consider the problem to be one involving Mie scattering by small dielectric particles.

Before discussing the reflection from a small cylinder, we shall have to review Thomson scattering, which applies to oscillating free electrons. The mean rate of energy scattered in all directions may be obtained by averaging Eq. (1.13) over a cycle, with the electron displacement obtained

Ratcliffe [ 1956~1 has reviewed the methods of autocorrelation functions and Fourier transforms, with particular application to diffraction phenomena in the ionosphere.

This statement may be readily proved for randomly distributed scatterers if one bears in mind that intensity is proportional to the time average of the square of the sum of the electric vectors. If, however, the volume elements reflecting an incident wave are in random motion, the superimposed reflected waves have different wavelengths, owing to the Doppler shifts. The net interference then varies along the wave train and an observer, recording the integrated spectrum, sees fading (Section 6.1.5). In this discussion we consider monochromatic waves and treat the scattering from individual volumes as being entirely independent of one another.


from Eq. (3.46) for vc = 0. The incident intensity Zo is related to the amplitude E, by Z, = E: cjSn. Since radiation is scattered in a direction perpendicular to the direction of oscillation, one may show (Problem 6.3) that with incident unpolarized radiation the intensity for Thomson scattering from a volume V is

V(1 + cos2 0) Ne e4 ITh(0) = 2 r 2 (6.10)

where r is the distance from the electron and 0 the angle of scattering (between the incident and emergent rays). This formula assumes that each electron scatters intensity independently of all the others in the volume and is strictly appropriate only if the electrons are separated by at least several wavelengths.

The actual scattering by a small cylinder containing free electrons may be computed by supposing that each electron gives Thomson scattering independently of the other electrons, and then adding wave amplitudes instead of intensities. This procedure is appropriate as long as the electron density is not high enough to make a large change in the index of refraction. That is, we assume that 1 1 - n I << 1, and for the moment we consider the cylinder to be immersed in vacuum.

Specifically, the scattered wave is obtained by adding the fields at a distant point from all the component waves scattered by electrons throughout the cylinder, with due regard for the interference between waves with different phases. Thus the scattered intensity is

(6.1 1)

where the interference factor, which depends on the geometry, is

9 = - &sdV (6.12)

for a homogeneous volume, and 6 is the phase lag, referred to some fixed origin.

Van de Hulst [1957a, p. 93 et seq.] has obtained a general solution for cylinders with arbitrary orientation. For a cylinder of length Z and diameter d, and backward scattering (0 = n), the interference factor is

V l J

(6.13)

where and Jl12 are Bessel functions, x = (2nd/h) cos i,h, y = (2nZ/h) x sin $, and i,h is the complement of the angle between the direction of incidence and the axis of the cylinder.

6.2. THEORY OF AURORAL REFLECTIONS 24 1

We shall be interested in cylinders aligned along the magnetic field and with d < 1 (thin rods). Reflection is observed to occur mainly for t,b - 0, so that we take both x and y < 1. Expanding the Bessel functions in power series, we obtain

for the intensity scattered from a single cylinder. If cylinders of density N e + d N e are imbedded in a background

medium with density N e , then in Eq. (6.14) NE is replaced with (AN,)’. This expression is equivalent to the scattering coefficient derived from the autocorrelation theory by Booker [ 1956~1. ’~

The angle + enters the formula only with the factor 1. Cylinder lengths 1 - 20 meters would give a good representation of the observed aspect sensitivity. The expansion of Eq. (6.14) assumed that h > 27rd; if this is not true the factor J1 in Eq. (6.13) would predict serious attenuation of the reflected intensity. Reflections detected in the 300-Mc/sec range thus suggest that d < 10 cm. From measurements of reflected intensity, Booker estimates that the root-mean-square fluctuations are [(dNe)2]1’2 - 500 ~ m - ~ , to be compared with Ne N los ~ m - ~ .

The scale size of the irregularities is thus much smaller than the scale of observed structure in visual aurora; and it is much smaller than one would anticipate for ionization produced by even a sharp beam of monoenergetic, spiralling electrons. Booker [ 1956a, b, 1958~1 has suggested, therefore, that the irregularities are -associated with ionospheric turbulence, which might create fluctuations in N e of the required scale size.

Too much emphasis should not be placed on the precise values of AN, and the scale sizes derived from the theory. The length factor supposes that aspect sensitivity is governed entirely by the interference phenomenon with a geometry that is cylindrically symmetrical. Actually

la A comparison of the formulae requires some algebraic manipulation. The equivalence of the two formulae requires one to replace in Booker’s Eq. (27) the transverse scale factor T with d/d8 and the longitudinal scale factor L with l/dg. Also replace his plasma wavelength, AN, with 2ac/wo, where wo is given by Eq. (3.54), and expand his exponential functions to the same order as we have the Bessel functions above. Finally, note that his scattering coefficient gives the scattered energy per unit solid angle, per second, per unit volume, per unit incident intensity and must be multiplied by lo V/rz to give the scattered intensity. With these changes, Booker’s formula differs from Eq. (6.14) by a factor of ( ~ r / 3 ) l ’ ~ . Before making comparisons with the observations, Booker integrates the scattering coefficient over the reflecting volume.


small departures from the simplified geometry could play a large role in this respect. And the derived fluctuations in Ne depend in turn on the volume of the cylinders. Further, if turbulence is in fact important, there is a correlation between neighboring cylinders, so that interference is even more destructive and the required AN, is higher.

6.2.4. Comparison of Reflection Mechanisms

Neither reflection by a surface with dimensions large compared with h nor scattering by small-scale structures seems entirely satisfactory. The difficulties associated with each have been discussed in the preceding sections and will be summarized here; they become worse toward higher frequencies.

Either mechanism might explain the aspect sensitivity: surface reflection, by the (ellipsoidal) shape of the surface; scattering, by the angular dependence of scattered intensity for a needle-shaped scattering volume.

Either process might also explain a decreasing reflected intensity toward higher frequencies, v. If reflection is from a surface, the question still exists as to whether critical or partial reflection is the mechanism. Partial reflection as given by Eq. (6.6) provides a rapidly decreasing intensity with v. If diffuseness of the surface is considered, the higher frequencies are reflected even more poorly. Critical reflections, on the other hand, require very high concentrations of ionization for the higher frequencies. The frequency dependence of reflection in this case would evidently arise from the probability of occurrence of reflecting centers with different electron densities. For the scattering mechanism, the higher frequencies are diminished by an interference effect. The observed intensity is then governed by the distribution function of diameters of the scattering cylinders.

For surface reflection one might suppose that each scattering center has a short lifetime. The fading might be ascribed to diffusion of ionization or, more probably, to apparent motions of the reflecting centers caused by a motion relative to the Earth of the point of particle bombardment. With scattering, the inhomogeneities have been attributed to turbulence, but the turbulent motions are not thought to be fast enough to account for the fading. It is also not very clear why the scattered intensity should be correlated with visual aurora, since only small fluctuations in the background electron density are sufficient to scatter, provided that their scale size is small enough.

Collins and Forsyth [1959a] have attempted to ascertain the reflection mechanism in their bistatic investigations, by examing the aspect


sensitivity and frequency dependence for the different types of radio- aurora. They conclude that A, and A, events arise from critical or near-critical reflection, whereas A , events arise from scattering by small volumes. However, the lack of aspect sensitivity found for A , events implies that the scattering volumes have roughly the same dimensions in all directions, and are not needle-shaped as discussed in Booker’s paper.

PROBLEMS

1. Starting with the boundary conditions on the tangential components of E and H, fill in the details of the derivation of Eq. (6.5) for the reflection coefficient of a plane wave that is normally incident on a large flat surface. Show that when Ne is well below the value for critical reflection, R is given by Eq. (6.6).

2. Suppose the electron density across a diffuse “surface” has a gradient diyejdz = (Ne,/a dr7 exp ( -z2/a2), where a is a constant and Ne, is the electron density far into the surface and is well below the value for critical reflection. Show that the reflection coefficient is reduced from the value for a sharp surface by a factor exp (- 8.rr2 a2/h2), where h is the wavelength in vacuum. Note that if the gradient is proportional to the Dirac &function, Eq. (6.9) reduces to Eq. (6.6).

3. Derive Eq. (6.10) for Thomson scattering.

Chapter 7. Physical Processes in the Auroral Atmosphere

The aurora results from energy being supplied to the upper atmosphere by a mechanism that is inoperative, or at least unimportant, during “normal” conditions. (A working definition of aurora is given in Section 6.1.1.) In this chapter we shall examine several possible means of depositing this energy and various ways in which it may be converted to electro-magnetic radiation. We shall also be concerned with, how these physical processes affect the general properties of the upper atmosphere.

7.1. Proton Bombardment]

Penetration of protons into the atmosphere during aurora is definitely established by the hydrogen emissions, discussed in Sections 4.3.2, 5.1.3, and especially Section 5.2.3. The H intensities vary by large amounts compared with other emissions and it seems clear that proton bombardment is not the only mechanism important as an auroral energy source. Indeed, we shall see later that protons seldom, if ever, supply the major portion of auroral energy, but instead seem to be merely an incidental phenomenon sometimes accompanying a display.

The theory is divided into two areas. On the one hand, we are concerned with the problem of H excitation and emission as a result of protons penetrating the atmosphere. The only observational data we need utilize are those on the H lines themselves. From this discussion we would hope to learn something of the proton flux, the initial energies of the particles, and the distribution of their orbits about the magnetic lines of force (Section 7.1.3). On the other hand, from the intensity in the Balmer lines we may estimate the energy deposited or ionization produced by protons and see how this energy or ionization rate compares

Helium and possibly heavier ions may also be contributors to the auroral bombardment. Helium lines have been suspected in the auroral spectrum (Section 5.1 .3) and some laboratory work (Section 7.1.2) has attempted to differentiate the effects of hydrogen and helium bombardment. But hydrogen ions are the only heavy particles that have been firmly established as auroral primaries and are the only ones that have received serious theoretical attention. The difficulties involved in predicting the emission from incoming particles other than hydrogen have been summarized by Bates [1956b].

244

7.1. PROTON BOMBARDMENT 245

with the total required to produce aurora (Section 7.1.2). Before proceeding with either program, we develop the basic theory for H-line emission.

7.1.1. Statistical Equilibrium for Hydrogen

Collisional Processes.-As a proton penetrates into the atmosphere it experiences successively a number of different types of collisions (see Section 1.5.2). For a fast particle the first collisions will be mainly those ionizing atmospheric atoms and molecules:

H+ + X + H + + X+* + e.

These collisions serve to slow down the proton and may leave X+ in an excited state (X+*).

When the proton is slowed to about 100 kev, charge-transfer collisions become important:

H+ -1 X -+ H* + X+*. ( 7 4

Neutral hydrogen atoms are thereby formed and in turn have collisions that excite or ionize H or the target atom or both:

(7.1)

( H * + X * H* + X+* + e H+ + X* + e (7.3)

[ H+ + x+* + 2e.

If the H atom is ionized by (7.3), it then suffers another collision of the type (7.1) or (7.2); the cycle between H and H + may be repeated several hundred times before the atom eventually comes to rest.

Equations of Statistical Equilibrium.-The excitation of hydrogen emissions may be calculated by the equations of statistical equilibrium (Chamberlain [ 195463). We may safely neglect captures of free electrons and take reactions (7.2) and (7.3) as being the only ones of importance.

An enormous simplification results if all the H atoms entering on the left of reaction (7.3) are in the ground configuration. Actually this is only approximately true, An electron will normally have time to cascade to ground between successive collisions except when it stops in the 2s configuration; here we shall ignore the metastability of 2s. Also, we do not distinguish between the various fine-structure levels (given by quantum number 1) within a given orbital (quantum number n). HOW- ever, this refinement would affect only the cascading terms in the theory,

246 7. PHYSICAL PROCESSES IN THE AURORAL ATMOSPHERE

which in turn contribute only 10 percent or so to the Ha intensity. The data used in the calculations scarcely justify attempts to perfect the theory to that extent.

Take the number density of atmospheric atoms (counting a diatomic molecule as two atoms) to be Na; the density of H in the nth orbital to be Nn; and the proton density, N p . The cross sections will always refer to collisions with an atom, and we take the cross section of a molecule to be twice that of an atom. For reaction (7.2) with capture into orbital n, the cross section is QKn. Similarly for excitation by the first two reactions in (7 .3) , the cross section is Qln; for ionization by the last pair in (7.3), it is QIK. The protons and H atoms are traveling with velocity v .

The equation of statistical equilibrium states the condition that the rate at which atoms enter the nth orbital by all processes equals the rate at which they leave:

The terms on the left give, respectively, capture, cascading from higher levels, and inelastic collisions; the right side gives the downward cascading.

T o this equation we add the condition of ionization equilibrium,

For the moment consider all the protons to be incident normally on the top of the atmosphere with a flux 9. At any depth the proton and hydrogen densities are related to the flux by 9- = (Nl + Np) v. With this relation and Eqs. (7.4) and (7.5), we may solve for N, as a function of 9, eliminating Nl and N p . I t is necessary to know only the velocity z,

to calculate the emission rate per cm3, Nn A,,,, in any H line. The solution would be quite simple were there no cascading term

on the left of Eq. (7.4). In that case we would have for Fnn,, the emission rate per unit volume,

m


Cascading may be considered by an iteration process of substituting Eq. (7.6) for Nnt lAnl rn under the summation in Eq. (7.4) and repeating the solution. The iteration may readily be carried further, but one such substitution is sufficient for our purposes. The solution is given in the original paper (Chamberlain [19543]) and need not be written here.

I t is convenient to carry out the calculations first of all for a homogeneous atmosphere with a density NB the same as that at sea level. For these calculations the emission depends only on the velocity or the residual range, r , of the fast particle. The most convenient independent variable in calculations of this sort is the residual range. It may be transformed to velocity or energy with experimental range measurements, listed in Table 7.1. The calculations may be referred to any height in the atmosphere for vertical penetration with the relation of equivalent depth versus height shown in Appendix IV, if the initial velocity or range of the protons outside the atmosphere is known.

TABLE 7.1

EQUIVALENT VALUES OF ENERGY, VELOCITY, AND RESIDUAL RANGE FOR PROTONS IN AIR

log E E W r (kev) (kev) (lo8 cmisec) (atm-cm)

- 0.25 0.00 0.25 0.50 0.75 1 .oo 1.25 1.50 1 . 7 5 2.00 2.50

0.56 1 .oo 1 . 7 8 3.16 5.62

10.0 1 7 . 8 31.6 56.2

100. 316.

0.33 0.44 0.58 0 .78 1.03 1 . 3 8 1.84 2.45 3.27 4.36 7.76

0.002' 0.0035' 0.0055' 0.0080' 0.014' 0.022 0.033 0.051 0.076 0.121 0.35

* Extrapolated values. Measurements are from Cook, Jones and Jorgensen [1953a], Reynolds, Dunbar, Wenzel, and Whaling [1953a], and Jesse and Sadauskis [195Oa].

Cross Sections.-For the ionization (loss) cross section, Q I K , I have used the experimental data of Stier and Barnett [1956a] and Barnett and Reynolds [1958a] for hydrogen atoms in N, and 0,. These data are in good agreement with Kanner's [1951a] measurements for H in air over the energy range common to both. Theoretical calculations by Bates and Griffing [19533, 1955~1 for H passing through H have been

248 7. PHYSICAL PROCESSES IN T H E AURORAL ATMOSPHERE

used as an aid in extrapolating the experimental data over the range from 1 to 10 kev. The fair agreement of these calculations with the experimental results for H in H, obtained by Barnett et al. and Ribe [1951a] suggests that, for purposes of the ionization cross section, it is reasonably accurate to consider a diatomic molecule as equivalent to two free atoms.

Experimental excitation cross sections, Qln, are not available, and the theoretical work of Bates and Griffing [19536, 1955al applies to H bombarding H. Judging from the measurements of Stier and Barnett [1956a] that the ionization cross section, Q I K , is about 3 times greater for H passing through air than for H through H, over most of the applicable energy range, we apply this same factor to the computed values to use them in the auroral problem.

Cross sections for capture (recombination) into the nth orbit, Q K n ,

have been computed by Bates and Dalgarno [19533] with the Born approximation for n 2 4 for protons passing through H. Measurements have been made of the total capture cross section,2 ZQKn, for protons in H, H,, N, and 0,. For energies exceeding about 25 kev the calculations adequately reproduce the experimental results for hydrogen, but the cross sections in air are slightly larger. Therefore, the theoretical results have been multiplied by varying factors between 1 and 3, depending on the energy, to bring .ZQKlp into accord with experiment.

The situation at very low energies is slightly more complicated because of the possibility that the near equality of the ionization potentials of H and of 0 may allow very large cross sections, as is the case for protons in H. Hence two cases have been treated: in case (a)any resonance collisions were neglected, and two 0 atoms were considered as the equivalent of an 0, molecule. At low energies the cross section QK1,

which is the predominant term in the total capture cross section, was taken from the experimental data, where oxygen and nitrogen are assumed to be twice as effective as hydrogen gas. In case (b) the same excitation and ionization cross sections were used as in case (a), but for capture into the ground configuration the cross section QK1, below 25 kev was taken from the perturbed-stationary-state calculations of Dalgarno and Yadav [1953a] for protons in atomic hydrogen.

Actually there is little difference in the results for cases (a) and (b) and it is much more convenient to use those for case (a), which do not depend on the composition of air. Hence the results quoted below are strictly for case (a) only.

See Kanner [1951a], Stier and Barnett [1956a], Barnett and Reynolds [1958a], Stedeford and Hasted [1955a], Fite, Brackmann, and Snow [1958a].

7.1, PROTON BOMBARDMENT 249

Dalgarno and Griffing [1955u] have made a theoretical study of the processes contributing to the slowing down of protons in passing through H. At energies below 30 kev resonance captures become significant. Measurements for protons in 0 are not available and proton velocities have been computed from range-energy measurements for protons in air (Cook, Jones, and Jorgensen [ 1953~1, Reynolds, Dunbar, Wenzel, and Whaling [ 1953~1, Jesse and Sadauskis [ 1950~1; see Table 7.1). If resonance collisions with 0 are important, the protons will be slowed more efficiently over the final 0.05 atm-cm of their paths.

Numerical Results.-After the publication of the original paper (Chamberlain [19546]), improved values of the cross sections as discussed above became available. Hence the calculations given here are slightly different from the data employed in that paper. Also, the model atmosphere in Appendix IV is probably more appropriate than the one used earlier, for the construction of brightness-height curves. Figure 7.1

Residual Range r (Atm - cm)

FIG. 7.1. Photon emission in H a , H/3, and Ly a: and ion pairs produced per incident proton per atm-cm path length. The Ha and L y a curves have been

multiplied by factors to make all three H curves have the same total area.


shows the emission rates for Ha, HB, and Ly a computed with allowance for cascading. The figure also contains the Bragg curve (Landolt- Bornstein [1952a]), which gives the rate of ionization produced by protons in air.

A fast incident proton has a total Ha emission, G ( H a I E,, +a),

(corresponding to the total area under the Ha curve in Fig. 7.1) of about 60 quanta. If the proton is incident with low velocity, the emission is correspondingly reduced. A fast proton gives an HB emission of 16 quanta and a Ly a emission of 460 quanta. For measurements in rayleighs, the Balmer decrement is G(Ha j E,, -a)/G(HB I E,, +a) = 3.7. If the decrement is measured in energy, rather than in photons, it is slightly less. It can be seen from Fig. 7.1 that low-velocity protons give a decrement somewhat larger than for faster particles. T h e Hy and higher- member intensities are not given here, as the required excitation cross sections have to be extrapolated and are therefore rather uncertain.

7.1.2. The Role of Protons in Producing Aurora

The N$/H Intensity Ratio.-It is of some importance that the ionization curve has quite a different shape from that for Balmer emission. As the initial proton energy is increased beyond 100 kev or so, the total H-line intensity changes very little, whereas the ionization produced, and hence the emissions resulting from this ionization, continue to increase. Therefore, an aurora produced by protons will have an intensity ratio of A3914 N$/H@, for example, that depends on the initial velocity or auroral height.

Figure 7.2 gives the ratio of the integrated ionization production to the Balmer emission as a function of the initial range, r,,, of the protons; i.e.,

where q is the rate of ionization production (ion-pair/cm3 sec). These values have been computed by numerical integration of the curves of Fig. 7.1. A similar curve extending to larger values of ro has been given by Omholt [1959a].

To use the data in Fig. 7.2 for estimates of the intensity ratios for a proton aurora, it is necessary to know what fraction of the ionizations lead to a photon of, say, h3914. This information is available for electron excitation. Massey and Burhop [1952a, p. 2651 tabulate the total cross

7.1. PROTON BOMBARDMENT 25 1

section for ionization of N, as a function of electron energy and Stewart [1956a, b] has measured the cross section for an ionization of N, into the B ZZ, o = 0 level of Ni-. The ratio of these two cross sections is nearly independent of electron energy over the region measured by Stewart, 20-200 ev. About 2 percent of the N, ionizations produce photons of h3914.

2.:

h L

0

N

uc 2.c P b0 \

0

0

P CS" v

m -0 I .5

I .( 0 0. I 0.2 0.3 0.4

Initial Ranqe ra (Atm-em)

FIG. 7.2. Ratio of the total number of ion pairs to the total number of H j photons (upper curve) produced by a proton with an initial residual range 7,. For Ha the shape of the curve is quite similar and the ratio is reduced by a factor of about 3.7

at the higher initial energies.

This ratio is not strictly correct for proton excitation at low energies, where charge transfer may produce much of the N,+ ionization, as advocated, for instance, by Shklovskii [ 195 1 c]. At the higher energies, where ionization produces a free electron, the situation is probably similar to the case of electron impact at the same velocities, especially since in both cases much of the ionization is produced by secondary


electrons. But at energies of only a few kev, Carleton and Lawrence [ 1958~1 found that the fraction of charge-transfer collisions yielding a A3914 photon is larger than the 2 percent found with electrons. A good estimate of the total yield of A3914 at low energies cannot yet be made, because the fractional cross section has not been measured over the entire energy range (it is quite sensitive to the proton energy), and the relative importance of A391 4 emission produced by reactions (7.3) and by secondary electrons formed by (7.3) is not well understood. For the present we shall therefore use a yield of 0.02 photon/ionization at all proton energies, bearing in mind that this value is appropriate for secondary electrons but not necessarily for primaries.

To compute the intensity ratio in the aurora, we must correct for the fraction of the ionization that is formed from constituents other than N,. For this purpose we take the ionization cross section per atom to be the same for all constituents and adopt the abundance ratios from Appen- dix IV. The results are listed in Table 7.2 as a function of initial range and energy of the protons and of their maximum depth of penetration (Appendix IV). The quoted abundance ratio of atoms, 2 N ( N J / N a ,

applies to the tabulated height. Actually the ionization and excitation are distributed over all altitudes above this height, where the abundance ratio is less. For the ratio .@(A4709)/9(Hfi), where A4709 is the 0-2 band of N;, the values in Table 7.2 should be multiplied by the ratio of transition probabilities Ao-,/A0-, = 0.057, according to Jarmain, Fraser, and Nicholls [1953a].

TABLE 7.2

THEORETICAL INTENSITY RATIOS OF A3914 AND HP FOR AN AURORA PRODUCED BY MONOENERGETIC PROTONS

Abundance Initial Initial Lowest height ratio Ion-pairs/HP Photon ratio

range T" proton of penetration 2N(N2)/Na photons Y(h3914)/ (atm-cm) energy c0 (kev) (km) (upper limit) (Fig. 7.2) 9(HP)

0.15 130 100 0.71 225 3.2 0.044 27 110 0.69 84 1 . 2 0.019 8 . 5 120 0.65 61 0 . 9

According to the observations reported in Section 5.2.3 and Table 5.5, an ordinary aurora invariably has an intensity rati09(A3914)/9(Hfi) > 10 and often much larger. Therefore, it is quite unlikely that any ordinary


aurora is produced mainly by proton bombardment3 (Omholt [ 1957c, 1959al). I t is true that the contribution to the excitation of A3914 from charge transfer may increase the ratios in the last column of Table 7.2. But direct ionization by neutral H and secondary electrons should always be important also, and it seems improbable that the ratios could be increased enough to satisfy observations.

Some of the observational work indicates that the H lines are relatively stronger in high-altitude aurorae, as suggested by the trend in Table 7.2. But an aurora due predominantly to protons should have HP of the same order of intensity as h3914, or even much stronger at high altitudes. The only aurorae for which photometric data support proton impact as the principal energy source are those rare cases in which H lines are abnormally strong, such as Montalbetti’s [1959a] H/3 aurora. The ratio of N,t/H as a function of height in a particular aurora depends on the angular dispersion and energy spectrum, and is discussed in Section 7.1.3.

The Proton Flux.-It is also illuminating to compare the total energy deposited in an aurora, as derived from the observations, with the energy carried by the incident protons. An aurora of IBCI I I has an emission rate in A3914 of about 100 kR, corresponding to a total rate of ionization of about 7 x lo1, ion-pair/cm2 sec, with the N, relative abundance at 110 km. A primary proton or electron loses on the average about 35 ev for every ion pair produced in air (Valentine and Curran [1958a], Lowry and Miller [1958a]). Thus the total energy deposited in a bright aurora is 2.5 x IOl4 ev/cm2 sec = 400 erg/cm2 sec. I t might be noted in passing that this figure is an order of magnitude greater than the energy of known or suspected optical emissions in Table 5.5, although the ultraviolet intensities in that table may be grossly underestimated.

T o derive the actual proton flux and energy from H-line intensities, one needs to know first the relative energy spectrum of the protons. But for first-order estimates, let us take all the protons with a constant initial energy. Table 7.3 gives some proton fluxes and total energy corresponding to zenith emission rates in Ha of 10 kR, about the maximum ever observed. Over a fairly wide range of particle energies, the total proton energy flux is around IOl3 ev/cm2 sec, an order of magnitude below the total required to explain the auroral ionization. (The

Vegard [1921a, 1939~1 first noted that with any appreciable spiralling protons could not be responsible for ray structures. At auroral velocities the radius of gyration from Eq. (3.18) is larger than the diameters of many rays, which are perhaps as sharp as 100 meters. Bates [1955c] has strengthened the argument by noting that the time-averaged charge on the particle is less than e, since part of the time the proton carries a captured electron with it.

254 7. PHYSICAL PROCESSES I N THE AURORAL ATMOSPHERE

proton flux is related to the H a intensity for the case of an energy dispersion of the incident protons in Section 7. I .3.)

TABLE 7.3

FLUX OF MONOENERGETIC PROTONS REQUIRED TO PRODUCE 10 kR OF Ha IN THE ZENITH

Minimum Initial Initial height of G(Hm 1 9) Proton Total incident

energy E~ range yo penetration (Ha quanta/ flux energy flux (kev) (atm-cm) tkm) proton) (cm-'%ec-l) (ev/cm%ec)

130 0 . 1 5 100 60 1 . 6 x los 2.1 x 1Ol9

8.5 0.019 1 20 7 14 x lo8 1 . 2 x lo1* 21 0.044 110 20 s x 108 1 . 4 x 1013

Laboratory Experiments with Proton Bombardment.-A number of laboratory experimental programs have been designed to simulate auroral processes induced by proton b~mbard rnen t .~ This work has given valuable information on some pertinent cross sections, but sometimes conclusions have been drawn too hastily in comparing auroral spectra with those from the laboratory. The experiments inevitably fail to reproduce auroral conditions entirely. If the gas density is low enough to approximate the auroral atmosphere, the incident particles are not slowed significantly over the length of the apparatus and the results apply only for a narrow energy range, whereas the auroral spectrum is an integrated result of stopping the particles. Also, if the mean free path is too long the effects of secondary electrons may be obscured, or one may measure excitation produced directly by protons without having enough neutral H atoms in the beam to see the effects of their collisions.

On the other hand, if the density is too high, collisional deactivation (or ionization of an H atom from an excited level) may become much more serious than in the aurora. These collisions probably explain why the Balmer lines were weaker in the experiments of Fan and Meinel [1953a] than those we computed in Table 7.2.

' Experiments with protons and helium ions were performed at Yerkes Observatory by Meinel and Fan [1952a], Fan and Meinel [1953a], and Fan [1954a, 1955a, 1956a, b] and are summarized in the last-mentioned paper. Other experiments on the spectra induced by fast ions have been reported by Branscomb, Shalek, and Bonner [1954a], Dieterich [1956a], Nicholls and Pleiter [1956a], Carleton [1957a], and Carleton and Lawrence [1958a]. Some of this work has compared ion impact with excitation produced by electron beams.


I t is usually impossible to state with certainty that a particular auroral feature is due to a specific kind of primary particle-electrons, protons, or helium ions-since the excitation produced may be quite sensitive to the velocity of the primary. Experiments of this nature must necessarily be carried out over wide ranges of energy and care is necessary to allow for the excitation by secondary electrons.

7.1.3. Hydrogen-Line Profiles and the Spectrum of Proton Energies

Introduction and Historical Summary,-After Meinel’s discovery of Doppler-shifted Ha, it was generally supposed that proton bombardment was responsible for homogeneous arcs, and in a number of papers devoted to quantitative treatments of auroral excitation, attempts were made to determine whether protons could explain the photometric data. Shklovskii [1951b, 1952a, 1958b], utilizing experimental cross sections, noted that protons and hydrogen atoms moving parallel to the magnetic lines of force would have to have initial velocities as low as 500 km/sec to produce the maximum in the zenith profile near that velocity (see Fig. 5.19). Table 7.1 and Appendix IV show that such particles would not, however, penetrate below 150 km height, whereas most arcs are lower. Another difficulty was that the H a profile does show a violet tail extending to 2000 or even 3000 km/sec.

The energy deposited by fast protons through ionizing collisions was computed as a function of height in the atmosphere by Vegard [1921a] and later by Bates and Griffing [1953a]. T o a first approximation, at least, this calculation should give directly the luminosity distribution, i.e., the observed distribution of brightness versus height in arcs (Harang [1945c, 1946a, 1951a, 1956a1). But Bates and Griffing found that the observed distribution was much broader than that computed for monoenergetic protons traveling straight along the lines of force. They noted in passing that some of the difficulties encountered with the luminosity distribution could be removed with an ad hoc assumption of an energy dispersion for the incident protons. Shklovskii has also pointed out this possibility for interpreting the zenith profile. But these workers did not combine the different types of observational data to show that such an assumption was unavoidable, nor did they examine the possibility that an angular dispersion could remove the difficulties. Griffing and Stewart [1954a] showed that the discrepancy was not due to the north-south extent of arcs, which might be thought to distort the observed luminosity distribution.

In the first detailed calculations of hydrogen excitation in aurora, Chamberlain [ 195433 pointed out that for monoenergetic protons the


hydrogen light should be concentrated lower in the atmosphere than the emissions produced by atmospheric ionization. This fact may be seen in Fig. 7.1, which shows how the hydrogen emission peaks at quite low energies. His conclusion seemed to be in accord with Meinel’s [1952u, 1954~1 observation that Ha was concentrated toward the bottom of arcs.

Later Chamberlain [1954c] showed that the main difficulties then encountered between theory and observation-viz., that the observed zenith profile was peaked at much lower velocities than the theoretical profile (Shklovskii [1952u], Chamberlain [1954b]) and the luminosity distribution was broader than that predicted (Bates and Griffing [ 1953~1) -might be removed by allowing for a dispersion of particle orbits about the lines of force. An angular distribution heavily weighted at large angles of inclination was required. The unsatisfactory nature of this explanation was first demonstrated by Omholt [1956b], who showed that such an angular distribution of monoenergetic particles predicted a horizon profile for Ha that greatly exceeded the observed width. An angular dispersion has also been discussed by Morel-Viard [1956u] and Bagariatskii [ 1958u, c, 1959~1.

The hydrogen-line profiles seem to be quite similar from one spectrum to the next. Whether or not protons cause any aurora, these profiles should give a consistent picture of the incoming particle orbits. An energy spectrum varying roughly as the inverse square of the initial velocity, as well as an angular dispersion, was therefore invoked by Chamberlain [ 1957~1 as being necessary for a qualitative explanation of all the data-the horizon and zenith profiles and the approximate luminosity distribution of Ha in a quiet arc. Galperin [1958b] independently noted that an angular dispersion alone could not explain the observations and suggested that a portion of the primaries had comparatively low velocities. The precise forms of the energy and angular dispersions are still rather uncertain, owing to the lack of precise data. But an energy spectrum now seems rather definite. In addition to the evidence presented below, it gives a plausible explanation for the lack of a large variation in the width of the horizon profile with height (for spectra obtained with the aurora imaged on the slit), although such a change was certainly to be expected with monoenergetic protons. Also an energy dispersion is found in the Van Allen radiation and has also been found in direct rocket measurements of auroral protons (see the end of this section).

In the earlier work the assumption was often made that protons are responsible for auroral arcs, which seems to be incorrect, as we have shown from the N$/H ratios in Table 7.2. Also, the hydrogen emission seems to be detected often in the upper parts of the display and not


always near the lower border, as earlier observations had suggested (see Section 5.2.3). Hence it does not now seem justifiable to try to derive the characteristics of the protons from an observed distribution of the total luminosity (i.e., the ionization rate versus height).

Fundamental Equations for Monoenergetic Protons.-First we examine the profiles produced by a stream of protons all with the same initial speed. These profiles may then be integrated over an initial energy spectrum of protons to derive the complete profiles. Also we shall see that the ratio of the moments of the zenith and horizon profiles is independent of the initial energy and can give information directly on the angular dispersion.

A profile in the magnetic zenith is inevitably integrated over height in the atmosphere; it is not possible observationally to sort out the radiation emitted at different heights. For horizon observations, however, one can in principle measure the profile as a function of altitude. The variation of the horizon profile with height for monoenergetic protons has been treated by Omholt [1956b], Chamberlain [1958c], and Bagariatskii [ 1959~1. One can see qualitatively that, since only protons directed nearly along the lines of force will reach the lowest parts of the aurora, the profile would increase in width with height. Of course, the total intensity of the profile varies with height also, in a manner to be discussed later, so that a measurement of the height variation in width would require rather good photometry. So far, no such variation has been detected, and it seems likely that it is obscured not only by the difficult observational problem of keeping the auroral arc focused on the same part of the spectrograph slit during the exposure, but by the energy spectrum as well.

Here we shall confine the discussion of horizon profiles to those that are integrated over height. Observationally this integration could be ensured by not focusing the auroral form on the spectrograph slit, but in any case, unless particular caution is taken to avoid it, the observed profile will probably be nearly the integrated one.

Throughout the theory we shall assume that protons and H atoms are undeflected in their collisions. Strictly speaking, these particles may go through small angles of deflection, especially at the lower velocities. The zenith profile (see Fig. 5.19) always shows some emission longward of the neutral line position, whereas it should not if there is no deflection at all. This so-called “red shift” may arise in part, however, from horizon light scattered in the lower atmosphere. In the same way, if the aurora is strong in the zenith, it may contaminate the shortward side of the horizon profile and make it unsymmetrical.


Let F(v) dv be the number of photons in a particular H line produced between v and v + dv per incident proton; that is, F(v) is the function Fnn./9 in Fig. 7.1 plotted against velocity instead of range. Then the zenith profile for monoenergetic particles moving parallel to the lines of force is simply proportional to F(v) . For particles entering at an angle 8 to the lines of force the emission between u Z and v i + dv, (parallel to the field-see Fig. 7.3) will be proportional to F(v , sec 0) sec 8. The

I I I 1 I I /

z axis = direction / of B

/

MAGNETIC NORTH ATMOSPHERE

FIG. 7.3. Geometry for auroral primaries. T h e magnetic field has an inclination i to the horizontal. A particle with initial speed q, enters the atmosphere at an angle 0

to the lines of force. Magnetic north is indicated for the northern hemisphere.

photon yield per proton is G(H 1 vo) = Jio F(v) dv, where vo is the proton speed outside the atmosphere. We shall suppose that the emission from each volume element is isotropic.

Consider now a stream of particles spiraling down the lines of force. Just above the atmosphere the intensity of particles in a given direction is q(8) proton/cm2 sec sterad, where the unit area is taken perpendicular TO the velocity vector. The spiraling will ensure that q is independent of azimuthal angle, +. The flux of particles across an area normal to the magnetic field is then5

9 = 277 S i i 2 q(0) cos 8 sin I9 do. (7.8)

If now I(vz) is the specific intensity in units of photon/cm2 sec sterad (unit velocity interval), the total emission from a square-centimeter column parallel to the lines of force is

In some of the papers on this topic the flux per unit solid angle, q(0) cos 0, has been denoted by N(O), which is the significant quantity in the theory. But the intensity q is the significant function in discussions of the particles in space (Chapter 8) and therefore will be the variable carried in this chapter.


where cos 8, = v,/v,,. Alternatively, the zenith profile may be expressed as an integral over v, instead of over 8, for a constant v,:

2’0 F(v) ~ ( 8 ) cos 0 4rrI(v,) = 2rr \ dv, . u* V

(7.10)

where 8 and ZI are related by v = v,/cos 8. Equation (7.10) will be especially useful in our later discussions.

The derivation of the horizon profile is slightly more involved. Here we will follow the procedure used by Omholt [ 1959~1 of transforming to some nonorthogonal coordinate system that includes the variables v, and o. By trial and error one seeks a third variable that will put the expression for the profile in the simplest form. The horizon profile will be expressed in terms of a function l’(v,) (which is not quite a specific intensity, since we are integrating the emission over height), where 4x l’(v,) is the emission in photonjsec (unit velocity interval) from a square-centimeter column in the atmosphere. The column is oriented now perpendicular to the line of sight. Writing the volume element v2sin 8 d8 d+ dv = dv,dv,dv,, we may obtain the horizon profile by integrating the angular dispersion over v u and vz:

li’ F(v) q(0) cos 0 47r1‘(vr) = dv, 4,

V2

where v, is held constant and v 2 = v: + vi + v:. (7.1 1)

FIG. 7.4. Geometry for the horizon profile. The angular variable 4 is measured between the z axis and the projection of the velocity vector onto the yz plane.


We may now transform to any other coordinate system by applying the Jacobian. With the variables v,, v, and $, where the latter is defined by cos $ = cos 8 (1 - ~ ; / v ~ ) - l ' ~ the horizon profile is (see Problem 7.1)

(7.12)

The geometrical meaning of I,L is illustrated in Fig. 7.4. In the event that the incident flux is isotropic, i.e., 7 cos 8 = const,

the profiles are identical for velocities toward the observer: I(vZ) =

2I'(v,) when v, = f v,. This identity was first pointed out by Omholt [19566] from symmetry considerations. The factor 2 enters because the horizon profile is always symmetrical, I'(v,) = 1'( - v,) and the radiation is emitted isotropically. In general we have the relations

4 ~ Y z 4~ I(.,) dv, = 4 ~ 9 b z 877 Z'(vU+) dv, = ,F F(v) dv. (7.13) /; 1; 1:" Angular Dispersion and Moments of the Profiles.-The angular distribution may be written, in a first approximation,

(7.14)

which has been normalized by Eq. (7.8). (As an alternative approach one could express 7 as a Legendre polynomial.) Defining

we may write the zenith profile (7.10) as

(7.15)

(7.16)

and the horizon profile (7.12) as

Whereas the horizon profile decreases monotonically away from the origin, the zenith profile is zero at the origin and passes through a maximum (except in the special case n = - 1).

The moments of the profiles may be used to gain some information about the exponent n in Eq. (7.14) for the angular dispersion (Omholt

7.1, PROTON BOMBARDMENT 26 1

1 1 1 1 1 1 1 1 1 0.637 0.500 0.424 0.375 0.340 0.313 0.291 1 0.500 0.333 0.250 0.200 0.167 0.143 0.125 1 0.424 0.250 0.170 0.125 0.097 0.078 0.065

[1959a]). For the zenith profile the mth moment, with 71 given by Eq. (7.14), is

4~ s” vy I(v,) dv,

4 T 9 Z

(n + 2) ro F(v) vm dv 0 - - . (7.18) 0

- vy =

(m + n + 2) r F ( v ) dv 0

qn+z/(n + 3) l/(n + 3)

qs+z/(n + 3) (n + 4) 2/(n + 3) (n + 5 )

Similarly, the semi-profile for horizon observations will have moments

where n/2

g,,m = J0 cos” 6 sinm 1 d< (7.20)

and 5 is defined by sin 5 = vx/v (see Fig. 7.4). The ratio of the horizon to zenith moment is

(7.21)

Table 7.4 gives the theoretical ratios for a range of n, along with the functions %?, and = (n + 2 ) ~ / 2 and (n + 1) en+1 = (n + 2) Wn-l.

In general we note that Y n

m \” 0 1 2 3

Qn+z

n + 3

TABLE 7.4

THEORETICAL RATIOS OF THE MOMENTS OF H PROFILES, w z / w T , AND THE FUNCTIONS Q, AND 9,,m

_ _

- 1 0 1 2 3 4 5 g n + z , m

71 2 371 8 577

4 3 16 15 32 35 256 - - - - 1 -


For n = - 1 the ratio of the moments of any order is unity, since the two profiles themselves are identical. The case n = 0, an isotropic distribution in the particle intensity, is of particular theoretical interest (Section 8.2.3).

Observational moments of the profiles might thus be compared with Table 7.4 to ascertain n in Eq. (7.14). The ratios are independent of the initial energy spectrum, since Eq. (7.21) is unchanged by integrating both (7.18) and (7.19) over vo. The practical difficulty is that the observational moments may be extremely sensitive to photometric errors. Even for m = 1 errors in the high-velocity tail of either profile could easily be important. For example, Omholt [1959a] found that the profiles in Fig. 5.19 have a ratio of first-order moments that imply n = 6. But the high-velocity tail of Ha in the zenith is blended with a First Positive band of N, and may well be too strong in the figure. I t also seems quite likely that the tail of the horizon profile can be underestimated, not only through inaccuracies in measuring at low intensities, but because the higher and weaker part of the aurora, which would contribute much of this emission, may often not be recorded.

Profiles for Fast, Monoenergetic Protons.-To obtain approximate analytic expressions for the profiles we may write the Balmer photon yield per unit velocity interval as

(7.22)

where K and /3 are constants. This equation gives only a fair fit with the F(v) curves (we Fig. 7.1) computed from the equations of statistical equilibrium, but is sufficiently accurate for many purposes. The maximum of F(v ) falls at v = /3 and for Ha, /3 w 2000 km/sec. Since Jr F(v) dv = 60 photons for Ha, we have K = 4 x 60/p dG = 6.8 x

With Eq. (7.14) for the angular dispersion, the zenith profile, Eq. (7.16), photon/km sec-'.

becomes

(7.23)

where we write u = vz//3z. The maximum intensity of the profile occurs at the value of u, = v:/Pz satisfying the equation

(7.24)


The profile is observed to extend to velocities several times the velocity of the maximum, so for an approximate solution replace uo bym in the integral. Then defining the exponential integral,

OD e-u

E,(u,) = uz-l Ju up du = .-".' de, P 1 5"

we have the condition for the profile maximum as

(7.25)

(7.26)

For the case n = - 1 the maximum is at the undisplaced line position and for n = 0 it is at o, m 1000 km/sec for Ha. For n = 1 it appears around 1300 km/sec and as n becomes still larger the maximum approaches a = /3 = 2000 km/sec. Thus for monoenergetic particles to produce the zenith profile in Fig. 5.19, a necessary condition is that - l < n < O .

But now consider the horizon profile. Equation (7.17) gives

(7.27)

Again with uo -+a, the velocity o, at which the profile falls to half the central (maximum) intensity is given by the value of u, in the relation

(7.28)

This equation is easily solved for u, for integral odd values of n. For n = - 1 , the half-maximum intensity of Ha occurs at o, = & 1700 km/sec. For n = 1 it is at & 1000 km/sec. Therefore, a large value of n is necessary to give the narrow horizon profile in Fig. 5.19.

Thus the horizon profile requires a narrow angular dispersion, with most of the particles in orbits with small pitch angles 0. This result is incompatible with the zenith profile, which requires a more nearly isotropic or even a flattened distribution function, with particles preferentially following helical orbits with large angles of pitch. The conclusion must be that the hypothesis of monoenergetic auroral protons does not give a consistent explanation of the profiles.

Energy Spectrum of Incident Protons.-If we assume that the angular dispersion and energy spectrum are independent, we may write


the differential intensity of incident particles between v, and vo + dv, as

where q(0) is given by Eq. (7.14) and where Y is normalized to unity. Representing Y by a power law, v;', to a sharp cutoff at some minimum velocity vmin, we have

At velocities v , > vmin the zenith profile from Eq. (7.16) is

(7.30)

(7.31)

With the photon yield given by (7.22) and writing u = vZ//3, we obtain

'The maximum occurs at the value of u , = v:/pz satisfying the

2 E(n+s)/z (4 = n+l e-uz,

(7.32)

relation

(7.33)

where E is given by (7.25). For a maximum other than at a , = 0, we must have s < 3, regardless of n ; this may be seen quite readily for the case of no angular dispersion, where the profile becomes simply

Equation (7.33) may be solved by expansions appropriate for small u , when (n + s)/2 is not an integer and with tables of E, when it is.6 If we take n = 0, the maximum occurs at v , = 0 for s = 3 and around v, = 600 km/sec for s = 2. T h e observed maximum near v, = 350 km/sec implies s - 2.6, but, of course, no great emphasis can be attached to this precise value.

s; F(uz) Y(v0) dv,.

Tables are given by Gold [1909a], Mian and Chapman [1942a], Jahnke and Emde [1945a], Placzek [1946a], Katterbach and Krause [1949a], Kourganoff [1952a].


In the same fashion we find the horizon profile from Eq. (7.17) to be

for U, > Umin. When Umin is very small we may compute the semiwidth of the horizon profile at half maximum (central) intensity. As with Eq. (7.28) a solution is readily obtained when n is an odd integer. For n = - 1, the observed semiwidth of v,/p a & 0.2 implies s a 2.5; for n = + 1, it gives s w 2.1. Hence we conclude that for n = 0, s = 2.3 would be appropriate.

The total zenith or horizon emission when there is a velocity dispersion is

Using the value of K given below Eq. (7.22), we find

(7.35)

(7.36)

where the integral is numerically 60 photon/proton for Ha-the total photon yield for fast particles. The flux required to produce a given intensity of Ha could well be one to three orders of magnitude greater than if all the protons initially had high velocities [v,, -+DO in Eq. (7.13)].

The moments of the profiles may also be computed (Problem 7.2) for the energy spectrum (7.30):

(7.37)

The horizon moments may be obtained from these zenith moments and the ratios in Table 7.4.

As we noted earlier, the observed profiles are likely to be considerably in error at the weak, high-velocity tails. But also the energy spectrum (7.30) is probably characterized by a constant value of s over only a moderate range of velocity; at low velocities s must decrease to keep the number flux finite. Therefore, the moments may be overestimated if they are computed with a value of s determined from the maximum of the zenith profile or the half-intensity width of the horizon profile. The zenith profile in Fig. 5.19 gives V, w 950 km/sec. If n = 0, this implies s = 2.5. And the observed V, m 250 km/sec implies s = 3.6 for n = 0. The latter value of s certainly cannot apply at low velocities,


vo, but may be appropriate at the higher velocities contributing most of the moment. The fact that the two observed moments give different values of s is a consequence of their ratio not being the correct value for n = 0 (Table 7.4).

We conclude that the momentum spectrum may follow a power law, vo3, where s a 2.5 in the velocity region of several hundred km/sec. In energy units the differential intensity spectrum varies as e;l*s. The main error in determining the exponents probably lies in the uncertainties in F(v ) , as approximated by (7.22), especially at low velocities. For an isotropic particle intensity [n = 0 in Eq. (7.14)], this power law reproduces the maximum of the zenith profile and half-intensity width of the horizon profile. The moments of the profiles, on the other hand, seem to imply an elongated angular dispersion [with large n in Eq. (7.14)], but the errors involved in measuring the moments are likely to introduce large errors in results based on them.

Luminosity Distribution for Hydrogen.-In principle the vertical distribution of Ha could be used to derive the parameters n and s for the angular and energy dispersions. In practice, little observational information is available on the luminosity distribution. Here we shall merely outline the approach. A similar analysis may be used to predict the ionization rate versus height from proton bombardment, which might be compared with a luminosity curve in integrated light. But as I mentioned in the introduction to Section 7.1, it now seems unlikely that proton bombardment alone is responsible for the auroral luminosity.

The curves in Fig. 7.1 may be represented by a function of the form Fnn,JF = C rb e-ar . (7.38)

For Ha emission, the parameters are a = 25.2, b = 0.83, and C =

2.3 x lo4, where r is in atm-cm and F32/.% in photon/atm-cm per incident proton. Similarly for the ionization, q/F, in ion-pair/atm-cm per incident proton, we have a = 4.63, b = 0.74, and C = 2.2 x lo5. At an equivalent depth 6 the range is related to the initial range r,, by

r0 - r = 6 sec 0, (7.39)

where 8 is the angle of incidence measured normal to the atmosphere. With the angular dispersion (7.14) and an energy spectrum varying as ~ ~ 7 0 , the luminosity distribution is

(7.40)


where E, is given by Eq. (7.25). The integration is accomplished by reversing the order of the integrals. For monoenergetic protons, the solution may be expressed as a series of incomplete r-functions. Equation (7.40) also applies for the ionization q:, when the appropriate constants are used.

Here F , and q: refer to the Balmer emission or ionization production in a homogeneous atmosphere a t depth 5. T o compare them with observations, they must be scaled to ionosphere densities by F , = - F , dtldz =

F , Na(Z)/Na(O) and similarly for 4;. These luminosity and ionization distributions are strictly correct only for particles spiraling about lines

IS0 -

- E - 1 - Y

5 140- u I - w

120 -

100 -

I I I I I I I 1 I I

0.2 0.4 0.6 0.8 I .o RELATIVE IONIZATION RATE

FIG. 7.5. Ionization production by protons. Solid lines are computed from Eq. (7.40) for I/g = 0.05 atm-cm; they show the variation with n, which describes the angular dispersion. The dashed line is computed for an isotropic, monoenergetic beam with r, = I/g, which is the mean value of r, for the particles in a beam with an exponential spectrum. These computed curves, plotted here on a relative scale for comparison, may be expressed in absolute units (ion-pair/cms sec) for a flux 9 = 1 proton/cm2 sec by multiplying by the indicated scale factors. The dots, showing an observed distribution for an auroral arc from Harang [1945c], are on

a relative scale only, fitted to the maximum intensity.


of force normal to the atmosphere. At auroral latitudes the errors introduced by the inclination are negligible compared with the uncertainties in the functions FS2(r) and q(r), the model atmosphere, and the observations.

Should accurate measurements of the Ha luminosity distribution become available, computations by Eq. (7.40) could show whether the proton energy spectrum can be adequately described by exp (- gr,) and, if so, provide values of g. Sample calculations for qz are shown in Fig. 7.5 and compared with an observed luminosity curve with a maximum at the same altitude as the computed distribution. The observed distribution could evidently be explained by proton ionization with an exponential energy spectrum. But as we have seen in Section 7.1.2, there appears to be a large discrepancy between the absolute amount of ionization produced by protons, as deduced from the Ha brightness, and the actual amount in an aurora, as derived from N,+ emissions.

With a spectrum that is exponential in ro, the ratio 4(h3914)/9(Hcu) varies with height, x, in proportion to the relative abundance of N,, since q,/F, is independent o f f . This behavior results from the particle spectrum, integrated over all directions, having the same exponential shape at all heights. I t would not be true for a power-law spectrum nor for monoenergetic particles.

Rocket Measurements.-During the IGY direct measurements of ions incident on the atmosphere were initiated. In a preliminary report Meredith, Davis, Heppner, and Berg [1958a] gave results of two rocket flights from Ft. Churchill. They find evidence for an isotropic ion intensity at high altitudes, which implies z = 0 in the above theory.

The energy spectra measured on the two flights were quite different, one varying as exp (- ~,/72), where e0 is the initial energy in kev, and the other following a power law, E ; ~ . ~ for 30 < E~ < 500 kev. These results are not directly comparable to those obtained from profile studies, as the velocities are somewhat higher than those important in producing, for example, the maximum of the zenith profile (see Table 7.1). This power law would, however, correspond to a momentum spectrum with s = 1.8 in Eq. (7.30).

Similar experiments have been reported by McIlwain [ 1959~1, who measured an energy spectrum varying as eo4 for eo > 70 kev. Simulta- neous photometry of HIS by Montalbetti showed that at least 70 percent of the proton flux was in the unobserved energy region below 70 kev.

The large difference in the energy spectra on the different flights seems inconsistent with the relative stability of the profiles on different spectra. Possibly the explanation is that the spectrum fluctuates, but

7.2. ELECTRON BOMBARDMENT 269

that over the long period required for photographic exposures the time-averaged spectrum is fairly constant. The rocket measurements also disclosed that proton bombardment was not confined especially to the visible auroral structures, which supports the conclusion reached from spectroscopic measurements that protons are not a predominant source of auroral excitation (Section 7.1.2).

7.2. Electron Bombardment

7.2.1. Bremsstrahlung X-Rays': Detection of Primary Electrons

Introduction.-Balloon and rocket flights detecting x-rays (10- 100 kev) in and near the auroral zone gave the first definite indication that primary (i.e., extraterrestrial) electrons contribute to the aurora. This x-radiation at the auroral zone was first found in daytime flights and seems to be a more or less continuous phenomenon. Later flights have established that it is enhanced during and directly associated with aurora. The only plausible interpretation of these measurements to be offered is that the x-rays are bremsstrahlung produced by energetic electrons. X-rays at the balloon altitudes are thought to arise from electrons stopped in the auroral region (- 100 km), whereas radiation in the auroral region itself may arise from electrons striking the apparatus and producing bremsstrahlung locally. These measurements have been summarized in Section 4.3.3.

Bremsstrahlung Spectrum.-As a fast charged particle passes close to an atomic nucleus and is accelerated in the Coulomb field, it radiates energy. At thermal energies (where the atomic field may differ greatly from a Coulomb field) the phenomenon is usually called a free-free transition, by analogy with captures (free-bound) and cascading (bound- bound). We are concerned here with electrons with energies up to several hundred kev-comparable to or less than the rest-mass energy of an electron, me2 = 520 kev.

before the encounter; it emits radiation between frequencies v and v + dv.

We will take an incident electron to have a kinetic energy

' The bremsstrahlung treated in this section arises from electrons passing through the Coulomb field of a nucleus, producing some high-energy photons. The same process produces emission at lower frequencies and even in the radio region, but for reasons discussed below, the cross section given here is not appropriate for low photon energies. Bremsstrahlung also arises from the deflection of low-velocity electrons in atomic collisions. An approximate treatment of this process, which is closely related to thermal emission and could contribute in the radio region, is presented in Section 7.3.3. Secondary ionization produced by the absorption of bremsstrahlung is discussed in Section 7.3.1.


The final energy is E = E, - hu, and the maximum frequency that can be emitted is u1 = .zl/h. The problem of computing the bremsstrahlung spectrum is one of expressing the cross section in terms of the initial kinetic energy E~ = hv, and the loss of kinetic energy, hu.

The spectrum can be derived from the classical electromagnetic equation (1.13) (see Panofsky and Phillips [1955a, p. 3081 or a more rigorous treatment by Landau and Lifshitz [1951a, p. 197]), but the more appropriate treatment is by quantum electrodynamics.

In the extreme relativistic case of E and el >> mc2, the cross section is given by Bethe and Heitler [1934a] for various degrees of screening (which is dependent on the incident energy) by atomic electrons. A better approximation for our purposes is the nonrelativistic formula, and here we shall neglect screening (using the Coulomb field of the nucleus) and adopt the Born approximation (the incident plane wave is perturbed only slightly). Sommerfeld [ 1950a, Chap. 71 has, however, treated the nonrelativistic problem with the exact wave functions, since the Born approximation breaks down at very low energies. Reviews of the theory are given by Bethe and Ashkin [1953a] and Heitler [1954a]. Experimental cross sections at 50 kev have been compared with the Sommerfeld theory by Motz and Placious [1958a].

The simplified, nonrelativistic formula for the total cross section is

8 Z2 a pt m c2 [(hul)l /z + (hu, - hu)1/2]2 @(ul [ v ) du = In du, (7.41)

3 hv, u hu

where Z is the atomic number of the nucleus, 01 = 2n e2/hc is the fine- structure constant, and po = e2/mc2 is the classical radius of the electron. The photon intensity is not isotropic, but has a maximum perpendicular to the plane of motion. In the aurora, however, the angular dispersion in the incident beam and that produced by subsequent electron scattering will reduce the anisotropy of the total emission integrated over a column.8

At the comparatively low energies of auroral electrons, the loss of energy from radiation (bremsstrahlung) is much less than the loss suffered through ordinary collisions. The number of photons emitted between v and v + du from an electron of initial kinetic energy hu, in path length ds is N@(v, I u ) dv ds, where N is the number density of atoms. The

Consider the particles at a particular energy vl. Their radiation from a specific small volume will be isotropic if the particle intensity ,I(€') (i.e., the number of particles crossing unit area normal to their own velocity vectors per second per steradian) is isotropic. But the angular distribution of the radiation emanating from particles in an energy range v 1 to v1 + dv,, (regardless of the corresponding height interval dz), depends on the angular fiux distribution, T ( 8 ) cos 8, since dz/dv, is proportional to cos 8.

7.2. ELECTRON BOMBARDMENT 27 1

energy loss computed from Eq. (7.41 ) would diverge logarithmically at small v, but this is due to the simultaneous neglect of screening and the use of Born’s approximation. The total energy loss in traversing unit path length may be found in the nonrelativistic case by allowing for screening (Heitler [1954a, pp. 249-2521):

l6 N Z2 01 p i m c2. (x)rad = - N JI hv @(v1 I v) dv m - - 3

(7.42) d.s

The nonrelativistic loss of energy in (ionizing) collisions is approximately (Bethe and Ashkin [1953a], Birkhoff [1958a]),

(7.43)

where hvion, the mean ionization-excitation potential, is of the order of 2 times 13.5 ev. The logarithmic factor is of the order of 10 in the energy range of interest, giving a ratio

(7.44)

where hv, is in Mev in the latter expression. For relativistic energies the ratio is essentially the same and radiation eventually dominates over collisional losses. But for electrons with hv, N 0.1 Mev in air (2- S), only about of the energy loss is spent in bremsstrahlung.

From the cross section (7.41) we see (neglecting the logarithmic factor) that the intensity in number of photons increases at small frequencies as dvlv. But intensity in energy units (per unit frequency interval) is nearly constant for v < v1 and vanishes for v > vl. Measure- ments of the bremsstrahlung spectrum (such as Anderson [1960a] has obtained for weak x-ray displays) could therefore yield the instantaneous spectrum of auroral electron energies, but to obtain the spectrum of initial energies outside the atmosphere, E,,, it would be necessary to consider the relative time that an electron spends in all intervals dE, as it is slowed down.

The total energy emitted in bremsstrahlung by an electron entering the atmosphere with energy E,, may be estimated by integrating Eq. (7.44). Thus we have, with energy again in MeV,

(7.45)

from which we can make some rough estimates of the electron flux at the higher energies.


For example, Winckler, Peterson, Arnoldy, and Hoffman [ 1958al measured from one electron burst an integrated emission rateg between 50 and 100 kev of 4779 = 2 x lop4 erg/cm2 sec = 1.2 x lo5 kev/cm2sec. In this energy region the primary electron spectrum is probably decreasing rapidly with increasing energy, so that 100 kev should be a safe upper limit for the mean initial energy E ~ . (Electrons at 100 kev could penetrate into the D region.) Their measurements recorded perhaps 10 percent of the total bremsstrahlung,1° most of the rest being absorbed above the balloon (Winckler, Peterson, Hoffman, and Arnoldy [ 1959a1). By Eq. (7.45) the total flux of incident particles was therefore 9 w 10 X 4?T9/(d&)rad > 2.4 X 10’ electron/cm2 sec. The total energy flux of primary electrons would be 9 c0 > 2.4 x lo9 kev/cm2 sec = 4 erg/ cm2 sec. The inequalities enter because a lower mean energy E~ would mean that a larger percentage of the bremsstrahlung was unrecorded and a larger flux would be necessary to give the same emission. In fact, a steep electron spectrum might provide a total energy and particle flux that would be orders of magnitude greater. We shall return to the question of the total flux in Section 7.2.4.

7.2.2. Cerenkov Radiation a t Radio Frequencies Basic Theory.-A charged particle moving with uniform velocity in a vacuum does not radiate energy. But when a charged particle enters a medium (refractive index n) with a speed v exceeding the phase velocity of light (c/n) in the medium, energy is emitted as Cerenkov radiation, which was first observed in the optical region, being induced by radioactive bombardment (Cerenkov [ 1937a1). In general, the electric and magnetic fields from an accelerated charge must be evaluated with the Lihard-Wiechert retarded potentials, which allow for the finite travel time of electromagnetic signals. The time dependence of the potentials at some fixed point leads to terms in E and B that vary as ljr. The Poynting vector, E x B c/477 then varies as l / r 2 and gives an outward flow of radiation. For the special case of uniform motion,. however, the coefficient of the l / r term vanishes unless v 2 cjn. The remaining terms vary as lj?, so the Poynting vector gives negligible flow of energy across a very large sphere. That is to say, destructive interference of the waves ordinarily removes the outward flow of energy, except in the case of Cerenkov radiation (Frank and Tamm [1937a]).

@We assume in deriving the numerical value of the emission rate that the radiation was isotropic and that their quoted flux is equivalent to a9. If the radiation was from a small region of sky, the indicated flux would be correspondingly larger.

lo This figure is quite uncertain, however, as it depends on the total atmospheric bremsstrahlung spectrum and not merely on the spectrum of E,,.


Classical treatments of the effect are given in the books by Panofsky and Phillips [1955a, p. 3091, Jelley [1958a, p. 151, and Schiff [1955a, p. 2671. Here we shall summarize the fundamental ideas and steps involved in the derivation.

All the time-dependent electromagnetic variables may be expressed in their Fourier components, as in

m

B(t) = I B , ciwt dw, (7.46) -m

where B(t) and B, are each functions of position in space. The inverse relation is then

B(t) eiWt dt. (7.47) B , = - I 1 " 27r -a

The general wave equation for the vector potential produced by an external current (the moving electron) is

where B = V x A, and the other quantities are defined in Section 3.3. For the case D = 0 and p = 1 the wave equation for the Fourier amplitudes A, is

(7.49) n2 w2

P A , + T A W = - 4 J,,

which may be integrated with a Green's function. We obtain

(7.50)

where r is the distance from the particle to the field point (where the potential is being evaluated) and the integration is carried over the entire trajectory of the particle.'l

l1 Incidentally, it may be shown that analyzing the potential through its wave equation in this manner is equivalent to adding all the components of the potential itself, from all along the trajectory, that arrive at the field point at time t. Thus with a transform of the type (7.46) we may show (Problem 7.3) that (7.50) is equivalent to

(7.50a)

where J is evaluated at time t' = t f m j c . In the last expression only the minus sign has physical significance; A is evaluated from the current J just as in the static or slowly varying case except that we use the current at each point on the path at the time t - m / c , which allows for the travel time of the electromagnetic disturbance. In the particular case of uniform motion it is thus possible to express the potential in terms of the particle's position at time t, which cannot generally be done in the case of accelerated motion.


The field component obtained from (7.50) is

e i o n r l c

(7.51) i w n

d r , - - - - J ~ , , , x r - r2

where dr is the differential volume of space. Here we have used only the plus sign (the physically meaningful one) from Eq. (7.50), and in the last expression a term varying as r2, which contributes to an induction field but not to radiation, is omitted. The current density of a single negative charge moving along the z axis with, velocity ZI may be written

(7.52) e v J 1 - - 6 ( ~ ) S(y) 6(z - at),

where 6 is the Dirac function. Then the Fourier transform to be substituted in Eq. (7.51) is

(7.53)

The Fourier amplitude is then

eiwnr,Jc B, = i---- sin 1 exp i [ (wx/v) - (wzn cos ejc)] dz, (7.54)

r0 277 c2

where I3 is the angle between r and v, and where ro is the distance of the field point measured from a fixed origin, r is its distance from the electron, and x is the distance of the electron from the origin (r = r, - zi, and

The electric vector for a wave is related to the magnetic vector by E, = H,/n. The total energy radiated is found by integrating the Poynting vector (E x Hc/4~r) over the surface of a large sphere; but to obtain the energy in a particular Fourier component, an additional factor 477 is required (see Panofsky and Phillips [1955a, p. 2181). The energy radiated in the interval du by a particle over its entire trajectory is therefore

70 >> 4.

(7.55)

where B, is to be substituted from Eq. (7.54).


The integral in Eq. (7.54) is essentially 6(1 - nv cos 6jc). I t gives

cos 0 = c/nv, (7.56)

for the direction of radiation; and it shows that when v < c/n there can be no emission at all, interference canceling all waves at large distances from the source. The wave front generated by the fast electrons bears some resemblance to a shock wave, propagating away from the axis of the particle in a "light cone" with half-angle 0. At v = c/n the wave accompahies the electron itself and as v increases, the angle 6 becomes larger. The &function gives an infinite amplitude in direction 6, but this peculiarity is a result of carrying the integral over all space. Actually, the electron's path is finite and when the integral is evaluated properly (see Panofsky and Phillips [1955a, p. 312]), it yields an energy emission per unit length of path of

the Cerenkov condition,

(7.57)

In ordinary air in the visible region, where n > I and does not change rapidly with v, the energy emitted is concentrated toward shorter wavelengths, giving a bluish light in laboratory experiments. Except for the frequency dependence on n, the number of photons emitted would be constant for all frequency intervals. But in the radio region it is precisely the dependence on n that makes the phenomenon important.

Emission Frequencies in the Radio Region.-From the Cerenkov condition (7.56) it is clear that for radiation to occur, we must have n > c/v . In the absence of a magnetic field and for zero collision frequency the index of refraction is n = (1 - where the plasma frequency wo is given by Eq. (3.54). For w < w,, the index is imaginary, which implies that such radio waves will be absorbed (Section 3.3.2). At higher frequencies, w > wo, we have n < I and Cerenkov radiation could not be produced.

If a magnetic field is present, the situation is quite different. When there are no collisions the Appleton-Hartree formula (see Mitra [1952a, p. 1871) gives

- 2(w&J2) (1 - w&2)

2(1 - w ~ / w 2 ) - ( w ~ / w 2 ) sin2 Ol~[(w;/w4) sin4 8,+4(1 -wg/w2))' (w,"/w2) C O S ~ ~ , ] ~ / ~ (7.58)


Here 8, is the angle between the direction of wave propagation and the magnetic field, wo is the plasma frequency given by Eq. (3.54), the gyrofrequency or cyclotron frequency is wc = e Blmc from Eq. (3.18), and w is the circular wave frequency, 27rv. For wo < w the minus sign in Eq. (7.58) applies if the electric vector of the wave rotates in the same sense as the electrons gyrate (extraordinary wave) and the plus sign applies for the opposite sense (ordinary wave). If wo > w the signs corresponding to extraordinary and ordinary modes are reversed.

We are concerned here with the situations wherein n may be greater than unity. If w > wo, which we shall call high-frequency emission, the condition for n > 1 at 8, = n-12 is that w < ( w i + ~ : ) l ’ ~ , although for 8, - 0 (longitudinal propagation-emission along the magnetic field) the condition is more stringent, w < wc. (For wc < wo, longitudinal high-frequency waves are forbidden.) Thus any high-frequency radiation from the Cerenkov mechanism propagates in the extraordinary mode and falls in the frequency band wo < w < (wi + w:) l iZ.

At low frepuencies, w < wo, there is no Cerenkov emission that will propagate transverse to the field, but in the longitudinal direction (0, sz 0), n may exceed unity in the extraordinary mode for w < wc.

Moreover, n will be its greatest in the neighborhood of w - w C and for w - 0, which might therefore be an indication of the frequency bands of strongest emission.

At the Earth’s surface the gyrofrequency for an electron is the order of wc = lo7 radianlsec. Hence the low-frequency band would be at v < wc/2n = 1.5 Mc/sec. On the other hand, if wc < wo the high- frequency Cerenkov emission will be produced near the local plasma frequency as the electron passes through the ionosphere. Should the auroral bombardment substantially increase the electron density in the higher regions of the ionosphere, it may even be that some VHF (v > 30 Mc/sec) emission is produced.

Cerenkov Emission f r o m Auroral Particles.12-For Cerenkov radiation from the ionosphere to be observed, it is necessary that the ionosphere below the level of production be fairly transparent to the waves. The frequencies that are reflected cannot be estimated with the

l2 Ellis [1957a, 1959~1 has discussed Cerenkov emission at very low frequencies. He estimated the intensity of emission, with certain assumptions for the electron flux and velocities, and with a crude model for the outer atmosphere. Hartz [1958a] has suggested that the mechanism may even be responsible for VHF auroral emission from the ionosphere.Previously Marshall [I 956~1 had attributed certain solar radio bursts to the Cerenkov process as particles ejected from the sun move through its atmosphere. The matters discussed in her paper are closely related to the terrestrial problem.


theory for zero magnetic field in Section 3.3.2 (which gave reflection when wo 2 w ) , because these waves propagate in the extraordinary mode, for which the magnetic field produces important changes in the index of refraction.

Consider first the high-frequency Cerenkov band, wo < w < (wi + w : ) ~ ’ ~ . Mitra [1952a] has plotted and discussed in detail Eq. (7.58) for several situations. For transverse waves (which will carry the highest frequencies) and when uc < w (the situation for VHF emission), n continually increases from unity at wo = w to infinity at wo = (wz - uE)l’z.

But where the plasma frequency drops below (w2 - w:)1/2, the index n has a discontinuity, becoming imaginary. The wave cannot therefore escape into a region of lower w,,.

The situation is not so clear if the emitting region has small (diameters of the order of a wavelength), localized regions of high electron density. If Cerenkov radiation could be produced in such a volume, it might be able to escape largely unimpeded. The wave would have to cross the discontinuity in n and reach a plasma frequency wo - w - ( 4 2 ) ; at lower values of wo, the wave would then be safely in regions of n2 > 0. Thus there are some serious difficulties in attributing the VHF auroral emissions to Cerenkov radiation, but the possibility deserves further exploration.

For the low-frequency Cerenkov band, w < wc, we have n --fa as w + wc. Auroral particles might therefore start emitting strongly at frequency w as soon as they reach a point, far above the F region, where wc = w . This frequency could be emitted over a path length of several thousand kilometers, until the particles are slowed down by collisions. As the electrons move through the far, outer atmosphere, approaching the Earth, wc increases and the emitted spectrum could include frequencies as high as 1500 kc/sec.

Again there is a problem of transmission of the wave through the ionosphere, but in this case it arises from a coupling of the transverse and longitudinal modes. In the pure longitudinal mode, there would be no reflection for w < wc. But for propagation at some finite angle 6 the transverse component introduces reflection at wo = w . Ellis [1957a] points out that in the D region, where this will occur, the collision frequency is high. The collisions have the effect of giving essentially a longitudinal mode of propagation (called the quasi-longitudinal mode) for angles 6 > 0. On the other hand, the collisions evidently do not produce much absorption at audio frequencies, or whistlers (Section 4.3.5) would not be detectable.

Probably a more serious obstruction is reflection by the tenuous ionosphere above the F region. Emission in what we have termed the


high-frequency band, w > wo, would be possible in the outer atmosphere in the longitudinal mode provided that w < we. But this radiation would be reflected as it entered the region wo = w, unless it is directed precisely along the magnetic field. Hence any higher frequencies emanating from a region of the outer ionosphere where wo < wc would be largely lost.

A factor that would help preserve low-frequency emission is that the refractive index tends to guide the wave along the magnetic field, especially when w < wc. This is the situation for whistler propagation (Storey [1953a], Garriott [1958a]). Very low frequency bursts may therefore be channeled, somewhere between their point of origin and the Earth, into the “wave guide” provided by the field.

The theory of the chorus (Section 4.3.5) developed by Gallet and Helliwell [1959a] and Gallet [1959a], exploits an analogy with traveling- wave tubes (Slater [1950a, p. 2801, Pierce [1950a]). But the excitation mechanism amounts essentially to Cerenkov radiation that is propagated from the outset along the magnetic field. In that case Eq. (7.58) gives for the extraordinary mode

(7.59)

Combining this with the Cerenkov condition (7.56), we obtain, when v cos 6 < c,

(7.60)

where 8 is the angle between the field and the electron’s velocity vector.

This equation gives the two frequencies that are emitted by a particle with velocity component v cos 6 along the field, as a function of wo

and wc at the place of origin. The lower frequency lies in the band 0 < w < 4 2 , and the upper, in the band wc > w > wc/2. If the factor in parentheses exceeds unity, there is no emission in any frequency directed along the field.

Since the particles travel along the field at the phase velocity of the wave, increasing the intensity of the wave all the while, they could generate a rather strong signal within a frequency interval dw. But Cerenkov radiation emitted in other directions from a discrete group of particles and during the same time interval would emanate from a large surface area and consequently not have the large intensity characteristic of the wave propagating along the wave guide (even if the transverse radiation can penetrate the ionosphere).


The observed spectral purity (at a particular instant) of many of the chorus signals implies, by this theory, that the responsible particles are indeed in discrete bunches and that the electrons in each bunch all have about the same velocity component along the field. This conclusion seems rather remarkable, but possibly is due to the interaction between the wave and the particles, as found also in traveling-wave tubes in the laboratory. The velocities required to explain the observations are of the order of lo9 cm/sec. Cerenkov emission is discussed in connection with gyro radiation in the following section; also see Section 8.2.1.

7.2.3. Gyro Radiation

Basic Theory.-As a charged particle moves in an external magnetic field, it gyrates about the lines of force and therefore is constantly being accelerated. The electromagnetic energy emitted is called synchrotron radiation if the particle is relativistic, but the more general term gyro radiation will be used here, where we are concerned principally with nonrelativistic velocities.

The total energy loss in the nonrelativistic case may be computed immediately from Eq. (1.13), where the Lorentz acceleration is equal to the centripetal acceleration, v y / p = vLwc. Here v L = v sin 6 is the velocity component perpendicular to B, p is the radius of gyration, and wc = eB/mc. Thus the rate of energy loss is

2 e4B2vi - - _ - de dt 3 r n 2 c 5 . (7.61)

The angular distribution follows directly from the consideration that the circular gyration is equivalent to two perpendicular oscillating dipoles, each with a dipole moment p = ex,, = ey, = ev , /wc . The electric vector from dipole radiation is proportional to sin X, where x is measured from the direction parallel to the dipole. Using cosx = cos+ sin 0 (0 is measured from the z-axis, along the field and + is azimuth measured in the xy plane), we average over + and obtain a mean rate of energy loss per unit solid angle, 8, of

(7.62)

With the electron gyrating at frequency wc and in the direction of circular polarization for an extraordinary wave, one would intuitively expect the emitted radiation to be monochromatic at the fundamental


frequency w1 w wc and extraordinarily p01arized.l~ T o a good first approximation, this is the actual behavior, but there are some departures from it. I shall merely summarize these points briefly.

First of all, higher harmonics of wp = q wl(q = integer) do appear, and become more pronounced at high particle velocities. The physical reason for their presence is that a finite time is required for the electromagnetic signal to travel a distance the order of the radius of gyration. Therefore, while the electron’s motion (or the current) has only a single Fourier component wC, a field quantity-for example, the vector potential A-does not vary in a simple harmonic fashion, and higher- order components are necessary to describe its periodic oscillations. The spectrum analysis, based on Eq. (7.50), proceeds in a manner similar to that given in the previous section for Cerenkov radiation (see Landau and Lifshitz [1951a, p. 21‘1).

The emission rate at a frequency wq varies as (vl/c)*q. At auroral energies the harmonics ( q 2 2) are much weaker than the fundamental. Each harmonic has its own angular dependence; but from what has been said above, it will be physically clear that along the axis of the magnetic field these harmonics are always absent. At relativistic energies (Schwinger [ 1949~1) the higher harmonics assume dominating importance and the radiation becomes directed within a narrow cone centered about the instantaneous velocity vector. Or, averaged over a cycle, the radiation is confined closely to the equatorial plane of the orbit.

T o obtain the proportion of radiation from each harmonic that is in the ordinary or extraordinary mode, it is necessary to compute the polarization from the field quantities and see how it is divided between the two categories. This has been done by Twiss and Roberts [1958u], who find that for the fundamental, w1 m wc, the energy radiated in the ordinary component is of the order of only ( v / c ) ~ of that in the extraordinary mode. In the harmonics q > 2 the total energy radiated in

la Strictly, the fundamental gyrofrequency is w c [ l - (v2/c2)]1/2, where w c is defined with the rest mass of the electron, rn. This relativistic correction is of little importance in free space, but if there is a background plasma the index of refraction for the longitudinal wave in the extraordinary mode has a singularity at w = w c . For propagation down through the ionosphere, we therefore require w < wc. A more important consideration in this regard will be the Doppler shift if there is uniform motion along the field. The fundamental frequency is then

(7.62a)

where 0 = 0 for motion toward the observer, along the magnetic field. Therefore, any observed radiation would come from particles near their mirror points (Section 3.2.4) or moving away from the observer ( 0 5 n/2).


the ordinary mode is a few percent of that in the corresponding extraordinary, but the intensity in the ordinary wave is always zero along the axis of the field and perpendicular to it.

All we have said thus far applies to gyro radiation in free space. If the background electron density should be great enough to give a plasma frequency wo - oc or greater, the emission would be altered because the phase velocity of the signal would be affected and, indeed, would not be the same in every direction. This complex problem has been treated in the paper by Twiss and Roberts [1958a].

Application to Auroral Particles.-Gyro radiation in the fundamental frequency, like Cerenkov emission, is important only in the extraordinary mode, the former because of the sense of gyration, the latter because n must exceed unity. Frequencies below the critical frequency of the ionosphere must propagate in the extraordinary mode to be detectable at the ground, unless, of course, the emission were produced below the ionosphere.

Ellis [1959a] has suggested gyro radiation as being a likely possibility for some of the very low frequency bursts. In the region of the outer atmosphere where emission is produced at frequency w - wc, there would be little guiding of the wave by the magnetic field. As the signal enters regions where wc > w, closer to the Earth, the wave could be guided in the fashion of whistlers, but the signal could nevertheless be observed at latitudes somewhat below the latitude of particle bombardment.

If only the fundamental is important, gyro radiation will contribute exclusively at very low frequencies, v < 1500 kc/sec, corresponding to 4 2 7 r near the Earth. The emission could, as with low frequency Cerenkov radiation, originate mostly in the outer ionosphere, far above the F region. Should the higher harmonics become developed, emission might be detected at very high frequencies and would then be plane polarized when observed perpendicular to the lines of force (see Section 8.2.1).

MacArthur [1959a] has stated that Eq. (7.60), which gives the emission frequencies for Cerenkov radiation along the magnetic field, may also be derived for gyro radiation from a particle with mass > m. Fast protons, he suggests, might therefore produce part of the chorus. His derivation assumes that the protons have velocity components v cos 0 w c /n , the phase velocity of the radiation. This condition gives a large Doppler shift, so that the protons radiate at much higher frequencies than their gyrofrequency [see Eq. (7.62a)], but it also approximates the Cerenkov condition (7.56).


However, as the Cerenkov condition is approached, the nonrelativistic theory for gyro radiation is invalid, and a simple application of the Doppler shift does not give the emitted radiation field. The relativistic theory shows that when the velocity of the particle is close to the phase velocity of the radiation, the intensity emitted along .the magnetic field becomes negligible. And when v < c/n, gyro radiation from heavy particles is much less intense than from electrons, as shown by Eq. (7.61); also, it would be ordinarily polarized when observed along the magnetic field. Gyro radiation from protons is therefore unimportant, and the spectrum derived by MacArthur is essentially the spectrum for Cerenkov radiation. This explains the equivalence of his result with that of Gallet and Helliwell [ 19594.

Cerenkov radiation in the outer ionosphere may also account for the discrete clustering of particles that is inferred from observations of the chorus. Modulations, in the manner of traveling-wave tubes, of the particles by the wave, may produce this clustering through the inverse Cerenkov effect.

7.2.4. Properties of Primary Electrons and Their Energy Deposition

General Considerations on the Energy Spectrum and Flux of Pr imary Electrons.-There is considerable evidence that primary (i.e., extraterrestrial) electrons, like auroral protons, possess a wide energy spectrum. Most of the arguments are based on the assumption that primary electrons are responsible for the majority of auroral excitation. This matter is certainly not proved, but with the evidence now against protons as being important energy contributors, it seems to be a justified approach.

1. Bremsstrahlung measurements, as discussed in Section 7.2.1, disclose electrons with energies exceeding 50 kev, which would penetrate below the height of most of the visible auroral radiation. An especially dramatic example of this discrepancy was the great red aurora of 11 February 1958, which occurred principally at high altitude, but which was characterized by strong radio absorption coincident with x-ray bursts (Section 4.3.3).14

2. The energy flux of these primary electrons (of the order of 4 erg/cm2 sec for the strong burst considered) is insufficient to explain the visible

in the Atmosphere

l4 In Section 7.3.1 we discuss the possibility that electron heating contributes to the excitation when the red lines are so strongly enhanced. That particle bombardment was nevertheless important is demonstrated by high-excitation lines in spectra of this aurora.


intensity (see below). Hence, we conclude that a large number of electrons with much lower energies are also important.

3. Direct rocket measurements by Meredith, Davis, Heppner, and Berg [1958a] indicated a spectrum that increased rapidly from 35 kev to 8 kev. [Electrons in the outer Van Allen regions (Section 8.2.1) also possess a wide energy spectrum. This point would seem to be pertinent to the question of whether trapped electrons eventually become auroral electrons or whether they are only the rejected particles that failed to penetrate the atmosphere directly from interplanetary space during past aurorae.] 4. The luminosity distribution with height is widely different for

different types of aurorae that have their lower borders at the same height. If all these aurorae are produced by electrons, a variable energy spectrum seems required. Indeed luminosity distributions offer the best potential means of deriving the spectrum from measurements at the ground.

In a particular collision a primary electron may lose the order of 100 ev, spent in ionizing the atom and in kinetic energy of the secondary, but some of the fast secondary electrons go on to produce further ionization and excitation. Each primary ionization may be accompanied by several secondary ionizations. On the average some 30 to 35 ev are lost by the primary for each ion pair produced in air (Valentine and Curran

A bright aurora (IBC 111) has an emission rate of about 100 kR in h3914. Adopting a ratio of 0.02 photons of A3914 per N, ionization (which has actually been measured only for electron energies below 200 ev) and a correction for the N, relative abundance at auroral altitudes, we obtain (Section 7.1.2) a total rate of ionization of 7 x lo1, ion- pair/cm2 sec. The total energy of ionization depositied in a bright aurora is around 2.5 x 1014 ev/cm2 sec = 400 erg/cm2 sec.

A rough estimate for the electron flux might be obtained by assuming an exponential spectrum. The flux of electrons per unit energy interval is then

[ 1958a1).

(7.63)

where 9 is total flux and a is a constant. The energy flux for particles with initial energy between E~ and very high energies is

(7.64)


To estimate 9 and a, we use the values quoted above for the total energy flux and for the energy flux for E~ > 50 kev. We obtain 01 = 7.5 kev and 9 = 3 x 1O1O electron/cm2 sec for a bright (IBC 111) aurora. It can be appreciated that numerous uncertainties are involved in this estimate. The total energy flux is based on average intensities, whereas the bremsstrahlung measurements were not accompanied by photometric observations, and refer to isolated bursts. Nevertheless, the ratio of the flux of electrons exceeding so = 8 kev to those exceeding 35 kev would be about 30, in fair agreement with the sort of variation derived by Meredith et al. from rocket measurements.

Some proton fluxes, for an Ha that is quite bright, were listed in Table 7.3, on the assumption of monoenergetic protons. But as we noted in discussing the proton spectrum in Section 7.1.3, the total flux might be much larger than those values, owing to the inefficient radiating ability of low-velocity protons. There is therefore no reason to suspect widely different proton and electron fluxes in the aurora.

General Considerations on the Penetration of a n Electron Beam into the Atmosphere.-As an electron spirals into the atmosphere and suffers ionizing collisions, it may be deflected through large angles. Hence even a first approximation to the luminosity distribution cannot be obtained with the techniques used for protons, which are deflected very little.

From the theory of electron-atom collisions one may compute the range of an electron with a given energy E (Bethe and Ashkin [1953a], Birkhoff [1958a]). The electron range is derived from the differential energy loss, Eq. (7.43), and hence is measured along the path of the particle and not in a straight line, as in the case of heavy ions. The angular scattering is the most important factor giving rise to a dispersion in the straight-line ranges of different individual electrons.

Table 7.5 gives some electron ranges. These data give, with a model atmosphere (Appendix IV), the maximum straight-line range or maximum depth of penetration of electrons with a given initial energy; they cannot be used to relate uniquely the energy to the depth of penetration. There is also some straggling or dispersion in ranges along the path due to statistical fluctuations in the energy lost per collision. This effect is ignored in what follows, where range will always apply to the average range measured along the path.


TABLE 7.5

EQUIVALENT VALUES OF ENERGY, VELOCITY, AND RESIDUAL RANGE' FOR ELECTRONS IN AIR

V

(loo cmisec) r

(atm-cm)

0 . 3 2 .6

10. 25. 50.

100. 200. 400.

1000.

1 3 6 9

12 17 22 25 28

0.01 0: 04 0.22 1 . 1 3 3.84

12.7 39.7

114. 385.

* The first and second values are quoted by Bates [19546] and are based on experimental data collected by Das Gupta and Ghosh [1946a]; the other values were computed from the Bethe formula by Spencer [1955a].

Computing the luminosity curve or energy deposition with height for electron bombardment is consequently rather involved. A theory, having an application to bombardment of tissues by 8-decay electrons from radioactive substances, as well as to the aurora, has been developed by Lewis [1950a] and Spencer [1955a].

Attention has been directed so far to the cases where the angular JEux, 71 cos 0, of the incident electrons is either isotropic or monodirectional. [We define q above Eq. (7.8).]

A plane source with an isotropic intensity, q, would probably be more pertinent to the auroral problem (Section 8.2.3). Calculations have not yet been made for 71 independent of 0 or for other more general distributions. In the aurora the guiding action of the magnetic field ensures symmetry in the azimuthal, 4, coordinate. I t also helps confine a fine beam of particles, even well into the atmosphere. If there were no magnetic confinement, a plane model of the source would be applicable only for uniform bombardment over wide areas. The field, on the other hand, guarantees that a fine beam of electrons will remain pretty much within a cylinder centered on a line of force and with a radius a few times the radius of gyration-at least, as long as the gyrofrequency, wc = eB/mc, greatly exceeds the collision frequency for scattered electrons.

In the theory below, we consider a plane source of electrons emitting in one direction, perpendicular to the plane. The source is surrounded above and below by a large, homogeneous atmosphere. Some of the


electrons that start initially into the upper half-atmosphere will be reflected through successive scatterings into the lower half. If auroral particles are initially directed only into the northern hemisphere, say, those reflected out of the atmosphere, with a certain pitch angle 8, will be guided by the field so that they enter the southern atmosphere with the same angle. These back-scattered electrons may therefore produce a weak aurora in the southern hemisphere simultaneously with a strong one in the northern, and a theory should give us the relative importance of the two displays.

Theory for a Monodirectional, Monoenergetic Electron Beam. -The theory of Lewis [1950a] and Spencer [1955a] has been developed for a source of monoenergetic particles. The energy deposition for a primary energy spectrum may be integrated from a number of monoenergetic solutions, but as I mentioned earlier, no numerical solutions have yet been obtained for a more realistic angular dispersion. At present, the theory is principally of interest for comparison with the distribution of ionization produced by monodirectional, monoenergetic protons (see Fig. 7.6).

Electron diffusion into the atmosphere is approached in a manner similar to that used in radiative transfer (Chapter 2), but with the added complication that the scattering function and the particle intensity depend on the residual range Y (or the energy) of the particle.

Let the path length traversed by the particle be denoted by s = ro - r , where yo is the range at the source. The infinite plane source is normal to the &axis, where 8 is then the perpendicular depth (in atm-cm) into the homogeneous atmosphere. The angle between the velocity vector and the (-axis is 8, which corresponds to the pitch angle of spiraling charges. The transport equation for an incident flux parallel to the &axis (which is analogous to auroral particles injected parallel to the magnetic field) is

Here T ( Y , p, 5 ) is the differential particle intensity in units of electron/ cm2 sec sterad per unit increment of range, where the area is measured normal to the velocity vector; Q is the differential cross section for


scattering of an electron with range r through an angle 0, between 8’, 4’ before the collision and 8, 4 afterward; N is the density of the atmosphere; 9 is the incident flux measured normal to the &axis; and p = cos 8. In the integral the first term in brackets gives the intensity scattered into the beam in direction p, and the second term is the intensity loss. The final term gives the electron source.

Taking Y, as the unit of length, we write T = r , ’~ , ; 5 = f ir , ; S(T, 0) =

7, N Q ( r , 0); and define I (T, p, 5) = ~ ( r , p, () r o / 9 . Then the transport equation in this notation is

T o begin the solution, the angular dependence of the scattering function, S(7, O), and the particle intensity are expressed in terms of spherical harmonics. Define

and

S,(T) = 277 J1 [l - P,(COS O)] S(T, 0) d(cos 0). -1

Then the particle intensity may be written as

(7.67)

(7.68)

(7.69)

and coefficients S , are determined by Eq. (7.68) from the theory and measurements of S(T, 0) for a particular substance-in this case, air.

The integration in Eq. (7.66) is carried out by use of the addition theorem for spherical harmonics (Morse and Feshbach [1953a, p. 12741). The angular distribution of the source may also be expressed in spherical harmonics. For an isotropic flux distribution we would take only the leading term. For a monodirectional source we use

(7.70)


After some reduction we obtain from Eq. (7.66) a system of differential equations,

(7.71)

These equations involve two independent variables and have not been integrated directly. They may, however, be solved in terms of their spatial moments. We define

(7.72)

Equation (7.72) then gives the double series of equations,

+ SZ(7)I ln(7) = S(T - 1) Sn0. (7.73)

This equation may be solved analytically for ILn(7) in terms of a double integration involving S1(7). Evaluation of the integrals must be done numerically and there are certain features associated with these computations that make it exceedingly difficult to obtain reliable results.

Spencer [1955a] has circumvented this difficulty by computing the residual-range moments of ILn , rather than I,, itself Defining

(7.74)

and representing S,(T) by a simple analytic expression, one multiplies Eq. (7.73) by and integrates, obtaining a recursion relation for Ipn which can be used to tabulate these moments. We shall see below how these moments are then used to obtain the energy deposition.

Energy Deposited Versus Depth in the Atmosphere.-It may seem at this point that the solution outlined above, giving the residual-range moments of the spatial moments of the electron intensity, is rather far removed from the electron intensity itself. The situation is actually not so bad, because the energy dissipation, which we are basically concerned with, also involves an integration over T .

= &(yo) its Let E ( Y ) be the kinetic energy of a single electron, and


initial energy. The energy deposited per cm3 per sec by particles of all ranges at depth ,$ is

where I, is defined by Eq. (7.67) and (d&/dr), is the stopping power when r = ro. The last equality above defines J c , which is the energy dissipation integral in the special units having ro as the unit of length. If we can obtain J t , we may compute the ionization rate per unit volume, qt = J E / d ~ l o n , where deion is the mean energy loss of a primary electron per ion pair, which is about 35 ev. Equation (7.75) gives the electron equivalent of the Bragg curve (Fig. 7.1) for protons. Both results must be scaled to atmospheric densities by writing

qz = - qc dE/dz = qg Na(z)/Na(O).

We now proceed to see how J c is computed from the known intensity moments The nth spatial moment of J c is

(7.76)

Approximating the stopping power by an expansion, for example, d&/dr = A, .-liZ + A, .liZ + A, T3'2, we obtain

(7.77)

The final moments in

step is to assume a functional form for J c and evaluate its terms of the unknown parameters in that function. Fitting

these moments with those computed from Eq. (7.77) determines the parameters and gives a complete analytic expression for Jc.

A rather extensive amount of computing is required for a numerical tabulation of Jc . Spencer [1959a] has programmed the calculations on a fast computing machine and published a number of results for electrons in air and other substances. Some of the details of defining and representing functions in that paper differ from the outline given here, but the fundamental procedure is the same.

The computations have not been carried out for initial energies c0 less than 25 kev, but as the curves at higher energies have nearly the same shape, it is possible to make a scale transformation for the energies


of interest in the aurora. The total energy dissipated is simply SF,. Equations (7.75), (7.76), and (7.72) give

which shows that J c is normalized to rate is therefore

= so/r0(ds/dr),. The ionization

(7.79)

The ratio J c / Js,o, is nearly independent of so; these values are tabulated in Table 7.6. The ionization production by electrons is compared with that produced by protons in Fig. 7.6 for an initial range for both

I2(

- E r

N

1

I- I ll( '3 W I

101

91

Observed Brightness

a

? I I I I 2 3

9 1

3 IONIZATION RATE - (~~-~ion-pair/cm primary partick)

FIG. 7.6. Ionization production by monodirectional (0 = 0), monoenergetic electrons and protons with the same initial range, Y,, = 0.22 atm-cm. The solid lines are computed from Eq. (7.79) and the ratios in Table 7.6. The proton ionization (dashed curve), taken from Fig. 7.1, is reduced by a factor of 20. The back-scatter ionization (increased by a factor of 10 in the figure) shows the aurora that would be produced in the southern hemisphere by monodirectional, monoenergetic electrons initially directed toward the northern hemisphere and subsequently scattered out of the atmosphere. The luminosity curve, shown in arbitrary

units for comparison purposes, is for an auroral arc (Harang [1945c]).


types of particle of ro = 0.22 atm-cm. Proton ionization is taken from the Bragg curve in Fig. 7.1. The electrons would have energies E~ =

10 kev, whereas the protons would have about 200 kev and produce much more total ionization per particle. Hence the proton curve is scaled down by a factor of 20. Here the curves have fairly similar shapes.

TABLE 7.6

FRACTIONAL ENERGY DISSIPATION BY MONODIRECTIONAL (e = o), MONOENERGETIC ELECTRONS

JglJl,o

Direct beam Back scatter 5 = Sir0

0.00 0.10 0.25 0.40 0.50 0.60 0.70 0.80 0.90 1 .oo

0.87 1.13 1.51 1.64 1.46 1.11 0.67 0.21 0.002 0.000

0.30 0.11 0.060 0.027

At values of ro considerably higher or lower than the example shown, the proton and electron curves would be more dissimilar. That is because the proton ionization has a broad maximum around values of Y (= ro - .$) between 0.1 and 0.2 atm-cm. The electron ionization, on the other hand, peaks at about .$ = 0.4 yo . At higher energies the proton curve is peaked lower than the electron curve. At lower energies, however, which are probably of more auroral interest, the electron curve is sharper and peaked lower than the proton curve.

It is not possible to make a good estimate of the effect of an angular dispersion of electrons, as it was for protons where the particles follow approximately straight paths. Nevertheless, it seems significant that low-energy electrons will not produce a luminosity distribution significantly broader than that produced by protons. In the case of protons we note from Fig. 7.5 that a reasonable angular dispersion with monoenergetic particles seems incapable of reproducing the luminosity distribution for arcs, whereas a combined angular dispersion (isotropic) and energy spectrum (exponential) is quite satisfactory. Quite possibly the same thing will hold true for primary electrons.


Certainly monoenergetic electrons do not seem capable of producing the long, nearly uniform luminosity distributions of rays. It was this consideration that formerly seemed to be the strongest argument against primary electrons as the source of ray structure and which pro- voked the development of a discharge theory (Section 7.3.2). In view of the evidence in favor of wide energy spectra for protons (Section 7.1.3) and electrons as well (see the introduction to this section), primary electrons might now be voted as the most important source of auroral luminosity.

7.3. Atmospheric Electrons

In this section we are concerned with two items that can not always be separated: mechanisms for producing energetic electrons and the characteristics of the auroral plasma. The detailed role played by atmospheric electrons in producing the auroralspectrum will be examined mainly in Section 7.4, but there will necessarily be some overlap between the subject matter of these two sections.

7.3.1. Secondary Electrons f rom Particle Bombardment

Production of Ionization.-Electrons produced within the atmosphere as an immediate consequence of particle bombardment are called secondary electrons, to distinguish them from primary electrons, those in the bombarding stream of particles. If we want to be fussy about it, we cannot distinguish quantum-mechanically which of two electrons emerging from an ionizing collision is the one that entered the collision. But if the ionization is produced by an electron with energy greatly exceeding the ionization potential, one of the emergent electrons will generally have much greater energy than the other, allowing us to tag it as the primary.

The average energy lost by the primary in each of its ionizing collisions is several times the ionization potential. For 30 kev electrons in air it is of the order of 80 ev (Mott and Massey [1949a, p. 2551). This much energy is lost partly because the primary also has excitation collisions without producing ionization and partly because of the kinetic energy imparted to the ionized electrons. Dalgarno and Griffing [1955a, 1958al have made detailed calculations of the processes by which the kinetic energy of a fast proton or electron is dissipated as it passes through atomic hydrogen.

7.3. ATMOSPHERIC ELECTRONS 293

Some of the jirst-generation secondaries have sufficient energy to produce additional ionizations, and in fact the larger fraction of the total ionization may well be produced by these secondaries. On the average one ion-pair is produced for roughly each 35 ev lost by the primary, regardless of whether the primary is a proton or electron and regardless of its initial energy. We noted in Section 7.1.2 that the N: intensity in a bright aurora implies a total production rate of 7 x 1012 ion-pair/cm2 (column) sec, provided that the ratio 0.02 photons of A3914 per N, ionization is valid for primary as well as secondary electrons.

For primary protons at auroral energies, Bates, McDowell, and Omholt [1957a] have computed the energy distribution of secondary electrons as they are ejected from the outer shell of neon (which behaves similarly for these purposes to oxygen and nitrogen). These calculations confirm that roughly half the secondaries have initial energies capable of producing at least one additional ion pair.

Almost all the secondary electrons are produced in the neighborhood of the primary impact, which is the assumption made in computing auroral luminosity distributions. For proton impact the maximum energy of the ejected electron is 4(m/M) E (where E is the incident energy), corresponding to twice the velocity of the proton. The penetrating power of these secondaries is very small compared with that of the proton.

Localized ionization is not the only case, however. Some secondary electrons may be produced at considerably greater depths in the atmosphere than the primaries penetrate, or at large horizontal distances from the locus of particle bombardment, through the action of x-rays or far-ultraviolet radiation. Bremsstrahlung x-rays, produced by fast primary electrons (see Section 7.2. l) , produce secondary ionization by Compton scattering, since the recoil momentum of the electron is sufficient to ionize it. These secondary electrons may then in turn produce further ionization by collisions. The ionization process is quite similar to ionization by an electron, with some 35 ev or so expended per ionization. At the higher frequencies, x-rays are much more penetrating than their parent primary and can reach balloon altitudes ( - 30 km). The softer component is more readily absorbed and may contribute to low-lying ionization associated with the aurora. Ionization in the D region during aurora is especially noticeable through radio absorption (Section 4.3.4). Possibly bremsstrahlung absorption also contributes to the fringe of E , ionization that advances ahead of an aurora as it moves toward lower latitudes (Section 4.3.4).

Chapman and Little [1957a] (also see Chapman [1959a]) have attributed much of the daytime radio absorption in the auroral zone


to the bremsstrahlung process. They maintain that is offers a natural explanation for the appearance of ionization at altitudes lower and areas more widespread than a typical visible aurora. The process was suggested for daytime absorption, because it operates at rather low altitudes. There electron attachment would rapidly deplete the free- electron density, unless photodetachment is also operative.

Without some definite knowledge about the energy spectrum of primary electrons, one cannot estimate reliably the relative importance of direct ionization by penetrating electrons and by bremsstrahlung. But as better information on the energy spectrum and geographic extent of electron bombardment away from the visible aurora becomes available, it should be possible to evaluate the importance of this mechanism.

Ultraviolet emission should also manifest itself through photoelectric ionization remote from the visible aurora. Some estimated lower limits of far-ultraviolet emissions are listed in Table 5.5. Following a suggestion of Bates [1955c], Omholt [1956c] investigated the possibility of auroral Ly a contributing to radio absorption through ionization of NO in the D region. I t has seemed likely that the D-region ionization may be attributed to solar Ly a. acting on NO, although the abundance of NO has been rather uncertain. If so, it is clear from a comparison of the auroral emission in Table 5.5 (4n-Y m 1.65 erg/cm2 sec for a bright aurora) and the solar flux (3.43 erg/cm2 sec, according to Aboud, Behring, and Rense [ 1959a]), that an extensive, bright display could compete with the daytime ionization rate.

Recombination and the Electron Density.-Knowing the total rate of production of ions from photometric observations and knowing either the electron density or recombination coefficient, one may estimate the remaining quantity for equilibrium conditions. Calculations of this sort have been made by Seaton [1954a] and Omholt [1954b], who assumed an effective recombination coefficient, aeff rn lops cm3/sec, characteristic of the normal E layer. Omholt [1955b] later measured the N,i- emission simultaneously with radio echoes (1-20 Mc/sec) from auroral E,s ionization, interpreting them as critical reflections. The electron densities obtained (up to lo6 crnp3) in this manner correlated very well with the N$ intensity and indicated - cm3/sec.

An increased recombination coefficient in the lower auroral region, compared with daytime values, seems plausible because of dissociative recombination of molecular ions. In the daytime recombination of 0: is probably the main process contributing to the effective recombination coefficient. In the aurora N,+ becomes relatively abundant and, as it


probably has a higher recombination coefficient, increases the value of cieff. Omholt [1955c] suggested that the increase could also be attributed to a difference in the negative-ion/electron ratio between daytime and au ro r a1 conditions .

Some idea of the electron densities might be obtained from the radio aurora, but as we have seen (Section 6.2.4) there is still some uncertainty in the reflection mechanism. The main objection to critical reflections at very-high and ultrahigh frequencies (Section 6.2.2) is the high Ne implied, even though these densities would occur in only small volumes at any instant. We should like to derive independently, or at least reconcile, these densities with optical evidence, considering plausible physical processes.

The local electron density changes at the rate

The first equality is essentially a definition of aeff while the second expresses recombination in terms of the coefficient for a given reaction and the abundance N+ of the relevant positive ion. We assume in this elementary discussion that at the height in question recombination is governed by a simple dominant process, and that attachment to form negative ions is negligible. (For low aurorae, attachment probably plays an important role in the recombination process and perhaps leads to the striking characteristics of a type-B red auroral spectrum; see Section 7.4.2).

Consider an auroral arc at average altitude, with its lower border around 110 km. The arc will have a vertical extent, measured between the heights of half-maximum intensity, of some 30 km. Hence a bright (IBC 111) aurora has an ionization rate near 120 km of q m 7 x l0lz/ 3 x lo6 m 2 x 106 ion-pair/cm3 sec. At this altitude N, contributes a major part of the abundance. Taking areC m lo-' cm3/sec for dissociative recombination (1.106) of N,+, we obtain an equilibrium abundance of Ne * 5 x lo6. Since N(N,) m 2 x 1011 at the altitude in question, its abundance would not be seriously modified by dissociation.

Even though this treatment is extremely crude, it nevertheless contains what seem to be the essential features of the problem. I t is not clear how N e could be greater, in small volumes or large, by a factor of 10' or more, to explain UHF radar echoes by critical reflection at this altitude. If the densities were so high, even for brief moments, very bright flashes in the visible aurora should accompany the formation of a reflecting volume.


Electron Velocity Distribution.-Secondary electrons, when they are first formed, have energies of several electron volts, as we have observed above. Recombination, on the other hand, involves principally electrons with thermal energies. Hence a secondary electron must be energetically degraded through successive inelastic and elastic collisions until it is moving slowly enough to be captured.

Bates [1949a] divides the electron population into two groups: active electrons, with energies of several electron volts, are capable of producing excitation, and the passive electrons are those in the thermal region, which is generally less than 0.1 ev. The majority will be passive, as we can see from the characteristic lifetimes for electrons in the two sets. A passive electron has a lifetime T~~~ - 1jNe meif, which is likely to be at least several seconds, except at quite low altitudes. A fast electron will be degraded mainly by inelastic collisions and will have a total rate coefficient for excitation, Sexc 2 cm3/sec. The lifetime, ‘Tact - l/Na sexc, is a small fraction of a second below 200 km. At higher altitudes both lifetimes increase; it appears that the active electrons will always be in the minority.

A calculation of the velocity distribution under equilibrium conditions would involve a knowledge of the energy distribution of ejected electrons and their rate of energy loss by different types of collision. Having this distribution, one might calculate the excitation rate of various molecular levels and the intensities to be expected in the different transitions. The data required for such an idealized program are not available and we must be content with some rough estimates.

Omholt [1959b] has estimated the distribution function for secondaries, on the basis of the energies of ejected electrons and selected inelastic collisions. While no great accuracy could be claimed, the general results are similar to those reached below by a more empirical approach. We shall merely attempt to draw some general conclusions regarding what must happen as an active electron is degraded in energy.

An important question in auroral excitation pertains to the relative intensity of [OI],, A5577 and N,+ A3914. These emissions show strong correlation, appearing with comparable intensities except under special conditions, such as sunlit aurora or at very low altitudes (Section 5.2.4).

If only about 2 percent of all ionizations of N, lead to a quantum of A3914 (Section 7.1.2), then the observations show that a comparable fraction of secondary electrons excites [OI],,, which has an excitation potential of only 4 ev. But we know that about half the first-generation secondaries produce an additional ionization.

Perhaps the primary electrons produce a much higher fraction of A3914 photons per N, ionization than do secondaries. For example, if


every primary ionization produced a quantum of X3914, the number of secondary ionizations (still about half the total) would be of the same order as the number of A5577 excitations.

Therefore, the number of secondary electrons exciting [OI],, is less, and perhaps much less, than the number ionizing N,. On the other hand, if the active secondaries were mostly concentrated at low energies, the green line should be far brighter than X3914. Deactivation is probably unimportant except at the lowest auroral heights. Even though the [OI],, cross section is an order of magnitude below the gas-kinetic value, the active secondary must pass rapidly through its low-energy range.

By assuming an analytic form for the distribution function, we may obtain a rough idea of the electron energies in a steady state (see Problem 7.5). The active electrons are evidently peaked at an energy much higher than 4 ev.

Why should the distribution function of secondaries contain relatively few electrons in the 4-15-ev region ? The steady-state distribution is governed partly by the initial energies of newly created secondaries and partly by the type of collision that is dominant in degrading the electronic energy. Omholt’s [ 195961 preliminary investigation of these effects gives plausibility to a distribution function peaked at high energies.

There is one type of collision, however, not included in Omholt’s treatment, which may be important in the aurora. Collisions involving electron exchange have a maximum probability close to the threshold energy. If nearly all an electron’s energy is likely to be lost in single encounters, the distribution function for secondaries can be greatly diminished in the low-energy active region (also see Section 7.4.1).

Emission Efficiency and Auroral Heating.-Another item of interest, which could best be treated with a distribution function for the electrons and all the relevant cross sections, is the emission efficiency 6, or the fraction of the total energy put into the atmosphere that escapes as nonthermal radiation. Not having all this information, we may try to estimate how the energy is dissipated by following the history of a single electron.

Virtually all the kinetic energy of the primary is lost by collisions, an average of 35 ev for each ion pair manufactured. A portion of this goes into excitation directly by the primary, possibly accompanying ionization. The secondary electron in turn expends most of its energy in excitation. It seems likely that almost all the excitation energy is eventually emitted. Deactivation of the Vegard-Kaplan bands is the main uncertainty here. Table 5.5 shows that the emission in this system is even less than would be anticipated from cascading alone. The de-


activating mechanism is not known, so we cannot be certain that the energy is really dissipated as heat.

In any case little of the electron's energy is lost by deactivating collisions, and probably little goes into molecular vibration as long as its energy exceeds 2 ev. Below that energy the red lines, [OI],,, can no longer be excited and elastic collisions and vibrational collisions of the homonuclear molecules 0, and N, offer the principal outlets. These collisions represent energy mainly lost as heat.

Another source of heat energy is the ionization potential. For atomic recombination this energy would be emitted, but for molecular ions dissociation generally accompanies recombination. Of the 7 ev or so difference between the ionization and dissociation potentials, a portion may go into exciting the newly formed atoms. Perhaps half goes into atomic kinetic energy. Much of the dissociation energy itself may also eventually go into heat, if association occurs by the three-body process. This energy would be released at 100 km or lower.

Altogether it does not seem unreasonable that at least 5 ev is dissipated into thermal motions for each 35 ev lost by the primary particles and that (5" 5 85 percent.

There are two outstanding questions on auroral heating: (1) Does the temperature increase significantly during a bright aurora ? and (2) Does particle bombardment affect the average temperature and structure of the thermosphere in the polar regions ?

We estimated in Section 7.1.2 that a bright aurora caused by particle bombardment may consume as much energy as 2.5 x 1014 ev/cm2 sec = 400 erg/cm2 sec. Possibly as much as 350 erg,/cm2 sec is radiated, which would mean that the ultraviolet emissions are far stronger than just those resulting from transitions that can be definitely inferred from cascading down from higher levels (see Table 5.5). The energy dissipated as heat will be of the order of 4 x ev/cm2 see = 60 erg/cm2 sec.

If the auroral luminosity distribution varied in proportion to the density of the atmosphere, we would infer that the heating was nearly uniformly distributed over all atoms in the auroral atmosphere. For an actual aurora, and especially ray structure, the luminosity may decrease upward much more slowly than the density. Even with this heat uniformly distributed among the particles above 110 km, each atom or molecule gains energy at the rate ds/dt = 3 x

The energy associated with T = 300" K is kT = 3 x lo-, ev. Hence the time scale for a significant increase is the order of lo3 sec. The time scale for cooling by downward conduction and radiation resulting from thermal collisions is the order of a few. days (Bates [1951a]). While there are several uncertainties involved here, it does seem plausible

evjsec.


that bombardment during a great aurora, especially a high-altitude one, might produce temporary but large changes in the temperature.

Section 5.2.7 and 5.2.8 contain summaries of rotational and vibrational temperatures of NZ. For some high sunlit aurorae there is evidence that the kinetic temperature approaches 2000" K during auroral bombardment. Perhaps these high temperatures are produced in part by the auroral particles themselves.

Bremsstrahlung measurements in the auroral zone (Van Allen [ 1957~1) show that particle bombardment at low intensity is a frequent phenomenon. Also, visible aurora, usually of low intensity, is observed during a substantial portion of the dark hours. For rough estimates, we assume that the energy deposited by particle bombardment is that of a continuous aurora of low intensity (IBC I), which gives an energy rate of 3 x lo-' evlsec per atom and a time scale the order of lo5 sec or about 1 day. Hence it is plausible that the temperature of the polar thermosphere is governed in large part by auroral particles. Auroral heating over the polar cap may therefore produce considerably greater thermospheric temperatures than are found at temperate latitudes. (See Section 12.2.1 for further discussion of a latitude variation of temperature. Also see Jastrow [1959u] and Ishikawa [1959u].)

Thermal Excitation of the Red Lines.-Should sufficient heating occur above 150 km, where deactivation of the red lines is not too important, thermal electron-atom collisions could become frequent enough to produce strong red-line emission. The discussion above shows that substantial heating by particle bombardment may reasonably be expected. If thermal excitation were important, the ratio of red/green intensities could become far greater than that due to newly created secondaries alone (Section 7.4.1).

We have little idea of the actual temperature structure of the auroral atmosphere and can only make an illustrative calculation. The rate of emission is obtained by integrating Eq. (13.21) over all heights. Suppose that effective values are Ne rn lo6 ~ m - ~ and T rn 2000" K for the region immediately above 200 km. The rate coefficient sI2 is treated in Sec- tion 13.3.1 and is 2.4 x cm3/sec for this temperature. The zenith emission would then be 47r9 = 0.4 kR. Thus a fairly modest amount of heating could account for enhanced A6300 in the airglow. Larger amounts might produce the faint, diffuse, red arcs that occasionally accompany an aurora at latitudes slightly lower than the main display (Section 5.2.3).

In using the Maxwellian distribution for the above calculations, we assume that the high-energy tail is not itself depleted by these collisions.


Elastic collisions, which redistribute the velocities, will be much more frequent than the inelastic ones, but the higher energies are nevertheless probably depleted.

Extreme conditions would be required to explain the enormous brightness of the great red aurora of 11 February 1958 (Section 5.2.2) and other strong displays with high red/green ratios as due to heating. The 11 February display had a brightness of only IBC I1 in the green line, indicating a total flux for particle bombardment that was not unusually large.

If Ne exceeds lo7 ~ m - ~ , electron deactivation is important, so that Eq. (13.21) is essentially independent of Ne, and the O ( l 0 ) population is in the thermal-equilibrium ratio with the ground term.15 An emission rate of lo4 kR would require a temperature of several thousand degrees extending down to 150 km or lower. A more precise estimate of conditions is scarcely feasible, since such high temperatures would make important modifications in the entire structure of the atmosphere. I t may be also that to explain the red/green ratios (Section 7.4.1) as well as the intensity of the red line, one would have to consider the depletion by inelastic collisions of electrons on the tail of the Maxwellian curve.

The required temperatures seem unreasonable, and the explanation for these aurorae may even involve the active, secondary electron distribution (Section 7.4.1). But any mechanism producing as much red-line excitation as this aurora demands an unusual situation. Particle bombardment is not the only means whereby auroral electron heating could occur. In particular, hydromagnetic waves (Section 7.3.2) may offer a means of producing thermal excitation without large amounts of auroral ionization.

7.3.2. Other Mechanisms for Producing Energetic Atmospheric Electrons

Although bombardment by extraterrestrial particles is generally thought to be the primary source of auroral energy, other mechanisms have been suggested for various reasons. The principal alternative or supplementary processes involve electric discharges or hydromagnetic waves.

Electric Discharges.-Auroral discharges have frequently been suggested in the literature (e.g., Lemstrom [1886a], Thomson [1917a]). A theory of auroral excitation based on electrical acceleration in the atmosphere was developed by Chamberlain [1955b, 1956bI because of a

l5 In this case the calculation may also be based on equations derived for thermal equilibrium; see Problem 7.6.

7.3. ATMOSPHERIC ELECTRONS 30 1

difficulty encountered in attributing auroral rays to particle bombardment.

The difficulty was that a wide spectrum of incident velocities would be necessary to reproduce the long, nearly constant luminosity distribution of some rays. W e have seen in Sections 7.1.3 and 7.2.4 that electrons as well as protons do bombard the atmosphere and that wide energy dispersions seem to be present, whether or not they fit our preconceived ideas about particle streams from the sun. Hence, the main incentive for a discharge theory-which was at best a negative reason, since the existence of the assumed electric field has never been convincingly demonstrated-has now disappeared.

The basic ideas and results may still find some application, and I shall summarize them briefly. A characteristic feature of long rays is nearly constant brightness over a change of atmospheric density by a factor of 100 or more. But high altitudes, where the mean free path is greater, are more effective for accelerating electrons. The number of target atoms and the number of fast electrons might therefore compensate one another over large ranges of density, without large changes in the electric field being required.

The first step is the calculation of energy distributions for electrons under the influence of an accelerating electric field along the geomagnetic field. The basic parameter governing the distribution function is = Eeh, where E is the field and X the mean free path. Then E l is the energy gained by the electron in falling down the field a distance of one mean free path.

Having approximate distribution functions, one may estimate the excitation of the [OI] red and green lines and the amount of ionization. The ionization and excitation (or the parameter E ~ ) , if known at some height, may be computed for any other height by imposing a condition on the current-for example, by requiring the total current to be constant dong the length of a ray-provided that the recombination coefficient is also known.

Without good information on the recombination processes, a more empirical approach is necessary. The approach I adopted was to assume a constant luminosity in the green line along the ray and to see what variation in (and in Ne, through the condition on the current) was implied. It was found that Ne and E decreased and increased gradually with height. The intensity ratio h3914/X5577 should increase markedly with height, however, contrary to observations (Section 5.2.4). This fact will be evident from the consideration that at high altitude & a is greater, giving a larger proportion of electrons that can ionize, as well as excite the green line. The comparable intensity of [OI],, A5577 and


N$ A3914 at all heights must evidently be attributed to particle bombardment. For the discharge mechanism a constant ratio is not consistent with a nearly flat luminosity distribution in either emission.

The spectroscopic evidence is therefore against a discharge mechanism for rays. The only type of spectrum that might fit pure discharge excitation is one in which N$ and other high-excitation emissions are far weaker than the forbidden lines. Seaton [1956a] applied the theory to low-latitude aurorae, which characteristically have a high redlgreen ratio. Their spectra also show strong N$ enhancements, which Seaton ascribed to resonance scattering from sunlit aurorae.

volt/cm) could be maintained solely along rays, with the electric conductivity being quite high throughout the ionosphere. Several mechanisms have been proposed, some quite independently of the atmospheric discharge mechanism, for producing electric fields in the upper atmosphere.16 For discharge excitation the field should extend only over the cross- sectional area of the rays and must continually be maintained against the large flow of current. These requirements seem to be exceedingly difficult to reproduce with a plausible model of the auroral energy source.

I t is not apparent how the required electric fields ( E -

Hydromagnetic Waves.-Oscillations in the magnetic field, traveling down the lines of force like waves on a vibrating string, will dissipate their energy in the relatively viscous upper atmosphere. This phenomenon duplicates one of the characteristic features of the discharge theory, viz., that low energy levels would be excited more readily than levels of high excitation. Like the discharge mechanism, hydromagnetic dissipation increases the energies of all electrons, so that their distribution function simulates one of very high temperature.

A hydromagnetic wave arises from a coupling of the electromagnetic and hydrodynamic properties of a fluid. If 6 , is a small perturbation in the main field, B,, in a medium of very high conductivity, it will propagate along the z axis according to the equation (AlfvCn [1950, P. 7 8 1 ~

(7.81)

where p is the mass density. The velocity of propagation of this transverse wave is BJ(47~p)l’~. In the event that collisions are important

1E For example, Wulf [1945a, 1953~1, Martyn [1951a], Alfvbn [1950u, 1955u, 1958~1. Lebedinskii [1952a, 1956~1 and Reid [1958a] have considered the rays as resulting from vertical discharges while arcs were attributed to a horizontal flow of current in the E region, closing the circuit. See Chamberlain [1958c] for a review.


during an oscillation of the wave, the equation must be modified to allow for dissipation. Longitudinal propagation of disturbances is also possible.

Dessler [1958a, 6 , 1959~1 has considered the possibility that hydromagnetic waves, generated in the outer atmosphere, might contribute to ionospheric heating during magnetic storms. As a wave propagates into the ionosphere, collisions will dissipate its energy into thermal motions. The heating becomes important where the collision frequency is the order of the wave frequency. Not much is really known about what kind of waves to expect, but there is some justification for taking a frequency around 1 sec-I.

The main region of heating is then around 200 km. Dessler estimates an energy dissipation rate of the order of erg/cm3 sec, which, if distributed among all the particles equally, would amount to ev/sec per atom. Over the period of a magnetic storm (several hours or a day) the heating could be comparable to the heat energy in the atmosphere. (At T = 1100" K, kT = 0.1 ev.) This rate is of the right order to compete with heating from particle bombardment (Section 7.3.1); it might be quite effective at the higher auroral altitudes (see, however, Akasofu [1960b]).

Exceptionally strong hydromagnetic waves might produce sufficient electronic heating to produce thermal excitation of the red lines (Chamberlain [1959b]; Section 7.3.1). Until more is known from satellite measurements about the actual waves entering the ionosphere, we can only speculate about their auroral importance.

7.3.3. Radio Emission

Here we are concerned only with radio-emissions generated by atmospheric electrons. Mechanisms depending directly on primary electrons are treated in Section 7.2.

Plasma Oscillations.-Suppose that an excess of ionization is produced in a localized region of the ionosphere. The electrons wifi diffuse outward much faster than the ions. A polarization field will be created from this charge separation, and the electrons will be accelerated inward. In this manner an oscillating motion of electrons will be established.

The polarization field, being proportional in a first approximation to the electron displacement about the neutral position, leads to a simple harmonic motion. For a one-dimensional oscillation, the electron's equation of motion, for zero collision frequency, is then

(7.82) d2 x d t2

m- = - e E = 4 n e P = -44nNee2x.


Assuming a periodic motion, x = x,, e - i m t , we obtain w = w,,, where wo is the plasma frequency given by Eqs. (3.54) and (3.56).

In this approximation no radiation could escape from the plasma, since the index of refraction, n = [ l - (W$W~)]~’~ , is zero. A more refined analysis that allows for the random thermal motions shows that the steady-state frequency is slightly higher than wo. The theory of plasma oscillations, and their excitation by beams of particles, has been examined by Tonks and Langmuir [1929a], Bohm and Gross [1949a], and Jaeger and Westfold [1949a], and is reviewed by Francis [1960a].

Each electron radiates as an oscillating dipole and its total energy loss, if there is no destructive wave interference, is given by Eq. (1.22). The difficulty in estimating the power output for a specific problem lies principally in the uncertainties as to the effective instantaneous volume that is emitting, and the amount of interference. The amplitude of oscillation may be estimated roughly from a mean velocity for ejected electrons and the frequency.

Theoretical treatments generally consider the one-dimensional problem, in which the disturbance is a function of x, say, and the time, but is independent of x and y . The electron oscillations in the x and y directions give radiation in the x direction. If the disturbance is a function of time (for example, a single burst of particles), the Fourier analysis predicts a continuum of emitted frequencies w > wo,

although as t -+ 03, the spectrum may settle into the steady-state frequency wo.

Forsyth, Petrie, and Currie [ 1950~1 proposed that plasma oscillations in the ionosphere were responsible for the auroral emission at very high frequencies (Section 4.3.5). If correct, the mechanism implies the existence of small volumes with high electron densities. T o produce emission at 3000 Mc/sec, densities of the order of loll electron/cm3 are required by Eq. (3.56).

Thermal Emission.-A surface radiating as a black body emits an isotropic specific intensity1’ according to Planck’s law,

2 h v3 1 2 kT I, = B,(T) ~ c2 (ehvlkT - 1) M - p (7.83)

where the approximate equality is the Rayleigh-Jeans law for long wavelengths. In a particular frequency the atmosphere may not be opaque enough to be considered as black surface, but if matter is in

l7 Note that in this section we write intensity in energy units, although photon units are used in other sections, where we are concerned with optical observations.


thermal equilibrium with its surroundings, Kirchoff’s law relates the emission rate, it,, to the absorption coefficient, k,, and Planck’s law. We have in volume dT an emission rate of d i v = k, 477 B,(T) dr , or, when the atmosphere is nearly transparent, an intensity of

m

1, = s, k, B,(T)dr, (7.84)

where the integral is carried over the line of sight and k, for radio frequencies is given by Eq. (3.57).

With these equations one might estimate the thermal emission in a particular frequency, using Eq. (7.83) when J k , dr 2 1, and eq. (7.84) when this integral is < 1. But it is necessary to bear in mind that these equations apply strictly for thermal equilibrium ; their application requires some judgment as to whether the departures from thermal equilibrium at the frequency in question are important (see Section 1.1). In this connection we must inquire into the physical processes on the atomic scale that are contributing to the emission.

Let us take the example of thermal emission in the radio region at frequencies above the local plasma frequency, v,, = W,,/~T. Forsyth, Petrie, Currie [1950a] suggested this as one mechanism for producing auroral radio bursts. From the discussion in Section 3.3.2, it is clear that absorption arises when an electron that has been set oscillating by an incident wave has a collision and loses its ordered motion.

The essential feature of thermal equilibrium is detailed balancing, in which every process cz -+ b is balanced by the inverse process b -+ a. Therefore, if we are to compute the thermal emission in the radio region with the equations for thermal equilibrium, it is sufficient that the energy lost by radiation is small compared with collisional losses, and that electrons receive as much energy from collisions as they lose. Then there will be an equilibrium between the electron temperature avd the ion or neutral-gas temperature. Such an equilibrium can be established after a few collisions, so the time required for it to be achieved is quite short over the lower ionosphere. Hence Eqs. (7.83) and (7.84) give us the radiation produced by the accelerations that electrons undergo in their collisions. The radiation process may be considered as the purely classical one in which an accelerated charge emits energy.

A more sophisticated approach would inquire into the quantum mechanics of the emission. We may neglect radiative captures and cascading for the radio emission, since the inverse processes are unimportant in producing radio absorption, as evidenced by the small absorption produced by the entire troposphere. For captures this point is not immediately obvious, because the amount of ionization present


is not the same as in strict thermal equilibrium at several hundred degrees. From Eq. (1.92) one may show that in thermal equilibrium the ionization would be greater. (In the atmosphere captures into excited levels are not balanced by photo-ionizations from the same levels.) Hence, the actual radio emission from the aurora by captures is even less than under the idealized conditions.

The mechanisms to consider then are free-free emissions (bremsstrahlung from thermal electrons) in the neighborhood of ions and in the neighborhood of neutral atoms. In the lower ionosphere the latter is more important because of the great number of neutral particles. We conclude that the principal source of thermal emission is probably free-free transitions-the quantum jumps that an electron makes even during “elastic” collisions with atoms. This supposition is tested below for decelerated auroral electrons by a rough argument from classical radiation theory. Forsyth, Petrie, and Currie [1950a] have made some numerical estimates for these various processes, and give references to the basic literature.

Consider now the black-body radiation from a surface at 600” K and at 30 Mc/sec (A = 1000 cm). The Rayleigh-Jeans approximation to Eq. (7.83) gives B,, = 1.7 x erg/cm2 sec sterad (unit frequency interval). (Multiply by for watt/meter2.) While few absolute measurements have been made, this figure is perhaps the observed order of magnitude at most frequencies (see Hartz [ 1958~1; however, the 10-cm observations of Forsyth, Petrie, and Currie [1949a, 1950~1 were much stronger), but it has not yet been corrected for the atmospheric opacity. Since the ionosphere is usually very transparent in the VHF range, it seems unlikely that an increase of temperature alone could account for radio emissions. But in times of auroral activity the atmosphere may become strongly absorbent (Section 4.3.4) and hence an efficient emitter. Auroral radio emission would then arise from the lower ionosphere, and be associated perhaps with bursts of highly penetrating electrons. Since B , varies as v2, and k, varies from Eq. (3.57) as v - ~ , the intensity I,, would be nearly independent of frequency. Radio absorption of several decibels at frequencies as high as 50 Mc/sec or so might therefore be accompanied by detectable thermal emission at the higher radio frequencies.

Radio Emission from Fast Secondary Electrons.-It might be supposed that secondary electrons produced in the atmosphere would have a much higher equivalent temperature (defined by the mean energy per electron) and would therefore radiate much more efficiently. Even for this situation a first approximation may be obtained with Eq. (7.84), since


the low temperature of the heavy particles will have little effect on their collisions with electrons. But the collision frequency and absorption coefficient from Eq. (3.57) would then involve only the active (high- temperature) electrons, and their low density will tend to counteract the advantage of the high temperature in Eq. (7.84).

With Eq. (3.27) for K,, the rate of emission is

(7.85)

where Ne is now the density of high-velocity, secondary electrons only, and Ne vc is the number of electron-atom collisions per cm3 per sec; a collision is counted if it substantially alters the electron’s momentum. With a mean electron velocity of 3 x lo8 cm/sec (= 25 ev) and 1013 effective collisions/cm2 (column) sec (probably a safe upper limit for collisions in this energy region in a bright aurora-see Section 7.2.4), we find I , m 2 x erg/cm2 sterad sec (unit frequency interval). This value is well below the value that might arise from ordinary thermal emission when increased ionization raises the opacity in the VHF band, and deceleration radiation can probably be discounted as a radio source. (It may be verified that J K , dr is only 3 x 10-2/v2, where v is in Mc/sec.)

Incidentally, it is of interest to derive Eq. (7.85) from a completely different approach, one that emphasizes the physical process that produces the emission. This process consists of free-free transitions, essentially the same mechanism as the bremsstrahlung discussed in Section 7.2.1. At low velocities the electrons collide with an atom and are deflected (i.e., accelerated) in a more complicated way than at high velocities, where they follow hyperbolic orbits through the nuclear Coulomb field. Nevertheless, a simplified classical approach will be instructive.

For a collision that produces a large deflection, the forward velocity component is altered by an amount 6v comparable to the initial speed v . Equation (1.13) for the classical rate of radiation is

- 2e2iisvj2 36-3 6t ’ 8& 6t _ _ _ _ (7.86)

where 6 t is the duration of the collision. One may do a Fourier analysis of 6v/8t, which is proportional to the total amplitude of the emitted radiation (see Panofsky and Phillips [1955a, p. 3041). If the collision is assumed to occur in a very short time, the energy radiated per unit frequency interval in a single collision is

4 e2 6 F , = -v2

3c3 ’ (7.87)


which is independent of U. The fact that there is no high-energy limit to the spectum is a result of approximating the deceleration as occurring instantaneously. But in Eq. (7.86), a time interval S t - u0/v, where a, is the Bohr radius, shows that Eq. (7.87) will be appropriate for frequencies as high as the visible region. Multiplying Eq. (7.87) by Ne vc/42r and integrating over d7 gives very nearly the specific intensity of Eq. (7.85), derived from considerations of thermal equilibrium.’*

7.4. Theory of the Auroral Spectrum

A wide variety of processes contribute to the optical emission of aurorae. Some of these mechanisms have already been discussed in the previous sections. Here we shall summarize what is known about the contributions of the various types of excitation process, referring when necessary to the earlier discussions.

7.4.1. Fast Particle Impact

General Considerations.-Since the fundamental source of aurora is the kinetic energy of charged particles, fast collisions are the most obvious excitation mechanism. Direct excitation by collisions accounts for most of the auroral spectrum, but there are still many uncertainties regarding the detailed processes.

First we may classify collisions according to the exciting particle:

I. Heavy particles A. Ions (H+) B. Neutrals (H)

11. Electrons A. Primaries (e 2 1 kev) B. Secondaries ( E 5 100 ev)

Some laboratory experiments on impact excitation, designed to simulate auroral conditions, have attempted to distinguish the qualitative appearance of spectra produced by heavy ions from that of spectra due to primary electrons. The results are still inconclusive (see references in Section 7.1 .2).4 Perhaps the most important difference between these spectra is the vibrational distributions in the band systems(Section 5.2.8).

The intensity of forbidden optical emissions may also be computed from the Kirchoff law for conditions where detailed balancing is approximated. This justification is left as an exercise (Problem 6).

7.4. THEORY OF THE AURORAL SPECTRUM 309

The distinction between primary and secondary electrons can be a bit nebulous in cases of high aurorae, which may arise from a high flux of low-energy electrons. For bright displays at the lower altitudes, most of the primaries were found in Section 7.2.4 to have energies of several kev.

Next we may ask what type of collision occurs. Each type of particle could theoretically produce direct excitation of the type that is optically permitted-specifically, when no reversal of electron spin is involved. Heavy ions are specially designed for charge-transfer collisions (1.103) and at the lower energies (5 30 kev) this process competes favorably with direct ionization (1.102b). Fast neutral atoms may produce excitations involving a change of spin, with electrons being exchanged between the particles.

Secondary electrons are likely to be far more important than primaries in exciting the atomic metastable levels and the triplet levels of N, (which give rise to the observed N, band systems). These excitations require electron exchange, which is favored by low impact velocities.

Impact excitation of a particular level might also occur in a slightly more subtle manner. For example, if molecular excitation from the ground level populates a singlet level, there may be an almost elastic collision, transferring the molecule to a triplet level. Impact may also produce excited atomic levels by dissociating a molecule and simultaneously exciting one or both atoms.

Excitation of H emissions from auroral protons is treated in Section7.1; here we shall be concerned only with atmospheric constituents.

Nitrogen Band Systems.-The principal problem with Ng emission arises from the different types of impact. Bates [1949a] showed that N,+ (in an aurora in the dark atmosphere) must arise from simultaneous ionization and excitation of N,. The intensity of N,+ excited from the ground state of N,+, relative to the intensity of the green line, would be of the same order of magnitude as the relative abundances of NZ and 0, since the excitation potentials and presumably the cross sections are comparable. Hence it is easy to see that a sizeable fraction of the auroral atmosphere would have to be ionized for this mechanism to be important.

Possibly half the total ionization is produced by secondary electrons (Section 7.3.1), which tends to obscure the effects of heavy-ion collisions. However, if protons are important in auroral excitation, charge-transfer collisions may contribute to raising the apparent temperatures. The vibrational distribution of the excited ions thus offers one means of detecting heavy-particle impact, but other possibilities exist for raising vibrational temperatures. These matters were discussed in Section 5.2.8 ;


we may conclude that electron collisions would explain most of the observations. For some reports of high vibrational development the interpretation could be either (a) the spectra were actually obtained from sunlit aurora, (b) the kinetic temperature at great heights was increased by the aurora (Section 7.3.1), or (c) proton impact was more important than is usually the case.

Rypdal and Vegard [1939a] and Stewart [1955a, 1956a, b] have measured the excitation functions (cross section versus particle energy) for electron excitation of the N,+ bands. Stewart’s measurements in absolute units are especially valuable in relating the N$ intensity to the total ionization rate (Section 7.1.2).

As noted in Section 5.2.8, the vibrational distribution of N, Second Positive gives no reason for doubting electron impact as the principal mechanism for this and perhaps the other N, systems. Direct excitation requires electron exchange and consequently the excitation functions are sharply peaked at energies just above the threshold (Rypdal and Vegard [1939a], Stewart [1955a]).

Excitation of the N, bands may consequerltly be a major factor in slowing down electrons in the 10- to 15-ev region. Since such collisions will take most of the electronic kinetic energy, they could be important in diminishing the distribution of active electrons between about 2 and 15 ev. If this is correct, then N, is important in suppressing the [OI],, green line-not through deactivation but by removing electrons that would otherwise excite the green line.

Differences (with time or with height) in the electron distribution function might manifest themselves in variations in the spectrum. Even two band systems with similar excitation potentials could show noticeable variations, if they had widely different excitation functions. These considerations may explain some variations of the N, bands compared with N,+ (Rypdal and Vegard [1939a]). Stewart, Gribbon, and EmelCus [1954a] have used this difference in the excitation functions of the N, First Positive and N$ Meinel systems to regulate their relative intensities in laboratory sources.

Forbidden Atomic Lines.-The cross section isgiven in terms of the collision strength, 52, by Eq. (1.99). Seaton [1953a, b, 1956~1 has calculated values of 52 for the forbidden atomic lines, summarizing his methods and results in the latter paper. The most complete discussion of excitation of these emissions in the aurora is also given by Seaton [1954b].

Were the distribution of electron velocities known, it would be a simple matter to compute the excitation rate in [OI],, red and [OI],,

7.4. THEORY OF THE AURORAL SPECTRUM 31 1

green lines. Reversing the procedure and using observed ratios to gain some information on the distribution function is not entirely straightforward, because of deactivation and additional excitation mechanisms, especially for the red lines.

Following Seaton we shall characterize the distribution function of active electrons by an effective temperature, T e A , remembering that a Maxwellian distribution has no special qualification other than its convenient analytic form. In the absence of deactivation the photon intensity ratio is then approximately

We have neglected a small correction factor for cascading in [OI],,, h2972, and have used the approximation that the Q s are constant, which gives Eq. (1.100). Anticipating the result, we adopt effective values of sZ( 1, 2) = 1.5 and sZ( 1, 3) = 0.30, which are strictly appropriate for electrons around 10 ev.

If the green line were excited directly, by some selective process, the red emission would still have about the same intensity as the green, just from cascading. And if, as we have considered here, the mechanism is inelastic electron collisions, the ratio of red/green intensities should be the order of 6 or greater. This ratio is about the maximum observed at great altitudes (Section 5.2.2) with the exception of the very large ratios sometimes seen at low latitudes, which require quite a different electron distribution function from the usual aurora (Section 7.3.1).

We conclude that deactivation of the red lines is important except at the higher altitudes, and that ordinarily kTeA >> 2 ev = - E,,.

That the distribution of active electrons has a maximum at rather high energies is in qualitative agreement with the conclusion reached earlier (Section 7.3.1) from the ratio of N,+ h3914/h5577 ’at lower altitudes.

-Since this distribution function is affected by inelastic collisions with N,, it could be greatly different at very high altitudes where the 0 / N 2 abundance ratio is large. If the distribution of active electrons is more heavily weighted a& low energies, the red/green ratio would be increased. This consideration offers a possible explanation for the high-altitude, faint red arcs (Section 5.2.2) and the brilliant red aurorae, such as that of 11 February 1958.

Seaton [1954b] concludes that for the [NI] lines to be excited by electron impact, analogously to [OI], rather large amounts of N, dissociation are required. Seaton’s adopted intensities for [NI],, and “I],, (which are less subject to deactivation than [NI],,) were considerably greater than those in Table 5.5. Nevertheless, the abundances of


N and 0 would have to be roughly the same for electron collisions to produce the observed intensity.

Another possibility involving fast particles is collisional dissociation of N, (Bates [1955c]),

N, + X - + N + N* + X, (7.89)

where X represents an electron, proton, or H atom. The same mechanism dissociating 0, could contribute to the [OI] lines.

The [NII] lines are most probably produced from dissociative ionization of N, (Seaton [1954b], Bates [1955c]),

N, + X - N + N+* + e + X. (7.90)

Bates, Massey, and Pearse [1948a] thought that [OII] lines should be present, since they expected the reaction

0 + X-+O+* + e + X (7.91)

to be important. The corresponding mechanism for N, produces the N,+ bands. The [OII] lines are now definitely identified, but are quite weak. Cross sections for electron impact with 0 and with N have been computed by Seaton [1959a] and measured by Fite and Brackmann [1959a]. It appears from these cross sections that [OII],,, which has a radiative lifetime of a few seconds, is strongly deactivated (see Problem 7).

Krassovskii [1958a] considers charge-transfer collisions (1.103) between protons and 0 atoms to be responsible for the red lines in high aurorae. After the O+ ion is created it has a slow collision with N, which leads to [OI],,. As Omholt [19596], has stated, it is unlikely that the process could dominate over electron impact.

Other processes than fast collisions may contribute to the forbidden lines, and slow collisions are responsible for deactivation. These matters are deferred to Section 7.4.2.

Other Emissions Excited by Fast Collisions.-Collisions by secondary electrons must produce some of the excitation of the metastable 0, states, but slow collisions are also important for the Atmospheric bands (see below).

The 0; bands will be produced in the same fashion (simultaneous ionization-excitation) as the N; systems. The enhancement of these bands in the low, type-B aurorae is usually attributed solely to the relative abundance of 0,. T h e bands are weak in any case, so this presumption is difficult to test quantitatively.


Permitted atomic lines of 01 and 011 could arise from collisions with either 0 or 0, as the target. The principal attention on this question has been centered on the ratio h7774/h8446, arising from a strong quintet and triplet in the same transition array. The intensity ratio seems to vary a bit, but the lines are of roughly equal intensity. Percival and Seaton [1956u] calculated cross sections for electron excitation of 0 and found that A7774 should be considerably weaker than A8446 and that both lines should be much fainter than h5577, contrary to fact.

That the mechanism is actually simultaneous excitation-dissociation of 0, is substantiated by electron bombardment experiments performed by Gribbon and Stewart [1956u], who obtained approximately the auroral ratio of intensities.

For the NI and NII lines, the target is most likely the molecule. Stewart [1955u] has produced the NI lines at 8200A in this way with fast electrons, and Carleton and Lawrence [ 1958~1 have measured excitation cross sections for proton impact.

Bates [1955c] noted that permitted atomic lines excited through molecular dissociation may show Doppler broadening from the kinetic energy of dissociation. From laboratory spectra Gribbon [ 1956aI has obtained a width in this manner, simulating 4000" K for one component of h8446, 01.

In the aurora 011 is weaker than 01 while NII is stronger than NI ; the same type of behavior is found in laboratory sources (Foss and Vegard [ 1949~1).

7.4.2. Therm at Collisions

Just as fast collisions deliver the power to an aurora, slow ones supply the finesse and subtlety. A variety of different processes undoubtedly occur, and we shall touch upon those that are suspected of playing principal roles (also see Section 7.3.1).

Dissociative Recombination,-For the forbidden lines of 01 and NI, dissociative recombination (1.106) may be important (Bates, Massey, and Pearse [1948u]). This mechanism proceeds much more rapidly than radiative recombination (1.94) and, except at low altitudes (which are discussed below), will be the principal recombination process. Even atomic ions such as O+ presumably recombine by first forming a molecular ion by an atom-ion exchange such as reaction (1.105).

These mechanisms are thought to be operative in the airglow, where they produce the [OI],, red lines and perhaps [NI],, as well; they are treated in Sections 11.5.3, 11.6.1, and 13.2. In the aurora dissociative


recombination may be relatively more important for [NI] than for [OI], as the latter is readily produced by inelastic electron collisions. However, Seaton [19543] notes that the mechanism may become important in producing the red lines below the level of maximum brightness.

Type-B Aurorae.-At the low altitudes of type-B red aurorae, negative ions are readily formed, and dissociative recombination is displaced by mutual neutralization as the mechanism for removing positive ions. Malville [I95961 has suggested two such processes that could cause the strong enhancement of N, First Positive bands in these aurorae. The reaction

N: + O--+Nt + 0 (7.92)

was proposed earlier by Nicolet [1945u], Mitra [1946a], and Ghosh [1946a] for the aurora, but was critized by Bates, Massey, and Pearse [1948u] on the grounds that electron collisions would be more important. The reaction would be energetically capable of exciting the First Positive but not the Second Positive bands if 0 were left in the lS term (the upper term for the green line). There is no particular reason to expect selective excitation of O(lS), but the First Positive bands might be selectively excited anyway. Malville has pointed out that the electron configurations for the N, bands favor excitation of the First Positive system in preference to the Second Positive for a transition from the ground state of N,+.

The D region also forms negative ions from 0,, and the relative abundances indicate that a more important reaction than (7.92) will be

N i + 0; -+ N,* + 0,. (7.93)

Again, the First Positive system is favored by the electron configurations. It could be that 0, is formed in a metastable state; if it is one of the Herzberg states (see Fig. 5.33) the reaction would have little energy in excess of what is necessary to excite the First Positive system.

T o explain the First Positive enhancement in type-B aurorae, it is not sufficient that a reaction merely becomes important at low altitude. It must also occur on a time scale consistent with the rapid brightness fluctuations and motions of structure characteristic of these aurorae. Malville has estimated the lifetime for negative ions following a burst of ionization to be the order of one or a few seconds.

First Positive bands are strong in some types of laboratory afterglows in nitrogen (Kaplan [ 1932~1, Thompson and Williams [ 1934~1, Bernard and Peyron [1948a], Bryan, Holt, and Oldenberg [ 1957~1, Oldenberg


[ 1959~1). Whereas some of these enhancements may arise from mutual neutralization, as we have discussed above, the Thompson-Williams afterglow does not. I t is produced by impact excitation to the metastable a l 1 7 state followed by collisional transfer to B 317, upper state of the First Positive (Ouenberg [1959a]; see Fig. 5.32).

Type-B enhancements may well be due to this same mechanism. The afterglow is observed at atmospheric pressures comparable to that of type-B aurorae. At higher altitudes the transfer collision would not occur, since there N, emits the Lyman-Birge-Hopfield bands in the ultraviolet. The lifetime of the a state is about 1.7 x lop4 sec (Lichten [1957a]), and there would be no observable lag between electron bombardment and red emission. Two-color photometric measurements -in the Meinel and First Positive bands-with good time resolution could distinguish between mutual neutralization and the mechanism suggested here.

An enhancement of N a D lines in type-B aurorae also probably involves a set of slow collisions. (Inelastic electron collisions are negligible because of the low Na abundance.) The reactions have not been established ; possibly the nightglow reactions are accelerated by auroral heating or some catalystic effect.

Deactivation Mechanisms.-A collision that deactivates an excited level may convert the excitation energy into either kinetic energy or excitation energy of another particle.

Electron deactivation of forbidden lines has been discussed in derail by Barbier [1948c] and Seaton [1954b, 1956~1. For the red [OI],, lines the rate coefficient is s,, m cm3/sec, becoming important when Ne exceeds lo7 ~ m - ~ (see Section 13.3.1). Perhaps electron deactivation contributes in some aurorae. If so, the ratio X6300/h5577 should be smaller for brighter aurorae, which presumably have a higher Ne. Electron deactivation is especially important for. the long-lived [OII],, and [NI],, transitions.

The [OII] and [NI] lines arise from upper doublet terms, whose component levels do not have the same radiative lifetime, as shown by the transition probabilities in Appendix VI. Hence the relative intensities of the lines within a multiplet will depend on how frequently collisions occur compared with the radiative lifetime. In the absence of collisions, the relative intensities vary as the rate of excitation and are proportional to the collision strengths, Q, which are in turn proportional to i3 of the upper level. At high densities the relative intensities are proportional to Gi Aij. The detailed theory is given by Seaton and Osterbrock [1957a], who also allow for cascading from higher levels. Comparison of observed


and theoretical ratios can be of use either in confirming identifications or for deriving electron densities.

Deactivation by atoms or molecules is much more difficult to predict on theoretical grounds. Kvifte and Vegard [1947a] measured a rate coefficient for deactivation of O(lS) (the upper term of the green line) of about 10-15cm3/sec. With a radiative lifetime of $see, the green line would then be unaffected by deactivation at any auroral height. However, there is always the possibility of a reaction that was not operative in the laboratory. Observations of the time lag in fluctuations of the green line, compared with N,+, offer a possible means of deriving empirically the deactivation rate. Omholt [19598] finds in this way no definite evidence for strong deactivation. Observing the decay of A5577 in meteor trains, Halliday [1960a] finds little deactivation as low as 80 km.

The intensities in Table 5.5 show that the Vegard-Kaplan bands of N,, being much weaker than the First Positive system, undergo strong deactivation. The mechanism is not yet known, but presumably atoms or molecules are responsible, as the bands become relatively stronger with height. In laboratory afterglows with pure N, these bands show a remarkable intensity and persistence, even at atmospheric pressure (Janin [1946a], Oldenberg [1959a]).

Herman, Morel, and Herman [1956a] conducted a laboratory investigation of Vegard-Kaplan deactivation by N, molecules and by electrons. They measured the relative intensity of the Second Positive and Vegard- Kaplan bands, so there is some uncertainty in the deactivation rate, depending on the relative amounts of excitation of various triplet levels of N,. However, for molecular collisions the ratio of the deactivation coefficient to transition probability is sAX/AAX m em3, so densities of the order of lo1* or higher are necessary for an appreciable effect. For electrons they find s A X / A A X * em3, requiring Ne 2 lo9 Probably atoms, rather than mol&ules, are involved in the auroral deactivation.

Molecular deactivation of O(l0) is interesting for several reasons. Collisions with 0, will not only deactivate the red lines, but contribute to the emission in the Atmospheric system. The 0, molecule in turn is vibrationally deactivated, so that most of the emission occurs from zi’ = 0. However, the zi’ = 1 level may, with this set of reactions, exhibit a rotational temperature different from v’ = 0.

A quantitative treatment of these processes has been presented by Wallace and Chamberlain [ 1959~1. Excitation of 0, and deactivation of 0 occur by energy transfer,

o(1q + o,(x 3z;, v’‘ = 0) -+ o(3q + o,(b iz;, I 2). (7.94)


Deactivation of v' = 2 could occur by the inverse process, but for v' 2 1, a reaction toward the left is energetically impossible. Vibrational deactivation (for v' > 0) occurs rapidly by a transfer of electronic energy only (Bates [19543]):

O,(b 'q, w' > 0) + O,(X 3z;, w" = 0) +

O,(X 3z;, w" > 0) + 0,(6 122;) w' = 0). (7.95)

In the latter reaction the rotational distribution of v' = 0 will be the same as in the ground state before the collision. Hence v' = 0 will have Trot Tkin. On the other hand, w' 2 1 may well have Trot quite different from Tkin; there is no reason to expect that reaction (7.94) would produce 0, molecules with Trot close to the gas temperature.

The observations yield Trot(1-1) m 700" K and Trot(0-1) m 200" K. The relative intensities of the 0, bands and the [OI],, red lines allow empirical determinations of the reaction rates. The rate coefficient for deactivation of the red lines by (7.94) was found to be 4 x < sZ1 < 10-lo cm3/sec. A value of 10-l1 cm3/sec is reasonably consistent with the available data.

We noted earlier that [OII],, is considerably weaker than would be expected without deactivation. Electron collisions are probably not important in this respect (Seaton [ 1954b]), but ion-atom interchange,

0+* + N, -+ NO+ + N, (7.96)

would be very efficient (Bates [1955b]). The ion O+ (,I' or 2D) is also energetically capable of simple charge transfer, leaving an excited N$ ( A ,17) ion and an 0 atom on the right side of (7.96) (Omholt [19573], Hunten [19583]).

7.4.3. Radiative Excitation

Several processes involving the absorption of radiation have been suggested as auroral mechanisms. The most definite of these is resonance scattering of the N,+ First Negative system in sunlit aurorae (Bates [ 1949~1). The observations of heights are summarized in Section 4.2.1 and the interpretation of the spectrum is reviewed in Section 5.2.7 and 5.2.8. Densities of N$ vary from lo4 cm-, at 200 km to lo3 cmP3 at 500 km for a bright aurora (Rees [1959b]).

Shefov [1961a] has proposed that the He I line h10,830 is excited in a similar fashion. Auroral excitation populates the metastable 2 3S term of atmospheric helium, which then scatters sunlight at 10,830 A. If


true, this explanation would mean that the auroral A10,830 emission does not indicate bombardment of helium ions in the same way that Ha. indicates proton bombardment.

Emission in the 0-0 bands of the 0, Atmospheric and Infrared Atmospheric systems may be continually absorbed and re-emitted by the large amount of 0, in the atmosphere until it fluoresces in the 0-1 transition (Bates [1954b]). If operative, this mechanism might explain the disparity in 0-1 and 1-1 rotational temperatures for the Atmospheric bands (Section 7.4.2). However, the main absorption will occur around 40 to 50 km altitude where the temperature is higher than the 0-1 band indicates. Probably 0, is collisionally deactivated at such low heights. This fluorescence is discussed further in Section , I 3.4.1 ; if applicable at all, it is especially important in the airglow.

A large amount of ultraviolet radiation must emanate from the aurora. Table 5.5 includes only those emissions that may be definitely inferred from visible observations, and undoubtedly greatly underestimates the atomic and molecular ultraviolet. Bates [ 1955~1 has drawn attention to some possible effects of this radiation:

1. Much of it will occur in resonance lines or other strong transitions ending on the ground level, with the emission being imprisoned. Some of this may be degraded to longer wavelengths by fluorescence, as in the 0, example discussed above, with observable emissions possibly occurring some distance from the aurora proper.

2. Some of the ultraviolet may dissociate 0, in the Schumann-Runge continuum, or 0, in the Hartley continuum, producing an O(l0) atom capable of emitting in the red lines.

3. Ionization may be produced by absorption of the ultraviolet. In particular, Ly a emission could ionize NO, as we have already discussed in Section 7.3.1.

A fluorescence mechanism, of the type first proposed by Bowen [1947a], was suggested as a means for enhancing A8446 01 by Swings [1956a]. The Ly /3 line has almost exact coincidence with an 01 transition between ground and an excited level. Hence 01 may absorb Ly /3, and would emit X8446. Omholt [ 1956~1, investigating the process quantitatively, found it to be unimportant in aurora. This Bowen mechanism does have some application, however, to the dayglow (Section 11.6.5).


PROBLEMS

1. Show that the horizon profile is given by Eq. (7.12). Adopting an angular distribution of the form (7.14), verify that both the zenith and horizon profiles give the total emission rate expressed by Eq. (7.13).

2. (a) Show that with the angular dispersion given by Eq. (7.14), the energy spectrum by Eq. (7.30), and the photon yield by Eq. (7.22), the moments of the zenith profile are expressed by Eq. (7.37). (b) Derive Eq. (7.40) for the H luminosity distribution with an exponential proton spectrum.

3. Show that the vector potential for charges in uniform motion is given by Eq. (7.50a), in which the current density is evaluated at the retarded time t'.

4. (a) Estimate the time required for an electron, with u = 0.1 c gyrating in a magnetic field of 0.1 gauss, to lose an appreciable fraction of its energy by Cerenkov radiation at radio frequencies. Take n as very large for w < wc and ignore radiation at other frequencies. (b) What is the ratio of the rate of energy loss in Cerenkov radiation (under these conditions) to the rate of loss by gyro radiation in free space? (c) What is the ratio for the two rates of loss for protons?

5. Represent the active secondary electrons by a Maxwellian distribution and find what effective temperature is necessary to give cQmparable intensities of A5577 and h3914. Take the 0 and N, abundances the same; use a constant N, cross section, equal to the gas-kinetic, above the ionization potential, and for 0 adopt a constant collision strength SZ = 0.3. Suppose that half of all the ionizations are by secondary electrons. Perform the calculation for two assumptions: (a) Two percent of all ionizations of N, give a photon of h3914. (b) Every primary ionization produces one photon of h3914.

6. Show that when collisional deactivation of a metastable atomic level is much more frequent than radiative cascades, the forbidden-line emission may be obtained from Kirchoff's law (7.84), provided that the electron velocities are Maxwellian. [That is, the emission rate computed on the basis of thermal equilibrium is in this case equivalent to that computed from consideration of the atomic processes by Eq. (13.21).]

7. Compute the ratio A7325 [OIJ],,/h3914 N,+ for electron impact, for cases (a) and (b) in Problem 5 , as a function of height. Take cross sections for N, from Massey and Burhop [1952a, p. 2651 and for 0 from Seaton [1959a]. How is the ratio modified with deactivation by (7.96) ? (Use a provisional rate coefficient of lo-" cm3/sec.)

Chapter 8. Auroral Particles in Space

We now leave the realm of the aurora itself and delve into questions of the origin of auroral particles and their properties outside the atmosphere. Many of these matters are highly speculative, with direct measurements and experimentation in this subject being inaugurated during the IGY.

An auroral theory must explain not only the morphological characteristics from Chapter 4, but the properties of the primary particles discussed in Chapter 7. The main conclusions of the latter chapter, insofar as they apply to this one, are that primary electrons and protons bombard the Earth with wide energy dispersions and that electrons usually carry most of the energy. The energy spectra were found to increase toward low energies and some quantitative estimates of the spectra were made. The angular dispersion is probably important also, and careful photometry of the H-line profiles, as well as rocket experiments, can give information on this point independently of any knowledge of the energy dispersion, provided that the two are independent.

The plan of the chapter is to review first the meager information available on the interplanetary medium, through which any disturbance from the sun must travel, and then to summarize various proposals for the transportation of solar particles to the Earth. The remainder of the chapter deals with the behavior of auroral particles in the terrestrial field. Primarily, we shall be raising questions and not, unfortunately, supplying many answers.

As a satisfactory and complete auroral theory has not been developed, our discussion is restricted to various hypotheses that have been invoked to explain certain features of the accumulated data. Perhaps a variety of these and other ideas will eventually be synthesiz5d into an auroral theory.

In the meantime it is perhaps well to remind ourselves occasionally in dealing with this subject that mathematical elegance cannot counteract incorrect physical assumptions, and that speculative suggestions, even when intuitively plausible, do not substitute for sound physical theory.

3 20

8.1. INTERPLANETARY SPACE 321

8.1. Interplanetary Space

8.1 .I. Properties of the Interplanetary Gas

Little information has been obtained on the interplanetary medium through observations from Earth. Direct exploration through space flights can supply data on densities, temperature, and the motion of the gas near the Earth, and these measurements should clarify ambi- guities and settle controversies that have arisen.

Some idea of the electron density of interplanetary space comes from the brightness and polarization of the zodiacal 1ight.l The densities derived are of the order of lo3 ~ m - ~ near the Earth, although if some of the polarization is supplied by meteoric material rather than electrons, the density is actually lower. In fact, Blackwell’s [1960a] observations of the Fraunhofer absorptions in the spectrum of the zodiacal light place an upper limit on this density of only 100 ~ m - - ~ .

Interplanetary temperatures and motions have been computed from theory, but the results are widely different for different approaches to the problem. Chapman [1957a] assumed a static solar corona, extending far into space, where the temperature was governed by conduction. At the Earth’s orbit the temperature would then be about 20 percent of the value in the corona proper, which is probably of the order of 2 x lo6 OK. Later Chapman [19593] revised his estimates slightly to give better fits with observed densities in the outer corona (or inner zodiacal light). He suggests that convective mixing is responsible for lowering the temperature to about half his previous estimate.

Parker [1958a, 195963 showed that such an atmosphere must actually expand and cannot remain static.2 Attacking the problem with the hydrodynamic equation of motion, he obtained outward velocities of the order of 500 km/sec, presumed to correspond to a solar wind (discussed further in Section 8.1.2).

The hydrodynamic solution contains an ambiguity, however, and Chamberlain [ 1960~1 has proposed that Parker’s large expansion velocities are based on an incorrect choice as to which mathematical solution was physically appropriate. With the alternate solution, the hydrodynamic expansion is equivalent to thermal evaporation and proceeds at much slower velocities.

Behr, Siedentopf, and Elsasser [1953a], Behr and Siedentopf [1953a], Elsasser [1954a], Blackwell [1956u, 1957~1.

From the point of view of individual particles this is true because a significant portion of the Maxwellian curve gives velocities exceeding the velocity of escape in the outer, tenuous atmosphere (see below).

322 8. AURORAL PARTICLES IN SPACE

The density and temperature out to the Earth’s orbit have been computed by Chamberlain [1960a] with the use of an evaporative kinetic theory of an outer atmosphere where collisions that redistribute particle energy were neglected. With this model, the temperature at the Earth’s orbit is between lo4 and lo5 OK, depending on how efficiently the high-energy Maxwellian tail is replenished in the corona. From the evaporative standpoint, T decreases outward more rapidly than with Chapman’s [ 1957~1 model, because the density is composed mainly of particles that have velocities less than the velocity of escape. Hydrody- namically, the reason is that the tendency to establish a conductive equilibrium will always lead to increased expansion, which in turn carries away heat energy. That is, with the hydrodynamic equations an outward expansion of an atmosphere held gravitationally is inevitable, if the temperature gradient is less steep than the adiabatic gradient. Therefore we can think of any conductive transport of heat as being the mechanism responsible for an outward flow of matter. This transport is basically similar to the evaporative loss of high-energy particles and their replenishment from below.

Chamberlain [ 1961 a] has also computed a hydrodynamic-conductive model of a slowly expanding corona, which predicts a temperature at the Earth’s orbit of 15,000-20,000° K. In contrast to the evaporative theory, this approach considers collisions that interchange kinetic energy to be frequent. Fitting the model with the corona out to 20 solar radii suggests that conduction is partly inhibited in that region, possibly by solar magnetic fields. The electron density at the Earth’s orbit is about 30 ~ m - ~ with this model.

An idea of the amount of neutral interplanetary hydrogen may be obtained from measurements of Ly a in the night sky (see Section 13.5.2). The degree of ionization then gives an empirical indication of the temperature, provided that we agree on the mechanisms for removing H atoms. (There is, however, still some question regarding how much of the night-sky Ly a is interplanetary and how much is terrestrial.)

Shklovskii [1958a] believes that the interplanetary gas has a lifetime of several thousand years, and considers radiative ionizations to balance recombinations, as in gaseous nebulae. Alternatively, if conduction were heating a static gas, electron-hydrogen collisions would keep it almost fully ionized for temperatures exceeding 20,000” K. Collisional equilibrium and a combination of radiative and collisional ionization have been treated for nebulae (Chamberlain [1953a, 1956~1).

On the other hand, the general circulation or diffusion of neutral atoms through the interplanetary gas may also be important in removing H. As atoms fall back toward the sun, into a region of much higher


temperature, they are rapidly ionized and are not replaced by outward diffusion. Another mechanism for removal is found in particle streams from the sun, passing through the interplanetary gas and ionizing H through charge-transfer collisions. These streams might effectively sweep H atoms out of the immediate neighborhood (say, I AU) of the Earth, to a distance where they would not be detected by resonance scattering of solar Ly a.

Should one of these processes give a mean lifetime for H atoms near the Earth of only a few months or less, it may be the governing factor. The temperature must then be less than in collisional equilibrium, so that some recombination can occur within the allotted time. In summary, it appears that temperatures exceeding 20,000" K beyond the Earth must be excluded and an extreme lower limit near the Earth is probably 5,000" K (see Brandt [1961a]).

The existence of weak magnetic fields in the interplanetary medium has been inferred from studies of cosmic rays. Fairly uniform fields exceeding gauss cannot exist through the volume inside the Earth's orbit, since otherwise low-energy cosmic rays from the sun would be shielded from the Earth. A nearly field-free cavity, changing with the solar cycle, could also explain long-period variations of the galactic cosmic-ray spectrum (Davis [ 1955~1, Meyer, Parker, and Simpson [1956a], Beiser [1958b], Hoyle [1956a]). Highly irregular fields do seem to be acceptable and even necessary to explain certain features of the delay times and direction of arrival of solar cosmic rays (Lust and Simpson [1957a]).

While these fields may be considered to originate from the general magnetic field of the sun or even from the galactic field, an alternative model conceives of large solar flares as exploding the field of a sunspot into interplanetary space. As solar gas moves radially outward, it pulls the field along with it, forming a magnetic cone, which affects cosmic rays and forms a channel for auroral particles (Piddington [1958a], Gold [1959a, b]).

8.1.2. Transmission of Geophysical Disturbances and Their Interaction with the Terrestrial Field

Solar Corpuscular Emission.-At the core of an auroral theory lies an hypothesis on the manner in which a solar disturbance is propagated. Usually the hypothesis has involved clouds or streams of plasma, for which there is some evidence. Several attempts have been made (Richardson [1944a], Bruck and Rutllant [1946a], Smyth [1954a, b]) to detect abnormal absorptions shortward of the solar H and K lines of


Ca I1 prior to magnetic storms, but the resuts have been mostly negative. Kraus and Crone [1959a] believed they detected such clouds by radio reflections, but their conclusion appears doubtful.

The angular diameter of geoactive streams is often thought to be several degrees (Gnevyshev and 01 [1945a]) as deduced from (1) the duration of strong magnetic storms of a few days at most; (2) the tendency for active solar regions to have their maximum geomagnetic influence near central-meridian passage ; (3) the yearly variation, interpreted as the Cortie effect (Section 4.1.3); and (4) the eleven-year cycle, with the lag in the geoactive maxihum behind the sunspot maximum attributed to the higher solar latitude of sunspots early in the sunspot cycle.

That corpuscular emission from the sun is more widespread and frequent than had been inferred from geophysical observations is indicated by the acceleration of comet tails away from the sun. Formerly attributed to radiation pressure, these accelerations now appear to involve particle collisions. Biermann [1951a, 1952a, 1953a, 1957al has developed this hypothesis and concludes that densities of the order of 100 ~ m - ~ and stream velocities of the order of 500-1500 km/sec are present at all times near the Earth, with a flux increased over 100 times during magnetic storms. The proposal for such a strong solar wind, as Parker calls it, offers difficulties in accounting for neutral H in the solar system and is not substantiated by observations of continuous outward motions in the Forona.

Solar particle streams appear to originate in the active regions around sunspots and may consequently carry magnetic fields (Hoyle [1949a]). Mustel [1958a] estimates that fields as high as gauss (the magnetic energy exceeding the kinetic) might be transported to the Earth in this fashion, “frozen” to the gas. Such fields would contribute to the large accelerations of ions in comet tails, reducing the momentum otherwise required for solar streams; they would have a profound bearing on the interaction of the streams with the Earth ; and they may account for time variations in cosmic rays, such as the Forbush decrease (Sec- tion 4.3.6).

Models for Particle Streams and Disturbances.-A considerable number of models for solar streams have been proposed. I have already published an extensive review, including historical references, of the work prior to 1957 (Chamberlain [1958c]) ; the serious reader interested in the details is referred to that summary or to the literature. Here I must confine the discussion to a brief resumk of the principal works.

Stormer’s [I 907a, 191 lc, 1955aI theory of single particles in a dipole field is the prototype for stream models in which the motions of charged


particles of one sign are predominant. A precursor to Stormer’s work was the theory for a particle in the field of a monopole developed by Stormer’s teacher, Poincark [ 1896~1. The stimulus was the experimental work of Birkeland [1896a] who fired particles at a magnetized sphere (terrella). A modification was proposed by Bennett and Hulburt [1954a, b] and Bennett [1955a, 1958~1, and it is also suitably illustrated by a modified terrella experiment designed by Bennett [1958b, 1959~1.

A stream composed of equal numbers of positive ions and electrons, all moving with essentially the same velocity, was first proposed by Lindemann (Lord Cherwell) [1919a] and subsequently developed by Chapman and Ferraro [1931a, 1940a, 1941~1 and Ferraro [1952a]. It was assumed that interplanetary space had little or noeffect on the stream, which carried no magnetic field of its own. Extensions have been proposed by Martyn [1951a], Landseer- Jones [1952a], and Warwick [1959a], regarding the interaction of such a stream with the terrestrial field to produce aurora.

Streams moving through an external field in interplanetary space or carrying a magnetic field frozen to the cloud have been considered by AlfvCn [1939a, 1940a, 1950a, 1955a, 1958~1, Astrom [1956a], Landseer- Jones [1955a], Piddington [1958a], and Gold [1959a, b]. Again appropriate terrella experiments have been designed in support of some of this work (Malmfors [1946a] and Block [1955a, 1956~1).

A frozen-in magnetic field offers an attractive possibility for explaining the energy spectrum of auroral primaries. The stream as a whole might travel with the conventional speed of 1000 km/sec deduced from 1-day delay times, while individual particles, trapped within the magnetized cloud, could have much higher velocities. A magnetic field to reconcile the travel time with speeds deduced from the optical aurora seems to have been first invoked by Beiser [1955a, b]. Such a field could greatly affect the interaction of the stream with the Earth’s field.

Most of the work mentioned so far has disregarded the possibility of a highly conducting interplanetary gas. Consideration of it has led to proposals that shock waves run ahead of the stream and produce preliminary effects (such as magnetic sudden commencements) at the Earth (Gold [1955a], Singer [1957a], Parker [1959a]). Also, the interactions between the Earth and stream are modified with a hydromagnetic coupling. For example, instead of picturing a stream approaching the Earth’s field and simply developing surface currents, which in turn modify the field, one now thinks of the stream as compressing the gas near the Earth and the terrestrial field simultaneously. The new concepts introduced by a hydromagnetic approach may be even more drastic, with hydromagnetic waves propagating magnetic energy rather efficiently.


Hydromagnetic theories of magnetic disturbances have been developed by Dessler and Parker [1959a] (also see Parker [I9586, 1959~1) and Piddington [1959a, 1960~1. There have also been one or two hydromagnetic questions regarding the ability of a ring current to make its magnetic field felt at the Earth.3

Dynamo currents generated by winds in the upper atmosphere may also contribute to magnetic storms, especially since the auroral ionization raises the ionospheric conductivity (Vestine [1953u, 1954~1, Obayashi and Jacobs [1957u]).

8.2. Auroral Particles in the Geomagnetic Field

A variety of mechanisms (see above) have been offered for injecting ionized particles into the terrestrial field, some requiring little modification of the dipole field by the incident stream and others insisting on a more violent departure from an unperturbed model. In any case this seems to be the most critical and the weakest point in our understanding of aurorae. In this section we will merely assume that particles are in the field-whether on a trapped, long-time basis or not-and consider what may happen to the particles and how they may affect the Earth.

8.2.1. Detection and Art i f ic ia l Production of Charged Particles

Direct 0bservations.-The most spectacular achievement of the IGY was the detection with satellites of energetic particles trapped in the Earth’s magnetic field (see Section 3.2.4 for a discussion of the trapping me~han i sm) .~ Detailed investigation of this radiation will undoubtedly continue, with high-altitude rockets as well as satellites, for some years before it becomes well understood, and in particular before we learn how it is related to solar streams and geophysical events.

The character of the radiation varies with distance from the Earth. The trapped particles follow geomagnetic lines of force, drifting gradually

Parker [1956a], Hines [1957n], Parker [1958c], Hines and Storey [1958a], Parker [1958d], Hines and Parker [1958a, 1960~1, Parkinson [1958a], Akasofu [1960a].

The principal accounts of the early observations and interpretations are given by Van Allen [1959a], Van Allen, McIlwain, and Ludwig [1959a], Van Allen and Frank [1959a], Vernov, Chudakov, Gorchakov, Logachev and Vakulov [1959a], Vernov, Chudakov, Vakulov, and Logachev [ 1959a1, Shklovskii, Krassovskii, and Galperin [ 1959~1, Rothwell and McIlwain [1960a], Yoshida, Ludwig, and Van Allen [1960a].

8.2. AURORAL PARTICLES IN THE GEOMAGNETIC FIELD 327

in longitude, with iso-intensity contours as shown in Fig. 8.1. The diagram shows two principal maxima, the so-called inner and outer Van Allen zones. The outer zone especially changes from time to time, evidently being affected by solar streams. I t appears that the inner zone,

FIG. 8.1. Schematic representation of the intensity of trapped radiation. Contours of constant intensity (labeled with the counting rates of the detecting instrument) and a satellite orbit are shown. The linear scale is in units of the Earth's radius.

Adapted from Van Allen [ 1959aI ; courtesy Journal of Geophysical Research.

which is characterized by protons with energies of the order of 100 MeV, is produced by ,%decay of neutrons. The neutrons are produced in the atmosphere through nuclear disintegrations induced by cosmic rays. Some of these neutrons will move outward and decay into charged particles while still within the magnetic field.

The outer zone is more probably produced by solar gas, although this conclusion has been questioned (Dessler and Karplus [ 1960al). Both electrons and protons probably have a steep energy spectrum, but most of the radiation intensity is contained in electrons. Van Allen [ 19594 has quoted some sample integrated spectral intensities, defined by

Here V ( E ~ 1 0) is the differential intensity in particle/cm* sec sterad (unit energy interval) and is essentially the same quantity we have used


in Chapter 7-see Eq. (7.29)-for the particle intensity above the atmosphere. Van Allen gives the summary in Table 8.1 for an altitude of 16,000 km above the geomagnetic equator.

TABLE 8.1

OUTER RADIATION BELT

Particles &l(kev) 411j(c1) (particles/cm2 sec)

Electrons

Protons

20 200

60,000

- 10" 5 108

5 108

The spectrum in the radiation belt is not necessarily the same as that of the particles that bombard the atmosphere. The spectrum of particles that escape into the atmosphere, whether these be the auroral particles or not, is affected by the frequency with which particles of different energies have collisions or are otherwise perturbed out of their trapped orbits. While some theoretical studies have been made on the stability of the radiation belts, several unknown factors are involved, including the density of the outer atmosphere and the importance of hydromagnetic waves as scattering centers for the particles.

At any rate it is of some interest that the electron intensities tabulated above are roughly similar to the electron spectrum we deduced for aurorae in Section 7.2.4. Representing the spectrum by an exponential law, exp (- t0/a), we find a < 25 kev, to be compared with a: - 8 kev for auroral electrons. The total integrated intensity is 4rJ(O) > 2.2 x loll, compared with a flux 9 = 3 x 101O electron/cm2 sec for a bright aurora. Hence, if the electrons normally present in the outer Van Allen belt were made isotropic over a period of a few seconds they would produce a bright, short-lived aurora (Section' 8.2.3). If the time scale for reorienting the electrons were longer, the brightness would be correspondingly reduced, but it would be longer before the electrons were depleted.

It appears, however, that the outer Van Allen zone is considerably closer to the Earth than it would have to be to feed electrons into the auroral zone. I t seems more reasonable that the outer zone, although regulated by and probably formed from solar gas, stores particles that eventually leak into the atmosphere at subauroral latitudes. These particles may be of sufficient importance to contribute to the nocturnal ionosphere, and may have a bearing on certain airglow radiations (Sec- tions 11.2.2 and 13.3.2) and low-latitude aurorae.


Continued experiments with satellites and interplanetary vehicles should help clarify the mystery of the injection of auroral particles into high latitudes. In Sections 8.2.2 and 8.2.3 we shall examine in more detail just what are the outstanding problems in this regard.

Indirect Detection of Particles in the Terrestrial Field.-Particles may also be detected by the radiation they produce. While these indirect means may in principle be used in satellites, they are of particular interest in that they afford means of detection from the Earth. They also involve more ambiguous theoretical interpretation and are never likely to offer the complete picture that can be obtained by carrying the laboratory into the cosmos. But in view of the gigantic expense involved in direct experimentation with satellites, further development of indirect, ground- based techniques (and associated theory) has become, not just a matter of present-day expense, but one of ultimate economy.

Radiation from fast particles outside the atmosphere was discussed in Chapter 7, along with emission produced locally within the atmosphere. There are two processes likely to be of some importance: Cerenkov and gyro radiation.

Cerenkov emission from particles with velocities of the order of lo9 cm/sec is probably the source of the chorus (Sections 4.3.5 and 7.2.2). In the very low (audio) frequencies, the index of refraction will exceed unity because of the magnetic field of the Earth. Then Cerenkov emission can occur from particles with only moderate (or higher) energy. The chorus has not been specifically related to aurora, but may arise from particles of solar dominion in the trapped radiation belt.

Electronic gyro radiation (Section 7.2.3) in the fundamental frequency would occur at very low frequencies, and may be responsible for some radio bursts associated with magnetic activity and emission in the red lines (Section 4.3.5). At relativistic velocities the higher harmonics become strong and merge together into a continuum. Dyce and Nakada [ 1959~1 have suggested that relativistic trapped electrons might be observed at very high frequencies. This synchrotron emission could perhaps be differentiated from the cosmic-noise background by its linear polarization, when observed perpendicular to the magnetic field. A precise calculation of the emission to be expected not only would involve the spectrum of particle energies but also must allow for the local plasma frequency. The latter consideration is likely to change the radiation field considerably from what would be found were the electrons gyrating in free space.

Indirect data on the background plasma has been derived from studies of radio whistlers (Section 4.3.5). Storey [1958a] has noted that precise


measurement of the dispersion of whistlers at middle latitudes could yield information about the molecular weight of the plasma ions. Such experiments would test the supposition that the main constituent in the outer atmosphere is hydrogen.

Artificial Injection of Particles and Production of Aurorae.-Atomic explosions at high altitude will inject ionized atoms into the geomagnetic field. A large part of this matter is radioactive and will emit /3-decay electrons with rather high energy. In this way it is possible to study the lifetime for trapped particles in the radiation belt and to produce artificial aurorae with nearly monoenergetic electrons. Charged particles might also be injected in a specified way by large amounts of radioactive substances or even by a particle accelerator packaged in an artificial satellite.

In the Argus experiment5 three bombs of the fission variety-so- called “small” bombs, in the 1- to 2-kiloton range-were exploded over the south Atlantic on three occasions in the late summer of 1958. All bursts were near 480 km altitude. Night explosions produced auroral emission above and below the bomb, extending along the magnetic field. At the magnetic conjugate point, near the Azores Islands, aurora was also observed.

The explosions produced radio-aurorae, detected at 30 Mc/sec, both near the bursts and at the conjugate point. Weak magnetic disturbances (less than 1 y ) at the conjugate point i w l i e d the existence of hydromagnetic waves with frequencies of around 1 sec-’ and velocities of several thousand kilometers per second. Although sporadic-E ionization appeared at the conjugate point and terrestrial radio signals at 20 kc/sec were weakened, there was no ionospheric absorption at the conjugate point in the very high frequencies. Perhaps the most valuable quantitative results of the experiment relate to the lifetime for trapped electrons, which allows some conclusions to be drawn as to the principal mechanisms for removing particles from a particular shell. (A geomagnetic shell is bounded by two neighboring geomagnetic surfaces; each surface is formed by rotating a line of force in longitude about the axis.)

Much more spectacular events accompanied the nocturnal Johnston Island explosions, called Teak and Orange, several weeks before Argus. Johnston Island is in the Pacific, some 14” N geomagnetic. The Teak

Several papers on Argus have been published together. Christofilos [1959a] has summarized the entire experiment; measurements on and interpretation of the trapped electrons are reported by Van Allen, McIlwain, and Ludwig [19596], Allen, Beavers, Whitaker, Welch, and Walton [1959a], and Welch and Whitaker [1959a]; for optical, radio, and magnetic observations see Newman [1959a] and Peterson [1959a].

8.2. AURORAL PARTICLES I N THE GEOMAGNETIC FIELD 33 1

explosion of 1 August 1958 was slightly above 60 km, according to press releases, and Orange on 12 August was around 30 km high. These explosions were of the thermonuclear (fusion) type, presumably therefore in the megaton class and triggered with garden-variety, fission-type bombs.

Aurorae were observed on both occasions at Apia, Samoa, near the conjugate point of Johnston Island (see Fig. 8.2). First reported by

Auroral ray -. -- ---_ seen from Apia _ _ _ _ _ _ _ _ 00

' N O 480km /'

/'

Mapnctic Equator

scotr - 0 200 400 hm

FIG. 8.2. The Teak experiment at Johnston Island, showing the conjugate point near Apia, the location of the high-altitude portion of the Apia aurora, and the auroral structure near the explosion as observed from Hawaii. After

Steiger and Matsushita [ 1960~1; courtesy Journal of Geophysical Research.

Cullington [ 1958~1 after Teak, these artificial aurorae clearly arose from P-decay electrons traveling along the line of force and bombarding the southern hemisphere (Fowler and Waddington [ 1958~1, Kellogg, Ney, and Winckler [1959a], Elliot and Quenby [1959a]).

The violet color of the auroral rays at Apia seems peculiar at first, but Malville [1959c] has called attention to the fact that the primary electrons were probably of higher energy than the majority of electrons in natural aurora. The lower height of penetration would therefore favor N l over 01 emission because of relative abundances and deactivation, the latter affecting at least the red lines. The diffuse red background may be attributed to one of the mechanisms proposed for reddening type-B natural aurorae (Section 7.4.2). Mutual neutralization by reaction (7.93) is perhaps the most attractive; a lifetime of a few seconds for this reaction would have produced a more diffuse glow for the First Positive bands than for N,+, owing to outward diffusion of the ions.

The rays lasted only a few minutes, gradually turning green. The color change is attributed by Malville to the fading of intensity, red and violet having higher color thresholds than green. An increase in the


height of the aurora may also have enhanced the green [OI] line, but without definite information on the primary electron spectrum and its changes with time, this possibility is entirely speculative. It might be noted that even if the /3-decay electrons were initially monoenergetic, their straggling as they escaped the atmosphere above Johnston Island would have introduced an energy dispersion, and vertical motions of the fission fragments would have changed the spectrum above Apia with time.

A “crimson arc” (presumed to be A6300 [OI],,), observed north of Apia at an altitude of 450-500 km, may have been produced by dissociative recombination as in the twilightglow (Section 11.5.3). This explanation is not entirely satisfactory, however. If the atmosphere were strongly ionized by charged particles at this height and below (see Fig. 8.2), the slowly decaying twilight-type emission should have extended down into the atmosphere below 200 km altitude. Hydromagnetic waves from the blast offer another possibility, again speculative, for accelerating electrons h the crimson arc.

Auroral rays were observed above Johnston Island at the Teak explosion (Steiger and Matsushita [1960a]), along with an expanding envelope of luminosity, evidently produced by a shock wave.

Magnetic disturbances exceeding 50 y were also recorded in the Pacific along with D-region absorption. These effects have been explained in part as a consequence of the ionization produced by y- and x-radiation and electrons from the blast. In addition, ionospheric winds generated by the explosion evidently accelerated the electric currents over Johnston Island through the dynamo effect. Over Apia the driving force for the currents could have been enhanced by convective circulation arising from heating-either by the particle ionization or by hydromagnetic waves.6

8.2.2. Questions concerning the Geographic Location of Particle

A proper theory of the manner in which charged particles enter the atmosphere via the magnetic field would explain not only the auroral zone but also the east-west orientations of auroral forms, daily variations, and very likely the systematic auroral motions. Various models of the auroral phenomenon have attempted to predict or explain these characteristics. A less ambitious approach to the problem, but one that promises

Preliminary reports of these effects were published by Maeda [1959a], Matsushita [1959b], Obayashi, Coroniti, and Pierce [1959a]. Extended analyses are given by Matsushita [1959c] and McNish [1959a].

Born bardrnent


a beginning to the ultimate solution, is to derive some general properties of the particle orbits from measurements of the geographic locations of bombardment. In this way one tries to work backward from the facts -in a deductive manner, with a minimum of ad hoc assumptions- to the source of injection of auroral particles into the field.

Particles from Infinity.-Stormer’s approach, upon which much of the later work has been based, was to assume a dipole field for the Earth and to compute the locus of bombardment for particles from a source at infinity. Consider particles of one sign with a single value of momentum. A line source at infinity along a magnetic meridian would give a locus of bombardment--a precipitation curve-as shown in Fig. 8.3. A point at a given latitude on the source line would precipitate particles onto a single point of the curve. Strictly, these monoenergetic particles from the sun would bombard only a small region of the curve at any one time. But as the sun moves during the day and through the year over a wide range of geomagnetic latitudes, this precipitation curve would give the average latitude of bombardment as a function of geomagnetic time.

It is well known that the particle momentum required for this curve to explain the auroral zone is greatly in excess of what is allowed by the heights of aurorae, unless the outer field is diminished in some way (for example, by a ring current, as Stormer proposed). This general type of spiral curve has been suggested by some analyses of geomagnetic daily variations (see the discussion in Section 4.1.3). The implication has been that orbits of the Stormer type, in which the momentumof the particle is sufficient for it to penetrate the field while being deflected in longitude, were somehow of importance. However, the monoenergetic requirement of this interpretation is difficult to reconcile with the energy spectra of auroral primaries.

Some modification of Stormer orbits does seem to be applicable to the low-energy cosmic rays from the sun (Section 4.3.6). But the departures of the Earth’s field from that of a dipole have an appreciable effect on the orbits (Quenby and Webber [1959-a]) and, more important, at very large distances from the Earth, the field must be diminished by the Earth’s rotation, which drags the field through the ionized interplanetary gas. Dungey [1955a] estimates that slippage of the outer field becomes serious at 8 Earth-radii in the equatorial plane. At times of magnetic storms the field is perhaps disrupted even closer to the Earth, as evidenced by the sudden appearance of low-energy cosmic rays at middle latitudes, which are normally inaccessible at these energies. Modified Stormer cutoff energies, with allowance for distortions


in the geomagnetic field, have been computed by Obayashi [19596] and Rothwell [1959uJ.

To the emanation point

t 0.931 '' 'OlUes

07

180

0.9 I

FIG. 8.3. Stormer's line of precipitation of positive particles. The Earth, viewed from above the north magnetic pole, rotates under the curve, which is fixed in space relative to the sun's longitude. Around the curve are indicated values of an impact parameter, yl, from the Stonner theory, the geomagnetic longitude measured from the sun, 4m, and the geomagnetic latitude of the sun, A?). The polar angle or colatitude is 8. For further explanation see text and Chamberlain

[1958c]. After Stormer [1955a] ; courtesy Oxford University Press.

Adiabatic Invariance.-Auroral isochasms, as shown in Figs. 4.3 and 4.4, are found to deviate appreciably from circles. Hultqvist [1959a] (see also Quenby and Webber [1959a]) has sought to explain these


departures by projecting a circle in the geomagnetic equatorial plane along lines of force onto the surface. Close to the surface, deviations from the dipole field become important and the projection is not a circle but an oval. The agreement with Vestine’s curves is only fair, but using some data collected in the IGY by Gartlein, Hultqvist obtains a better representation of the isochasms.

If these are indeed accurate representations of the isochasms, they would lend support to the idea that particlesbombardthe atmosphere at about the geomagnetic longitude at which they are injected into the field. Pre- sumably the injection process is a function of the local field strength, and an isochasm computed from constant equatorial fields would then correspond to contours of equal injection.

A rather different explanation for the isochasms is proposed by Vestine and Sibley [1959b], who in effect consider the bombardment to be independent of the longitude at which particles are injected. If the particles remain trapped in the geomagnetic field, drifting in longitude (Section 3.2.3) until they are somehow ejected, we would expect the average amount of bombardment to be the same all along the drift trajectory. The problem, then, is whether auroral isocontours represent equal amounts of particle injection in the equatorial plane (that is, where the field is weakest), or whether they represent a longitude equality dictated by particle drifts. With either point of view the isochasms might also be parallel to the mean east-west extension of auroral forms.

In Section 3.2.4 we showed that a particle moving into a converging magnetic field will tighten its spiral until it is finally reflected-at its so-called magnetic mirror point-in accordance with the transverse adiabatic invariant. In the terrestrial field a particle that does not strike the atmosphere will thus oscillate along a line of force, back and forth between the northern and southern hemispheres.

At the same time it drifts in longitude. If the field were perfectly dipolar, the drifts would be circular. The technique of computing the actual surfaces swept out by a particle oscillating between magnetic mirror points and drifting is of rather fundamental importance. I t is based on the second or longitudinal adiabatic invariant, whose existence was suggested by Rosenbluth. The first mention of it in the open literature is by Rosenbluth and Longmire [1957a]. A relativistic proof and applications to the Van Allen radiation are given by Northrop and Teller [1960a], who also derive the third or JEux invariant, necessary to describe the motion in a time-dependent field (as during a magnetic storm).

The adiabatic invariants are valid in a magnetic field with time and


space variations small compared with the period and radius of gyration. The particle is then represented as moving in a circle whose guiding center moves rapidly along the field and slowly perpendicular to the field. The longitudinal invariant, then, states that

is a constant. Here vlI is the velocity component parallel to B, the integration is carried along a line of force from the southern mirror point, ss, to the northern, and B, is the field at these mirror points. The second equality is valid when the total velocity is constant (no electric fields), and follows from Eq. (3.37).

The mirror points are on a surface of constant B = B,. Given the line of force occupied by a particle initially, we ask what line intersecting this surface will it follow later; it is the line satisfying Eq. (8.2). For one thing, the particle, after drifting all around the Earth, will return to the same line of force. Thus the particle trajectory lies on a closed surface, which is intuitively clear for a pure dipole field, but not a trivial result for the more irregular real field.

Vestine and Sibley [19593] integrated Eq. (8.2) for a large number of lines of force in the auroral zone with B, = 0.45 gauss. Thus the particular mirror point chosen as parameter occurs at higher altitudes for higher latitudes. The aurora might actually be described better with the mirror point occurring at a constant height of several hundred kilometers at all latitudes, but little difference in the shape of the computed isochasms would be expected. The agreement with observed isochasms is good, and it is not possible to decide whether Hultqvist or Vestine and Sibley have adopted the more realistic approach.

The southern isochasms, Vestine and Sibley [1959a] find, are linked to the northern ones by theoretical lines of force. This result would be expected, of course, if there actually were a stable magnetic connection between the two auroral zones, but it is not necessarily an indication that a simple and permanent connection exists. The degree to which solar streams distort the field at several Earth radii is a critical point in auroral theory, and one that is intimately associated with the question of simultaneity and similarity of individual northern and southern auroral displays.

Equation (8.2) has also been applied by Vestine [1960a] to the problem of daily variations in the aurora and especially the occurrence of aurorae at night. Suppose that particles are injected on the day side while the


equatorial field is compressed by solar gas, as shown in Fig. 8.4. Those particles with mirror points above the ionosphere will drift to the night side, the positive particles moving westward and the electrons eastward, in such a way that I = constant. As they drift into a region of uncom- pressed gas, the mirror points must move lower in latitude. If they did not, I would increase, since B in the equatorial regions would decrease.

/ I

I I \ \

\ - 1 - 1 - 1 +War Stream-

// *+- ’ - Compressed Field

I .

FIG. 8.4. Drift of trapped particles according to the longitudinal invariant. Solar gas incident from the right compresses the field and injects particles with mirror points on the surface of constant B. In drifting to the night side, the particles

must move even closer to the Earth to conserve I .

As the particles move to lower latitudes their mirror points are lowered in altitude, emptying them preferentially on the night side. The same reasoning holds if the field on the night side is distended by a solar stream.

Particles will be emptied from the magnetic field much more effectively if they are accelerated locally, parallel to B, while they are trapped. The quantities p and I are still adiabatically invariant, and the mirror point is then lowered, since B, increases as the kinetic energy, Chamberlain, Kern, and Vestine [1960a] have noted that a local acceleration mechanism would thus not only serve to empty auroral particles from their trapped orbits, but their precipitation curve on the Earth would be a spiral, not unlike the Stormer spiral of Figure 8.3. Particles might in this fashion move toward lower latitudes, and individual auroral arcs and bands would be slightly tilted to parallels of geomagnetic latitude.

Other effects may be present, of course, but these applications of the adiabatic invariants serve to illustrate what powerful tools they are. Many problems remain essentially untouched, such as auroral motions and differences in the drifts of positive and negative charges. Shaw [1959a], Vestine [1960a], and Chamberlain, Kern, and Vestine [1960a],


have speculated on the ionospheric currents induced in the auroral zone by a magnetic separation of bombarding particles.

8.2.3. Questions concerning the Energy Spectra and Angular

Two alternatives have been proposed to explain the energy spectra in auroral primaries. Either the particles are accelerated locally, presumably within the Earth’s field (Chamberlain [1957a]), or, if they are accelerated near the sun, they must be constrained by magnetic fields to within the neighborhood of the Earth. Otherwise fast and slow particles would not bombard the atmosphere at about the same time. The lag of a day or so of geophysical events following solar events implies velocities of - lo3 km/sec, at least an order of magnitude less than the largest velocities required by auroral observations (depth of aurora and bremsstrahlung). On the other hand, the evidence from H-line profiles is that the bulk of auroral protons have velocities of only a few hundred kilometers .per second. Thus it appears necessary to justify not only velocities that exceed the net sun-Earth travel speed, but others markedly below it as well.

Local acceleration is inherent in the speculative auroral models involving large-scale electric fields in the region around the Earth (see the review by Chamberlain [1958c]). A fundamental objection to the use of this acceleration mechanism is that propulsion into any one place on the atmosphere would involve particles of only one electrical sign at a time. But the evidence of Chapter 7 is that whenever protons are bombarding the atmosphere, primary electrons are entering simultaneously. We shall return to the matter below, when we discuss electron energies.

Distribution of Auroral Particles

Proton Acceleration.-Acceleration of protons or heavier ions in the Earth’s field by a modified Fermi mechanism has been suggested by Parker [1958b, el and Singer [1958a]. The original Fermi [1949a, 1954~1 mechanism accelerated cosmic rays by collisions of particles with moving interstellar gas clouds. A converging magnetic field attached to the cloud would cause an incident spiraling particle to be reflected. In a head-on collision the particle gains energy, and in an overtaking collision, it loses it. But as head-on collisions are the more frequent, there is a net increase of energy, which enters the equations as a second-order effect in the cloud velocity.

One may think of the colliding particles and clouds as statistically seeking the same mean energy, just as electrons and heavy ions in a


plasma exchange energy until both types of particle have the same temperature. The result is that the cosmic-ray particles attain tremendous energies.

As an auxiliary process to the Fermi mechanism, Davis [1956a] and Fan [1956c] have proposed the betatron effect, in which a changing magnetic field induces a faster gyrational motion by Faraday’s law (3.39). Fermi acceleration from collisions of a particle with traveling hydromagnetic waves (instead of with magnetized gas clouds) appears to be especially efficient. As two approaching waves converge on each other with a particle trapped between them, the betatron effect, as well as Fermi acceleration, are operative. The betatron effect not only accelerates the particle but, by increasing the magnetic moment, allows Fermi acceleration to continue longer before the particle breaks through the magnetic trap. In this fashion the net acceleration may become a first- order effect in the hydromagnetic-wave velocity. AlfvCn [1958b, 1959~1, who incidentally considers cosmic rays to originate for the most part in the solar system, has treated basically the same mechanisms but with some modifications.

In applying these considerations to auroral protons, where the accelerating hydromagnetic waves may be initiated by solar streams colliding with or blowing past the outer regions of the Earth’s field, Parker finds an energy spectrum similar to that derived empirically in Sec- tion 7.1.3.

Curiously, the differential energy spectrum of auroral protons actually striking the atmosphere (Section 7.1.3) follows about the same power law as protons in the inner Van Allen belt (Freden and White [1959a]). These spectra vary as or, in velocity or momentum units, the exponent is about - 2.5. AlfvCn [I95961 has drawn attention to the fact that the momentum spectrum of the inner Van Allen protons follows, in turn, the same power law as do (relativistic) cosmic rays. He further suggests that this coincidence is not fortuitous but arises because the Van Allen protons are accelerated by the cosmic-ray mechanism within the terrestrial field. It is tempting, although perhaps a bit rash, to extrapolate the same speculative conclusion to the acceleration of auroral protons.

Electron Acceleration.-Fermi acceleration of electrons in the same manner as protons is not generally thought to be very efficient. Each head-on collision with a moving magnetic constriction gives a definite increment to the velocity (not the energy) of the particle, regardless of whether it is a proton or electron. However, Crawford [1959a] has proposed that electrons in the outer Van Allen regions are accelerated


in closed magnetic loops. Presumably such loops are formed by instabili- ties in the region where a solar stream penetrates through the terrestrial field. Crawford shows that the process may reasonably give an exponential velocity distribution.

As I mentioned earlier, acceleration by a large-scale separation of charge (by Lorentz force in the outer terrestrial field) has been invoked by several writers,’ and the process might be considered appropriate for electron, if not proton, acceleration. Electrons would then derive energy essentially from the kinetic energy of protons, since any initial separation of charge must consume kinetic energy. In making calculations of this sort, one often assumes that the maximum separation of charge occurs (this maximum depending on the approach and assumptions with the particular model discussed), and that neutralization or discharge then converts the electrostatic potential into kinetic energy. However, even for a stream in vacuum there are difficulties in supposing the processes of separation and neutralization will be so accommodating. In a highly conducting plasma, such as surrounds the Earth, the mechanism seems more unsatisfactory in that it operates on all electrons in a large region. What is needed is a process for transferring large amounts of energy to a few select electrons.

Smaller scale, transient electric fields offer an alternative mechanism for accelerating auroral electrons. Parker [1958f] and Cole [1959a] have suggested that the penetration of solar gas into the terrestrial plasma (held by the geomagnetic field) sets up running plasma waves. The waves are readily damped by transferring their electrostatic energy into kinetic energy of the particles. Thus the mechanism basically transforms the energy of a solar stream into the energy of trapped particles. It works on protons as well as electrons, but is more spectacular for the latter in that it tends to equalize the energies of the two species.

Local Acceleration or Magnetic Constraint of Solar Plasma? -It has not been established that local acceleration occurs, but the matter can probably be settled by satellites or interplanetary vehicles that penetrate a solar stream outside the Earth’s field. All the particle acceleration may occur at the sun, provided that the particles are constrained by magnetic fields. It may readily be shown that even the

’ Notably AlfvCn [1950a, 1955a, 1958~1, Hoyle [1949a], Martyn [1951a], Landseer- Jones [1952a, 1955~1, Kellogg [1957a]. Also see Veksler [19580], who considers a situation where charge separation would not occur but the electrostatic acceleration supposedly proceeds continuously. This paper appears to be based on the misconception that protons and electrons experience the same degree of convergence of the magnetic field and omits allowance for their different radii of gyration.

8.2. AURORAL PARTICLES IN THE GEOMAGNETIC FIELD 34 1

proton velocity spread required by the H-line profiles could not be contained in an unmagnetized cloud (e.g., Bagariatskii [ 1958b]), and the electron velocities make the total spread far greater.

If a cloud of gas with magnetic fields imbedded in it breaks away from the sun, the fields may keep fast and slow particles together, so that all arrive at the Earth simultaneously. Such models have been envisioned by various people (Section 8.1.2) and offer an obvious mechanism for preserving an energy spectrum. One variation if this idea is contained in the model of Piddington [1958u] and Gold [1959u, b] who picture the magnetic field as being stretched radially outward by the gas cloud, remaining attached to the sun and forming a channel of communication with the Earth.

In Chapter 4 we noted several morphological changes that often accompany a change from positive to negative values of the magnetic disturbance: (1) the visible structure of the aurora changes from a homogeneous arc to a rayed form (Section 4.3.1); (2) the amount of proton bombardment decreases markedly over a period of several minutes (Section 4.3.2); (3) possibly there is an increase in the high- energy component of the electron spectrum (Section 4.3.3); (4) ionization is detected in the very low ionosphere, by radio absorption and even occasionally by reflection (Section 4.3.4); (5) the radio-aurora also may assume a different character during homogeneous and rayed visible forms, and its east-west direction of motion seems to be related to the sign of magnetic disturbance, the direction of positive current being opposite to the drift of radio-aurora (Section 6.1 .S).

Thus the whole character of auroral bombardment seems to change with magnetic activity. However, we have little understanding of what changes are occurring in the outer magnetic field-whether these changes involve local acceleration of particles or whether they merely alter the mechanism for dumping trapped particles into the atmosphere.

Angular Distribution.-In the calculations of hydrogen profiles and luminosity distributions in Chapter 7, we assumed that the incident particles were oriented isotropically over a hemisphere. For protons some information on the actual distribution may be obtained from zenith and horizon comparisons of Ha, although for electrons we must rely on rocket measurements exclusively. With an isotropic distribution, the same proton energy spectrum reproduces the maximum of the zenith profile and the semiwidth of the horizon profile. On this basis isotropy seems consistent with the data. But the moments of the profiles indicate a distribution elongated along the field. The discrepancy may be due to observational errors in the moments or may arise from


departures from isotropy, possibly with the angular distribution depending on particle energy.

At any rate we shall show that an isotropic distribution is to be expected for particles propelled toward the atmosphere from an injection source or center of acceleration located far above the atmosphere.* For more complex situations, such as continuous acceleration along lines of force or a scattering mechanism that operates on trapped particles immediately above the auroral atmosphere, the distribution function could depart from isotropy to produce either an elongated or flattened distribution.

We assume that the particles from the source that are able to reach

FIG. 8.5. Motion of a homogeneous group of particles with constant energy down a converging tube of magnetic lines of force. T h e particles crossing an element of the area A, into solid angle dSZ, later cross an element of area A into

solid angle dQ.

The intensity distribution urouortional

the atmosphere without being magnetically reflected are initially oriented isotropically. If the source is far above the atmosphere only a small cone of particles will eventually penetrate into the aurora, and isotropy does not have to extend over the whole sphere. Consider a group of particles all with the same total velocity, which does not change as the particles spiral in. Their intensity in a given direction, measured across an area normal to the particle motion, is everywhere independent of azimuthal angle 4 and is written T(0) particle/cm2 sec sterad. Hence the number of particles per second crossing area dA into solid angle dQ is 7 dA dQ.

For particles that are confined to a flux tube with cross-sectional area = const/B, the element of area traversed is proportional to (cos 0)/B (see Fig. 8.5). At a different point on their trajectory the particles will have a different

to cos 0 quoted by Chamberlain [1957a, - - 1958~1 and Bagariatskii [1958a, c] for this situation is incorrect. That result actually applies to the angular flux, not the intensity. Omholt [1959a] wrote down the correct angular dependence, but retained a normalization factor depending on the field strength.


angle. In order that the particles be conserved, we must therefore have the relation between two points on the trajectory,

(8.3) ~ ( 0 ) cos B sin 8 d0 - q0(0,) cos 8, sin 0, doo

B BO

Another relation between the two points is the adiabatic invariant from Eq. (3.37),

sin2 0 sin2 B0

-

(8.4) -

B Bo *

Differentiating this equation shows that q(0) = qo(O0), provided that 0 and 8, are related by Eq. (8.4).

Not only is the angular distribution isotropic at the top of the atmosphere if it is isotropic“initial1y”in a small cone, but the absolute intensity is the same. There are two compensating effects. As particles move toward increasing field, their orbits open outward and some are eventually reflected. But the convergence of the lines of force tends to increase the intensity.

The conclusion that q remains isotropic, proved here only for adiabatic invariance, is actually quite general, provided that the particles are not accelerated continuously. For example, it holds true for cosmic rays, showing that if the intensity is isotropic within allowed angles of entry (for some angles there are no orbits to infinity), the radiation is isotropic in space. A derivation follows immediately from Liouville’s theorem (see Janossy [1950a, p. 2681).

PROBLEMS

1. (a) For electrons with a spectrum extending up to velocities capable of penetrating to 100 km and with small pitch angles 0, show that the longitudinal drift acquired between the equatorial plane and the auroral atmosphere is less than the fine-structure width of rays (see Chapter 3, Problem 3). (b) If the fine structure on a beam of electrons was imposed on the day side of the Earth, would the structure be preserved after the electrons had drifted to the night side ? (c) If the drift is greater at large pitch angles of inclination, in what sense would rays deviate from being parallel to lines of force ?

2. Suppose a plasma stream bombards the Earth. Assume that a density of 10 ion/cm3 at a speed of lo8 cmjsec pushes on the field until the initial kinetic-energy density of the stream equals the magnetic-


energy density, B2//8.rr. (a) How far does the stream penetrate in the equatorial plane? (b) Compute the disturbed field at the Earth on the equator by considering the surface of the stream as a “mirror” that reflects the magnetic field, so that the disturbance is equivalent to the field produced by an image dipole twice as far from the real dipole as the stream surface (Chapman and Ferraro [ 19314). (c) Suppose the terrestrial field becomes merged with lines of force in the stream so that plasma is injected into the auroral zones. Also suppose that the velocities in the stream become isotropic over a cone of at least several degrees about the field. What is the energy flux that would actually strike the atmosphere and how does it compare with the observed flux in a moderate aurora ?

Chapter 9. The Airglow Spectrum

9.1. Nightglow

9.1.1. On the Distinction Between the Airglow and Aurora

We shall here consider the airglow to consist of the nonthermal radiation emitted by the Earth’s atmosphere, with the exceptions of auroral emission and radiation of a cataclysmic origin, such as lightning and meteor trains. This definition is purposely left somewhat ambiguous and vague, but it is to be hoped that as greater understanding of atmospheric radiation is accumulated, a more rigorous description will become feasible ; this is essentially the same definition first proposed by Elvey [1950a].

The lack of precise limits to the Earth’s atmosphere may cause some ambiguity; if Lyman and Balmer lines are emitted or scattered from sunlight by hydrogen in a large, tenuous geocorona, should this radiation be counted as airglow or zodiacal light or as still something else ?

But the most frustrating aspect of defining the airglow lies in distinguishing it from the aurora. In the event of weak airglow or a bright auroral display, there is no doubt in anyone’s mind what to call the phenomenon; for the borderline cases of a bright airglow or faint aurora, however, there is considerable doubt! Generally one distin- guishes between the two on physiological grounds, calling a structure

aurora” if it is bright enough to be seen. But according to Roach, McCaulley, and Marovich [1959a] there is no abrupt change at the visual threshold in the frequency distribution of intensities of the green line, h5577; thus it is not evident on the hasis of brightness alone that there is a physical distinction between auroral and airglow green-line emission. (In this regard also see Cabannes and Dufay [1935a]). Further, as F. E. Roach delights in pointing out, it is ridiculous at the present time to say that there is an aurora only if there is a simultaneous magnetic disturbance. The relationship between two such phenomena is one of the answers we seek; but the problem evaporates when the two phenomena are defined to be practically identical. Nor does it seem possible at the moment to differentiate clearly between the two on the basis of structure or motions, since the airglow green line can exhibit changing patterns not unlike auroral arcs, and the aurora can be rather amorphous and quiescent.

345

6 6

346 9. THE AIRGLOW SPECTRUM

The spectra are one possible basis for separating the two, up to a point. Rayleigh [1931a] measured a night sky of exceptional brightness, but concluded that the absence of N l bands ruled against an auroral interpretation. Roach, McCaulley, Marovich, and Purdy [1960a] have insisted, however, that the tremendous reciprocity failure of photographic emulsions for long exposures makes any quantitative comparison of relative intensities between airglow and auroral spectra quite suspect (see, however, Problem 1). Dkjardin [1936a] was impressed with the qualitative difference between auroral and night-sky spectra. Although many of the identifications of airglow band systems were wrong in 1936, the belief at that time that the aurora has a spectrum with much higher excitation than the airglow was correct. We might therefore conclude, for example, that O H bands always indicate airglow and N, First Positive bands, an aurora.

Barbier [19583] has suggested a similar pragmatic approach for distinguishing the presence of an aurora at low latitudes. By simultaneous photometry in different wavelengths he finds that the green line, h5577, and the 0, Herzberg bands, measured at h3670, are well correlated (Section 12.3.3). When individual measurements show an appreciable divergence from the established correlation, he concludes that aurora is present.

As a working rule of thumb this procedure is partly satisfactory; as a basic definition, it is not. It is always possible that N, bands are weakly present in the airglow (as they were formerly thought to be), in which case the distinction becomes only quantitative, not qualitative. And we must readily admit the possibility-indeed, the likelihood-that the different radiations in the airglow arise from a variety of separate and independent causes. How, then, do we decide whether a particular enhancement of, say, the green or red [OI] lines is due to auroral activity ?

Any meaningful and valid distinction between aurora and airglow must eventually look to the cause of the excitation. In Section 6.1.1 the aurora was defined as the sporadic electromagnetic radiation that is emitted from the atmosphere and induced by extra-atmospheric atomic or subatomic particles. But we cannot exclude the possibility that some of the airglow has an incident-particle 0rigin.l At a later

Indeed, the faint Cerenkov radiation, which is emitted in the lower atmosphere by cosmic rays and which forms a “limit to the darkness of the darkest night” (Blackett [1948a]) would be counted as airglow radiation according to our definitions. For actual measurements of the brightness of this component of the night sky, see Jelley and Galbraith [1953u, bl and Goldanskii and Zhdanov [1955a]. A review has been published by Jelley [ 1959ul.

9.1. NIGHTGLOW 347

date it may prove expedient to resurrect the term permanent aurora or nonpolar aurora to describe a component of the airglow.

The precise meanings to be ascribed to aurora and airglow also bear on the problem of what to call emission that is detected from the dark hemispheres of other planets. For Venus Kozyrev [1954a] first reported some weak emission bands that may include the First Negative system of N2+. This work was partially confirmed by Newkirk [1959a], who used a coronograph to reduce the scattered light from the bright part of the planet. These observations hold great potential importance both from the standpoint of solar-planetary relationships and for an understanding of the chemical composition and photochemistry of Venus’ atmosphere.

9.1.2. Historical Summary of Early Work

In the years around 1900 several astronomers began to recognize the existence of a terrestrial component to the light of the night sky. How- ever, there are observations on record (see the historical review by Yntema [1909a]) as early as 1788 of nights with an unusually large brightness over the sky and a gradual increase in brightness from the zenith toward the horizon.

The existence of what is now termed airglow2 was established photometrically by Yntema [1909a]. He gave the name Earthlight to the night-sky light emitted by or scattered in the Earth’s atmosphere. Besides the variability in the brightness of the sky from night to night, Yntema noted on the basis of star counts that scattered starlight was insufficient to explain the increase of intensity away from the zenith. These points were noted earlier by Burns [1906a], who also suggested a terrestrial emission but who did not rule out the possibility that scattered starlight might explain the increase of intensity toward the horizon.

Another line of evidence in favor of an airglow was that the brightness of the light of the night sky was not concentrated toward the Milky Way to the extent that one would expect on the basis of star counts in the Milky Way and near the galactic pole. Newcomb [1901a] and Bu ns [1902a] were the first to measure this effect visually; Townley [1903a] and Fabry [1910a] made photographic measurements of sky brightness.

Finally, there was the powerful spectroscopic evidence that the A5577 green auroral line was present at all times over the entire sky.

The word airglow was introduced by Elvey [1950a] at the suggestion of Otto Struve. Roach and Pettit [195lb] began using nightglow to mean the nighttime airglow.


Angstrom [1868a, pp. 41 -421, Vogel [I 8724, and Wiechert [ 1902~1 suggested that the green line could be present even when visible auroral structure was not. Campbell [1895a] and later Fath [1908a] noted that the line seemed to be present at all times and in all parts of the sky. Slipher [1919a] obtained a large number of spectrograms with the green auroral line and confirmed the conclusion that there was a permaeent aurora as Yntema [1909a] called it, or a nonpolar aurora in Rayleigh’s [ 1924al terminology.

Yntema’s photometric investigations at Groningen were extended and his conclusions in favor of the Earthlight were confirmed by van Rhijn [1919a]. In a more extensive account of his researches, van Rhijn [1921a] first gave the rather simple expression (see Section 12.1.1) for the increase of intensity with zenith distance for a homogeneous, thin emitting layer in a spherical atmosphere, with no extinction (i.e., with a perfectly transparent troposphere). The expression involves the height of the emitting layer and so the measurement of the intensity variation with zenith distance forms a possible means of deriving the airglow height. As we shall see in Section 12.1.3 the practical difficulties of correcting for the lower atmosphere render these so-called van Rhijn heights quite uncertain.

Fabry [1919a, 1921al drew attention to one of the major problems of the light of the night sky: the sorting out of the contributions from the stellar background, from scattering of sunlight by interplanetary gas, scattering by interplanetary dust, and atmospheric emission. With this end in view, Rayleigh [1919a] and Babcock [1919a] looked for polarization in the light of the night sky and found i t to be almost completely absent. Later Dufay [1928a, 1929al found a weak (between 2 and 4 percent) polarization whose plane remained in the azimuth of the sun. He concluded that about 15 percent of the light of the night sky arose from the zodiacal light. Further, Rayleigh [1920a, 1921al began his studies of the color of the night sky by photographic and visual photometry with various filters. Rayleigh’s [ 1924a, 19254 program of observations gave the first quantitative information on time variations of intensity in different parts of the spectrum. He also determined relative intensities in different spectral regions and sought correlations with sunspot area and magnetic disturbance.

Using very low-dispersion instruments, Rayleigh [ 1922a, 1922c, 1923a, 1928a, 1931al also investigated the spectrum of the night sky. His studies were particularly concerned with the variation in brightness of the green “auroral” line, h5577. He concluded that the terrestrial component of the light of the night sky was qualitatively different from the aurora, as there seemed to be no particular enhancement of the green

9.1. NIGHTGLOW 349

line toward the north, and the negative nitrogen bands, always present in the aurora, were absent from the night sky. The first absolute measurements of the brightness of the green line were expressed by Rayleigh [1930a] in terms of the number of atomic transitions per second in a column along the line of sight, and accordingly the photometric unit used in airglow and auroral observations has been named after him (see Appendix 11).

Both Rayleigh [1923a] and Dufay [1923a] noted the presence of what seemed, on their low-dispersion plates, to be a continuous spectrum in the ultraviolet and blue, crossed with several of the stronger Fraunhofer absorption lines.3 The question was whether this backgrounci continuum arose from starlight or from the zodiacal light (i.e., sunlight scattered by the interplanetary medium). Rayleigh also measured two emission features in the blue.

Babcock [1923a] photographed the night sky in the light of green- line interference fringes formed by a Fabry-Perot etalon. The wavelength he obtained was 5577.350 A on the international scale, which was 0.48 A less then Slipher’s [1919a] measurement on the auroral spectrum.4 Babcock’s work also set an upper limit of the line width of 0.035 A ; such measurements may be used as indicators of the temperature of the emitting regions (see Section 12.2).

The identity of the green line was a perplexing problem for many years. Vegard [1923a, b, c, d] suggested that it might arise from solid nitrogen, but McLennan and Shrum [1924a] were unable to produce it by bombarding solid nitrogen with cathode rays. Shortly afterward, McLennan and Shrum [1925a] succeeded in producing the green line in a laboratory discharge tube containing oxygen and helium, and correctly concluded that it arose from some previously unknown spectrum of oxygen. In an extension of this work McLennan and McLeod [1927a] measured the laboiatory line with an interferometer and obtained a wavelength of 5577.341 & 0.004 A, in excellent agreement with Babcock’s value.

Investigation of the Zeeman pattern by McLennan and others5 indicated that the green line probably arose from the “forbidden” transition, ‘D, - lSO. The first identification of forbidden lines had

I t is now known that the blue continuum and the absorption lines are, to some extent, illusory, with many close emission bands resembling a continuous spectrum. See Sec- tion 9.1.3.

Cabannes and Dufay [1955a] quote the probable wavelength of the green line as 5577.345 4~ 0.003 A.

McLennan, McLeod, and McQuarrie [1927a]; McLennan, McLeod, and Ruedy [1928a]; McLennan [1928a]; and Sommer [1928a].

3 50 9. THE AIRGLOW SPECTRUM

just been made by Bowen [1927a, 1928~1 in an analysis of the spectra of planetary nebulae. Frerichs [1930a] confirmed the identification of the green line and predicted the energy of lD, and ‘So on the basis of ultraviolet spectra of oxygen. This analysis predicted the oxygen red lines, 3P - ID, near 6300 and 6364 A, which were identified in laboratory spectra by Paschen [1930a] and in planetary nebulae by Bowen [1930a].

The red lines, as well as the Na D lines, were first recorded in the airglow spectrum by Slipher [1929a]. The first measurements of the red lines showed only a strong feature “near X6315,” but later spectra by Sommer [1932a, 1933~1, Slipher [1933a], and Cabannes [1934a, 1935~1 resolved the lines and made the identification rather definite.6 These early spectra of the red and near infrared also disclosed a number of bands that have since been identified as OH (see Section 9.1.4).

McLennan, McLeod, and Ireton [ 1928~1 and Rayleigh [1929a] independently reported a daily maximum in the green-line intensity occurring near midnight. Spencer Jones [1930a] did not find such a variation in South Africa but did find yearly variations in the southern hemisphere that seemed to be opposite in phase to those in the northern hemisphere (see Section 12.3.2).

Other important photometric and spectral studies were carried out by McLennan and Ireton [1930a], Dufay [1928a, b, 1929~1, Cabannes and Dufay [1934a, 1935a, b], and Brunner [1935a]. Dufay found that the green line carried about one third the energy of the continuous spectrum between 4960 and 6000 A and between 6 and 9 percent of the total visual brightness of the night sky. The latter figure agrees well with Rayleigh’s [1930a] result that 7 percent of the light seen by a dark-adapted eye arises from the green line (see Section 12.3.1). Early attempts at theoretical explanations of the airglow were made by Chapman [1931a] and Cabannes [1934b]; an excellent review article on these early researches was prepared by Dkjardin [1936a].

9.1.3. The Ul t rav io le t and Blue Spectrum

The blue and near ultraviolet regions of the night-sky spectrum have been investigated extensively, but the problem of identifications of the features is still not completely solved. I n the blue region especially, numerous bands are crowded together and overlap, making it most difficult with low resolution to decide where band heads or maxima occur.

a The wavelengths for the red doublet, as given by the interferometric work of Cabannes and Dufay [1955a, b, 1956a, b] are 6300.308 A for sP2 - ‘D, and 6363.790 A for 3P, - lD,.

9.1. NI1;;HTGLOW 351

The Blue Pseudo-Continuum.--A portion of the light of the night sky arises, of course, from direct starlight plus the diffuse galactic light and from zodiacal light (Section 12.3.1), and these astronomical components will have spectra roughly similar to that of the sun.' Rayleigh [1923a] noted the apparent presence of the H and K absorption lines of Ca I1 and Dufay [1923a, 1928~1 listed a large number of absorption lines between 3047 A and the G band at 4300 A. Cabannes and Dufay [1944a], in their extensive study of the blue and violet regions, also listed many absorption as well as emission features.

Other investigators, such as Elkey, Swings, and Linke [1941a], did not list any absorption lines, and Barbier [ 19454 specifically rejected them since a number of prominent Fraunhofer lines, especially in the ultraviolet, did not appear in the night sky. Nevertheless, the appearance of a continuum remained, and Kastler [19466] suggested the presence of an airglow emission continuum In the blue. Barbier [19473] ascribed 80 percent of the light in the blue-violet region (longward of 3900 A) to an apparent continuum, but over half of this was assigned to the airglow (unresolved bands and emission continuum). Meinel [1953a] and Chamberlain and Oliver [19530] suggested that the blue continuum arose from the astronomical components of the night sky, with the weakness of some lines that are strong in the solar spectrum due to overlapping emission bands.

Spectra with higher resolution than was formerly possible (Cham- berlain [1958d]) show that a continuum in the blue-violet region is actually not nearly so important as was often believed. Rather, the impression of a continuum that one obtains from low-resolution spectra is due largely (albeit not entirely) to numerous close, discrete bands.

The airglow emission continuum, that is so predominant in the green region (see Section 9.1.4) probably contributes somewhat in the blue as well. However, the blue spectrum between some of the discrete emission bands is very faint, suggesting that continuous radiation must be relatively unimportant in the region around 4000 A and shortward. Further, the astronomical component does appear weakly; for example, the depressions at the H and K lines (3933, 3968 A) are considerably deeper than between other bands in the region. But on low-dispersion

The color and spectrum would not be precisely those of the sun: the spectra of the Milky U'ay, star clusters, and other galaxies are composites of light from stars over a wide range of temperatures, but they still resemble the solar spectrum (Fath [1912a, 1913~1). Scattering in the lower atmosphere would also make the light bluer than direct sunlight. Incidentally, Fath's spectra seem to include some airglow emission, especially around 4165 A.

3 52 9. THE AIRGLOW SPECTRUM

spectra the importance of H and K is exaggerated by the fortuitous placing of neighboring emission bands (see Fig. 9.3).

Herzberg bands of 02.-J. Dufay [1941u, 194733 first suggested that the forbidden Herzberg bands, A 3Zz + X 3Z;, might be present in the airglow (see Fig. 5.33). Swings [1943a] concurred in this proposal, assigning many additional Herzberg bands to the airglow spectrum. Barbier 11947~1 also supported these identifications on the basis of his careful studies of the spectrum between 3100 and 5000 A (also see Barbier [1945a]).

The identification was established definitely by an ultraviolet spectrum with a dispersion of 23 A/mm (Chamberlain [1954d, 1955a]), which resolved most of the rotational structure and which is reproduced in Figs.9.1 and 9.2. Additional bands appear in the blue region (Chamberlain [1958d]), as shown in Figs. 9.3 and 9.4.

The bands have been studied under high resolution in absorption by Herzberg [1952a]. Broida and Gaydon [1954u] first produced the bands in emission in laboratory afterglows and revised Herzberg’s vibrational numberings for the upper state by one unit. Other laboratory studies of the bands have been made by Gaydon [1956a] and Barth and Kaplan [1957a, b, 1959~1.

Bands with v’ (upper state) as high as 7 have been observed. (In the laboratory afterglows a few bands with v’ 2 8 have been detected shortward of 3000A.) The prominence in the airglow of bands with the higher values of v’ is noticeable, both in the ultraviolet and blue regions; bands with v’ = 0, 1, and 2 are quite weak compared with their relative intensities in the laboratory spectra.

Other Attempted Identifications, 3100-5000 A.-The Herzberg bands do not by any means explain all the emission bands in the blue region, and numerous proposals have been made for other identifications. Electronic bands of OH were suggested for the ultraviolet spectrum by Dkjardin and Bernard [1938b] and Nicolet and Gotz [1951u]. The Vegard-Kaplan forbidden band system of N,, A “.c,+ -fXIZ$+, was thought for many years to be in the airglow. Kaplan [1935u, b] first proposed that the 2-14 and 3-14 bands were responsible for the strong peaks near 4425 and 4171 A, Rayleigh’s so-called XI and X, bands.8 Cabannes and Dufay [1935u, 1946~1, Elvey, Swings, and Linke [1941a], and Barbier [1947u] listed a number of other features that might arise from

These features actually arise from blends of several distinct bands, the strongest of which belong to the Herzberg 0, system.

FIG. 9.1. Nightglow spectrum, 3130-3550 A. The upper part of the spectrum was photographed with light from the north horizon; the lower part, with light from the zenith. Differences between the two make it possible to identify auroral contami- nations. The mercury (Hg) line is a contamination from artificial lights. Herzberg bands of 0, are labeled H. Dashed lines above the spectrum indicate expected but unconfirmed positions of band heads in the 34 + 14 system of 0,. From Yerkes Observatory plate no. 19, dispersion 23 A/mm, projected slit width 0.8 A. For microphotometer tracings see Chamberlain [ I 955aI.

354 9. T

HE

A

IRC

LO

W

SPECTR

UM

FIG. 9.2. Nightglow spectrum, 3410-3830 A. See legend to Fig. 9. I . The position of [OII],, is indicated, but the identification is doubtful. FromYerkes Observatory plate no. 19,dispersion 23 A/mm, projected slit width 0.8 A. For microphotometer tracings

see Chamberlain [ 1955~1.

FIG. 9.3. Nightglow spectrum, 3720-4100 A. See legend to Fig. 9.1. The N, and N; bands marked with dashed lines beiow the spectrum are aurora1 contamination. From Yerkes Observatory plate no. 129, dispersion 21 A / m , projected slit width I .2 A.

After Chamberlain [ 1958d] ; courtesy University of Chicago Press. wl wl

FIG. 9.3. Nightglow spectrum, 3720-4100 A. See legend to Fig. 9.1. The N, and NH bands marked with dashed lines below the spectrum are auroral contamination. From Yerkes Observatory plate no. 129, dispersion 21 A / m , projected slit width 1.2 A.

After Chamberlain [ 1958dJ ; courtesy University of Chicago Press. VI VI

356 9.

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n \ - I

FIG. 9.4. Nightglow spectrum, 4060-4400A. See legends to Figs. 9.1 and 9.3. From Yerkes Observatory plate no. 129, dispersion 21 A i m , projected slit width 1.2 A. After Chamberlain [19584; courtesy University of Chicago Press.

FIG. 9.5. Nightglow spectrum, 4300-4900 A. See legend to Fig. 9. I . From Yerkes Observatory plate no. 83, dispersion 35 A / m , projected slit width 1.7. A. After Chamberlain [l958dJ; courtesy University of Chicago Press.

~

CA 4


the Vegard-Kaplan system. I n later work the identifications became questioned (Meinel, [1951a], Barbier [1953c], Chamberlain and Oliver [1953b]) and high-resolution spectra (Chamberlain [1955a, 1958d1) show no Vegard-Kaplan radiation.

Various other proposals, especially of N, and 0, band systems, have been made on the basis of coincidences between predicted wavelengths and emission peaks on low-resolution ~ p e c t r a . ~ Nevertheless, only the Herzberg 0, bands have been definitely established. The N,+ First Negative system, especially A3914 and X4278, may emit weakly in the nightglow, but its presence is not certain.

In Figs. 9.1 through 9.5 several bands are indicated in the B 34, -+ a ld, system of 0,, as proposed by Chamberlain [1958d]. Tables of wavelengths of band positions, for both the identified and unidentified features, are given in the papers by Chamberlain [1955a, 1958dl.

Far Ultraviolet Radiations.-By means of rocket flights or Earth- satellite experiments, the spectrum of the airglow shortward of the ozone cutoff near.3100 A can be measured. Observations of this nature made from Aerobee rockets have been reported by a grouplo at the Naval Research Laboratory. The Lyman cy line of hydrogen at 1215 A was observed with an emission rate of about 2500 rayleighs, nearly omni- directional over the upper hemisphere, but with a slight minimum in the antisolar direction. This radiation is probably related to the Ha line detected in the airglow by Prokudina [1959a] (see Section 9.1.4). If it arises from resonance scattering of sunlight by H atoms in interplanetary space or a geocorona, it may show polarization (see Section 1 1.1.2).

When observing downward from above 120 km, the rocket detected another source of Ly a radiation. This emission is perhaps extraterrestrial, being scattered by H atoms in the upper atmosphere. The effective albedo of the Earth for L y a was thus found to be about 40 percent. The remaining radiation, which is absorbed in the atmosphere, may provide a means of exciting some additional airglow emissions.

See especially the spectroscopic analyses by Elvey, Swings, and Linke [1941a], Dbjardin and Dufay [1942a], Dufay and Dkjardin [1946a], Cabannes and Dufay [1944a, 1946~1, Barbier [1945a, 1947a, b, c, d, 1948b, 1953c, 1955~1, DLjardin [1948a], Pearse [1948a], Hunaerts and Nicolet [195Oa], Herzberg [1953a], Auberger [1953a], Broida and Gaydon [1954a], M. Dufay [1954a], and M. and J. Dufay [1955a].

lo See Byram, Chubb, Friedman, and Kupperian [1957a], Kupperian, Byrarn, Chubb, and Friedrnan [1958a, 1959~1.

9.1. NIGHTGLOW 359

9.1.4. The Green, Red, a n d Infrared Spectrum

Atomic Lines.-The early work on the discovery of the [OI],, green line ( lD, - ‘So) at 5577 A, the [OI],, red doublet (3P,,, - lD,) at 6300 and 6364 A, and the Na D or resonance lines (2S1,2 - 2P3/2, at 5890 and 5896 A has been summarized in Section 9.1.2, where the most recent interferometric wavelengths are also recorded. In addition to these strong lines, which have received a great deal of photometric attention (see Chapter 12), a weak doublet of [NIIz1 at 5199 A (4St/, - 2D$2, 3,2) seems to be detectable in the nightglow (M. Dufay [19596], Krassovskii [19583], Blackwell, Ingham, and Rundle [ 1960~1). This line was previously observed in twilight (Section 9.2.4). Interferometer studies of the widths of the [OI] lines have provided information on the temperature of the emitting atoms (Section 12.3).

The red lines should appear with a photon intensity ratio for A6300/ A6364 of 3 to 1 , the same as the ratio of their transition probabilities (Appendix VI). For sodium a ratio of 2 to 1 for D,, A5890/D,, A5896 would be expected if the upper levels are excited in proportion to their statistical weights and if the nightglow D-line radiation is not subsequently scattered by atmospheric Na. I t seems likely that there is sufficient Na in the high atmosphere in winter to cause an appreciable deviation from this ratio (Donahue and Foderaro [1955u], Chamberlain and Negaard [1956u]), but the quantitative results depend not only on the Na abundance but on the zenith angle of observation, the relative position of the free Na atoms and the nightglow emitting layer, and the kinetic temperature of both the scattering Na atoms and the excited “nightglow atoms.” Measurements by Cabannes, Dufay, and Gauzit [1938c], Berthier [1952u], and Nguyen-huu-Doan [1959u] show that D,/D, is approximately 2, but accurate simultaneous measurements throughout the year both in the zenith and near the horizon are needed for an adequate interpretation in terms of the theory.

A weak Ha emission in the airglow has been reported by Prokudina [1959u] (also Kvifte [19596]). Its breadth of less than 2 A corresponds to a Doppler broadening of less than 50 km/sec, which may be compared with widths of several hundred kilometers per second for auroral hydrogen lines. The emission rate varies between 5 and 20 R, and is thus the order of one tenth the brightness of A6300 [OI],,.

The Green Continuum.-Quite distinct from the blue pseudo-continuum, produced on low-dispersion spectra mostly by unresolved bands, there seems to be a real emission continuum that is strongest in the green. This continuous radiation was first indicated by the photometric


5 -

4 -

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R/ A

Apr 4 -Apr5'57

Nov 19 -Nov2&

-- -_- Oct22-0c t23 7 ------

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I I L I I I I 1 1 1 1 1 1 1 1 =-

0, Atmospheric Band System.-Investigations of the infrared airglow were unrewarding for many years because of the low dispersions (usually less than 2000 Ajmm) that were used. An important advance was made by Meinel [1948a], whose first airglow-aurora spectrograph utilized a replica transmission grating and gave a dispersion in the first order of 250 Ajmm. The system worked at an effective speed of fj1.0, having a Schmidt camera with a field-flattening lens immediately in front of the focal plane.

With this spectrograph and a later one of higher resolution, Meinel [1948a, 1950a,f] identified the 0-1 band of the 0, Atmospheric system, b lZ; --f X ";. This band has its origin at 8645 A, with the P- and R-form branches giving maxima at about 8659 A and 8629 A, respectively. Kaplan [ 1947a, b] had previously produced the 0-1 band in emission for the first time in laboratory afterglows. The 0-0 band at 7619 A must

observations of Barbier, Dufay, and Williams [1951a, 1954~1 and confirmed by Chuvayev [1952a] and Barbier [1956a]. The photometric studies do not in themselves exclude the possibility that the emission detected arises from discrete bands; however, the spectra in Figs. 9.3 to 9.5, obtained with rather high dispersion, show progressively less structure toward the long wavelengths, suggesting that there is a continuous emission which is relatively much stronger in the green than in the blue.

An accurate measurement of the intensity distribution with wavelength is rendered quite difficult by the overlying bands. However, a first attempt to measure this distribution has been made by Shefov [1959a], whose results are given in Fig. 9.6.

9.1. NIGHTGLOW 361

also be emitted in the upper atmosphere, but it is reabsorbed by the great mass of 0, that it must penetrate. Night-sky spectra thus show an absorption, corresponding to the Fraunhofer A band, around 7619 A.

Bates [I95431 pointed out that some of the 0-0 emission might become degraded into the 0-1 band through successive scatterings. This

FIG. 9.7. Nightglow spectrum 4800-6100 A, obtained by Mironov, Prokudina and Shefov, dispersion 80A/mm. The 9-2 OH band overlaps A5200 [NI],,, but

does not show clearly in this print. Courtesy V. I . Krassovskii.

radiative-transfer effect was investigated by Chamberlain [ 1954~1, who found that the conversion would occur mainly near the 50-km level. However, it is likely that deactivation of 0, is important at and above this height, so that actually little of the 7619 A emission is converted into the 8645 A band.

FIG. 9.8. Nightglow spectrum, 5400-6530 A, dispersion 78 A/mm. After Blackwell, Ingham, and Rundle [ 1960al; courtesy University of Chicago Press.

362 9.

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10

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FIG. 9.9. Microphotometer tracing of nightglow spectrum in Fig. 9.8. After Blackwell, Ingham, and Rundle [ I960a] ; courtesy University of Chicago Press.

9.1. NIGHTGLOW 363

OH Meinel Bands.-Although bands in the near infrared had been detected previously, it was not until Meinel [1950b] resolved their rotational structure that an identification of the vibration-rotation bands was possible. An emission near 6500 A, thought possibly to be due to Ha (Elvey" [1950a]), was shown by Meinel [195Oc] to belong to OH. Meinel [1950d, el later presented a detailed analysis of the new band system. Additional photographic studies were reported in France.12

FIG. 9.10. Nightglow spectra; 7800-1 1,100 A, obtained by Mironov, Prokudina, and Shefov, with the aid of an electron image converter, dispersion 130A/mm.

Courtesy V. I. Krassovskii.

The use of electronic techniques in the observation of the infrared was begun by Elvey [1943u] and Stebbins, Whitford, and Swings [1944u, 1945a1, who used filters with fairly wide band passes to isolate particular spectral regions. The measurements suggested an emission near 10,400 A, which was tentatively attributed to the 0-0 band of the N, First Positive system. Rodionov and Pavlova [1949a] carried out a similar investigation with four overlapping filters, but were unable to

l1 This emission was described by Elvey as being quite broad and therefore is not to be confused with the narrow airglow line identified more recently as Ha by Prokudina

l2 See Cabannes, Dufay, and Dufay [195Oa], J. Dufay [1949a, 195101, J. and M. Dufay [ 1959al.

[1951a], M. Dufay [1951b], L. and R. Herman [1955a].

364 9.

TH

E

AIR

GL

OW

SP

EC

TR

UM

m-

365


identify the radiation with any greater certainty. Later Kron [ 1950al placed an infrared photocell behind the exit slit of a monochromator and scanned the spectrum between 9000 and 11,000 A. Although the resolution of this instrument was only about 400 A, he was able to show that the spectrum agreed reasonably well with the expected OH bands and did not disclose a strong First Positive band.

Meanwhile in the Soviet Union spectroscopic investigations in the near infrared had begun with an electron image converter under the

t A 1.8 1.9

FIG. 9.12. Nightglow spectrum, 1 .Op to 2.0p, obtained with a scanning spectrometer, projected slit width 200A. T h e origins and expected intensities of OH bands are shown by vertical lines; the horizontal strokes indicate the reduction due to water vapor. After Gush and Vallance Jones [1955a]; courtesy Pergamon

Press.

direction of Krassovskii [1949a]. Although the sensitivity of the instrument extended to 12,000 A, it was usable on the airglow only to 11,000 A because of telluric absorption bands. These early measurements were made with very low resolution, and the emissions were not identifiable with much confidence. The steps in the gradual improvement of the instrumentation and in the measurements have been reported in a series of notes and in reviews.13 Spectra made with the aid of an image

la Krassovskii [1949a, 1950a, b, c], Lukashenia and Krassovskii [1951a, b], Krassovskii and Lukashenia [1951a], Bagariatskii, Krassovskii, and Mordukhovich [1952a], Krassovskii [1952a, 19546, 1956~1, Bagariatskii and Fedorova [1956a], and Fedorova [1957a].

9.1, NIGHTGLOW 367

converter are shown in Fig. 9.10. Soon after the publication of Meinel's [1950b] first note on OH, Shklovskii [1950a, b, 1951~1 identified the infrared bands found by Krassovskii et al. with the Meinel bands.

M. Dufay [1957a] used a photoelectric spectrometer to resolve partially the O H band structure between 7,000 and 11,000 A. Gush and Vallance Jones [1955a] (see also Vallance Jones and Gush [1953a]) have obtained spectra in the 1-2p region with a scanning spectrometer equipped with a lead sulfide (PbS) detector (Fig. 9.12). Similar instruments have been used by Noxon, Harrison, and Vallance Jones [1959a] to record the spectrum from 1.4 to 4.0p, and by Moroz [1959a] from 1.2 to 3 . 4 ~ . Vallance Jones [19553] also obtained a spectrum near 10,000 A on Eastman I-Z(2) emulsion (see Fig. 5.26). Thus far no emission bands other than OH have been identified in the near infrared, but longward of 2 . 5 ~ the thermal radiation from the lower atmosphere becomes too bright to allow the detection of further OH.

The Meinel system of OH is composed of the vibration-rotation bands formed within the ground, ,l7, state. Each band has P, Q, and R branches, with the latter forming the band head on the shortward side. The ground state is designated 2173,, and gives rise to the so-called P,, Ql, and R, lines. Because of spin doubling the z17n,,, state lies approximately 140 cm-l higher. Its P,, Q2, and R, lines are weaker than those in the lower, more populated state, and consequently there is an alternation in intensity between P, and Pz lines in the band (see especially Fig. 9.11). There is also a A-doubling which has been observed in the high- resolution laboratory spectra but not in the airglow.

These laboratory spectra have been obtained from oxyacetylene flames by Dkjardin, Janin, and Peyron [1953a] and by Herman and Hornbeck [1953a]; who analyzed the 4-0, 5-1 and 6-2 bands in detail. The energies of the lowest vibrational levels are given by analysis of ultraviolet electronic bands. Chamberlain and Roesler [1955a] combined improved measurements of some of the airglow bands with these laboratory data to obtain the energy levels up to v = 9 and an improved set of vibrational constants. Table 9.1 gives the predicted positions of the origins of OH bands with v 5 9 along with R and P lines. No bands with v 2 10 have been detected in the airglow, an interesting fact whose interpretation is discussed in Chapter 13.

The Far Infrared.-Although thermal radiation dominates longward of 2.5p, the emission spectrum of the atmosphere in the infrared differs greatly from that of a black body. Since water vapor plays such an important role, the spectrum is critically dependent on humidity and cloud coverage; the spectrum changes little between day and night. The


TABLE 9.1

PREDICTED POSITIONS OF MEINEL OH BANDS

An asterisk denotes the R, and Re lines forming the band heads. The band origins are those listed by Chamberlain and Smith [1959u] as computed

from the energy levels tabulated by Chamberlain and Roesler [1955u]. The rotational and spin constants used were those given by Herman and Hornbeck [1953u], which are now known to be somewhat in error for w 2 7 (Blackwell, Ingham, and Rundle [1960a], Wallace [1960b]). For accurate wavelengths of lines involving these levels, a correction will be necessary. Kvifte [ 1959~1 has tabulated the rotational energy levels, deriving those for z1 = 7, 8, and 9 from his airglow spectra, and Wallace [1960b] has derived the molecular constants, by combining the best data available, from which the energy levels may be computed. Accurate wavelengths have been measured in the laboratory for 4-0, 5-1, and 6-2 by Herman and Hornbeck (1953~1 and Dejardin, Janin, and Peyron [1953a]. The most accurate wavelengths measured on airglow spectra are probably those of Kvifte [1959b, c] for 8-2,5-0,9-3, and 6-1 (photographed at 35Airnm); Chamberlain and Roesler [1955u] for the P-branch lines of 5-1 and 6-2 (70 Aimm); Wallace [19606] for 8-3 and 9-4 (30 A/mm); and Vallance Jones [1955b] for 8-4, 3-0, 9-5, 4-1, and 5-2 (85 A/mm).

Rands origins Lines Xair (A) Band

(w' - v") Xai, (A) vVac (cm-I) K" Rl RZ Pl PZ

9-0 3816.6 26193.9 1 2 3 4 5 6 7

8-0 4172.9 23957.9 1 2 3 4 5 6 7

9- 1 4418.8 22624.3 1 2 3 4 5 6 7

3 809.6' 3810.1 3812.2 3816.1 3821.7 3829.2 3838.5

4136.9 4163.7* 4165.4 4168.8 4174.1 4181.4 4190.6

4409.1 * 4409.2 4411.3 4415.3 4421.5 4429.8 4440.4

3811.8 3811.1" 3812.5 3815.9 3821.2 3828.5 3837.7

4166.6 4165.1 * 4165.8 4168.7 4173.7 4180.7 4189.8

4412.3 4410.9' 4411.9 4415.4 4421.1 4429.2 4439.6

3830.1 3839.2 3849.9 3862.6 3877.2 3893.7

4189.0 4199.2 4211.4 4225.6 4241.8 4260.1

4436.1 4447.3 4460.7 4476.3 4494.2 4514.4

3826.5 3835.6 3846.5 3859.4 3874.2 3891.0

4184.5 4194.9 4207.4 4221.9 4238.5 4257.1

4431.5 4442.8 4456.4 4472.3 4490.6 4510.5

9.1. NIGHTGLOW 369

TABLE 9.1 ( c o n t . )

Band origins Lines h,i,. (A) Band

(w' - w") A,,, (A) vVac (cm-') K"

7-0

8- 1

9-2

6-0

7- 1

8-2

4640.6

4903.5

5201.4

5273.3

5562.2

5886.3

2 1543.2

20387.9

19220.3

18958.2

17973.6

16983.9

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

R, P,

4628.6 4627.6' 4628.4 463 1.2 4636.0 4642.9 4651.9

4890.7 4889.8' 4891.1 4894.5 4900.1 4908.1 4918.4

5187.6 5187.0' 5188.7 5192.8 5199.5 5208.7 5220.6

5256.9 5254.3 5253.9' 5255.6 5259.6 5265.9 5274.5

5544.7 5542.2 5542.1. 5544.4 5549.1 5556.4 5566.3

5867.2 5865.2' 5865.5 5868.5 5874.2 5882.7 5894.2

4632.0 4629.4 4629.2' 4631.3 4635.7 4642.3 465 I .2

4894.7 4892.1 * 4892.1 4894.7 4899.9 4907.5 4917.7

5192.3 5189.6' 5189.9 5193.2 5199.3 5208.2 5219.9

5261.4 5257.0 5255.2. 5256.1 5259.5 5265.5 5273.9

5549.8 5545.3 5543.7* 5545.0 5549.1 5556.1 5565.7

5873.4 5868.8 5867.4' 5869.3 5874.3 5882.4 5893.6

4660.3 4672.3 4686.5 4702.8 4721.5 4742.3

4924.7 4937.8 4953.3 4971.2 4991.5 5014.5

5224.3 5238.7 5255.7 5275.4 5297.9 5323.3

5298.6 5313.3 5330.5 5350.1 5372.2 5396.9

5589.3 5605.2 5623.8 5645.2 5669.3 5696.2

5915.4 5932.9 5953.2 5976.6 6003.0 6032.7

4654.8 4667.1 4681.7 4698.5 4717.6 4738.8

4918.8 4932.3 4948.1 4966.5 4987.3 5010.6

5218.2 5232.8 5250.1 5270.3 5293.3 5319.0

5291.4 5306.7 5324.5 5344.8 5367.5 5392.7

5581.7 5598.2 5617.4 5639.4 5664.1 5691.6

5907.3 5925.3 5946.3 5970.3 5997.4 6027.6


TABLE 9.1 (cont.)

Band origins Lines hair (A)

(w' - w") Xair (A) Yvac (cm-') K" R , R , PI p2 Band

5-0

9-3

6-1

7-2

8-3

4-0

6168.6

6256.0

6496.5

6861.7

7274.5

7521.5

16206.7

15980.1

15388.6

14569.6

13743.7

13291.5

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

6144.6 6139.6 6136.9 6136.6' 6139.0 6143.9 6151.4

6235.8 6233.7* 6234.5 6238.3 6245.2 6255.3 6268.3

6471.0 6466.0 6463.6' 6463.8 6466.9 6472.8 6481.7

6834.5 6829.4 6827.3' 6828.1 6832.0 6839.2 6849.6

7244.8 7239.8 7238.0* 7239.2 7244.2 7253.3 7265.1

7483.6 7473.8 7466.8 7462.6 7461.4' 7463.3 7468.3

6151.1 6143.6 61 32.9 6137.8' 61 39.4 6143.8 6151.0

6242.6 6237.9 6236.9* 6239.4 6245.5 6255.0 6268.0

6478.5 6470.5 6466.2 6465.2' 6467.4 6472.8 6481.4

6842.6 6834.6 6830.3 6829.7' 6832.7 6839.6 6849.3

7254.0 7245.7 7241.6* 7241.6 7245.5 7253.5 7265.3

7494.0 7480.6 747 1 .O 7465.7 7462.8' 7464.0 7468.5

6202.9 6221.9 6243.7 6268.5 6296.2 6326.8

6287.6 6306.8 6329.2 6355.1 6384.4 6416.9

6533.1 6553.7 6577.3 6604.1 6634.2 6667.5

6901 .O 6923.3 6949.0 6978.2 701 1 .O 7047.4

7316.4 7340.8 7369.0 7401.0 7436.1 7476.7

7571.9 7598.6 7628.8 7662.5 7699.8 7740.7

6193.1 6213.1 6236.0 6261.7 6290.2 6321.6

6279.2 6298.7 6321.7 6348.2 6378.1 641 1.6

6522.8 6544.3 6569.0 6596.7 6627.7 6661.7

6890.0 6913.2 6939.9 6970.1 7003.8 7041 .O

7304.5 7330.0 7359.1 7392.2 7429.1 7470.1

7557.7 7586.2 7618.0 7653.3 7691.8 7733.7

9.1. NIGHTGLOW 371

TABLE 9.1 (conf . )

Band origins Lines hatr (A) Band

R , R2 Pl p, (w' - w") X,I, (A) vyaC (cm-') K"

9-4

5- 1

6-2

7-3

8-4

3-0

7748.3

7911.0

8341.7

8824.1

9373.0

9788.

12902.4

12637.1

11984.6

11 329.4

10666.0

8 1021

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

I 2 3 4 5 6 7

1 2 3 4 5 6 7

7716.7 771 1.7 7710.4. 7712.9 7719.4 7729.9 7744.6

7870.9 7860.8 7853.7 7849.8 7849.3 * 7852.1 7858.4

8299.0 8288.7 8281.7 8278.3 * 8278.5 8282.5 8290.4

8778.4 8767.8 8760.9 8758.1 * 8759.2 8764.6 8773.6

9323.6 9312.8 9306.1 9303.9' 9306.3 9313.4 9325.4

9720.2 9699.6 9682.5 9668.9 9659.2 9654.3

7727.3 7718.6 7714.7. 7715.4 7720.6 7730.2 7744.4

7882.1 7868.1 7858.4 7852.7 7850.9' 7852.9 7858.7

8311.4 8296.8 8287.0 8281.5 8280.3' 8283.5 8290.7

8792.2 8777.0 8766.9 8761.8 8761.4' 8765.7 8774.7

9339.2 9323.3 9312.9 9308.3' 9308.9 9314.8 9325.8

9738.3 9711.9 9690.7 9674.4 9662.9 9655.5

7794.4 7821.3 7852.4 7888.0 7928.0 7972.6

7964.8 7993.5 8076.9 8062.3 8102.6 8146.9

8399.3 8430.2 8465.4 8504.8 8548.6 8596.8

8886.0 8919.7 8958.0 9001.0 9048.8 9100.8

9439.9 9476.8 9518.8 9565.9 9618.6 9676.9

9872.5 9914.9 9962.2

10,014 10,071

7782.0 7809.6 7841.7 7878.1 7919.1 7964.6

7949.5 7980.0 8014.2 8052.1 8093.7 8139.1

8382.9 8415.7 8452.6 8493.6 8538.8 8588.1

8868.6 8904.0 8943.9 8988.5 9037.8 9091.7

9420.9 9459.7 9503.4 9552.2 9606.4 9665.9

9848.5 9894.6 9945.0 9999.8

10.059 9651.7 9653.1 10;133 l0;lZZ


TABLE 9.1 (cont.)

Band origins Lines Xsir (A) Band

(w' - w") hair (A) vyBc (cm-') K" R, Rz PI p,

9-5

4- 1

5-2

6-3

7-4

8-5

10,010

10,273

10,828

11,433

12,115

12,898

9987.2

9721.9

9233.1

8744.4

8251.7

7750.8

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

9956.1 9974.4 9947.9 9957.6 9938.6 9947.1 9937.3% 9942.9' 9941.2 9944.8 9950.5 9952.6 9965.4 9966.4

10,211 10,231 10,190 10,204 10,172 10,182 10,159 10,165 10,149 10,154 10,144 10,147 10,143 10,145

10,751 10,773 10,729 10,744 10,711 10,721 10,697 10,704 10,688 10,693 10,684' 10,687 10,685 10,686;

11,351 11,375 11,328 11,345 11,310 11,321 11,296 11,303 11,288 11,293 11,285 11,288 11,286 11,289

12,028 12,054 12,004 12,022 11,985 11,998 11,971 11,981 11,964 11,970 11,962' 11,966; 11,966 11,969

12,803 12,834 12,778 12,800 12,758 12,774 12,745 12,756 12,739 12,746 12,739' 12,744' 12,745 12,749

10,083 10,124 10,170 10,223 10,281 10,346

10,373 10,418 10,469 10,525 10,586 10,652

10,924 10,973 11,027 1 1,087 11,153 11,225

11,536 11,589 11,648 11,713 11,784 11,861

12,226 12,284 12,348 12,419 12,497 12,583

13,018 13,081 13,152 13,230 13,317 13,411

10,063 10,106 10,154 10,208 10,268 10,334

10,348 10,397 10,451 10,509 10,573 10,641

10,896 10,949 11,007 1 1,070 11,138 11,212

11,507 11,563 11,625 11,693 11,768 1 1,848

11,195 12,256 12,323 12,397 12,478 12,566

12,984 13,051 13,125 13,207 13,296 13,393

9.1. NIGHTGLOW 373

TABLE 9.1 (cont.)

Band origins Lines hair (A) Band

(w' - v") hair (A) vyaC (cm-') K" R1 R2 P I P,

9-6 13,817 7235.7 1 2 3 4 5 6 7

2-0 14,336 6973.6 1 2 3 4 5 6 7

3- 1 15,047 6644.2 1 2 3 4 5 6 7

4-2 15,824 6317.9 1 2 3 4 5 6 7

5-3 16,682 5992.9 1 2 3 4 5 6 7

6-4 17,642 5666.7 1 2 3 4 5 6 7

13,712 13,685 13,665 13,653 13,647. 13,649 13,659

14,183 14,130 14,083 14,041 14,004 13,973 13,948

14,884 14,829 14,780 14,736 14,698 14,669 14,642

15,651 15,593 15,542 15,497 15,458 15,426 15,401

16,498 16,438 16,384 16,338 16,298 16,266 16,239

17,445 17,382 17,326 17,278 17,238 17,206 17,183

13,747 13,711 13,684 13,665 13,656 13,656' 13,664

14,223 14,159 14,104 14,055 14,015 13,981 13,953

14,929 14,861 14,803 14,752 14,710 14,676 14,648

15,700 15,629 15,567 15,515 15,472 15,436 15,409

16,550 16,476 16,411 16,357 16,312 16,276 16,249

17,503 17,424 17,356 17,300 17,253 17,218 17,192

13,948 14,018 14,096 14,183 14,279 14,385

14,516 14,601 14,695 14,796 14,905 15,022.

15,237 15,329 15,428 15,536 15,653 15,778

16,027 16,124 16,23 1 16,347 16,472 1 6,607

16,899 17,004 17,119 17,244 17,379 17,522

17,876 17,989 18,114 18,249 18,395 18,554

13,912 13,985 14,067 14,157 14,256 14.364

14,465 14,560 14,660 14,767 14,881 15,001

15,183 15,284 15,391 15,505 15,627 15,756

15,969 16,076 16,191 16,313 16,443 16,582

16,836 16,95 1 17,074 17,206 17,346 17,496

17,808 17,931 18,063 18,206 18,358 18,521


TABLE 9.1 (cont.)


(u’ - u”) hair (A) uyae (cm-’) K ‘ R, R, PI p2

7-5

8- 6

9-7

1-0

2- 1

3-2

18,734

19,997

21,496

28,007

29,369

30,854

5336.5

4999.3

4650.7

3569.6

3404.0

3240.2

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 I

1 2 3 4 5 6 7

1 2 3 4 5 6 7

18,521 18,454 18,395 18,345 18,304 18,272 18,250

19,766 19,694 19,631 19,579 19,537 19,507 19,485

21,241 21,164 21,098 21,042 21,000 20,969 20,95 1

27,397 27,171 26,956 26,752 26,560 26,381 26,214

28,723 28,486 28,259 28,046 27,845 27,658 27,485

30,166 29,916 29,679 29,455 29,245 29,058 28,869

18,586 18,501 18,430 18,371 18,323 18,286 18,261

19,838 19,748 19,672 19,609 19,559 19,522 19,497

21,324 21,227 21,145 21,078 21,027 20,989 20,967

27,557 27,287 27,040 26,813 26,605 26,415 26,240

28,898 28,613 28,353 28,115 27,897 27,698 27,516

30,356 30,056 29,782 29,531 29,303 29,094 28,904

18,986 19,109 19,244 19,391 19,552 19,725

20,271 20,407 20,555 20,717 20,894 21,085

21,798 21,949 22,114 22,296 22,494 22,708

28,691 29,003 29,337 29,695 30,073 30,475

30,094 30,426 30,781 31,160 31,563 31,990

31,625 31,977 32,356 32,760 33,190 33,647

18,913 19,046 19,190 19,345 19,511 19,689

20,192 20,338 20,495 20,666 20,849 21,045

21,713 21,873 22,048 22,238 22,443 22,663

28,499 28,847 29,211 29,592 29,988 30,402

29,889 30,258 30,645 3 1,047 3 1,470 31,913

3 1,404 31,796 32,207 32,637 33,087 33,559

9.1. NIGHTGLOW 375

TABLE 9.1 (cont.)


(v’ - w ” ) ,lair (A) vVBc (cm-’) K ’ R, R2 p1 p2

4- 3

5-4

6-5

7-6

8-7

9-8

32,483

34,294

36,334

38,674

41,409

44,702

3077.7

2915.2

2751.5

2585.0

2414.3

2236.4

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

31,752 31,488 31,238 3 1,002 30,782 30,578 30,382

33,514 33,233 32,969 32,721 32,490 32,277 32,083

35,495 35,197 34,916 34,654 34,412 34,198 33,988

37,764 37,444 37,144 36,864 36,607 36,371 36,158

40,414 40,068 39,744 39,445 39,170 38,920 38,697

43,599 43,218 42,866 42,542 42,245 41,979 41,741

3 1,957 31,641 31,351 31,088 30,847 30,628 30,414

33,716 33,398 33,091 32,812 32,560 32,331 32,124

35,740 35,382 35,057 34,761 34,494 34,254 34,038

38,036 37,652 37,302 36,986 36,699 36,444 36,215

40,719 40,302 39,925 39,584 39,277 39,005 38,764

43,954 43,489 43,077 42,705 42,374 42,080 41,823

33,304 33,681 34,085 34,519 34,980 35,521

35,176 35,580 36,015 36,480 36,976 37,501

37,281 37,718 38,188 38,691 39,230 39,803

39,702 40,176 40,687 41,234 41,821 42,446

42,532 43,055 43,618 44,222 44,871 45,564

45,950 46,534 47,164 47,841 48,568 49,350

33,067 33,485 33,924 34,383 34,865 35,372

34,9 15 35,361 35,831 36,325 36,844 37,391

37,002 37,482 37,988 38,522 39,084 39,678

39,398 39,916 40,465 41,045 41,657 42,304

42,193 42,767 43,370 44,010 44,686 45,403

45,581 46,213 46,885 47,599 48,357 49,163


spectrum between 4p and 1 5 . 5 ~ has been studied by Sloan, Shaw, and Williams [1955a] and between 1 4 . 5 ~ and 2 2 . 5 ~ by Burch and Shaw

The most prominent emission features are due to CO,, 0,, H,O and, longward of 15p, N,O. For every strong emission in the sky spectrum, there is a corresponding absorption minimum in the solar spectrum. The maximum intensity appears between 7p and 8p, but major bands appear at 43p, 6.3p, 9.611, and 15p.

[ 1957al.

9.2. Twilight and Day Airglow

The twilightglow is the airglow emission at a time when sunlight is shining on the emitting region of the atmosphere from below. The dayglow is similarly defined, except that the sunlight enters from above. For a particular emission the twilight and day airglow need not necessarily be enhanced over the nighttime brightness, and could conceivably be suppressed.

The twilight and day airglow introduce new possibilities for significant observations beyond those found in the nightglow. Measurements of the intensity of the twilight emission in different directions and throughout twilight and into the night provide data that may yield the height of emission, the excitation process, and the abundance and vertical distribution of the emitting substance.

The dayglow similarly holds great promise for study of the upper atmosphere. In the case of sodium, for example, where the excitation mechanism seems to be definitely established as resonance scattering, extended monitoring of the dayglow from a balloon could give valuable data on the geographic and time variations in the sodium abundance. These data should materially assist, and may even provide the crucial clue to, an explanation of the origin of atmospheric sodium.

It is not necessarily the case that the twilight intensity will drop to the average nighttime value when the sunlight leaves the emitting region. In the case of the [OI],, red lines, for example, there is a post- twilight enhancement, wherein the airglow emission continually decreases in brightness long after the sun has left the ionosphere. Strictly speaking, this post-twilight effect is part of the nightglow, but it is not always convenient to insist upon definitions sharply differentiating between day, twilight, and night airglow, as for some emissions they may all arise from the same excitation process.

In the twilight spectrum there are three emissions that have been studied longer and more extensively than the rest. They are the N,+ First Negative bands, B ,ZC,+ -j X ,Z; (in particular the 0-0 band at

9.2. TWILIGHT AND DAY AIRGLOW 377

3914 A and the 0-1 band at 4278 A), the Na D, and D, lines at, respectively, 5896 and 5890 A (3s 2Sliz - 3p 2P& ,,,J, and the [OI],, resonance lines at 6300 and 6364 A (2p4 ,P,,, - 2p4 lD2) .

Also, the close [NI],, doublet (2p3 4S30,z - 2p3 2D$2, 5,2) at 5199 A appears as a weak feature. Recently the 0-1 Infrared Atmospheric ( d d , --f X ,Z;) band at 1 . 5 8 ~ has been studied, and the Ca I1 H and K resonance lines (4s 2S,,2 - 4p ,P:,,, 3 1 2 ) at 3968.5 and 3933.7 A have been seen on some occasions. The analogous transition in Li I, which gives a close doublet at 6708 A, has also been discovered. We shall discuss these emissions in more detail below.

In addition, enhancements in twilight have been reported for the 0, Atmospheric ( b l,Y; --f X ”;) 0-1 band at 8645 A (band origin) by Meinel [1951a] and Berthier [1953b, 1956~1 and for the Meinel OH bands in the infrared by Berthier. Sholokhova and Frish [1955a] have also reported twilight emission in the neighborhood of 1p and, to a less extent, around 8000 A, which comes from the 100-km region. These enhancements may arise from OH, but quantitative confirmation is desirable. An OH enhancement, if real, is probably photochemical in origin, as fluorescence of solar radiation absorbed in the Meinel bands is expected to be negligible. For the 0, Atmospheric 0-1 band, a strong enhancement through absorption in the 0-0 band could occur only in early twilight, when the shadow is in the neighborhood of 100 km or below. But screening by the lower atmosphere greatly increases the shadow height in the 0-0 band over the height of the solid-Earth shadow (Section 10.1 and 10.2). Hence some other explanation must be sought for Meinel’s and Berthier’s observations. A precise calculation of the expected intensity in the very early twilight is rendered difficult by the radiative transfer problem (Chamberlain [1954a]) that must be considered.

Dufay and Dufay [1948a] maintained that the green line, A5577 of [OI],,, has a twilight enhancement of at least a factor of two over the nightglow. Although other investigators were not able to observe it for many years, a twilight effect has been substantiated by observations with a birefringent filter by Megill [1960a]. The expected photon emission in A5577, arising from fluorescence of A2972 (cf. Appendix VI), is about 45 times smaller than for resonance scattering of A6300 [OI],,, for negligible deactivation and negligible screening by the lower atmosphere. Although deactivation is probably much more effective in suppressing A6300 at low altitudes, screening of the solar flux at A2972 is so important that no detectable A5577 enhancement can be expected from scattering of sunlight during middle or late twilight, when observations are normally made (see Table 11.1).


9.2.1. N2+ First Negative Bands

In his George Darwin lecture to the Royal Astronomical Society, Slipher [1933a, see p. 6661 first reported a twilight enhancement of the airglow: the First Negative bands prominent in auroral spectra. The observation was confirmed by Elvey [ 1942~1, although Gauzit [ 1938~1 and Cario (see Gauzit [1938a]) did not detect it. That the intensity of the emission was actually variable from night to night was demonstrated by J. and M. Dufay [1947a]. They found a correlation of the enhancement with magnetic activity and with the occurrence of aurorae far to their north in the auroral zone. A relationship between N,f twilight emission and magnetic activity was further demonstrated by M. Dufay [1949a, 1953~1 and Costello, Serson, Montalbetti, and Petrie [ 1954~1.

Swings and Nicolet [1949a] made a preliminary analysis of a series of spectra obtained at McDonald Observatory in Texas and compared, in particular, the Na and N,f emissions. They found the ratio Na/N,+ to be larger in morning than in evening twilight and attributed the change mostly to Na. In general, N,f seemed to be a more stable emission from point to point in the sky, as well as from evening to morning, than did Na. The available spectra were obtained only during magnetically quiet periods, and so no new information was obtained on the variability found by the Dufays [1947a]. However, only two out of 50 sets of spectra failed to show the N,f emission. In France M. Dufay [1953a] found N,f absent 4 times in 28.

The decrease of intensity as the shadow height increases is generally slower than for Na D, corresponding to the slightly greater apparent height and thickness of the emitting region (Section 12.3). In all, some 8 or 9 bands may be recorded photographically, and M. Dufay [1953a] has measured the relative intensities of A3914 (0-0), A3884 (1-1), A4278 (0-1), and A4737 (1-2).

An accurate photometric study of the N,+ emission has not been made. However, Bates [1949b] has made some rough estimates from reports of the observations and the conditions under which they were made, He concludes that during disturbed conditions the brightness in the direction of observation may exceed one kilorayleigh. Judging from Swings and Nicolet’s [1949a] comparison of the Na and N,+ flash, it appears that Bates’ estimate is on the conservative side. T o appear of comparable strength to the sodium emission in winter on a panchromatic plate, A3914 probably approaches one kilorayleigh referred to the zenith, under quiet magnetic conditions and when the height of the solid- Earth shadow is well below 100 km.


9.2.2. N a D Lines

The first systematic and extensive investigation of the sodium enhancement i n twilight was made by Bernard [1938a, b,f]. Earlier observations by Currie and Edwards [1936a] at Chesterfield during the second Inter- national Polar Year 1932-33 may also have disclosed a twilight enhancement, although there has been some controversy on the matter between Cabannes, Dufay, and Gauzit [1938u, 6, c] and Bernard [1938d, 1939a, b]. Also, Cherniaev and Vuks [1937u] at Mt. Elbrus in the Caucasus reported the sodium flash before Bernard. Their observations were rather remarkable in that they were made in August, when the twilight D lines in the northern hemisphere are ordinarily more difficult to detect than in the winter months. (Their paper also reported a small twilight enhancement of the green line.)

Height a n d Identification.-Bernard’s observations were made first at Tromso, Norway and later at Saint Auban, Basses-Alpes, France. He found a rapid decrease of intensity corresponding to an apparent height (i.e., the height of the shadow of the solid Earth with refraction ignored) of 80 km on the assumption of excitation by resonance scattering. Bernard corrected this apparent height for refraction, but not for atmospheric screening (which Cario and Stille [1940a] showed to be appreciable even for yellow light), and consequently obtained a real height of only 60 km. (A height of about 85 km was found by Hunten and Shepherd [1954a] from a more extensive analysis; see Section 10.3.2.)

While the measured wavelength of 5893 A suggested sodium as the emitting gas, the identification was not certain until the interferometric studies of Bernard [1938c,f] and Cabannes, Dufay, and Gauzit [1938c]. Bernard estimated that the D,/D, intensity ratio in twilight was of the order of two, which is now known to be too high (Section 11.3.3).

Origin of Atmospheric Sodium.-The positive identification of sodium emission in the nightglow accompanied the work on the twilight and immediately gave rise to speculation on the cosmic or terrestrial origin of atmospheric sodium (Dkjardin [1938a]). Bernard favored a terrestrial origin, with sodium being carried to great altitudes in the form of NaCl and then dissociated. The origin of the sodium was presumably the sea (Bernard [1938e]), although sodium ejected by volcanic activity might also be significant. It was thought that the D lines were always absent from auroral spectra and that this absence implied there was no sodium at auroral heights.I4 This conclusion seemed to

I4 Chapman [1939a] pointed out that this argument overlooked the question of the excitation mechanisms in aurora and twilight and was therefore not particularly pertinent.


favor a terrestrial origin, with sodium concentrated at the lower altitudes. Cabannes, Dufay, and Gauzit [1938a, 1938~1 rejected the idea that solid NaCl crystals could be transported to high altitudes and accordingly favored the cosmic origin. They considered sodium to be distributed over the entire upper atmosphere, as their van Rhijn analysis of Garrigue’s measurements of the nightglow intensity gave a height of 130 km. Hence it seemed that sodium might enter the Earth from meteors and be deposited over the entire high a tm0~phere . l~ Chapman [ 1938~1 and Vegard and Tonsberg [1940a] suggested a cosmic origin involving streams of gas from the sun, which might be identified with the streams believed to produce aurorae. Fabry [1938a] and Dauvillier [1959a] offered the speculation that the Earth would sweep up interstellar sodium as it moves through space with the solar system.

As Cabannes, Dufay, and Gauzit [1938c] wrote, “The problem is twofold: What is the origin of the atmospheric sodium, and why does it become luminous in the upper atmosphere ?” The investigation of the source of sodium has become a complex problem. Photometric observations in twilight can give information on the abundance and vertical distribution of sodium atoms, but except for close to the ground we have no information on the sodium abundance at lower altitudes, where it is in the form of molecular compounds. The problem is perhaps closely related to an explanation of the seasonal variation, which is discussed in Section 11.4.

Twilight Excitation.-The excitation mechanism is closely related to the abundance problem, as it is only through an understanding of the excitation that we can derive the abundance. It now seems definite that the Na D lines in twilight are excited predominantly by resonance scattering of sunlight, as Bernard [1938a, b,f] originally supposed, and in Chapter 11 we give a detailed theory for the scattered D-line intensity with this hypothesis. There are several reasons for accepting this excitation mechanism:

The resonance-scattering theory makes possible independent determinations of the abundance from the total D, + D, intensity and from the DJD, ratio. These abundance estimates agree remarkably well (Chamberlain, Hunten, and Mack [1958a]; Vallance Jones and McPherson [1958a]) and also agree with abundances obtained from the terrestrial component of the D-lines in the absorption spectrum of the sun (Scrimger and Hunten [1957a]). This consistency

1. Intensity and Line Ratio,

l5 The D lines appear in the spectra of meteor trains, but Roach [I94961 has pointed out that their origin may nevertheless be atmospheric sodium atoms.

9.2. TWILIGHT AND DAY AIRGLOW 38 1

of theory and observations, which holds over a fairly wide range of sodium abundances, would be most unlikely were the theory based on an utterly false premise.

2. Screening Height. The effective screening height of the atmosphere for the incident, exciting solar radiation should give a clue to its wavelength. While some of the earlier results indicated screening heights of the order of 40 km, which were interpreted as evidence that ultraviolet radiation was the exciting agent, the present evidence favors a lower height, more consistent with yellow light (Section 10.3.2).

I t was suggested by Kastler [1938a], Franck and Rieke [1939a], and Cario and Stille [1939a] that a study of the width of the twilight sodium lines might give information on the excitation mechanism. With resonance scattering the lines should be narrow, indicative of the Doppler broadening for the temperature of the sodium

layer.” But with ultraviolet light as the exciting agent, the lines would most likely result from photodissociation of a sodium compound, with Na left in an excited state. These dissociated atoms would acquire additional kinetic energy in the process, so that the D lines should appear wider than with optical scattering.

The line width was measured by Kastler [1940a] and Bricard and Kastler [1944a] by placing a cell containing sodium vapor between the sky and the spectrograph slit. Knowing the density and temperature of sodium in this cell they derived the spectral width, effectively, over which the cell would filter out the twilightglow. Two other spectra were made simultaneously as controls: one of twilight emission without a sodium filter and the other through a filter with a high pressure of sodium. The latter gave complete line absorption and provided a measurement of the background intensity. Their detailed theory of absorption by the sodium cell follows Mitchell and Zemansky’s [1934a] treatment of resonance radiation.

Bricard and Kastler [1944a] concluded that the width of the twilight D lines indicated a Doppler temperature of the order of 240” K. This temperature should not be taken literally as indicating the kinetic temperature in the twilightglow layer, even if the accuracy of the measurement were high. Although they took proper account of the hyperfine structure of the lines, the individual line components will deviate from their assumed Doppler profiles because of absorption within the sodium layer itself. This effect, treated by radiative-transfer techniques in Chapter 11 (see Fig. 11.6), becomes serious in winter, when Bricard and Kastler’s observations were made and when the sodium abundance is greatest.

3 . Line Width .

< <


4. Polarization. Kastler [1938a, 1946~1 pointed out that the twilight D lines should show a small polarization if the excitation mechanism is resonance scattering. The D lines excited by photodissociation of a sodium compound are probably not significantly polarized (Mitchell [1928a]). Measurements of the polarization of the twilight emission were successfully made by Bricard, Kastler, and Robley [1949u] (also cf. Bricard and Kastler [1950a]). They isolated the emission lines with a Savart-Lyot polariscope (Bricard and Kastler [1947a, 1948a]), as in their study of nightglow polarization (Section 12.3.1). The instrument utilizes monochromatic interference fringes produced by a thick quartz crystal between two polarizers. To diminish the background sunlight, which is strongly polarized by Rayleigh scattering when observed 90 degrees from the sun, the fringes were focused on the slit of a spectrograph of high dispersion. When the incident light is partially polarized the instrument gives fringes even when the polarizer in front of the quartz is removed.

The theory and laboratory measurements for the sodium lines predict a maximum polarization for the combined D, + D, twilight lines of 6 or 7 percent.16 The expected degree of polarization will depend on the D,lD, ratio (which is shown in Section 11.3.2 to depend on the sodium abundance), since the D, line line is completely unpolarized. A measurement of the order of 9 percent (the value they expected from the theory) was reported by Bricard, Kastler, and Robley [1949a].”

Thus the evidence is greatly in favor of resonance scattering. The favorite alternative process for excitation has been dissociation of a sodium compound, such as NaCl or NaO, into the ,P term of Na, as first tentatively suggested (but not favored) by Bernard [ 1938~1. Penndorf [1950a] proposed an alternative mechanism that involved a series of photochemical reactions wherein the D lines were excited by

NaO + Na, --f Na,O + Na*(,P). (9.1)

The Na was converted back to NaO by a collision with N,O, and Na,O was partially dissociated by ultraviolet light ( A < 2031 A) to replenish Na,. Kahn [ 1950~1 discussed the equilibrium abundances, however, and pointed out that the mechanism required a prohibitive amount of NaO. At present the need for an excitation mechanism involving ultraviolet light has been abolished.

This calculation is made in Section 11.1.2. l7 Barber [1957a] has reported that on some occasions following enhanced solar activity

the twilight radiation observed through a filter (width at half intensity, 260 A) centered on the D lines is highly polarized. These observations have not yet been explained.


Absolute Intensity and Its Variations.-When the sun is about 6 or 7 degrees below the horizon, the exciting sunlight suffers very little extinction by the lower atmosphere, whereas at larger angles of the solar depression, p, the shadow of the Earth begins to affect the twilightglow brightness. The intensity then drops rather abruptly nearly to the nightglow level, in the order of 20 minutes. At smaller angles of fl, scattered light becomes so important that the Fraunhofer spectrum may obscure the D lines. Consequently, the region around /3 = 6g is the most appropriate for intensity measurements except, of course, those dealing with height determinations. Bricard and Kastler [ 1944~1 first made a reasonably accurate measurement of the D-line intensity on a November evening in France. Their result, reduced to the zenith, was 7.2 kR,18 with the angle of solar depression, /3, about 6 or 7 degrees. This result is somewhat larger than the winter average of the measures by Hunten [19566], who found about 4.3 kR in Saskatchewan in February and about 0.8 kR in June and July. However, there is a large day-to-day fluctuation and the seasonal variation may be associated with an important latitude variation. The twilight enhancement is thus of the order of 15 times the nightglow in winter; the summer enhancement may be around the same factor, but the nightglow intensities are less certain than in winter because of OH blending.

The seasonal variation has been studied spectrographically by Bricard and Kastler [1944u], with a polarization photometer by Barber [1954u], with a photometer equipped with interference filters by Cronin and Noelke [ 19.55~1, with a photoelectric scanning spectrometer by Hunten [19566], and with a photomultiplier equipped with a magnetic sodium cell by Blamont [1956a]. All these data are not identical. For example, Blamont found a maximum in November, with a secondary maximum in March. Cronin and Noelke reported similar results, but Hunten finds only a single maximum in February. While these differences may be systematic and associated with the different latitudes of observation, they may also result from the strong irregular fluctuations that appear from day to day. More extended measurements on an absolute basis at different locations are badly needed.

There are severe difficulties involved in making absolute measurements. Besides the usual troubles that go with absolute photometry, there is the problem of elimination of background radiation in the Fraunhofer spectrum. Hunten and Shepherd [1954a] have used a scanning spectrometer with several angstroms resolution. The brightness of the neighboring solar spectrum and a knowledge of the profiles of

' 8 For definition of the rayleigh (R) see Appendix 11.


the Fraunhofer D lines makes it possible to correct for scattered sunlight. Donahue [1956a] has suggested that the Fraunhofer lines in the background scattered light would be diminished by Na extinction when the sunlight enters the atmosphere, whereas the neighboring continuum would not. Thus any subtraction of scattered light based on the brightness of the neighboring spectrum would overcorrect the measurements. Hunten [1957a] has pointed out that while this effect is negligible with the existing abundances of sodium, there are various difficulties involved in making suitable corrections (depending on the instrument) to the background Fraunhofer lines. The photometric corrections are especially difficult with a sodium cell, as used by Blamont [1953a, 1956~1, and with a birefringent filter (Blamont and Kastler [1951a]). If the high accuracy of these instruments is to be carried to the final results, considerable care is required in calibrating and reducing the measurements.

Observations made in the southern hemisphere have disclosed that the intensity variations depend on the local season (i.e,, high in winter, low in summer) rather than on the month of the year (Bricard and Kastler [1950a], Mayaud and Robley [1954a]). The latter behavior would be anticipated if the intensity variations arose from changes in the amount of sodium captured from interplanetary space or from gas clouds ejected by the sun.

A morninglevening ratio greater than unity was suspected by Swings and Nicolet [1949a] from a spectrographic investigation and verified in a later investigation by Cronin and Noelke [1955a]. Blamont [1956a] also found the intensity slightly greater in the morning when he compared observations corresponding to the same day ; for pairs of observations referred to the same night, the morning-evening effect was not apparent. Much more extensive data seem necessary to obtain a quantitative ratio that is free from errors introduced by what seem to be random fluctuations. Blamont, Donahue, and Stull [ 19584 also suggested that part of the morning-evening effect might be due to a Doppler shift of the Fraunhofer line because of relative sun-atmosphere motion, which is different in morning and evening.

In Chapter 11 the theory of the morning-evening, seasonal, and latitude variations is discussed from the standpoint of the abundance of neutral atomic sodium. While changing water vapor absorption (Bricard and Kastler [1944u]) may have some bearing on the intensity variations, it alone cannot explain the main effects.

9.2.3. [0 1121 Red Lines

The twilight enhancement of the airglow oxygen emission at 6300 and 6364 A was first reported by Garrigue [1936a]. (Currie and Edwards


[ 1936~1 independently reported enhancements in the red lines during the long twilight periods at Chesterfield-on Hudson’s Bay in Canada- during the 1932-33 Polar Year. It was not evident, however, that the Chesterfield spectra represented a twilight airglow rather than auroral activity.) A systematic height analysis of observational data was carried out by Cabannes and Garrigue [1936a], and since that time the foremost question has been the excitation mechanism. Cabannes and Garrigue showed that resonance scattering implied a large scale height for atomic oxygen, and suggested dissociation of 0, (into 0 and 0,) by ultraviolet radiation in the Hartley continuum ( A < 2680 A) as an alternative means of exciting the term.

Other investigations of the rate of change of the twilight intensity have been made spectrographically by Elvey and Farnsworth [1942a], Elvey [ 1948~1, Dufay and Tcheng [1946a], Barbier [1948a], and Berthier [ 1953~1. Robley [ 19564 has measured the intensity variation in twilight in several directions by means of an interferometer. Barbier [1956a, 19574 has studied the late twilight with a photoelectric photometer utilizing two interference filters around 6300 A. One of the filters provides a much wider band pass than the other, allowing a correction to be made for background radiation.

The intensity in early twilight in A6300 may be in the range 500 to 1000 rayleighs (reduced to the zenith), which is some 10 or 20 times the average nightglow brightness. The intensity decrease in evening twilight decays with a half life of 15 to 30 minutes in early evening and at a slower rate during the first part of the night. The [OI],, twilight thus persists much longer than in the Na D lines, with the slow decrease often referred to as the post-twilight enhancement (see Figs. 9.13 and

An interpretation of the slow rate of decrease of evening twilight in terms of resonance scattering alone would, at best, imply an enormous scale height for oxygen atoms above 100 km. There are also other difficulties with this interpretation, which are discussed in Section 10.3.3. In Section 11.5 it is shown that dissociative recombination probably accounts for the major part of the evening twilight, with dissociation of 0, by sunlight in the Schumann-Runge region contributing somewhat.

An important observational problem is the comparison of morning and evening twilights. Comparative observations have been published by Elvey and Farnsworth [1942a], Elvey [1948a], Berthier [1953a], Robley [1956a], and Barbier [1956a, 1957~1. The morning enhancement is usually considerably less than for the corresponding times (i.e., the same angles of solar depression) in the evening. Barbier’s observations indicate a strong yearly variation, with a pre-dawn enhancement promi-

10.10).


nent in winter months and absent in the summer (Fig. 9.13). This pre-dawn increase is analogous to the post-twilight decay, and may begin several hours before sunrise. Evidently it is not a result of the direct action of solar light; whereas some suggestions have been made

APRIL SEPT. +I: 4 0 0 c L14" 0 t 0

4 0 0 K : 4r,. , ? T O O

'18 21 0 3 6 18 21 0 3 UT UT

FIG. 9.13. Mean curves by month for the daily variation of A6300 [OI],,. Note the slow post-twilight decay and the pre-dawn enhancement. The main twilight effect is not included in the figure. Based on observations from May 1957 through

April 1960. Courtesy D. Barbier.

toward its explanation (Section 13.2), the phenomenon still has no satisfactory theory. The nightglow red lines also experience semiregular enhancements near the middle of the night, at le.ast at some latitudes and times of year (Section 12.3.2).

9.2.4. Other Twilight Emissions

&sides the three major twilight emissions discussed above, there are a few other lines and bands definitely established that present interesting problems of their own. Although a large number of weak lines and bands have been reported in the range 5400-6800A by Khvostikov and Megrelishvili [ 1959~1, their reality is considered to be doubtful.

[N Ilzl Lines.-A weak feature around 5199 A, believed to be the forbidden nitrogen doublet A5198 and A5200, was first detected by

N;

I I

FIG. 9.i4. Tracing of twilight airglow spectrum in the visible region. The N; bands and [NI],, line are abnormally strong, suggesting an auroral effect. After Nicolet [ 195433 ; courtesy University of Chicago Press.

388 9. THE AJRGLOW SPECTRUM

Courtks [ 19504. Subsequent observations of the emission have been made by M. Dufay [1951a, 1952a, 1953~1 and Nicolet and Pastiels [1952a] (Fig. 9.14).

According to Dufay’s observations extending over two years, A5199 shows no significant correlation with magnetic activity, in contrast with the N,f bands. There does seem to be a seasonal variation, with the line more regular in its appearance and somewhat stronger in summer than in winter.

Dufay [1953a] also made some rough estimates of the average emission intensity. From several spectra, obtained with exposures upward of one hour, when the angle of solar depression at the observer, a, was between 12 degrees and 18 degrees (or sometimes greater), he obtained the ratio of A5577/h5199. The green oxygen line has little if any twilight enhancement and its average nightglow intensity is known with fair accuracy. On this basis it appears that the emission rate for the doublet, reduced to the zenith, is ~47~9- 10 rayleighs, where p = cos 0, B is the angle of emergence from the emitting layer (measured from the normal), and ,9 is the integrated intensity.

0, Infrared Atmospheric Band,-Vallance Jones and Harrison [ 1958al discovered the 0-1 band of the 0, Infrared Atmospheric system, a ld, ---f

X 32;, at 1.58p, in the wing of the Q-branch of O H (4-2). No emission has been detected in the 0-0 band, 1.27p, which is evidently absorbed by the lower atmosphere. The situation is analogous to that of the Atmospheric system A-band (0-0) absorption and 0-1 emission in the nightglow.

The emission was first detected with an infrared spectrometer that utilizes a lead sulphide cell (Gush and Vallance Jones [1955a]). Although the 0, band nearly overlaps the Q branch of the 4-2 O H band, the failure of other OH bands to show an enhancement favored the 0, identification. This assignment was later confirmed by increasing the resolution from 200 A to 25 A and calculating synthetic profiles. There seems to be no morlling enhancement, only an enhancement in the evening twilight.

The absolute rate of emission in the zenith (p4n.Y) of the 0-1 band, is around 15 to 20 kR in early t ~ i 1 i g h t . l ~ The emission rate of the 0-0 band should be approximately 10 times that of 0-1. These rates of emission may be compared with those of other airglow-aurora emissions in Appendix 11.

l9 The time used by Vallance Jones and Harrison to compare observations from different nights is when the shadow cast by a screening layer at ha = 40 km intersects the line of sight at Zo = 70 km (see Fig. 10.3).


39llOA 120

Ca I1 H and K Lines.-Vallance Jones [1956a, 1958~1 first observed the H and K lines at 3933.7 and 3968.5 A from Saskatoon with high dispersion (10 and 20 A/mm). M. Dufay [19586] reported confirmatory observations from southern France and Antarctica. The lines are quite variable from night to night, but seem to be strongest at times of great

30 0 5 0 6 0 3 9 7 0 A

meteor showers. The perseids especially, which appear in August, appear to be associated with strong calcium emission. This correlation naturally suggests that meteors are responsible for introducing calcium into the atmosphere.

The maximum intensity of the lines is always low. However, Vallance Jones [1958u] estimates that for A3933 the emission rate referred to the zenith, ~4779, may sometimes be as high as 150 rayleighs. Thus calcium may have a considerably greater photon emission rate than A5199 [NI],,. T h e latter emission seems to decay rather slowly, if at all, after sunset, and is consequently easier to detect with long photographic exposures at low latitudes. At Saskatoon the twilight can b t very long. With the spectrograph directed so that its line of sight intersects the solid-Earth shadow at a constant height of, say, 100 km, according to a precalculated program, exposures of three hours or more are possible on a summer’s night. Thus if the calcium emission arises from resonance scattering of sunlight, as seems likely (although it is not proved), it


could be present for long periods at high latitudes, which would aid spectrographic observation.

Little is known about the emission height. At least part of the emission arises from a solid-Earth shadow height (denoted by z , in Figs. 10.1 and 10.3) greater than 120 km. Observations with z , = 80 km showed no detectable emission, which means that the increase in background continuum (from Rayleigh scattering in the lower atmosphere) was much greater than the increase in C a I I emission, as z, was changed from 120 to 80 km. Thus all we can say is that the region just above z , = 80 km does not emit strongly, compared with some higher region.20

Li I Resonance Lines.-In connection with a spectrographic program on the aurora in the southern hemisphere (66" S) during the Inter- national Geophysical Year, Delannoy and Weill [ 1958~1 obtained some long twilight exposures that showed a new line at 6708A. The most likely identification seems to be the lithium resonance lines, X6707.89 and h6707.74. According to their report, the height distribution is similw to that of the N a D lines and the intensity is the order of one tenth that of D,. Similar results were obtained independently at Hallett Station, Antarctica, and Invercargill, New Zealand, by Gadsden and Salmon [1958a]. Later measurements\are mentioned in Section 11.6.4.

9.2.5. The Dayglow

A dayglow must exist, and in the case of some emissions we can predict a lower limit to the brightness with some confidence. Some attempts have been made to observe the dayglow from rockets. Miley, Cullington, and Bedinger [1953a] reported high absolute intensities in eight spectral regions between 4200 and 6400A, each about 2 0 A wide, with little variation'in intensity with wavelength. The photon emission in each of these regions was of the order of lo6 R. Later results (Bedinger [1954a]) obtained at a different time of day were similar, but the intensities were an order of magnitude fainter, which was ascribed to a daily variation.

These observations inspired an important paper by Bates and Dalgarno [1954a] in which theoretical estimates of the dayglow intensity were made. This topic is discussed further in Chapter 11. Briefly, however, they concluded that the reported intensity from the rocket experiment

2o The problem of converting z, to an actual shadow height is discussed in Chapter 10. While the actual shadow is not sharply defined, its effective height would probably be some 10 km above 2,. The difference between the two heights will depend, however, on the vertical distribution of Ca I1 and will vary with zenith distance during the observations.

9.2. TWILIGHT AND DAY AIRGLOW 39 1

could not be reconciled with an excitation process depending on the direct action of sunlight. James [1956a] also concluded, from some laboratory experiments on fluorescence induced by ultraviolet radiation, that the dayglow produced by this mechpism was probably insufficient to account for the rocket observations.

Morosov and Shklovskii [1956a, b] have shown that the observations of the sky brightness during the solar eclipse in Brazil in 1947 by Richardson and Hulburt [ 1949~1 contradicted the rocket observations of a dayglow. Were the dayglow as bright (about one percent of the daytime sky brightness) and as high (> 135 km) as the rockets implied, then the amount of sunlight striking the upper atmosphere during the Brazilian eclipse should have been sufficient to make the sky at least several times brighter than it was. Kaiser and Seaton [1954a] have excluded the zodiacal light and scattering by dust particles in the Earth’s atmosphere as explanations for these experiments. It appears, therefore, that the earlier rocket measurements were spurious and that the photometers did not actually detect the dayglow.

On a later rocket flight described by Berg [1955a], photographic exposures in integrated light were made of the sky. The sensitivity of the film was too low for a definite measurement over most of the flight, but the results showed the integrated brightness above 80 km to be less than that reported by Miley et al. However, this flight apparently did not record the dayglow, either.

T h e dayglow spectrum almost certainly contains the same features, and with intensities at least as great, as are observed in twilight. Consider, for example, the sodium emission, arising from resonance scattering. The Na abundance probably changes very little from night to day. Further, the intensity can be increased somewhat by ground reflection of sunlight. I n the case of excitation produced by ultraviolet dissociation or recombination in the ionized layers, there will be less attenuation of the incident solar radiation and these processes could therefore be much more efficient in day than in twilight. Each of these mechanisms will produce the [OI],, red lines, and in Section 11.5.4 we discuss the enhancement of dayglow/twilight to be expected.

In addition, there are probably several fairly strong features that are absent in twilight. For example, Shklovskii [1957a] has suggested that certain infrared lines of 01 may be excited in twilight as a result of a fluorescence mechanism (Section 11.6.5), and Brandt [1959a] has shown that these lines will be far stronger in the dayglow.

The dayglow of other planets may also be of considerable interest. If line or band emission were sufficiently strong relative to the reflected sunlight, fluorescence would be a means of identifying constituents that


do not show in the planetary absorption spectrum. Urey and Brewer [ 19574 have discussed some possible consequences of fluorescence in planetary atmospheres.

PROBLEMS

1 . Suppose that particle bombardment in the E region is sufficiently intense to double the intensity of A5577 [OI],,, compared with the normal airglow background. On the basis of auroral intensities (Table 5.5 and Section 5.2.4) estimate the enhancement of A3914 N,+. How would it compare with the intensities of Herzberg 0, bands in the same region (Section 12.3.1 ; Appendix 11) ? Would it be feasible to detect such correlations (a) with patrol spectra ? (b) with photoelectric photometers having 30-A band passes ?

2. Assume that one photon of A3914 is emitted at night for every 50 N,f ions formed and that N,+ ions have a mean lifetime of 100 sec, regardless of height in the atmosphere. Using Eq. (1 1.6) and the g-value in Table 11.1, estimate the intensity of the N: twilight airglow (when the E region is fully illuminated by blue light) with the particle bombardment implied in Problem 1. Compare with the observed values.

Chapter 10. Analysis of Twilight Observations for Emission Heights

Twilight observations of the airglow can be a powerful tool for investigating the physics and chemistry of the upper atmosphere. Theoretical interpretations of these data will be considered in the next chapter, with the present one devoted to the problem of reducing the observations to a convenient form for interpretation.

Just how these data should be finally expressed depends, first of all, on the type of theoretical explanation we are examining. If the emission is believed to arise from the direct and immediate action of sunlight, as with resonance scattering or excitation through dissociation by ultraviolet light, the intensity may be plotted against the height of intersection of the shadow line with the line of sight. As the true shadow is not sharply defined, allowance may have to be made for a transmission function for the lower atmosphere, which governs the extinction near the edge of the shadow. The extent of extinction or screening by the atmosphere on the incident beam depends on the frequency of the exciting radiation. For the far ultraviolet, radiation grazing the atmosphere tangentially will suffer appreciable extinction even above 100 km. The calculation of the screening height (i.e., the height above ground of the atmospheric layer producing the effective shadow) and the complete transmission function will be considered in Section 10.2.3.

Before considering the presence of an absorbing atmosphere, we shall compute heights of intersection of the line of sight with the imaginary

To Sun

LL

FIG. 10.1. Simplified three-dimensional diagram for twilight observations. The point P, is the intersection of the solid-Earth shadow and the observer’s line of sight. I t has a zenith distance t and an azimuth 44 from the sun. The great circles on which a and /3 are measured are perpendicular to the terminator (sunset line)

and intersect at the subsolar point. 393

394 10. TWILIGHT EMISSION HEIGHTS

shadow produced by the Earth’s surface. The atmosphere will be considered later and a correction derived for the case when atmospheric extinction can be represented by a simple screening height.

Figures 10.1 and 10.2 show the relationship between the observer 8, the sun, and the intersection of the shadow line with the line of sight when atmospheric screening is neglected. Figure 10.3 shows the more complicated situation when refraction and screening by the atmosphere are allowed for. T o retain the simplicity of a two-dimensional drawing, the point 0 (observer) in Fig. 10.3 has been projected onto the plane containing the great circle /3.

The calculation of heights of intersection of the Earth’s shadow and the observer’s line of sight is also of interest for sunlit aurorae.

10.1. Apparent Heights zs : The Shadow of the Solid Earth

Here we shall be concerned with the shadow that would be formed by an Earth with no atmosphere illuminated by a parallel beam of light; we thus neglect attenuation and refraction of the incident beam and consider the shadow to be perfectly sharp.

10.1 .I. General Solutions for the Apparent Height

The problem may be defined in terms of the seven parameters a, p, y , Os, 5, A+, and z, (see Figs. 10.1, 10.2, and 10.3). Of these quantities 5 and A+ (the zenith angle and azimuth of observation) are known and 01

(the observer’s angle of solar depression) may easily be obtained from known quantities. (We shall see in Section 10.1.4 how 01 may be computed for a given date, place, and time of observation.) To obtain x, we require four equations relating the four unknown parameters.

FIG. 10.2. The geocentric celestial sphere illustrating the angles pertinent to twilight reductions. Pi is the projection of P, (Fig. 10.1) onto the celestial sphere.

The length of the arc y has been exaggerated for clarity.

10.1. APPARENT HEIGHTS 2s : THE SHADOW OF THE SOLID EARTH 395

From triangle CP,Q, in Fig. 10.3 (where C, not marked in the figure, represents the center of the Earth), we have cos /? = CQJCP, or

- -

z, = u(sec ,8 - I ) , (10.1)

where a is the Earth’s radius. Similarly, triangle COP, gives two relations: from the law of sines, we have the van Rhijn formula,’

(10.2) U sin 8, = ___ sin 5 = cos /3 sin 5 ,

where the second equality follows from Eq. (10.1). Further, the angle y is simply

y = 5 - 8,. (10.3)

The final required relation is given by the spherical triangle in Fig. 10.2: (10.4)

a + z,

sin ,6 = cos y sin cy - sin y cos cy cos A+.

FIG. 10.3. Two-dimensional geometry of twilight scattering. The incident ray that passes just above the screening height, &, intersects the line of sight at height z,,, where the lowering of the incident ray by refraction is also included. The angles B and y are not in general in the same plane, in which case a # B + y.

Observers who make a large number of twilight observations in a few particular directions ( 5 , A+) may find it convenient to tabulate x, as a function of 01 for these various directions. This tabulation may be

* This equation is fundamental in the van Rhijn method of height measurements of the nightglow. See Section 12.1.1.


done most easily by first plotting f l versus a from Eq. (10.4), with different curves on the graph for different y (and different sets of curves for the various A$). For an assumed value of y and the 5 of observation, one computes 8, from Eq. (10.3), then f l and z, from Eqs. (10.2) and (10.1). With this value of p, one then enters the graph of Eq. (10.4) and reads a.

These equations are also readily adaptable to an iteration solution (Chamberlain [1958a]). We may start the solution with a fixed assumed height, x i o ) , or compute a rough starting value through an approximate solution. A first value of 8,(= O i l ) ) is obtained from Eq. (10.2), then y ( l ) is found from (10.3), /3(l) from (10.4), and zgl) from (10.1). The process is then repeated and, happily, converges. Equation (10.1) may be omitted from the iteration procedure and a final z, computed only when successive values of f l converge satisfactorily. L. R. Megill has prepared a program of this type for use with an electronic digital computer at the Bureau of Standards in Boulder, Colorado. Two or three iterations are usually sufficient to give an accuracy to within one km.

A closed solution for a general direction of observation is most conveniently expressed in terms of the distance OP, = p in Fig. 10.3. From triangle OCP,, we have

f2 =)'''- 1 !? (2 + cos 5) , (10.5) a 2a a

3 = (1 +s + (1

where the approximate equality holds for small heights, z, < a.

ties. From the law of sines and Eq. (10.3), we relate p and y : The value of p / a may be expressed exactly in terms of known quanti-

alp = sin 5 ctn y - cos 5. (10.6)

And finally, ctn y may be computed by elimination of /3 and 8, from Eqs. (10.2), (10.3), and (10.4):

cos O1 cos A+ cos 5 + sinzol sin 5 ctn y = sin 01

C O S ~ 5 C O S ~ a cos 5 cos a cos A+ sin 5 sin3 a

1'2

. (10.7) 1 + (x + sin2 5 sin4 a +

Equations (10.7), (10.6), and (10.5) thus form the exact, closed solution for x,. The closed solution has been expressed in a rather different way by Wark [1960a].

Whether one adopts the closed solution, the iteration solution, or prepares special tables will depend on individual circumstances of the accuracy required, the number and variety of observations, etc. The

10.1. APPARENT HEIGHTS 2s : THE SHADOW OF THE SOLID EARTH 397

closed solution is rather cumbersome to use and the iteration method is therefore often preferable, especially if a good starting value, xjo), is available. If the observation is near the zenith, a rough starting value is, from Eq. (10.1) for a - jl,

sin2 a -secci-l w- zs a 2 . _ - (10.8)

Lugeon [ 19344 has prepared some twilight tables, giving the height of the solid-Earth shadow in the zenith versus the observer's latitude, the sun's declination, and the time since sunset (or before sunrise). With these tables it is not necessary even to compute the angle of solar depression, a, if no more than the zenith shadow height is required; the height is simply read (or interpolated) from the table for each observation. For horizon observations, values to start the iteration may be obtained from the approximate equation (10.21) below.

10.1.2. Solutions for the Vertical Plane Through the Sun

Often the observations are made only in the plane of the vertical circle through the sun, as the reductions are then considerably simplified. In this case the angles a, jl, and y are in the same plane, and as a = y, Eq. (10.3) gives2

6 , = (5 F a) i B. (10.9)

With this value of 0, placed in Eq. (10.2), we obtain

Then Eq. (10.1) gives

[sin ( 5 a) - sin 512 - 1, - = / 1 + z,

a cos2(5 F a) \

( 10.10)

(10.11)

which is exact. This solution may also be obtained from the general closed solution given by Eqs. (10.5), (10.6), and (10.7) (see Problem 1).

A simplified expression is possible for z,/a Q 1, when Eq. (10.11) expands into

z, 1 [sin (5 'F a) - sin 512

a - j: COS'(5 F a ) * (10.12)

Throughout the discussion on observations in the plane of the vertical circle through the sun, double signs will appear in the equations. The upper sign refers to the half- plane between the observer and the sun (A+ = 0) and the lower sign refers to A+ = 180°.


An alternative expression is found from Eqs. (10.6) and (10.7); when A+ = 0 or 180" (see Problem l ) , we find

P = sin2 a

a (1 + cos a) cos ( 5 a ) - (10.13)

Then with the approximate equality of Eq. (10.5), the height in the azimuth plane of the sun becomes

sin2 a sin2 a F8 + cos 11 . (10.14) z, -

a (1 + cos a) cos (1 T a) [2(1 + cos a) cos (1 F a)

Equations (10.12) and (10.14) are identical approximations (see Problem 1).

The exact solution for the vertical plane in the azimuth of the sun may be written in still another way, which may be more convenient to use than Eq. (10.11). From Eq. (10.1) we write

( 10.1 5 ) Z S - = sec (a F y) - 1, a

where we compute y from the simplified Eq. (10.7):

1 - cos 01

ctn 5 f sin a tan y = (10.16)

10.1.3. Approximate Solution for Horizon Observations

Twilight observations near the horizon take on special significance. The intensity increases toward the horizon, owing to the increased layer thickness in the line of sight, although very close to the horizon it will start to decrease again because of increased extinction. Consequently, observations are often made at 5 = 75" or 80", where the brightness is usually greatest in the visual region of the spectrum. For some purposes (see Section 10.2) zenith-horizon comparisons have been made. There is no difficulty in deriving the apparent zenith height, as then ,B = CL in Eq. (lO.l), and the height is easily computed or may be read from Lugeon's [1934a] tables.

If the observations are precisely in the azimuth of the sun, the reductions may be made with the formulae in the preceding section. Often, however, the observations are made for a constant azimuth and do not follow the vertical plane of the sun, or a circle parallel to the horizon is swept over by the photometer. Hence it is convenient to have a

10.1. APPARENT HEIGHTS Zs : THE SHADOW OF THE SOLID EARTH 399

simplified formula applicable to observations near the horizon but at any azimuth.

First consider an observation made precisely on the horizon. From Eqs. (10.6) and (10.7) we find p for 5 = x/2, which we shall denote by p H . Also for 5 = 7712, p = y = pH. Then

sin 01 p_H = tan pH = a 1 + cos 01 cos A+ '

(10.17)

From Eqs. (10.1) and (10.5) the apparent shadow height on the horizon, zH[= z,(( = x/2)], is

(10.18)

Near the horizon the height may be expressed in terms of y by a Taylor series about pH. Thus

(10.19)

As p H and y are small quantities, they can be evaluated from Eqs. (10.17) and (1 0.7). We find, after some simplification of terms,

In the limit, then, of observations near the horizon,

(10.21) 1 . a 2(1+ cos a: cos 4412 (1 + sin a sin2 01 2 ctn 6 cos A+ z.=

This expression is almost identical to one presented by Cabannes and Garrigue [1936u]. The approximation should not be trusted very far above the horizon; in taking the limit (10.20), we consider terms of the order of tan ( to be much larger than ctn a. Hence, when a is small, the formula will not be accurate except extremely close to the horizon. I t is interesting to note that Eq. (10.21) for the azimuth of the sun (A+ = 0) agrees with Eq. (10.14) in the limit as 5 + n/2. But for Aq5 = x ,

the two expressions do not agree, evidently because the assumption that z$a < 1 , involved in both the approximations, is not valid near the horizon away from the sun.


10.1.4. Computation of the Angle of Solar Depression and Solar Azimuth

In the preceding discussion we have treated the angles a and A+, the solar depression at the observer and difference in azimuth of the sun and the observed direction, as known quantities. We shall show here how the zenith distance (90" + a ) and azimuth of the sun may be computed. Figure 10.4 illustrates the problem for an observer in the northern hemisphere. (For the southern hemisphere the problem is essentially the same if the solar declination and observer's latitude are measured positive toward the south pole instead of the north.) The sun's FIG. 10.4. The celestial sphere,

illustrating the calculation of oL declination is 6, the observer's latitude after in the northern on Earth is h, the hour angle of the sun

is T , and its hour angle at sunset was T ~ .

Applying the law of cosines to the triangle formed by sun-pole-zenith,

hemisphere.

we obtain s i n a = -sin 6 sin A - cos 6 cos h cos 7. (10.22)

The azimuth of the sun, measured from the north point and positive toward the east, may then be derived from the same triangle and the law of sines :

cos 6 sin +,, = - -~ sin T. cos a

(10.23)

Usually a human computer will have no difficulty in deciding which quadrant +,, is in, although near 90" and 270" there may be some uncertainty. But if computations are being performed by an automatic machine, some provision not involving judgment must be made to obtain the algebraic sign of cosC$,. The most straightforward way is to compute cos 4" directly from the cosine law:

(sin a sin h + sin 6) cos +" = --__-__- cos a cos h (10.24)

Equations (10.22) and (10.23) involve the hour angle of the sun, T ,

which must be obtained from the time of the observation, t . The difference T - t changes very little over several days, so that a convenient way of finding this difference for a particular night's observations is to

10.1. APPARENT HEIGHTS zB : THE SHADOW OF THE SOLID EARTH 401

calculate it for the time of sunset, to. The time to is given for the Green- wich meridian for various latitudes and dates in the year in ephemerides. This time is very nearly the same on any other standard meridian (i.e., a meridian whose longitude is a multiple of 15 degrees). The observer must then correct the tabulated value to the longitude of his station by adding (or subtracting) four minutes for each degree the station is west (or east) of his standard meridian.

At sunset and sunrise the hour angle is given by Eq. (10.22) for ff = 0:

cos T,, = - tan 6 tan A. (10.25)

With T~ computed by this equation and to obtained from the ephemeris, one may find T = t + T~ - to. This method is especially convenient if annual tables already exist for sunset and sunrise at the station.

If one has to go to the ephemeris, he may find it more convenient to use the equation of time directly. If t is the standard time at a station and A l is the difference in longitude of the station and the standard meridian, then t - 12” A1 is the hour angle of the mean sun. The + sign is used when the station is east of the meridian, the - sign when it is west. The equation of time, E, is defined as the hour angle of the true sun, T, minus the hour angle of the mean sun. Hence T = t - 12” AE + E , where E is given in ephemerides; approximate values of E are given in Table 10.1, along with the sun’s declination 6 .

Equations (10.22) and (10.24) may be solved by means of Hunten’s [1958a] nomogram for spherical triangles (Fig. 10.5). The nomogram may be constructed for any latitude in a few hours, and will be a marvel- ous aid if many observations or reductions are to be made.

If the hour angle of an observation is known, one places a straight edge on the value of T , as read from the line on the left, and on the solar declination, which appears on the circle. He then reads the altitude, - a, from the center line. Similarly one may use the nomogram to find the hour angle when the sun is at a particular angle of depression, a. When T is then converted to t by the equation of time, this procedure can be used, for example, to compute the time of astronomical twilight ( a = 18”), civil twilight (a = 6”) , or sunset (a = 0 ) ; the latter case is also given by Eq. (10.25). The procedure is the same for relating the solar azimuth, declination, and solar depression, where the scales are used as labeled at the bottom of the figure.

402

Hour angle

*T

DEGREES H M S

azimuth

*t

FIG. 10.5.

10. TWILIGHT EMISSION HEIGHTS

altitude -0

declination

declination

8 ;L 9 42' 34' 12"6

Hunten's nomogram for solving spherical triangles, drawn for the latitude of Yerkes Observatory., 42"34'12I'6.

10.1. APPARENT HEIGHTS zs : THE SHADOW OF THE SOLID EARTH 403

TABLE 10.1

APPROXIMATE SOLAR DECLINATION, 6, AND EQUATION OF TIME, E

s E Date (degrees) (minutes

of time)

Jan. 1 8

15 22 29

Feb. 5 12 19 26

Mar. 5 12 19 26

Apr. 2 9

16 23 30

May 7 14 21 28

June 4 11 18 25

July 2

- 23 - 22 -21 - 20 -18 - 16 - 14 - 12 - 9 - 6 - 4 - 1 t 2 + 5 $ 7 + 10 + 12 + 14 + 16 + I 8 + 20 + 21 + 22 + 23 + 23 + 23 + 23

- 3 - 6 - 9 -11 -13 - 14 - 14 - 14 - 13 -12 - 10 - 8 - 6 - 4 - 2

0 + 1 f 3 t 3 t 4 + 4 + 3 + 2 + l - 1 - 2 - 4

6 E Date (degrees) (minutes

of time)

July 9 + 22 16 + 22 23 + 20 30 + 19

Aug. 7 + 17 14 + 15 21 + 12 28 + 10

Sept. 3 + 8 10 + 5 17 1 - 3 24 0

Oct. 1 - 3 8 - 5

15 - 8 22 -1 1 29 -13

Nov. 5 -15 12 -17 19 -19 26 -21

Dec. 3 -22 10 - 23 17 - 23 24 - 23 31 -23

- 5 - 6 - 6 - 6 - 6 - 5 - 3 - 2

0 + 3 -I- 5 + 8 + 10 + 12 + 14 + 15 + 16 +16 +16 +15 -c 13 +11 + 8 + 4 + I - 3

10.1.5. Time of Sunset at a Particular Height and Direction from the Observer

When the twilight emission is produced directly by incident sunlight, as with resonance scattering or excitation by ultraviolet dissociation of molecules into excited atomic levels, the observations will normally be expressed in terms of the intensity versus height of the shadow. After corrections for atmospheric screening, these data are then in a convenient form for interpretation and comparison with theory. Thus far in this


chapter we have been concerned with transforming the time of an observation to shadow height. Alternatively, in planning the observations, one may want to know at what time the shadow may be expected to cross the line of sight in a particular direction and at a particular height.

Furthermore, if a twilight effect arises from a more indirect result of sunlight, as from molecular association or recombination, the radiation from a particular volume will continue with a certain lifetime after the sun has set. The pertinent way to represent the observations would then be a plot of intensity versus the time since sunset at a point in the direction of observation and at the height where the radiation is believed to originate. This problem may also be solved, in the absence of atmospheric extinction and refraction, by the basic equations (10.1) to (10.4).

The solution is now straightforward. The height z, is known or assumed, 5 and A+ are known. Hence we may calculate p, O,, y , and 01

in that order. Since 01 is generally a small angle, it may be most easily calculated from Eq. (10.4) by first taking cos 01 = 1 and computing sin 01. The second approximation should suffice. The sun’s hour angle, at the instant of sunset on the chosen point, is then obtained from Eq. (10.22). With hour angle related to the observer’s local time, as discussed in the preceding section, the intensity measurement through twilight can be plotted against the time interval since sunset at a particular height.

10.2. Height Measurements with Atmospheric Screening

From the analysis of t‘he preceding section, one may derive an apparent height z, for any observation in a given direction and at a known instant. When the shadow is not cast by the solid Earth but by the atmosphere at height h,, we may find a correction to the computed height of intersection (see Fig. 10.3). We shall call h, the screening height (Vegard [1940a]), and the height of the intersection of the unrefracted shadow line with the line of sight will be zl. When the small correction for atmospheric refraction of the incident sunlight is applied, the actual height of intersection will be called x,,. Actually, of course, the shadow does not have a sharp boundary, as we assume here, but in the limit of the approximation that the boundary is sharp, z, is the height most generally of physical significance.

Our procedure of correcting the apparent height z, for screening, almost as an afterthought, may appear to be an indirect way of solving the problem. It is possible, of course, to set up the geometry without

10.2. HEIGHT MEASUREMENTS WITH ATMOSPHERIC SCREENING 405

ever explicitly considering z,, but in practice the screening height may have to be determined from the observations or may be uncertain, so that the present procedure will often possess definite advantages. The discussion here is limited, however, to small screening heights (h , < a).

10.2.1. Actual Shadow Height zo, for a Known Screening Height h,

The geometry of the shadow with and without a screening height is illustrated in Fig. 10.6. The vertical plane through the point P, and perpendicular to the azimuth of the sun is shown. The point P lies on the shadow cast by a screening layer at height h,. We want to find the

of earth

height.

difference in heights, zo - z,, for an arbitrary direction of observation. In this discussion superscripts ( l ) will refer to heights measured in the observer’s zenith.

First of all, we note that in the azimuth perpendicular to the sun,3

FIG. 10.6. Three-dimensional geometry of twilight observation with a screening

The azimuth in this discussion should strictly be the azimuth of P as measured from P,. In practice this is very nearly the same as the azimuth of P and P, as measured from C. Thus for observations perpendicular to the sun’s azimuth, the great circle containing the projections of 0, P, and P, is nearly identical to a small circle parallel to the terminator, over the small distances involved. Similarly, the angle f l refers to the sun as seen from P, although in practice it is derived for the point P, (Section 10.1). These limitations on the derivation given here should be borne in mind in case the equations are to be applied to large heights.


the difference in height due to extinction alone between the unrefracted shadow of the screening layer (at height xll)) and the apparent shadow (at height z,) is zil) - z, = h, sec p.

The actual height is also lowered slightly by refraction. A star rising or setting, as observed from the ground, is refracted 35‘ = 0.010 radian. A tangential ray passing completely through the lower atmosphere, with closest approach at height x, would then be refracted through 0.020 N(z)/ N(0) radian. From Fig. 10.3 we see that the change in height from refraction alone, for a zenith observation (or one in the plane perpendicular to the sun’s azimuth), is

(10.26) where the approximate equality is valid for h, < a and where the numerical value 127 applies to heights measured in kilometers. For an azimuth 90” from the sun the total change in shadow height, due to the lower atmosphere, is

x:) - z, = h, sec /? - Sz. (10.27)

The refraction term 62, which decreases as h, increases, is much smaller than the screening term.

We may now proceed to compute the effect of a screening layer for observations in an arbitrary direction ( c , A+). It will be sufficient to express z,, in terms of xi1) and x,. In Fig. 10.6 the perpendicular distance from the point P (intersection of the actual shadow and the line of sight) to the vertical plane aligned perpendicular to the sun’s azimuth is denoted by q. The distance between P and P, is s, and the angle at P between these two lines is x.

In the triangle just described, we have the relation

q = s cos x. (10.28)

The difference between xi11 and zo is4

z t ) - zo = q tan 8, (10.29)

and by projecting the length s onto the vertical, we find

zo - z, = s cos 8,. (10.30)

Strictly, if zo is the height of the projection of P onto the plane containing P,< and aligned perpendicular to the sun’s azimuth (as shown in Fig. 10.5), then the height of P above the ground is approximately zo + q*/(a + zo). The correction term is entirely negligible for small screening heights h,.


From the angles 8, and x formed at P, we find

cos x = sin 8, cos A+. (10.31)

Eliminating q, s, and cos x from Eqs. (10.28) to (10.31), we obtain

(10.32)

Combining this equation with Eq. (10.27), we find

(10.33)

When the screening height is known, the solution for zo thus proceeds as follows: The apparent height z, is found from Section 10.1 ; once z, is known the angles 8, and B follow immediately from Eqs. (10.2) and (lO.l), respectively. Then 6z (the refraction term) is found from Eq. (10.26) and the actual height, z,, from Eq. (10.33).

h, sec 18 - Sz

1 + tan 8, tan 18 cos A+ *

2, - Z,? =

10.2.2. The Zenith-Horizon Method of Height Determinations

When the screening height can be estimated with some precision (see Section 10.2.3), the method given above is adequate for deriving the height of the twilight shadow. If the excitation mechanism is not known, however, the screening height cannot be computed. For example, suppose that it is not known whether the excitation of a resonance line arises from simple resonance scattering of sunlight in the visible region or from excitation accompanying molecular dissociation, produced by ultraviolet radiation. I n the two cases the screening height would usually be vastly different and one would like to derive h, as well as x, from observations. The investigation of this particular problem for the case of the Na D lines inspired the development of the zenith-horizon method.

This method has been used with several modifications, all making use of the fact (see Fig. 10.7) that when two observations (one near the horizon and one near the zenith) correspond to the same actual height, z,, the apparent heights, z,, will ordinarily be different. The method requires that the observer should be able to tell from his data which horizon and zenith observations correspond to the same actual height. The accuracy of the zenith-horizon method depends on the accuracy with which these corresponding observations can be specified, and this very point has been the source of some controversy over the usefulness and reliability of the method.


The first zenith-horizon comparisons on the Na D lines were reported by Vegard [1940a] and Vegard and Tonsberg [1940a, 1941~1. The observations were reduced at first by a graphical method, but analytic techniques were soon adopted by Vegard and Kvifte [1945a], Penndorf [1946a, 1948~1, and Cario and Stille [1950a]. Critical discussions and

FIG. 10.7. T h e zenith-horizon comparison method for observations in the azimuth plane of the sun. T h e observer at O1 computes an apparent height zp) when the actual height is zo. When the same observer is at O,, relative to the sun’s rays, and again sees the actual shadow at z,, the apparent shadow will be at zj2). For

simplicity, refraction is not shown in the figure.

modifications of the method of twilight analysis have been made by Bricard and Kastler [ 1944a, 1952~1 (who, incidentally, introduced the term zenith-horizon method), Dufay [1947a], Kvifte [1951a, 1953~1, and Hunten [1954a, 1956~1.

For purposes of the present discussion we assume that two corresponding observations have been chosen, which implies the following: (1) The observed intensities must have been corrected for scattered light in the troposphere (Chapter 2) and (2) reduced to the zenith by multiplying the observed intensities by cos 0 (where 0 is the angle of emergence of the beam from the layer, measured from the normal). (3) An additional small correction may be necessary if the scattering layer has an appreciable thickness5 (Bricard and Kastler [1952a]). (4) For the D lines a correction may be required because D, is not isotropically scattered. The scattering phase function is related to the polarization and is discussed in Section 1 1.1.2. (5) Finally, there may be a small radiative-transfer correction to the zenith and horizon intensities

See Fig. 10.7. The incident sunlight illuminating a particular height zo + dz will suffer slightly more atmospheric attenuation when the observation is in the zenith than when it is near the horizon toward the sun.


for multiple scattering in the luminescent region for the particular case of the Na D lines (Rundle, Hunten, and Chamberlain [1960a]).

We shall denote by zv) the apparent height of an observation in the zenith, and zv) will be the apparent height for a corresponding observation near the horizon,, in the azimuth plane of the sun. For the zenith observation, Eq. (10.33) gives

zo = ~ $ 1 ) + h, sec /3(l) - Sz(/3(l)), (10.34)

where now ,!I(1) = a(1) and the superscript refers to the zenith observation.

I t is evident from Eqs. (10.33) and (10.4) that for observations that are made in the plane perpendicular to the azimuth of the sun, Eq. (10.34) is still a good approximation with ,!I(1) = c ~ ( 1 ) . Hence it is not necessary to restrict the observation at Ol (see Fig. 10.7) to the zenith, and if it is made at the same zenith distance as the observation from O,, differences in the length of the emitting path and in extinction will largely disappear. Scattering into the line of sight will not be the same in the two cases, and a correction must be applied according to the methods of Chapter 2. But there is probably less difficulty in picking out corresponding points on the two intensity (versus time) curves, at least for thin emitting layers, if both sets of data are for the same zenith angle.

For an observation in the azimuth plane of the sun, we have, similarly,

(10.35)

Subtracting Eq. (10.35) from (10.34) and neglecting second-order terms in j?, we obtain

[h, sec z ( 2 ) - (1) = - Sz(/3)] tan 8, tan /3 s zs 1 + tan Os tan /3 (10.36)

It is unimportant whether p in Eq. (10.36) is obtained from the zenith or horizon observation. The screening height is thus

h, = cos /3 [(ctn B,$ ctn /3 + 1) (2:) -zp)) + Sz(/3)]. (10.37)

All the quantities on the right except the refraction term may be computed for a given observation (Section 10.1). If refraction is important, it can be included in a second approximation.

If corresponding points on the intensity curves for the zenith and the horizon could be picked out, h, could be readily computed. The data


obtained by Hunten [1956c] and shown in Fig. 10.8 illustrates the difficulty. The fact that the horizon intensities have been divided by 3.3 is of no special significance. Hunten estimates that with allowance not only for the increased path length of the horizon observations (sec 8) but also for the increased extinction, the correct intensity ratio should be about 2.6. This means that the horizon points should be raised slightly,

loo !r-

2s KM

FIG. 10.8. Zenith and horizon ( 5 = 750) intensity of Na D lines obtained at Saskatoon and plotted against apparent shadow height. The line is a theoretical curve for an adopted height distribution of Na atoms and screening appropriate

to yellow light. After Hunten [1956c] ; courtesy Pergamon Press.

and it develops that over the entire set of points the average horizontal shift of zenith and horizon observations is about zf) - zp) = 3 km. With refraction neglected and sec 8, = 3.3 (judged appropriate for the height of the emission and zenith angle of observation) and with p = 7P5 (or z , = 55 km), Eq. (10.37) yields h, = 10 km. As this equation is not very sensitive to 8, we would expect the zenith and horizon points in Fig. 10.7 to form nearly parallel curves, as indeed they seem to do.

We might ask how much significance can be attached to this precise screening height. T h e attempt to compare zenith and horizon observations photometrically invariably involves uncertain corrections. The emitting path length and tropospheric scattering have already been mentioned. In addition, if the layer is not thin and the shadow is not sharp, then the concept of a screening height begins to lose physical significance ; the distribution of sunlight through the emitting layer is different when the layer is viewed in the zenith than when it is on the horizon.

One might also try to fit the zenith and horizon curves without any preconceived ratio for the intensities. Again the result is bound to be

10.2. HEIGHT MEASUREMENTS WITH ATMOSPHERIC SCREENING 41 1

uncertain, as there are no definite corresponding points on the smooth curves. Nevertheless, with intensity plotted as ordinate on a logarithmic scale, one may move one curve vertically (versus intensity) until the nearly horizontal portions (the plateaus) cqincide approximately or until there is a constant horizontal separation between the sloping part of the curves.

An error of 30 percent in the relative zenith and horizon curves in Fig. 10.8 would correspond to an error in the screening height of about 6 km. Therefore, it does not seem likely that Hunten’s screening height of 10 km for the D lines could be in error so much as to indicate screening of ultraviolet radiation by the ozone layer. When one postulates an exponential distribution of Na with height, an effective screening height of 10 km appears quite reasonable for incident yellow light (Section 10.2.3 ; Hunten [ 1956~1).

10.2.3. Calculation of Transmission Function and Screening Height

For a more accurate treatment of the twilight shadow than can be accomplished with a screening height, we consider the transmission function at height z defined by

where the solid-Earth shadow is observed at height z,. Here CY,, is the absorption coefficient per particle (atom or molecule) and %(h) is the total number of particles in a column, of unit cross section, tangent to a sphere of radius a + h about the Earth’s center. For a given observation we must relate x and h.

Following Hunten [1954a] we may express %(h) in terms of the density at the closest approach, h, of the column to the Earth. If the scale height is H at height h, the total density traversed is (Fig. 10.9)

m cc

%(h) = N(z ’ ) ds N(h) e-(z’-h)lH a dP’, (10.39) -m -m

as the integrand is significant only when ,8‘ is small. The exponential may be expressed in terms of ,8‘ by writing cos ,8‘ = (u + h)/(a + 2’).

Expanding both sides in series, we find z‘ - h = a,8’2/2; then

(10.40)


Strictly z and h are related by Eq. (10.33), where z, and h, are replaced by z and h, respectively. But to a good approximation for small /3 (within one percent throughout the sodium twilight for zenith observations), z - z , m h , when refraction can be ignored. This procedure

FIG. 10.9. Geometry for calculation of transmission function.

is adequate for the transmission function of the lower atmosphere, although it may be necessary to consider a refraction correction (see below). In addition, atmospheric ozone produces appreciable absorption over most of the visible spectrum (see Table 2.2) and must be treated numerically, as the ozone distribution does not follow a barometric law.

A simple screening height, h,, might be estimated by finding the height h at which the transmission function is one half, provided either the emitting layer is very thin or the emitting atoms are uniformly distributed with height within the layer.

In the absence of secondary scatterings within the airglow layer, the integrated intensity of a twilight line due to scattering of sunlight in the transition /3 + y is (see Section 11.1. I )

(10.41)

Here nE is the solar flux (measured across a unit area normal to the sun’s rays) entering the Earth’s atmosphere: fa# is the oscillator strength for absorption from the ground term (a); A,, is the transition probability for emission of the line /3 + y ; 0 is the angle of emergence of the scattered light, measured from the normal to the scattering layer; and JV&(ZJ is the effective number of fully illuminated atoms when the solid-Earth shadow is at height z,, computed with allowance for the influence of the Earth’s actual shadow:

(10.42)

10.3. HEIGHT AND VERTICAL DISTRIBUTION 413

where N , is the density of atoms in the ground term. If N , varies with a constant scale height, then an effective screening height may be estimated by finding the h at which N , T,, is one half its maximum value. But even this procedure is not very satisfactory, as the whole concept of a definite screening height loses much of its usefulness when neither the screening atmosphere nor the scattering layer is sharply defined.

In Eq. (10.41) dCq is the only factor that changes as the sun rises or sets. If something is known (or can be assumed) about the variation with height of the density, N,, we may compute Nee; as a function of z , by evaluating the integral in Eq. (10.42). For the case of sodium, Hunten [1954a] has done this for three assumed distributions, in an effort to find which gave a better fit with observations. I t appears that the intensity variation is not very sensitive to the precise distribution function (Hunten and Shepherd [1954a]). This means that it is difficult to obtain the height distribution from observations, but that, alternatively, an assumed distribution used in Eq. (10.42) is likely to predict a reliable

J&(zs). It is at least possible, therefore, to test a given hypothesis for the excitation mechanism in twilight and to obtain a good estimate for the mean height of the emission.

Hunten's [1954a] calculations of the transmission function T,. have allowed for two additional but small effects. Refraction not only tends to lower the incident beam, so that a correction is necessary in relating h to z when '91 is computed by Eq. (10.40), but the change of refraction with height attenuates the beam slightly so that the scattered intensity is diminished. Secondly, he has made a rough allowance for the finite diameter (one half degree) of the sun; the transmission function computed for a point source at the center of the sun's disk is thus blurred over a vertical distance of the order of

Link [ 1958~1 has also computed transmission functions with allowance for molecular scattering, refraction, finite size of the solar disk, ozone absorption, and (non-Rayleigh) scattering by aerosols in the atmosphere. His results for 5893 A are presented in tabular form.

5 km in the atmosphere.

10.3. Height and Vertical Distribution of Observed Emissions

Only the three principal emissions in the visible are treated here; for other height estimates see Section 11.6.

10.3.1. Ionized Nitrogen Bands

It seems most likely that the N: twilightglow results from resonance scattering (or fluorescence for some vibrational transitions) by NZ ions


(in contrast to simultaneous ionization and excitation of N, by ultraviolet radiation). T h e evidence for this conclusion is outlined in Sec- tion 11.2.1. However, a height analysis in terms of excitation by blue light may give an erroneous height unless the N: abundance remains constant through twilight. Thus the twilight curve may actually depend on the ionizing radiation rather than on the exciting radiation (Sec- tion 11.2.2).

J. and M. Dufay [1947a] discussed a series of twilight spectrograms showing the N,+ bands. For the most part their spectra were obtained when the apparent height of the shadow, z,, was in the range 70 to 150 km, but a detailed height analysis of the data was not made at that time. Shortly afterward, M. Dufay [1948a, 1949~1 made the first serious height estimate and reported that the emission arose from an apparent altitude of about 100 km.

Dufay [1953a] later made a more extended study of the problem. The bands were rarely detectable when z, < 90 km or when z, > 125 km. The lower limit probably has no significance insofar as the emission height is concerned, because for low values of x , ~ the strong solar continuum completely obscures the emission. With the low dispersion of Dufay’s spectra the bands were effectively masked below 90 km ; Swings and Nicolet [1949a] could detect the band A3914 at much lower apparent heights. The upper height (125 km) is probably indicative of a true decrease of N,+ ions.

The actual height z, is not so readily obtained, however. Dufay [1953a] was not able to make a precise estimate of the screening height, and so the actual height of emission is not known directly from observations. A screening layer around h, = 20 km did not seem inconsistent with Dufay’s rough comparisons of zenith and horizon observations, and a screening height of this order would be expected for violet light (Bates [1949b]). For ionizing ultraviolet or x-radiation, h,, would be much greater.

The observational problem for N: is more difficult than for the yellow Na lines. Rayleigh scattering of sunlight in the violet is more of a nuisance, which considerably hampers zenith-horizon comparisons and intensity measurements in general. Further, the N: bands often undergo strong variations from night to night and it is uncertain whether these enhancements are localized geographically; they seem to be associated with magnetic activity. At higher latitudes low-level auroral activity often hampers pure twilight observations. Thus the observational problems are not easy, but the N: flash deserves much fuller investigation.


10.3.2. Sodium D Lines

The twilight emission that has attracted the most attention by far is the resonance doublet, Na D. Bernard [1938a, b,fl estimated the apparent height, z,, to be around 80 km, and supposed the rapid6 decrease of intensity to indicate a thin layer of atomic sodium. Chapman [1939a] suggested that at low altitudes the sodium would be in the form NaO, but that above the peak concentration, Na might be expected to decrease exponentially with the barometric law. He also pointed out that the intensity decrease would still be fairly rapid. Elvey and Farnsworth [1942a] were later able to represent their twilight observations adequately by assuming an exponential distribution of atoms.

While the zenith-horizon method is fairly straightforward in principle, the necessary corrections (e.g., for the longer emitting path and greater extinction and scattering for observations near the horizon) have invalidated many of the Na height results based on this method. Several analyses’ have favored a screening height of about 40 km and Na heights around 90 to 115 km. This screening height seems too high for yellow light and it has been interpreted as indicating excitation by ultraviolet solar radiation.

Cario and Stille [1940a] first pointed out the necessity for considering a finite screening height even for visible light. The screening height to be expected for resonance scattering, with allowance for extinction by ozone as well as by ordinary air, was first calculated by Bricard and Kastler [1944a]. J. Dufay [1947a] obtained an emission height of 80- 90 km and a screening height of 25 km, and showed that the latter is not unreasonable when extinction by ozone in the Chappuis band is considered. Barbier [1948a] also computed a screening height from an adopted ozone distribution and derived from spectrographic observations a vertical distribution for Na that had a sharp lower boundary at 70 km and a scale height of 8 km. Later Barbier and Roach [1950a] carried out observations in late twilight and, adopting an effective screening height, they interpreted a small post-twilight and predawn enhancement as arising from resonance scattering by sodium atoms at great heights. This interpretation led to a very slow decrease in sodium density (scale height, 250 km) above 200 km altitude. The enhancements observed at these heights were only of the order of magnitude of the nightglow

Bernard’s estimate of the time for the intensity to drop to a few percent of its maximum twilight value was too short; the decay actually takes some 15 or 20 minutes. ’ Vegard and Tonsberg [1940a], Vegard and Kvifte [1945a], Vegard [1948a], Kvifte

[1951a], Vegard, Tonsberg, and Kvifte [1951u], Vegard, Kvifte, Omholt, and Larsen [1955a], Cario and Stille [1950a, 1954~1.


and, as the filter used could have admitted other radiations, the results must be treated with caution.

Blamont and Kastler [1951a] observed the late twilight with a photoelectric photometer that rejected the continuous Fraunhofer spectrum and recorded only the D-line emission. They computed a transmission function and, like Barbier and Roach, interpreted the intensity as resonance scattering from free sodium. The result was a scale height of 85 km for sodium in the region 130 to 200 km. Again we may question whether the interpretation is correct; a slow post-twilight variation in the nightglow, due to photochemical processes, might simulate a late twilight scattering.

The thickness of the emitting region was discussed also by Vegard [ 1948~1 and the subsequent papers from his laboratory have included thickness measurements. However, as Kvifte [ 1953~1 has pointed out, the thicknesses derived by these methods are not too convincing, as a sharp screening height is assumed. The finite slope of the curve of intensity versus time, as the shadow sweeps across the Na layer, is then explained solely by the vertical distribution. But actually since the shadow itself is not sharp, the rate at which the intensity falls off depends on the transmission near the edge of the shadow as well as on the Na distribution.

A more appropriate way to derive a vertical distribution is to combine an accurate transmission function with various assumed sodium distributions and then compare these computations with observations. We shall call this the method of the transmission function.8 Hunten and Shepherd [1954a] performed an extensive analysis of this type. They compared an entire evening’s observations with computed curves (based on various Na models) to derive the height and vertical distribution as described in Section 10.2.3 (see Fig. 10.8). A good fit was obtained for a peak concentration of Na at 85 km, with an exponential decrease above and below this height with a scale height of about 7.5 km.

Similarly, Blamont, Donahue, and Weber [1958a] assumed a Gaussian distribution and obtained a peak height of 88 km and a thickness at half-peak of 14 km. Hunten [19566] found virtually no seasonal variation in the height of the peak, upon introducing variations in the ozone content and their effect on the transmission function into the analysis. This result is of considerable interest in view of the large seasonal variation in total Na content. Observations from the zenith and horizon

Cronin and Noelke [1955a] call this the curve:ftting method. It may be contrasted with the zenith-horizon method, which attempts to derive the screening characteristics of the atmosphere, as well as the emission height and distribution, from a judicious comparison of two sets of data.

10.3. HEIGHT AND VERTICAL DISTRIBUTION 41 7

should give consistent results, but the height deduced by this method of the transmission function does not require that the zenith and horizon data be compared at all. On the other hand, Hunten [1956c] has derived a screening height from some of his data by zenith-horizon comparisons, to show that the methods of zenith-horizon and transmission function do give reasonably consistent results. Hunten has not attempted to compare observations in the zenith and horizon on the basis of only one or two corresponding points (such as the time or apparent height z , of disappearance of emission); rather, he has fitted the two entire sets of observed points together. This technique might be called the generalized zenith-horizon method. The effective screening height (see Section 10.2.3) was h, = 10 km. Hunten mentions that while this value is not inconsistent with excitation by yellow light, the precise h, should not be given too much significance.

In order to compute an effective screening height from the transmission function by setting T,,(h,) = 1/2, some definite information is required on the vertical distribution of Na and of ozone, which is responsible for most of the screening. Alternatively, precise observations and corrections for scattered light are necessary to derive h,, from zenith- horizon comparisons. Ordinarily one does not have the necessary data to use either method to full advantage. The ozone content and distribution is uncertain and variable both with the seasons and sporadically. And the difficulties and uncertainties in photometric comparisons and corrections are formidable (Kvifte [ 19534) and are most likely responsible for the large screening heights (around 40 km) deduced in several investigations.

Also, zenith-horizon comparisons in the past have invariably assumed the scattering to be isotropic. Actually, the phase function for D , slightly favors forward and backward scattering, as shown in Eq. (1 1.44); for D, no correction is necessary.

In Chapter 11 we shall discuss the transfer of radiation through the Na layer in some detail. While the transfer problem is concerned primarily with the absolute intensity of the twilight flash, the change of intensity with time is also affected by the Na layer itself. The main effect takes place at the first passage of sunlight through the Na layer; the optical path length through this layer is nearly proportional to csc p, where ,f3 is the angle of solar depression. Hence as /I changes during twilight, the observed intensity changes. (This change is in addition to that produced by the lower atmosphere.) Therefore, in any derivation of the Na distribution, from a consideration of the curve of intensity versus time, scattering in the Na layer should be allowed for (Donahue, Resnick, and Stull [1956a]). While this effect was not included in Hunten


and Shepherd’s [1954a] analysis, it has since been considered by Rundle, Hunten, and Chamberlain [1960a] and by Hunten [1960a].

The method of the transmission function meets with practical difficulties of interpretation in terms of the vertical distribution of sodium. From Eq. (10.42) we may see that errors in the transmission function could appear in the derived height distribution of atoms. But an even greater source of error lies in the fact that to obtain the vertical distribution from a series of measurements of the total intensity, one must take the difference between successive measurements, and the errors in these differences may be very large. An alternative approach is to measure directly the derivative of brightness (with respect to shadow height) and compare the observations with the derivative of Eq. (10.42).

Observations of this type have been made at Saskatoon with a birefringent photometer that is rotated around the zenith in a small circle, with the amplitude of the varying output recorded. The results have been corrected for height variations in the transmission function and for radiative-transfer effects produced by D-line scattering within the Na layer. Uncertainties in the transmission function are the limiting factor in the accuracy of the height distributions. The first results obtained by this technique (Rundle, Hunten, and Chamberlain [ 1960~1) give heights and distributions similar in form to the earlier results discussed above, but show greater detail and indicate rather substantial variations from day to day. The method seems promising.

10.3.3. Oxygen Red Lines

For some time it was thought that the [OI],, red lines, A6300 and h6364, might originate from resonance scattering. In their early work, however, Cabannes and Garrigue [1936a] analyzed the intensity of the evening twilightglow as a function of shadow height z, and, neglecting deactivation, noted that the slow decrease of intensity would then imply a large scale height for 0 atoms in the ionosphere. Elvey and Farnsworth [1942a] and Elvey [1948a] showed that the gradual decay of the evening twilightglow extends well into the night and that the red lines are enhanced even when the shadow height is 1300 km. Similar results were obtained by Dufay and Tcheng [1946a]. But the observation of a morning as well as an evening enhancement suggested a mechanism, such as resonance scattering, that depends on the direct action of sunlight.

Bates [1948a] compared Elvey and Farnsworth’s [ 1942~1 data, placed on an uncertain scale of absolute intensity, with the intensity to be expected from resonance scattering with an adopted model atmosphere. At that time it appeared that the absolute intensity could be satisfactorily


explained and that with allowance for collisional deactivation of metastable 0 atoms and for observational uncertainty, the slow decrease with height might also fit the theory.

More recent calculations have been carried out by Chamberlain [1958a] with an improved model atmosphere and with allowance for deactivation. It appears that resonance scattering is incapable, after all, of providing more than a minor contribution to the [OI],, twilight (see Chapter 11). Not only is the observed absolute intensity too great and the decrease of intensity after sunset too slow to be explained by the 0 atoms in the upper atmosphere, but in different azimuths the observed intensity, when plotted against shadow height, gives a set of curves that do not coincide. The situation is illustrated in Fig. 10.10, based on data obtained by Robley. The discrepancies between the curves are much too great to be reconciled with a mechanism resulting from

and immediate action of sunlight. Figure 10.10 may be the direct

70C

60C

2 rn .-

- I 5oc d

2L 8 .s 4oc

'I .%

I

300

2OC

100 I

I I I I I

1 150 200 250 300 350

Height zo (kml

FIG. 10.10. Evening twilight observations of [OI],, in different directions, from data provided by R. Robley. The height scale has been fitted to the data with the assumption of a screening height h, = 25 km. From Chamberlain [1958a];

courtesy University of Chicago Press.


compared with Fig. 1 1.1 1, which shows the theoretical intensity allowed by resonance scattering, and with Fig. 11.12, which shows the same data fitted with the theory of dissociative recombination.

The failure of resonance scattering to explain the data also accounts, in part at least, for other apparent inconsistencies. For example, Robley [ 1956~1 has compared zenith and horizon observations in the following manner: neglecting screening and refraction, he selected corresponding observations on the zenith and horizon intensity curves, thus presuming the height z, and angle p to remain constant for the two observations. Substituting Eq. (10.9) in Eq. (10.2) we obtain

Z S - = (sec /3 - 1) = tan (a - 8) ctn 5 + sec (a - 18) - 1, a

(10.43)

which gives the height z, for an observation at an arbitrary in terms of the difference in angles, a - p. Robley's method consists, essentially, in obtaining ,8 from the zenith observation; a proper zenith-horizon comparison means that the same p applies to the horizon observation, for which 5 and 01 are known. In this fashion Robley found that the height at which his [OI] intensity curves for 6 July 1956 seemed to drop most abruptly (i.e., the point of inflection) was x, = 73 km. I t is interesting to note, however, that if the heights for the same inflection points on his two curves of intensity versus time are derived separately by Eq. (10.12), instead of by Eq. (10.43), his zenith curve gives zf) =

191 km and the horizon curve, z',") = 173 km. The discrepancy between the two procedures is in the wrong direction

to be explained by a screening height; from Eq. (10.37) we see that the h, necessary to reconcile the data would be negative. Evidently Eq. (10.43), which depends on the difference 01 - p of two uncertain quantities, is not appropriate for reliable heights. The difficulty is present to some extent in any zenith-horizon comparisons. But for the [OI],, lines the facts that the intensity decays slowly and the excitation does not depend in the first place on the scattering or absorption of sunlight at the time of observation make it virtually impossible to choose empirically corresponding points on the two curves.

Inasmuch as the red-line twilightglow probably arises largely from the same process as the nightglow, other techniques are required to derive the emission height. A discussion of these methods is deferred to Section 12.1,

10.3. HEIGHT AND VERTICAL DISTRIBUTION 42 1

PROBLEMS

1. (a) Show that when A+ = 0 or 180", p is given by Eq. (10.13), and that alternative choices of algebraic sign that appear in the derivation of Eq. (10.13) may be rejected. (b) Show that the exact closed solution for the apparent height, as given by Eq. (10.5), then reduces to a form equivalent to Eq. (10.1 1). (c) Show that the approximations (10.12) and (10.14) are identical.

2. (a) What is the transmission T, of the lower atmosphere for a beam of yellow light that just grazes the Earth's surface (h, = O ) ? Take the extinction coefficient as Na, = 8.98 x lo-@ cm-I for air at sea level (van de Hulst [1952a, Table 4, p. 551); take H = 7 km as an average value for the troposphere. (b) With this extinction coefficient, at what height h, does T, become equal to one half? (c) With Dufay's [ 1947al distribution of ozone, and the ozone absorption coefficients given in Table 2.2, compute h, for 5893 A and for 6300 A. (d) At what height h, is T,. = & for ultraviolet radiation in the Schumann-Runge region (A < 1750 A) ? Take as an average value ti, = 2 x lo-'@ cm*/ molecule. (e) How much does refraction lower the zenith height of a ray of visible light that just grazes the Earth's surface when = 6" ? How much decrease in height is there for the ray that grazes the screening height h, computed in part (b) ?

Chapter 1 1 . Theory of the Twilight and Day Airglow

The most obvious mechanisms to investigate for the production of a twilight airglow are resonance scattering and fluorescence. In the absence of secondary scatterings, deactivation, and polarization, the theory is quite straightforward. The addition of some of these complicating features requires more elaborate analyses, but the problem is still amenable to analytic treatment.

Scattering will not explain the entire twilight airglow, however, and in later sections of this chapter, we shall discuss other theories for particular emissions.

11.1. Resonance Scattering and Fluorescence for An Optically Thin Layer

11 .I .I. Scattered Intensity with Allowance for Deactivation

In presenting the theory it is convenient to consider a particular example, but the modifications required for any other atom will be straightforward. We will treat the problem for h6300, [OI],,, which arises from the 3P, - lD, “forbidden” transition (see energy level diagram, Appendix IV). The discussion follows that given in an earlier paper (Chamberlain [1958a]).

Let there be no attenuation of ?T e, the incident flux of solar photons’ per unit frequency interval per unit area normal to the beam above height x,. Then above x, the number of photons per unit frequency interval at frequency v in the line J - J‘ absorbed in one cubic centimeter per second is T NJ(x)ay, where N,(z) is the number of oxygen atoms at height x in the lower level J , and a , is the absorption coefficient. Of this number of absorbed photons the fraction (1 - uD) AZ2/(A2, + &) is re-emitted in all directions in the 6300 A line. Here uD is the

The intensity and flux of radiation will be treated here in number of photons rather than in units of energy. This procedure avoids factors of hv when contributions from absorption or emission at two wavelengths are considered together. The flux at the surface of the sun’must be reduced by a factor (radius of suniradius of Earth’s orbit)2 = 2.15 X

to give ~ 9 - at the Earth.

422

1 1.1. RESONANCE SCATTERING AND FLUORESCENCE 423

fraction of atoms in the 'D term that are collisionally deactivated before they can radiate by a downward transition, and A is the radiative transition probability, with subscripts referring to the upper and lower J values, respectively, of the atomic levels. (Since A,, is negligible, we have ADP = A,, + A,l.)

If the radiation is re-emitted or scattered isotropically by a plane- parallel layer, the photon intensity, from the atmosphere above x,, in the 6300 A line will be

where p = cos 8 and 8 is the angle of emergence of the observed beam from the layer, measured from the normal to the layer., T h e summation extends over J = 2 and J = 1 (A6300 and X6364) in the case of the oxygen atom, as absorptions in each of these lines populate the lD term. The factor l / I p I on the right gives the increased number of atoms in the line of sight for oblique observations, and 11477 results simply from the choice of units forY (photon/cm2 sec sterad). The scattered photon intensity is independent of the angle of incidence of sunlight, 8,, for an optically thin atmosphere.

When %is constant over the width of the line, we find with Eq. (1.54) that

where NJ refers to the population in the Jth level of the ground (") term.

T h e populations are given in terms of the total atomic oxygen density by Eq. (1.7). Bates and Dalgarno [1954a] have pointed out that the Boltzmann factor in Eq. (1.7) has an appreciable influence on the ground-term populations at atmospheric temperatures. For many purposes, however, the accuracy lost by ignoring this factor is not important (see Problem 2, Chapter 1).

In general, we shall use the notation established in Chapter 2. In particular, 0 is measured from the normal on the same side of the plane-parallel atmosphere as the external source of radiation (i.e., the sun). In twilight this is the lower side; in the dayglow, 0 is measured from the upward normal. Hence the absolute value signs around p,

424 1 1 . THEORY OF THE TWILIGHT AND DAY AIRGLOW

Since line strengths may be added to give the multiplet strength, we have from Eq. (1.57),

i 3 2 f 2 2 + & f I 2 = i 3 P f P D * (11.3)

If we now understand gV to be the weighted average of 96300 and 96364, we obtain

where N ( 0 I z ) is the number density of 0 atoms at height z. Alter- natively in Eq. (1 1.4), f p D &/ADP may be replaced with f Z z B,/Gp =

If deactivation is produced by a constituent X with a rate coefficient 5 SfiZ.

sD, we may use

(11.5)

At a time when the shadow of the solid Earth is at height z,, the photon emission in A6300 may thus be written

where

and

(11.6)

(11.7)

(11.8)

Here xo is the height of the actual shadow in the exciting wavelength. We may relate x, (which is easily computed for a given time of observation and thus serves as a convenient independent variable) to z, (which is the theoretically important variable) by Eq. (10.33) for an arbitrary direction of observation. Physically, g is the number of photons that would be scattered per second per unit atom if there were no deactivation, and Jlseq(x,9) is the equivalent number of atoms without deactivation in a square centimeter column above the ~ h a d o w . ~ If TFav and g

We assume throughout that the atmosphere is in a state of quasi-equilibrium such that the incident solar radiation remains constant for periods long compared with the lifetime of an excited state. For A5199 for example, the “twilight” emission actually may continue long after sunset.

1 1.1. RESONANCE SCATTERING A N D FLUORESCENCE 425

are expressed in units of lo6 photons, 4 7 ~ 9 in Eq. ( 1 1.6) will be in rayleighs (see Appendix 11). Table 1 1.1 gives representative values of g.

TABLE 11.1

REPRESENTATIVE VALUES OF g (PHOTON/SEC ATOM)

~~~ ~

Atom Line or band A (A) g Notes

3P2 - ‘DZ 6300 4.5 x 10-10 1

‘D2 - ‘So 5571 1 x 10-11

=Pl - ‘So 2972 6 x

“I121 4s0 3/2 - ,Do 312, 6/2 5199 7.5 x 10-11 2

Op Atmospheric b 1 C ; + X 8 < 8645 5 x 10-10 3

0, Infrared alAo -+ X 3C; 15,803 1.2 x 10-11 4

N a I D, + D2 %/2 - 2p;/2,3/z 5893 0 .888 5

0’ = 0 + V’’ = 1

Atmospheric 0‘ = 0 + 0’’ = 1

C a I I K ZS1p - 2P& 3933 0 . 3 6

Li I

K I

2s1/2 - 2 p y / 2 , 3 / 2 6708 7 . 4 7

,s1/2 - ,p;/, 1699 0 .67 8

N; First Negative B ,Z; + X =Z; 3914 0.20 9

H Lyman m Is 2s - 2p 2PO 1215 1.0 x 10-a 10

H Balmer a 2s 2s - 3p ZPO 6563 2.3 x lo-‘ I I

v’ = 0 4 0’’ = 0

NOTES:

1. For A6300 the g-value is from Chamberlain [1958a]. 2. For [NII2, the computedg-value is due almost entirely to fluorescence; the absorption

rSo - 3. For A8645 of O3 the g-value neglects any degradation of the 0-0 band into the 0-1

transition through Bates’ [ 195463 fluorescent mechanism (see also Chamberlain

4. For the 1 . 5 8 ~ band of 0, the g-value neglects any degradation of the 0-0 band into 0-1 (see note 3). Theg-value is based on Vallance Jones and Harrison’s [I95801 semiempirical calculation of transition probabilities.

is followed by cascading from ,Po to ,Do. From Nicolet [19526].

[ 1954al).

5 . For Na I the g-value is from Chamberlain, Hunten, and Mack [19580]. 6. For Ca I1 the g-value is from Vallance Jones [1958a]. 7. For Li I the g-value is quoted as 8.34 times the value for Na I), t D, by Barbier,

Delannoy, and Weill [1958a].

426 11. THEORY OF THE TWILIGHT AND DAY AIRGLOW

8 .

9.

10.

11.

For K I the g-value is from Lytle and Hunten [1959a]. Although the other line of the doublet, h7665, would otherwise be stronger, it is obliterated by a strong line of the 0, Atmospheric system's A band. The g-value for the A3914 band poses additional complications (see Section 11.2). The value quoted (in photon/sec molecular-ion) is from Bates r194961 and Shull[1950a] and assumes that all excitation occurs from the ground vibrational level (v" = 0) of N;. The A3914 band is responsible in this situation for about 60 percent of the entire First Negative emission. Calculation assumes that total solar Ly a flux is 3 erg/cm2 sec, distributed over an effective width of 0.9 A. Adopted f-value from Allen [1955a]. Calculation assumes that total solar Ly 8 flux is 0.5 erg/cm' sec with an effective width of 0.9 A. Note that scattering is assumed to occur only from ,Po term; f-values and Einstein A's taken from Allen [1955a]. For Ly 8 the g-value is then 7.5 times greater. Any Ha transitions originating from 3 2DD,, 3, because of the degeneracy of this level with 3 2Pa,,, would tend to increase g ( H a ) at the expense of g(Ly 8). (See Bethe and Salpeter [1957a].)

In the case where the shadow cast by the lower atmosphere is not sharply defined, ./cq in Eq. (1 1.6) must include the transmission function, T,, defined by Eq. (10.38). Then if z , ~ is the apparent height of the shadow in the direction of observation,

(1 1.9)

becomes the equivalent number of fully illuminated atoms without deactivation in a vertical column of 1 cm2 cross section. In twilight when deactivation is still important above the shadow height, Eq. (1 1 .8) may be used and the value of zo is unimportant.

When the shadow enters the emitting region, Eq. (11.9) is more appropriate. However, the approximation of a simple screening height, h,, is equivalent to adopting T, = 1 above height zo and T, = 0 below z,, where zo is given in terms of x, and h, by Eq. (10.33). Then Eq. (1 1.9) reduces to Eq. (1 1.8).

Equation (1 1.9) is also applicable to the dayglow, as long as secondary scatterings may be neglected. The transmission function T, must be chosen appropriately, however. In the dayglow T, becomes an attenuation factor exp [- Ty(X)/p,], where p, = cos 8,, 8, is the zenith angle of the sun, and T ~ ( z ) is the vertical optical thickness in the exciting frequency above height x. Of course, if T, is strongly dependent on v over the applicable range of frequency, we must return to Eq. (11.1) and evaluate T,,(z) under the integral.

With the values ofg in Table 11.1 we may readily make some estimates of the upper limit of the emission in [OI] lines to be expected from resonance scattering and fluorescence at a given instant in twilight. Let


us ignore collisional deactivation and take the actual shadow to intersect the line of sight at 110 km. (The height of the shadow of the solid Earth will be somewhat lower, depending on the wavelength of the exciting radiation and the direction of observation.)

Then by Eq. ( 1 1.6) the emission referred to the zenith, ~ 4 ~ 4 , will be less than 310 R for h6300, 7 R for h5577, and 0.42 R for A2972. Deactivation will most probably affect A6300 at this altitude, but the estimate for the other two lines may be close to the correct value. However, these rates of emission are quite low, as we may appreciate by recalling that the twilight Na D emission may be as high as 5000 R in winter, and is usually about 800 R in summer (Section 9.2.2).

T o evaluate Eq. ( I 1.8) we shall assume that the rate coefficient for deactivation, sD, is independent of height. Actually it may vary considerably with height for any particular process. The rate coefficient for a given reaction may be temperature-sensitive, and an even more important variation in sD may result if the deactivation process is a near-resonance collision, as in Eq. (1 1.75). In that case the reaction could also proceed to the left, re-exciting the 'D, level. The effective value of sD would then depend on the probability of the reverse reaction occurring, which would be dependent on the density. In the general case one might thus treat the deactivation probability, N(X I z ) sD(z), as a single function of height.

With sD a constant and N(X I z ) and N ( O I z) expressible in terms of constant scale heights Hx and H,, respectively, about height z,, we define

11 = t( & z - z , ) / H ~ (11.10)

where uo = N(X 1 zo) s ~ / A D ~ . Then Eq. (1 1 .S) becomes

(1 1.1 1)

where b = ( H , - Hx)/Ho 5 1. Whenb = 1 (i.e., H , = O),Eq. (11.11) is indeterminate. But in that case there is no deactivation, and it is clear from Eq. (1 1.8) that

N e s ( Z J = Ho N ( 0 I zo). (11.12)

Equations (I 1.6), (1 1.7), and (1 1.11) represent the formal solution of the twilight intensity for an actual shadow at zo, for isotropic scattering (or fluorescence) by a substance with a constant scale height, and when the deactivation probability follows a constant scale height. For further discussion of the case b = 3, see Section 11.5.1.


11 .I .2. Polarization of Resonance Radiation

Although for some elements the polarization of scattered resonance radiation may be explained with some success by the classical theory of an oscillating dipole, this theory fails in the case of the Na D lines. The situation is analogous to the theory of the Zeeman effect, where one must use the quantum theory for a satisfactory discussion.

A complete and accurate theory of polarization can become most complicated. A complete treatment would include the hyperfine structure of the line, allowance for elliptical polarization of the incident radiation, evaluation of the depolarization due to collisions and a magnetic field, and consideration of secondary scatterings (imprisonment of radiation).

Polarization of resonance radiation is a direct consequence of the Zeeman effect. Hence, depolarization may result when an excited atom experiences a collision that transfers it from one Zeeman state to another. The cross section for such a collision depends, of course, on the gases involved, but from typical cross sections obtained experimentally (Mitchell and Zemansky [1934a, p. 31 11) it appears that atmospheric sodium in the 80 km region will be immune to collisional depolarization. Here we shall neglect secondary scatterings; a t the end of this section we shall discuss their effect briefly.

The theory of polarization of resonance radiation has been treated with the old quantum theory by Van Vleck [1925a] and is summarized by Mitchell and Zemansky [1934a, p. 272 et seq.]. Weisskopf [1931a] has considered the problem from the standpoint of Dirac’s [ 1947~1 theory of radiation. The Weisskopf treatment has been reviewed in detail and extended somewhat by Breit [1933a].

Hamilton [ 1947~1 has used the Dirac-Weisskopf treatment to represent scattered light in terms of the four Stokes parameters. Any radiative- transfer problem (i-e., any situation involving multiple scattering) that deals with polarized radiation must be treated in terms of the Stokes parameters. Chandrasekhar [ 1950a, p. 501 discusses this problem and gives Hamilton’s table (properly normalized and with definitions slightly different from Hamilton’s), which allows the scattering matrix to be calculated readily for a given transition. This table is not applicable, however, when the line has hyperfine structure (hfs) ; the interchange among different hfs levels is not properly accounted for by treating each hyperfine line as due to a resonance transition and then adding the separate intensity components. In this section the coefficients in the scattering matrix are expressed in terms of transition probabilities and can be computed for any given line whose total transition probability, A, is known. We shall consider the incident radiation to be plane polar-


ized or unpolarized and shall not consider the general case of incident radiation that is elliptically polarized, which has no application to the airglow.

If the incident radiation is isotropic and unpolarized and there is no magnetic field, there will be no polarization, as all directions are equivalent. But when the exciting radiation is incident from predominantly one direction, the scattered light will ordinarily be polarized, although in specific cases (such as D l ) there may be no polarization. The presence of a strong external magnetic field will also affect the polarization, as the axis of quantization of the Zeeman states is fixed (relative to the electric vector of the incident light) and this orientation thus determines the Zeeman components that will be absorbed,

For the upper energy levels of the Na D lines, the Zeeman splitting produced by the Earth's magnetic field is small compared with the natural broadening of these levels. Hence we shall consider the polariza-

M; . +2 +I

0 - I - 2

MF = - + I - 0 --I

FIG. I 1.1. Energy levels of the 3s and 3p configurations of Na, showing hyperfine structure for I = 3/2. The Doppler blending of various hyperfine lines into hyperfine groups (Dlo, D,, , D,,, D2*) is discussed in Section 11.3.1 ; these groups are of no importance to the polarization. The right side of the figure shows the Zeeman states of F = 2 and F = 1, and the polarization of the various Zeeman

components of the hyperfine line is indicated below the diagram.

430 11. THEORY OF THE TWILIGHT AND DAY AIRCLOW

tion in the absence of a magnetic field. On the other hand, the hyperfine splitting of levels, due to a nuclear spin with a quantum number I = 3/2, is large compared with the natural broadening, so that the hyperfine structure must be considered in detail (see Fig. 11.1). It is important to note that the polarization with hfs ignored would be equivalent to postulating I = 0 or very great natural broadening. Indeed, the measurement of polarization for a given resonance line offers an experimental means of ascertaining the amount of nuclear spin.

Scattering Perpendicular to Incident Beam.-The geometry of scattering is illustrated in Fig. 11.2. The beam, incident along the x axis, is scattered at the origin and observed along the y axis (perpendicular to the incident beam). The xy plane is called the plane of scattering.

2

JL

SCATTERED LIGHT

LIGHT

FIG. 11.2. Geometry used in the calculation of polarization of resonance

scattering.

We shall denote-by 4 the scattered intensity polarized with the electric vector perpendicular to the plane of scattering (i.e., parallel to the x axis). Similarly, 9,, is polarized in the xy plane, which means parallel to the x axis for scattering along t h e y axis.

Let the incident light with flux ~9~ be continuous (with wavelength) and polarized with the electric vector along the z axis- that is, perpendicular to the plane of scattering. We want to find the

scattered intensities 4 and $ 1 1 in the absence o f a magnetic field. But as the polarization depends on the relative intensities of the Zeeman components, it is nevertheless necessary to choose an axis of quantization for the magnetic quantum number M(= MF), By an extension of the principle of spectroscopic stability, Heisenberg [ 1925~1 pointed out that the polarization without a field should be the same as with a very weak field parallel to the electric vector of the incident light. Breit [1933a] has shown that this way of treating the problem is consistent with the Weisskopf theory.

The scattered intensities of a line are then

(11.13)

1 1.1. RESONANCE SCATTERING A N D FLUORESCENCE 43 1

and

( 1 1.14)

Here ij('S) is the statistical weight of the ground term (taken as 2S in these equations), C is a proportionality constant of no importance to this discussion, and is the total transition probability to all Zeeman states in the lower level with emission of a 7r Zeeman component (electric vector polarized parallel to the magnetic field) from a state F M ' . Similarly, is the probability of a transition emitting a u component (polarized perpendicular to the field). T h e total transition probability is

n (1 1.15) A = A F ' M ' + A C ' M ' ,

which is independent of F' or M . That Eqs. (1 1.13) and (1 1.14) are correct may be seen from the follow-

ing considerations. The number of absorptions along 7r components from sodium in all (lower) states in ?!3,,, to a given upper state F'M' is proportional to the sum of the strengths of these transitions divided by &(%') [compare Eq. (1..57)]. But the sum of the strengths is proportional to the transition probability, as shown by Eq. (1.50), since the statistical weight of a Zeeman state is unity. Of those atoms entering F'M' a fraction AE'M'/A emits 7r components, and the portion APM'/A emits D components. With the incident beam polarized along the magnetic field, the atoms will absorb along 7r components only. Thus Eq. (1 1.13) is proportional to the emission absorbed in 71 components and re-emitted in 7r components. In the same fashion Eq. (1 1.14) represents light absorbed in 7r components followed by emission in CT components. The factor $ enters because, in a direction perpendicular to the field, u components radiate with one half the efficiency of 7r components (relative to their respective transition probabilities). This will be apparent when one considers that circularly polarized light may be represented as a sum of two linearly polarized components aligned perpendicular to one another.

We now define the auxiliary quantities

a(F') = ___ 4&(2S) [ x , ( A E ' M ' ) Z + (2F' 3 + '1 A 2 1 (11.16)

and

432 11 . THEORY OF THE TWILIGHT AND DAY AIRGLOW

We previously noted that the scattered radiation must be unpolarized when the incident radiation is isotropic and unpolarized and in the absence of a field. According to the principle of spectroscopic stability, the polarization of a line is still zero in the presence of a weak magnetic field, as long as the incident radiation remains unpolarized and isotropic. For isotropic, unpolarized radiation the number of absorptions to any state is proportional to A. Thus for the emitted line to be unpolarized when observed perpendicular to the field, we must have

Also, summing Eq. (1 1.15) we obtain

x + A F M ' ) = (2F' + 1) A. MI

(11.18)

(11.19)

With these relations it readily follows that

I,= 2 [a(P') + 215(F')] F, ; 9,, = 2 [a(F') - 2P(F')] FL. (1 1.20) F' FI

Thus the degree of polarization PL(r /2) of light scattered through an angle ~ / 2 , when the incident beam is polarized perpendicular to the scattering plane, is

(11.21)

T o find the polarization of scattered natural light we must add to Eq. (1 1.20) the intensities 3L and Y,, when the incident radiation in Fig. 11.2 is polarized with the electric vector parallel to the y-axis with a flux T%I. Applying Heisenberg's rule, we now take the weak magnetic field also along the y axis. For this component of the scattered light, we find

9, =41, = 2 [a(F') - 2/3(F')] F,I. (1 1.22) F f


The degree of polarization Po(rr/2) when the incident light is unpolarized and observed at 0 = ~ 1 2 , is thus

1 3 z (AC‘M’)Z - j (21’ + 1) (21 + 1) A2

(21‘ + 1) (21 + 1) A2 - F‘& (AZ’M‘)Z ( I 1.23)

F’M‘ - - *

Scattering in a n Arbi t rary Direction.-In the event that the scattered light is observed at some scattering angle 0, measured from the x-axis, the polarization may be computed by means of a scattering matrix (Chandrasekhar [1950a, p. 51]), where the intensities are given by

Here 7~911 and rFl are the incident fluxes polarized parallel and perpendicular, respectively, to the scattering plane.4 The first matrix in Eq. (1 1.24) is of the form appropriate to Rayleigh scattering, and the second matrix applies, of course, to isotropic scattering. Resonance scattering in general is described by a linear combination of these two scattering matrices.

When the incident beam is plane polarized in the perpendicular direction (9 = S1), the polarization is the same at all 0 and is given by Eq. (1 1.21). When the incident light has 9 = 911, the polarization of the scattered intensity depends on 0; along the y-axis the light is unpolarized, and along the x-axis its polarization is opposite to that from SL, so that natural light remains unpolarized when scattered along the x-axis. The general formula for unpolarized incident light observed in direction 0 is < @(F’) sina 0

F Po(@) = 5 [cy(F’) - B(F’) sin2 01 * (1 1.25)

If the incident light is plane polarized in some arbitrary direction, it is necessary to consider also the Stokes parameter U, which can be incorporated into the matrix equation (1 1.24). The intensity components are as given above, although they are no longer parallel and perpendicular to the scattering plane. In the general case of elliptically polarized light with the major axis in an arbitrary direction, the Stokes parameter V should be considered as well. See Chandrasekhar [1950a, p. 25 el seq.].


T o compute the polarization for a particular line from Eq. (1 1.23) or (1 1.25), it is first necessary to obtain APMf in terms of A, for the various i~ Zeeman components. For dipole transitions these values may be computed by application of the intensity rules of Burger, Dorgelo, and O r n ~ t e i n . ~

Polarization of the Sodium D Lines.-When the scattered light is observed along the y-axis, the maximum degree of polarization is obtained if the incident light is plane polarized along the z-axis (see Fig. 11.2). For this arrangement, which is generally used in laboratory measurements, the polarization is given by Eq. (1 1.21). If there were no nuclear spin (I = 0), Pi would be 60 percent for D,. Ellett [1930a] pointed out that the much smaller value observed could perhaps be reconciled with the theory if nuclear spin were included in the calculations. Heydenburg, Larrick, and Ellett [1932a] have computed P , = 18.6 percent for D, with I = 312.

When D, and D, are excited by light in the flux ratio F1 /F2 , the scattered light integrated over all directions will be in the ratio ,F1/2 F,.

See, for example, White [1934a, pp. 161, 2111. The transition probabilities between two particular Zeeman states, AF‘M‘F”M“, may be written, for F’+ F’,

AF’M’F’M’ = &ff2 n

and AF’M‘F’(M’*l) = (F’ 5 M’ + 1) (F’ &f’). a 2

For a transition F’+ F’ + 1 ,

AF’M”F’+1)M’ = b (F’ + M’ + 1) (F’ - M’ + I ) n

and b

2 AF’m(F’+1)(M’*1) = - (F’ f M’ + 1) (F‘ & M‘ + 2).

U

ForF’+F’ - 1, /pM”F’-l’M’ = c(F’ + M’) (F’ - M’) n

and

/JF’M”F’-l”M‘*l’ = E (F’ - 1 M’) (F’ M’). a 2

Here (I, b, and c are constants that can be expressed in terms of A through Eq. (11.15) by summing the Ax’s and A,’s over all lower states F ” W and by considering the ratios of the strengths for the different hfs components, F’ --f F’. The latter may be obtained from the Table in the Appendix of White’s [1934a] book by replacing the quantum numbers S, I., and J with I, J , and F , respectively. For quadrupole radiation, see Rubinowicz and Blaton [1932n].


Since D, is unpolarized its intensity in any direction will be F l / 2 F , times the mean D, intensity. We find from Eq. (11.24) that the mean intensity of a line is

(1 1.26) 4 ‘ 3 = 2 [2 a(F’) - 3 p(F’)] 9,

F’

where rF is the total incident flux in the line. In this manner we find

where P,(D2) is given by Eq. (1 1.21). If the incident light is in the ratio 9,/ S, = 1/2, we find P , (D , + 0,) = 15.1 percent, according to Heydenburg et al. The calculations have assumed throughout that the hfs is well separated, compared with the natural widths of the levels. For further accuracy one can allow for the small but finite overlapping of hfs levels. Breit [1933a] has shown that in this manner the theoretical polarization, P , (D, + Dl) , would be one or two percent higher, which gives excellent agreement with the observations.

Now we consider the problem appropriate to the twilight airglow, viz., polarization of the combined D, and D, lines excited by natural light. When 9!, = Fl = Q F,, Eq. (1 1.24) gives

S(0, I 0) =9,1 +.YI = 2 2 [a(F’) - p(F’)sin2 O] 9,, (11.28) F‘

where the summation is performed over the hyperfine levels of 2P&. Similarly the difference 4 -9,, may be expressed for an arbitrary direction in terms of a and /?. Proceeding as in the derivation of Eq. (1 1.27), we find the following alternate expressions for the degree of polarization:

C /3(F‘) sin2 O

- - POP, I 0) 1 + (S t l /2F2) + ( S 1 / 6 F 2 ) (1 - 2 ctn2 0) P0(D2 1 0) ’

(1 1.29) where the summation is over the hfs of D, only and where P0(D2 I ~ / 2 ) or Po(D, I 0) may be obtained from Eq. (1 1-23) or (1 1-25), respectively.


By way of illustration let us compute the expected polarization for an incident flux ratio 9,/9, = 1.17, which is appropriate for the central intensities of the Fraunhofer lines (Scrimger and Hunten [1956a]). Since P, (D,) = 0.186 according to the calculations of Heydenburg et al. [1932a], we find from Eq. (11.21) that Z/I(F’)/Za(F’) = 0.093, which can be used in the first expression in the set (1 1.29). Alternatively, we can obtain Po(D, I n/2) = 0.1025 from Eq. (1 1.23) and use the second expression in (1 1.29):

sin2 0 15.64 + cos2 0 *

Po@, + D2 I 0) = (11.30)

The maximum polarization occurs for scattering at right angles to the incident beam and is 6.4 percent.

When the sodium abundance is near its winter maximum, the absorption of D-line radiation on the first passage through the atmosphere (see Fig. 11.4) is important. This absorption diminishes D, more than it does D,; hence, 6.4 percent is the maximum polarization that is to be expected from the theory.‘j If we take 9,/ 3, = 2, which is probably near the maximum value to be encountered in the twilight problem, the theoretical polarization normal to the incident beam is reduced to 5.0 percent.

Measurements of the polarization are difficult; not only is the light intensity very low, but the background sunlight provided by Rayleigh scattering is strongly polarized. Measurements by Bricard, Kastler, and Robley [1949a], discussed in Section 9.2.2, seem to be in satisfactory agreement, however, with expectations for resonance scattering.

Secondary scatterings within the sodium layer have been omitted from all the above considerations. With the sodium abundances encountered in the upper atmosphere, multiple scatterings are relatively unimportant compared with primary scatterings and with the differential loss of light between D, and D, on the first (inward) passage through the atmosphere. On the one hand these scatterings would tend to increase the polarization, inasmuch as they tend to enhance D,, especially if the sodium layer is not too optically thick and is aligned perpendicular to the line of sight. But on the other hand, as the radiation field within the layer approaches isotropy, the polarization of outgoing light diminishes accordingly.

Adopting the measured value (Heydenburg e t a / . [1932a])of P , ( D , + DJ = 16.48 percent f o r 9 J F 2 = 1/2, and using Eqs. (1 1.27), (1 1.23), and ( 1 1.29), we obtain a maximum polarization of 7.0 percent for twilight.

11.2. EXCITATION OF N l FIRST NEGATIVE BANDS 437

An accurate treatment of the polarization by radiative-transfer theory can in principle be accomplished. In practice, however, the problem presents enormous difficulties, which have not been overcome. We shall have more to say on this topic in Section 11.3.1.

11.2. Excitation of NZ+ First Negative Bands

11.2.1. Excitation Mechanisms

The negative system of nitrogen arises from the electronic transition B zZ; --f X ",j!. The two excitation processes that have been discussed seriously for twilight are simultaneous ionization and excitation (Saha [ 1 9374 1,

N,(X lZ;) + hu + N:(B 2Zz) + e , (1 1.31)

and resonance scattering' (Wulf and Deming [ 1 9 3 8 4 ,

(1 1.32)

Bates [19493] made a comparative study of the two mechanisms, concluding that resonance scattering was likely to be the more effective by far.

Simultaneous Ionization and Excitation.-The main difficulties with the Saha mechanism were (1) it required more solar radiation in the far ultraviolet than seemed acceptable, and (2) it implied a higher rate of ionization for the F region than seemed consistent with radio observations. We shall review the essential arguments briefly.

Process (11.31) requires 18.7 ev of energy, or photons shortward of 660 A. If the sun were a black body at 6000" K, the flux of quanta at the earth with X < 660 A would be several powers of ten less than the number of ionizations in an atmospheric column required by process (1 1.31). Hence Saha suggested that the solar spectrum in this wavelength region is much brighter than would be expected on the black-body approximation. Bates pointed out that immediately shortward of 910 A (the ionization wavelength for 0 and the position of the Lyman dis-

' The mechanism (1 1.32) may be considered as resonance scattering insofar as the electronic transition is concerned. If we consider individual vibrational transitions, the 0-0 band at A3914 is still in resonance, but the next strongest feature, 0-1 at A4278, arises from fluorescence, since not all the excitation energy is emitted in a single transition.


continuity in the solar spectrum) the solar flux could not be greatly in excess of 6000" K, according to the theory of ion production in the Fl layer (Bates and Massey [1946a]). It thus seemed most unlikely that the flux would be as great as Saha expected at 660 A.

Also, Bates has computed the maximum N; emission that could arise by (1 1.31) even if the ionosphere were due entirely to N, ionization. From a knowledge of the maximum density of electrons and the effective recombination coefficient one can estimate a semiempirical rate of electron production. Bates' procedure was to relate the rate of ionization to the semiempirical rate of electron production at noon at the height of maximum absorption. In this manner it was unnecessary to make any assumption regarding the absorption coefficient or solar flux. Inte- grating over a column along the direction of observation, he found the rate of ionization-and thence the maximum rate of photon emission in the 0-0 band at h3914-during twilight. Because of atmospheric screening in twilight, the ionization, and therefore the emission by (1 1.31), occurs only at very high altitudes.

The height measurements are discussed in Section 10.3.1 ; the main emission arises at apparent heights immediately below 125 km. With excitation by (1 1.31) the screening height may be several hundred km, so that the actual height of emission would be much greater than the apparent height, For this reason the photon emission available from Eq. (1 1.31) turns out to be inadequate to explain the observed intensities (Section 9.2.1).

These arguments are now not so apodictic as they once seemed, because of the likelihood that the upper atmosphere has a substantial production rate of ions that is rather effectively hidden from radio observations (Bates [1951a]). The solar flux from coronal emission lines, rather than continuous radiation, may be the chief ionizing radiation in the F region. This emission could be quite effective in ionizing N, without producing more Of than is acceptable, And since N,+ has a high recombination coefficient, these ions could still form only a minority of the ionization density and not contribute to the effective recombination rate determined from radio evidence.

Nevertheless, the Saha mechanism may be discarded, since Bates has shown that with the ionization rate of N, required to explain the data, the ionospheric abundance of N,+ would be sufficient to make process (1 1.32) dominant anyway.

Resonance Scattering.-For the Wulf-Deming hypothesis of resonance scattering by pre-existing NJ ions, we can use the theory of Section 1 1.1.1 with slight modifications for a molecule instead of an atom. Ordinarily

11 -2. EXCITATION OF N l FIRST NEGATIVE BANDS 439

in the upper atmosphere, all molecules in the ground electronic state will be also in the ground vibrational state (see Section 1.1.3). But if the gas is excited with a large flux at extremely low pressure, a molecule may remain in the ground electronic state for a short time compared with the time between vibrational collisions (i.e., collisions that deactivate an excited vibrational level). In this case the higher v” levels (in the ground electronic state) may attain appreciable populations after the gas has been excited for a time. These populations and, indeed, the entire excitation problem must be handled by a statistical-equilibrium approach (see introductory remarks to Section 1.1). Conditions of this sort may obtain in high, sunlit aurorae (Section 5.2.8); the limiting case of no collisional redistribution in the ground state has been treated by Bates [1949a].

For the twilight emission, collisions may be sufficiently frequent to maintain the X 2,Z; molecules in v” = 0. In this case the photon emission per second per N; ion in the v’ - v” band is, from Eq. (1 1.7),

(11.33)

where f,,, is the f-value for absorption from v” = 0 to v’ in the upper state. By means of Eqs. (1.57) and (1.70) we may write fovt w fxB q(v’O), wherefxB applies to the entire band system (i.e., all upper vibrational levels) and q(v’0) is the Franck-Condon factor. For this relation we neglect the small variation of f o v , with frequency among different bands of a progression and recall that L’,! q(v’0) = 1.

Similarly, the A’s can be written in terms of Franck-Condon factors by Eqs. (1 -50) and (1.70). Thus for the v’ - ZI” transition we find*

(11.34)

The relevant q’s have been computed by Bates [1949a, 1952~1 and Jarmain, Fraser, and Nicholls [1953a] and measured in the laboratory by Wallace and Nicholls [1955a]. Bates [19493] computed f X B w 0.04 and estimated this to be correct within a factor of about three. A more elaborate computation by Shull [1950a] gave f X B = 0.12. This value corresponds to an electronic transition probability of ABx = 5 x lo7 sec-l.

Bates formulated the calculation of g in somewhat different notation from that used here. In particular, his quantity G is equivalent to (64nd/3hcS)R:, where Re is the matrix element of Eq. (1.68).


In the computation of ~ 2 % particular care is necessary, since the solar spectrum contains numerous strong absorption lines in the violet and blue regions. Thus there is more incident flux in the wavelengths of some rotational lines than in others. Bates evaluated T by weighting the solar flux according to a rotational temperature for the ground state of 273” K [cf. Eq. (1 1.39)]. The totalg-value for the entire First Negative system [obtained by summing Eq. (11.34) over v” and v’, where we must, of course, include T%,, under the summation] is about 0.33 photon/N,+-ion sec. About 60 percent of these photons are in the 0-0 band, h3914, whose g-value is thus given in Table 11.1.

If the zenith emission rate, ~ 4 ~ 2 , in A3914 is of the order of 1 kilorayleigh (Section 9.2. l), the equivalent number of N,+ ions, from Eq. (11.6), is Neq * 5 x lo9 ion/cm2 (column).

It is not known whether the N,+ twilight curve (intensity versus time) has a plateau, where the intensity is approximately constant for a while, as the photographic spectra alone are not sufficiently accurate photometrically. But if the N,+ ions were actually present only above 100 km or so and decreased above that point with a scale height of, say, 25 km, the Nes estimated above would imply a maximum N,+ density of 2 x lo3 ion/cm3. In the next section we discuss the origin of N,+ ions and the actual height of emission.

11.2.2. The Production of NZ+ in the Ionosphere

There seems little doubt that resonance scattering, as discussed above, is the mechanism for N,+ excitation. As shown in Table 11.1 every fully illuminated N,+ ion will scatter one A3914 photon on the average of every 5 seconds. For any indirect mechanism to dominate over resonance scattering it would have to destroy and reform the ions with even greater efficiency. The particular alternative of simultaneous ionization-excitation of N, must be rejected on this basis.

On the other hand, resonance scattering by pre-existing N,+ ions also poses some problems. Bates [19498,19543] has shown that the upper limit placed on the N,+ abundance in the F region (by the fact that A3914 is too weak to be observed when the actual shadow in the violet is above 200 km or so) is so small as to contribute a negligible amount to the F-layer ionization in late twilight. Still, the rate of ionization may be sufficient for N,+ to contribute to the net ionization of the F layers earlier in the twilight and daytime, since N,+ will recombine rapidly after sunset in the ionizing wavelengths (see below). The situation for the F region is somewhat confused, as the photochemistry of atmospheric nitrogen is still not adequately understood (see Bates [1952a, 195481). In

11.2. EXCITATION OF N: FIRST NEGATIVE BANDS 44 1

particular, the degree of dissociation of nitrogen obviously has an important bearing on the ionization problem, as well as on the [NI],, twilight and on sunlit and normal aurorae. Alternatively, the study of these spectra may help clarify the question of dissociation at various altitudes.

In the E region solar x-radiation probably produces some ionization of N,, although not enough to explain the E layer itself (Nicolet [1952a]). If the height measurements (Section 10.3.1) are interpreted in terms of a screening height corresponding to violet sunlight (with the N; abundance remaining constant throughout twilight) the emission appears to arise from the upper E region. I t has been generally supposed, therefore, that x-ray ionization in the E region accounts for the N: seen in twilight, but this hypothesis is not without difficulty. Bates [1950b] has suggested on theoretical grounds that dissociative recombination,

N,+ + e + N * + N*, ( 1 1.35)

should proceed quite rapidly. Also, laboratory measurements by Biondi [ 195 I a], Faire, Fundingsland, and Aden [ 1954a1, and Bialecke and Dougal [1958a, b] do indeed indicate a rate coefficient of mrec - lop6 cm3/sec at room temperature (and somewhat lower for F-region temperatures). The lifetime for N: is of the order of l/arec Ne. Even if mreC in the ionosphere is only lo-' cm3/sec, we would expect a considerable loss of N; ions during the night. However, the study of spectrograms by Swings and Nicolet [ 1949al revealed remarkably little difference between morning and evening twilights. Hence for the emission to come from the E region either the recombination coefficient is greatly overestimated or N,'. is formed by some process throughout the night. In the latter case one possibility is particle bombardment, suggested also by the enhanced twilight emission during magnetic activity.

Another possibility is that N,'. emission actually arises from the F region, being produced there by photoionization and then scattering of violet light. Since the ionizing radiation has a much higher twilight shadow than violet light, it would govern the actual height of emission. The N; ions, with this interpretation, would approach daytime equilibrium shortly after being first illuminated in the far ultraviolet in the morning, and would disappear soon after the shadow appeared in the evening.

These two possibilities have been examined by Chamberlain and Sagan [1960a]. Each seems feasible but the uncertainty in the solar ionizing flux in He 11, A304 made it impossible to reach a final decision. Permanent particle bombardment might be attributed to leakage from the Van Allen radiation belt (Section 8.2.1).


11.2.3. Rotational Structure

An interpretation of the NJ twilight in terms of ions in the F, rather than the E, region seems plausible although the arguments used are not conclusive, and confirmation (or rejection) by accurate photometry is needed. Observations should also demonstrate that excitation is by resonance scattering. Although there seems little reason to doubt this mechanism in view of Bates’ arguments (Section 11.2. l), an experimental verification is possible and should, of course, be made.

Swings [1948a, 1949~1 has proposed that the rotational structure of the emission band should show the effect of absorption lines in the exciting Fraunhofer spectrum, since no rotational redistribution is expected in the excited electronic state. A distorted profile appears, for example, in the CN bands in cometary ~ p e c t r a . ~ Bates [1949b] also allowed for the irregular flux distribution in computing the g-value of N,+ (cf. Table 11.1). Here we shall outline the computation for the profile of a branch of a First Negative band, v’ - v” , for infinite resolving power. In the event that the spectral resolution blurs the rotational structure, the computed profile must be modified according to the discussion of Section 12.2.

The rotational structure for one of these bands (“Z;. -+ ”:) under fairly high resolution is shown in Fig. 5.10. The reader may refer to Herzberg [1950a, p. 2471 for details of the band structure. We shall ignore the small spin doubling and consider the structure as composed of simple P and R branches. Let the initial (lower) rotational level of the absorption be K , the upper level be K’, and the final (lower) level of the emission be K“. With the N,+ population almost exclusively in the ground vibrational level and collisions in the excited state negligible, the total band intensity,.Y, is given by Eq. (1 1.6), where g is obtained from Eq. ( 1 1.33) or (1 1.34). The fraction of this intensity in a particular line is then

m

~ ( K J K J ) ) [q fK0.K.v’ j, NK (z) dz] A K ’ ~ ’ . K”v”

, (11.36)

where %depends on the upward transition from K , v = 0 to K’, v‘. The f-values and transition probabilities may be written in terms of

of strengths (Sections 1.3.2 and 1.3.3). Recalling that the rotational line strength, S(K’K”), is that part of the square of the matrix element

- - 9 ~ a v f o , , ~ , , A,.,..

*Additional comparisons of cometary spectra with those of the airglow and aurora have been made by Barbier [1952c].

11.2. EXCITATION OF N$ FIRST NEGATIVE BANDS 443

that depends on the K’s as in Eq. (1.80), we obtain for an isothermal atmosphere,

Z [3f NK S(K’K”) S(K’K”)/GK GK,] . (11.37)

The relative populations in the Kth level, N,/N, depend on the temperature by Eq. (1.7), and are computed with the energy relation (1.84) for the ground state.

The level K’ may be excited by incident radiation in both the R branch from K = K’ - 1 and the P branch from K = K’ + 1. We shall denote the incident radiation in these two frequencies by F g , and Fg,, respectively. The line strengths may be written S,(K’K) =

( K + l)Gfc/(2K + 1) and S,(K’K) = K sK/(2K + I ) , where the statistical weight o must include the effect of nuclear spin I, to give the alternation of intensities (in the ratio 2 : 1 for nitrogen) between even and odd rotational lines (Herzberg, [ 1950a, pp. 250, 1331). We thus obtain for a line in the R branch,

$(K’K’’) - fc -

.a 9 a v N

4R(K’, K’ - 1) 9

( 1 1.38) K ’ f l 1 K‘ K’

2K‘+3 2K’+ 1 ’ + 9;. N K ” ~ = - [.Fg, NKw1 2K, - I 1 .Fa“N

With this equation one may compute the fractional intensity in any R line for an assumed rotational temperature in the ground state.

For investigations of the N: profiles, only relative intensities are required and the value of &v is unimportant. However, if we add to this equation the intensity appearing in emission in the P branch from level K‘ and then sum over all K’, we obtain an expression for the weighted incident flux, which was used in the discussion of absolute intensities [see Eq. (1 1-33)]:

It may be verified that when Fw is independent of wavelength, it is equal to Fa”. It is generally more convenient when FK. is independent of wavelength, however, to use an approximate equation that considers the relative populations in the upper (K’) levels to be the same as in the lower ( K ) levels (see the discussion at the end of Section 1.4.2). But if there were strictly no change in the angular momentum upon


excitation, the alternation in emission intensities would be the converse of the normal pattern (in which lines of even K or K” and odd K’ are the stronger-see Problem 3).

11.3. Photon Scattering by Atmospheric Sodium

11.3.1. Introduction: The Physical Theory a n d Approximations

There is little doubt that resonance scattering of sunlight is the source of the twilight airglow in the D lines (Section 9.2.2); the atomic transitions are shown in Fig. 11.1). This excitation mechanism makes it possible to obtain extensive information on atmospheric sodium, even though it is a very minor constituent.

It is now possible to do rather accurate photometry on the sodium airglow and the subject thus demands a detailed theory relating Na abundance to the D-line brightness. The amount of sodium in the upper atmosphere is sometimes large enough that secondary scatterings within the sodium “layer” should be considered in the theory for the D, + D, brightness. If each photon underwent only one scattering, the D,/D, ratio (averaged over all scattering directions) would be just twice the ratio at the bottom of the Fraunhofer lines. But additional scatterings also modify the ratio ; hence measurements of the ratio can be used to derive the abundance only if an accurate theory is available.

In the radiative-transfer theory, we shall treat the D lines as though they arose from resonance transitions, were scattered coherently and isotropically, and were unpolarized. None of these four conditions is strictly true for D,; and even D, is not actually a resonance transition when hyperfine structure is considered,1° nor is it scattered coherently, since the atom can emit a slightly different frequency than it absorbs. We shall examine the errors introduced by these approximations and indicate the corrections required for them.

Resonance Scattering.-The transitions involved in the D lines, with hfs of the various levels considered, are shown in Fig. 1 1.1. The separation of the hyperfine components in the ground level is considerably

lo We shall use the term resonance scattering to imply that exactly the same “line” or component is emitted as is absorbed, so that (in the absence of deactivation) no radiant energy is lost or gained in the process in any “line.” However, when an upper level can be populated by absorptions in more than one component and then emits in these components in the same proportion as it absorbed, the net result is still entirely equivalent to strict resonance scattering. Departures from this situation are discussed below.

20

INTENSITY 4

I5

10

4co.-

300'

(KELVIN: ZCO' TEMPERATURE

* 100"-

a DOPPLER HALF-INTENSITY WIDTt L---

F4 0.33. I03CM-'=NATURAL HALF-INTENSITY WIDTI APPROACH 2oow

PODU/SEC , ,

SODIUM RESONANCE LINE SHAPES AT DIFFERENT TEMPERATURES

FIG. 11.3. Line profiles for DI and D, emission at various temperatures. The inserts show the Doppler half-intensity widths, the natural half-intensity width, and the broadening due to winds. See Section 11.3.3 for discussion.

From Chamberlain, Hunten, and Mack [ 1958~1; courtesy Pergamon Press.


more than in the upper, so that each D line is divided into two hyperfine groups of fine structure lines. These groups, labeled Din, Dlb, D2,, , and DZb, are important in the airglow, as Doppler broadening at the temperature of the sodium layer (probably 200-250” K) effectively blends together the hfs lines within one group, without much overlapping of the profiles between different groups. The situation is illustrated in Fig. 11.3.

The intensity of a single hfs component scattered isotropically is obtained in the same manner as Eqs. (11.6), (11.7), and (11.9), where we shall now neglect collisional deactivation. For single scattering and an incident flux re that is constant over at least the width of one hfs component, we have, for the scattered intensity of a component,

We use unprimed symbols for initial lower levels, single primes for upper levels, and double primes for final lower levels; and ..P& is the equivalent number of fully illuminated sodium atoms in a vertical square-centimeter column. If the incident radiation is also constant for all hfs components in one line, Eq. (1 1.40) when summed over F“ and then F’ gives

(11.41)

which is the simple expression for a resonance line. Thus for single scattering of sunlight, the hyperfine structure may be ignored.

Suppose, however, that the incident radiation, n- 3$,F, is dependent on F (the initial hfs level), but not on F‘. This is the situation in the twilight problem, where the hyperfine groups described above depend only on the lower hyperfine levels. We shall use the subscript a for F or F” = 2 and b for F or F” = 1. The scattered intensity in a hyperfine group (J’ + F”) is then given by

( 1 1.42) where the strength S is related to A and f by Eqs. (1.50) and (1.57). This equation would be in the correct form for pure resonance scattering if the summation were replaced with r 3$... When F(, = F b this is, in fact, the case, and Eq. (1 1.42) becomes Eq. (1 1.41) when the former is summed over F“.

11.3. PHOTON SCATTERING BY ATMOSPHERIC SODIUM 447

When Fa f Fb and Eq. (1 1.42) is summed over F”, we obtain an expression for the total intensity in the line J‘+ J”:

Hence the total J’+ J” intensity after the first scattering is given correctly by treating the hyperfine groups separately as though they each involved pure resonance scattering. I t is to be emphasized, however, that the correct relative intensities in groups a and b [given correctly by Eq. (1 1.42)] will not in general be given accurately by the resonance- line approximation. Further, it is necessary that the correct values of .%, and Fb be known in order for the J’ -+ J“ (total line) intensity to be correctly computed; an average of

Here we have discussed only single scattering of an incident parallel beam of light. But the implications for secondary scattering in twilight are now clear. The Fraunhofer line is nearly the same intensity for a and b components and the extinction on the first passage through the sodium layer can be expressed accurately in any wavelength by an exponential absorption law. Thus the flux incident on the observed scattering layer, n q , can be represented properly. The total line intensity after the first scattering is then given correctly by a resonance-line treatment, but the computed relative intensities in a and b components will be incorrect. The total intensity of light scattered a second time will therefore not be accurately represented by the resonance approximation.

In the twilight airglow, however, the error thus introduced is small. Secondary and higher order scatterings are probably never responsible for more than 20 percent of the total intensity. And sample calculations’l indicate that the intensity of that part of the light scattered twice is easily correct to within 10 percent, by the resonance treatment. The total error involved is thus ordinarily less than 2 percent.

+ 3 will not suffice.

Coherent Scattering.-The transfer theory is developed for radiation at a particular frequency v. We postulate monochromatic radiative equilibrium: in the scattering process precisely the same v is re-emitted as was absorbed. While this may be nearly correct in the atom’s frame of reference12 it is not true in the observer’s frame if the photon is

l1 See Problem 2, which contains an extreme example. When Pa m Pb appreciable

Noncoherent scattering is also possible in this frame, but since the natural broadening errors do no enter until the third scattering of a photon.

of the levels is small compared with Doppler broadening, we may neglect it.

448 11. THEORY OF THE T W I L I G H T AND DAY AIRGLOW

scattered in a direction other than its incident direction. Donahue has made computations on this effect and finds that although it is usually negligible, a small error may be introduced into the multiple-scattering component when the profile becomes strongly self-reversed (see Fig. 11.6).

Isotropic Scattering.-The assumption that light is scattered isotropically in the sodium layer simplifies the radiative-transfer theory enormously and allows the solution to be expressed in terms of certain X- and Y-functions already tabulated. The D, line is, in fact, scattered isotropically, but D, is scattered according to a phase function13 p ( D , 1 O), given by Eq. (1 1.28) and normalized with Eq. (1 1.26) so that J p dS2/4rr = 1. We find

Z [ol(F’) - B(F’) sin2 01 = 0.967 (1 + 0.102 C O S ~ @), (1 1.44) F P(Q I 0) = g M F ’ ) - $ B(F’11

where the numerical values are taken from the discussion above Eq. (1 1.30). Conservative isotropic scattering is, of course, characterized by p ( 0 ) = 1. Even if the angular dependence is neglected altogether, the error is not very serious.

Consider first the secondary scatterings. Here the incident radiation (i.e., the light that has already experienced one scattering) is most intense in directions nearly parallel to the plane of the layer and is about equally important in all azimuths. If one observes near the zenith (0 -x/2), the secondary component will be less than 4 percent different from what would be expected with isotropic scattering. For observations near the horizon the phase function is even less important. So long as the secondary component is a relatively small portion of the total, isotropic scattering is quite suitable as a basis for computing the radiative-transfer effects.

The phase function is of slightly greater importance to the primary scatterings and should be considered in accurate zenith-horizon comparisons for height measurements and for D,/D, ratios. Suppose horizon observations are made in the azimuth of the sun at a zenith distance 5 = 75”. From Eq. (10.3) the angle of emergence, for a scattering height of 85 km, is 0 = 7 2 3 . If the observations are made at a solar depression angle of p = 63, the scattering angle is 0 = 90 - 0 + p = 24”. For

l3 There should be no confusion between the phase function p ( 0 ) (see Section 2.2) and the degree of polarization denoted by P ( 0 ) (Section 11.1.2).


a zenith observation at the same /3, we have 0 = 963. Thus the ratio of zenith and horizon phase functions for D, is

p z 0.968 - 0.92. -

PH 1.049 (1 1.45)

For accurate zenith-horizon comparisons, the D, intensities, computed from the transfer theory should be corrected for the phase function before they are added to D, intensities. Since secondary scatterings account for a small portion of the total, one might apply the correction deduced for the primary component to the total computed D, intensity.

For observations of the D,/D, ratio the phase function is readily computed for a given scattering angle and multiplied times the theoretical ratios. When long photographic exposures are required to observe the resolved D, and D, lines, 0 will change during the twilight and an average value has to be estimated. When the spectrograph is pointed at a constant zenith angle, 0 changes only as /3 (angle of solar depression) changes, which is very little during the usable twilight. However, the ratio is more sensitive to /3 than to 0 and it is better to make observations by varying the zenith angle through twilight, so that the Earth's shadows and the line of sight intersect at a constant height. This procedure also allows longer exposures with a minimum of background scattered light (if the height is chosen appropriately).

The angle 0 might vary from, say, 90 degrees to 25 degrees, with the smaller values of 0 carrying greater weight. Then p would vary between 0.97 to 1.05. The net correction factor under these circumstances will therefore be very near unity,14 and can safely be neglected.

Polarization.-In the above discussion I have used a phase function, p ( 0 ) , that describes the angular distribution of scattered natural light. The total intensity in a particular line can be described adequately by such a function for the first or primary scattering. Further, we have seen that the effect of the anisotropic phase function on secondary scatterings will have little bearing on the total emergent intensities.

Nevertheless, if one were to extend the theory to allow for p ( 0 ) f 1, it would be desirable to allow for polarization as well. The anisotropy of the phase function is a direct consequence of the existence of Zeeman states, which scatter 7r and (T polarization components in different

lo The phase function p(D, I 0) = 1 for cos2 0 = or 0 = 54"44'. For a height of = 6?5, and an observation in the azimuth of the sun, the corresponding zenith 85 km,

distance is 5 = 42:s.


fashions. Therefore, after the primary scattering, radiation will be partially polarized, as discussed in detail earlier in the chapter.

T o describe the secondary scatterings accurately we should use a scattering matrix, which treats the different polarization components separately. The scattering matrix would be composed actually of two matrices, one representing the isotropic component and the other the Rayleigh-scattering component, as in Eq. (1 1.24). (However, the matrices would have to be enlarged to three-by-three form to include the scattering of the Stokes parameter U.)

This is the manner in which the problem of Rayleigh scattering in the daytime sky has been treated by Chandrasekhar [1950a]; this problem forms the basis of photometric corrections for airglow photometry (see Section 2.5.2). However, the treatment of resonance scattering by the transfer equation poses difficulties not encountered in Rayleigh or isotropic scattering alone. Chandrasekhar [ 19.50a, p. 2851 has shown that the failure of the so-called “characteristic equation” to factorize in the general case (as it does for Rayleigh scattering) prevents the exact solution in closed form from being obtained.

11.3.2. Scattered Intensity of a Resonance Line from the Theory of Radiative Transfer for a Plane-Parallel Atmosphere

In the twilight airglow, extinction of sodium radiation at the first, incident passage of sunlight through the high atmosphere and again at the second, emergent passage, where the sodium layer is observed, is the most important modification that must be made to the theory of single scattering in Section 11.1.1. That resonance extinction might be important was mentioned in the work of Bricard and Kastler [1944a], and detailed calculations have been made by Donahue, Resnick, and Stull [1955a, 1956al and Blamont, Donahue, and Stull [1958a] for a spherical atmosphere and by Hunten [1956c] for a plane-parallel atmosphere and a variety of sodium abundances.

Secondary and higher-order scatterings have been considered by Galperin [1956a, b] , who was concerned with the twilight D,/D, ratio only, and in a series of papers entitled Resonance Scattering by Atmos- pheric Sodium.15 The discussion in this and the next two sections will, for the most part, follow the latter papers, which for brevity will be referenced as “Paper I,” “Paper 11,” etc.

l5 Paper, I, Chamberlain [1956a]; 11, Chamberlain and Negaard [1956a]; 111, Hunten [1956a]; IV, Chamberlain, Hunten, and Mack [1958a]; l’, Brandt and Chamberlain [1958a]; VI, Brandt [1958a]; VII, Rundle, Hunten, and Chamberlain [1960a]; VIII Hunten [1960a].

1 1.3. PHOTON SCATTERING BY ATMOSPHERIC SODIUM 45 1

Theory for Zero Ground Reflection.-If monochromatic radiation of frequency v is incident in a parallel beam on a plane-parallel atmosphere wherein radiation is scattered isotropically, there is no difficulty in obtaining the exact solution for the emergent intensity 1,. Therefore we approximate the airglow geometry by Fig. 11.4, and consider the

0 m

I I I

FIG. 1 1.4. Idealized atmospheric layers. The dashed lines show plane-parallel layers I , 11, and 111 , which represent an approximation to the spherical atmosphere.

From Chamberlain [ 1956al; courtesy Pergamon Press.

emitting layers to be plane parallel. The departures from a plane atmosphere become important only for angles of solar depression, ,8, of less than 3 or 4 degrees, so that the theory is appropriate for the entire range of ,8 ordinarily observed from the ground.

In the theory the radiation scattered out of the beam in layer I (Fig. 11.4) is presumed lost. It can be shown that the scattered radiation from layer I makes a negligible contribution to the incident radiation at layer I11 for all but very small values of 8, where the theory is inaccurate anyway (Paper I).

The exact solution for the plane-parallel atmosphere is given by Eq. (2.50) and Eq. (2.51). For twilight, the first of these equations is appropriate. Writing T F ~ ) as the flux incident on layer 111, we have, for conservative scattering and no ground reflection,

If we let TE be the flux outside the Earth’s atmosphere at frequency Y

452 11 , THEORY OF THE TWILIGHT A N D DAY AIRGLOW

in the Fraunhofer spectrum, the incident flux on layer I11 is obtained from

(1 1.47)

For a line broadened by thermal motions (Section 1.1.4)’ the optical

= 9 Y e-zpl/% .

thickness of the atmosphere in frequency u is

T , = T~ exp (- x2),

where - y o ) x =

y o lJ

(1 1.48)

(1 1.49)

and the most probable velocity U is given by Eq. (1.4). At the line center 70 - - .&,, where 41; is the number of sodium atoms in a vertical square- centimeter column in the lower level, F, of the line. The absorption coefficient at the line center is obtained from Eq. (1.12):

c nez

T mc (Yo = ~ d- -fFF.

Writing the scattering function from Eq. (2.46) as

( 1 1.50)

(where X and Y are functions of 7”) and integrating Eq. (11.46) over the entire spectrum, we obtain

For an adopted set of parameters p, p,,, and ro, the integrand may be computed for various values of x and the integral evaluated numerically. By changing T~ and repeating the calculations, one can obtain a set of points for a given pair of directions. The numerical computations from Paper IV for several p and po, for the incident flux in the Fraunhofer D, line and for T = 200” K are given in Table 11.2.

It is also possible, however, to obtain an analytic solution to Eq. (1 1.52) by expanding the integrand with Taylor’s series in r, about an arbitrary point T, = a (Paper V). Since S(T, = 0) 3 0, the expansion can be written in the form

S”‘(u) + ...( 11.53) T,”- 3 U T : + 3U2T, 6

1 1.3. PHOTON SCATTERING BY ATMOSPHERIC SODIUM 453

Then defining 2 "

d n ( w ) = z/n Jo exp (-we-$) ecnX2 dx, (1 1.54)

we find from Eq. (1 1.52),

where S'(T") = ~ S ( T ~ ) / ~ T , . A simplified expression for small values of ro may be obtained by

discarding terms in S"'(a) and higher order in Eqs. (1 1.53) and (1 1.55). Then with S'(a) in Eq. (1 1.55) expressed in terms of S"(a) and S(a), the intensity is

[$ap (3) --al ($j]l . (11.56) + sf'(: To PO

The value of a is still arbitrary; if we set

the intensity at small T~ becomes

( 1 1.57)

(1 1.58)

Since &'1(70/p0) = exp (- ~ ~ / . \ / 2 p ~ ) at small 70 (Paper 111), Eq. ( I 1.58) may be written

This expression is analogous to that for monochromatic light [Eq. ( 1 1.52)] with an effective optical thickness ~ ~ p p = rO/2/2. Hunten (Paper 111) first showed that for small optical thicknesses, one might use this effective value Tere in the monochromatic intensity formula and thereby avoid the integration over frequency ; the derivation from the general formula


was first given in Paper V. It is a useful relation for computing small corrections, such as the effect of a finite ground albedo in twilight. The factor 6 Uu,/c in Eq. (11.59) is the effective line width.

The above equations may be simplified further and reduced to the equation for single scattering in Section 11.1.1 by using the asymptotic relations, X * -+ 1 and Y* --+ exp (- 7,/p0), as T , -+ 0.

For purposes of evaluating the general series (1 1.55), a = 7,/3 was found empirically to be a good working value over the range of T~ of interest. Consequently in Paper VI Brandt has tabulated not only the gn(7 , /po ) functions but some auxiliary functions to speed the solution of Eq. (1 1.55) for a = ~ , / 3 . I t is also shown in Paper VI how 5" and S" may be obtained with the aid of tabulated functions. When S"' is required it is best computed simply by numerical differentiation of S". Thus all the functions necessary for the analytic evaluation of the scattered intensity are available, including a number of X * and Y* functions for small 7,, which were published in Papers V and VI and serve to supplement those of Chandrasekhar and Elbert [ 1952~1.

TABLE 11.2

INTENSITY FOR A SINGLE DOPPLER COMPONENT^

Zenith ( p = 1.0)

CLO \ 0.04 0.08 0.12 0.16 0.32

0.04 0.701 0.06 0.940 0.08 1.099 0.10 1.210 0.12 1.293 0.15 1.383

0.694 1.110 1.447 1.722 1.944 2.202

0.612 0.549 0.447 1.062 0.979 0.765 1.499 1.442 1.147 1.887 1.893 1.589 2.226 2.314 2.071 2.649 2.869 2.821

Horizon ( p = 0.3)

0.04 0.685 0.671 0.591 0.530 0.433 0.06 0.916 1.061 1.010 0.928 0.725 0.08 1.068 1.381 1.411 1.349 1.069 0.10 1.175 1.636 1.765 1.753 1.452 0.12 1.255 1.843 2.073 2.127 1.862 0.15 1.341 2.083 2.456 2.618 2.487

Computed from Eq. (1 1.52) for T = 200" K and rl = 0.0590. The table gives values of in kilorayleighs.


Discussion of Results.-Table 1 1.2 gives numerically computed values of ~ 4 x 9 for a single Doppler-broadened line at 200” K. The solar flux adopted for these calculations is 7rz= r, TZ, where = T x 205 quanta/cm2 sec sec-l is the flux in the continuum near the D lines (Minnaert [1953u, Table 11); and the central intensity of the broad Fraunhofer- D, line, relative- to the continuum, is r1 = 0.0590 (Scrimger and Hunten [1957u]; for other measures see the same authors [1955u, 1956~1, Priester [1953u], and Shane [1941a]).

T o derive the intensity for a line with an effective temper- atureI6 Tefr but with the same T ~ ,

the values read from Table 11.2 should be multiplied by (Tm/ 200)’’*. For a line excited with the Fraunhofer D, residual intensity, the values in the table should be multiplied by rz/rl = 0.0506j0.0590 = 0.858 (Scrimger and Hunten [1957u]). The values of p4z-9 are rather insensitive to p ; hence, one set of computations for use near the zenith ( p = 1) and one for near the horizon ( p = 0.3) are given.

5 (optical depth at centre of a line cmponen t )

FIG. 11.5. Absolute horizon intensity of a single hyperfine component of the Fraunhofer D, line versus the optical depth at the center of the component for /3 = 6 3 . See the text for discussion. From Brandt [ 1958~1; courtesy Pergamon Press.

The dependence of the line intensity on T~ is illustrated in Fig. 11.5, where the absolute values of.9 pertain to T = 200” K and excitation by the residual intensity in the solar D, line, as in Table 11.2. The points represent values computed from the analytic integration. If there were no extinction on the first passage and only single scattering at layer 111, the intensity would be represented in Fig. 11.5 by the straight line

70 = 43.3 To. (11.60)

The numerical value applies for T = 200” K and for 47r9 in kilo- ray1eighs.l’

G UYo ~ 4 x 4 = r , x .C C

An “effective temperature” for two close hyperfine components is discussed in the

In this approximation 9 does not depend on T; although U = (2kT/M)’12, T@ varies following section.

as T-’1*. Hence ~ 4 x 4 varies only with abundance -+> in the lower hyperfine level.


Figure 11.6 shows how the profile for a single resonance line can become distorted by multiple scattering and extinction in the sodium layer. The radiative-transfer profile was computed for ~ ~ / p ~ = 0.8, and it can be seen that self-reversal (a minimum superimposed on the profile

D

c b - yo) ” ’ ygu FIG. 11.6. Comparison of a normal profile for Doppler broadening with the distorted profile of a resonance line for T,, = 0.08, = 0.10, and p = 0.3 computed from Eqs. ( 1 1.46) and ( 1 1.47) and fitted to the Doppler profile asymptotically

at large x .

maximum) is just beginning to show. The difference in area under the two curves gives the net loss of radiation scattered toward the observer and is related to the departures of the curve in Figure 11.5 from the linear relation of Eq. (1 1.60).

Effect of Ground Reflection.-When the ground has an albedo h, we may express the observed intensity l v ( O I + p ; Ao) in terms of the intensity l v ( O 1 + p ; 0) given by Eq. (1 1.46) for no ground reflection. The twilight illumination of the sky in sodium light is highly nonuniform, but since the albedo corrections are small, we may obtain approximate values for early twilight on the basis of a plane-parallel sodium layer


illuminated uniformly by sunlight. The solution (Paper I ) is obtained in a manner similar to that given in Section 2.5.1 and is

where s(p) is given by Eq. (2.53) and S by Eq. (2.58). The corrections are always small in the twilight problem, and the intensity ratio in Eq. (1 1.61) may be evaluated with Hunten's approximation (Paper 111), at reif = ro/l/z. It will then be nearly equivalent to the accurate correction factor for the integrated intensity of a line with optical thickness T~ at the line center. Results for A,, = 0.15 (applicable to average ground conditions in the absence of snow) and A, = 0.75 (for a snow-covered terrain) are given in Table 11.3.

TABLE 11.3

INTENSITY CORRECTION FACTORS ARISING FROM GROUND REFLECTION^

I"@ I + P ; &)/Id0 I + P ; 0)

Teff & = 0.15 X, = 0.15

0.05 0.10 0.15 0 . 2 0 0 .25

1.006 1.012 1.018 1.023 1.027

1.034 1.067 1.099 1.128 1.158

a The table gives average values for the range of solar depression angles 3" < < 9", and for observations in the zenith and at 5 = 75". Individual values in this range deviate from the average by amounts that are small compared with the differences between successive entries versus ~ ~ f f . Correction factors refer to a single wavelength or to one entire hyperfine group, where is the effective optical thickness of the layer for the group.

Since the table is computed with the Earth's shadow neglected, the correction factor will usually be closer to unity than the computed values. T o a first rough approximation, the component of the intensity arising from ground reflection will be proportional to the fraction of the sodium layer illuminated by sunlight, as seen from the ground directly below the area being observed. Thus just before the shadow crosses the observed region of the layer, the ground below that point is illuminated by only half the sky, and the albedo correction is correspondingly diminished. The correction factors in Table 11.3 are not valid at all,

458 11, THEORY OF THE TWILIGHT AND DAY AIRGLOW

however, after the shadow encroaches on the observed point, with the actual relative correction becoming larger as the directly scattered light diminishes.

O n the Accuracy Lost and Simplicity Gained with the Plane-Parallel Model.-Donahue and Stull [1959a], Donahue, Resnick, and Stull [1955a, 1956~1, and Blamont, Donahue, and Stull[1958u] have developed and applied a somewhat different theory for the intensity of the sodium lines as a function of abundance. Their calculations are based on a spherical-shell model for the atmosphere, with a Gaussian distribution of sodium. Discarding the plane-parallel geometry also means that a concise analytic theory is sacrificed for the secondary scatterings, which then must be accounted for in a most laborious manner requiring high-speed machine calculations. Donahue et al. allow for secondary scatterings in a given volume by first computing the primary scattering in all the surrounding elements of volume.

We shall see below that considerations of resonance absorption make a major difference in the wintertime abundances derived from the total intensities. There are, however, several limitations to the accuracy attainable that obviate attempts at this time to improve on the plane- parallel model:

1. Inaccuracies in the observational data themselves are important. The seasonal abundance curves derived from total intensities and from D,/D, ratios are in rather good accord-enough so to justify the postulate of resonance scattering and to justify the further use of ratios in abundance determinations. (Note, however, the limitations on the use of ratios discussed in the next section.) But the accuracy of either type of measurement is not often such that one can be reasonably certain that the abundance is correct to within, say, 30 percent.

2. Uncertainties in the sodium-layer model, aside from the vertical distribution, involve the temperature and patchiness. If the Na layer is above the mesopause, where the temperature may vary considerably over a short vertical distance, a constant temperature may even be a poor assumption. The patchiness could seriously distort the resonance absorption computed at the first passage. In addition, there is appreciable uncertainty in the central intensities of the Fraunhofer lines.

3. Departures from the physical theory of resonant, isotropic scattering without polarization are not entirely insignificant, as we saw in Sec- tion 11.3.1.

Should greatly improved values of the temperature or the Fraunhofer central intensities become available, it would be a fairly simple matter to recompute the D-line emission rates. Of course, for very small angles


of solar depression, /?, the curvature of the atmosphere is important. The theory of Donahue et al. gives a minimum scattered intensity at /? N 2" instead of @ = 0" as would be the case in the plane-parallel model. However, observations at such small p are not only difficult with current instrumentation, but there is no compelling reason to observe at such angles. Abundances can be obtained with better accuracy at slightly larger p, and changes in abundance with time are best studied by observing both morning and evening twilight, possibly supplemented by balloon observations of the dayglow.

At /3 N 6 to 7 degrees-i.e., at p's just smaller than that at which the shadow starts to cross the sodium layer along the line of sight- the shadow may diminish the amount of secondary scattering compared with the amount computed for uniform illumination. Donahue et al. have allowed for this effect also in their work, but as long as abundance observations are made on the intensity plateau, where the intensity is constant or changes very slowly with time, the error introduced is not important.

Depending on the function the theory is to perform, one may choose either the exact, analytic solution of the approximate problem (which may be of some benefit because of its simplicity and flexibility) or the approximate, numerical solution of the exact problem (which will be more useful for certain observations requiring a large correction to the simple theory).

11.3.3. Twilight Airglow: The Na Abundance and Seasonal Variation

T o compute the intensity of the D, and D, lines, we must add the separate intensities of the hyperfine components in each line. The absorption coefficient per atom at the center of a line is, by Eq. (1,12),

(1 1.62)

Since the populations of the lower levels will be distributed in proportion to the statistical weights, the vertical optical thickness for the center of the line F - F' is

where&- is the total sodium abundance in a square-centimeter column. The T'S of the various components are thus proportional to their strengths (Section 1.3.2).


Since the components are not precisely superimposed, the T~ for a hyperfine group is not simply the sum of the component parts. I n Paper IV a formula is derived whereby two close lines with Doppler profiles for the kinetic temperature T may be approximated by a single Doppler profile for an effective temperature, Ten. The effective value of cyo (= agff) for a hyperfine group will then be slightly less than the sum of the individual so's, being smaller for wider separations. In order to keep the integrated absorption coefficient or f-value constant, cvff must decrease as Teff increases.

Table 11.4 gives the effective temperature and absorption coefficient for a kinetic temperature of 220" K for the various hyperfine groups. For a given assumed abundanceN the separate D, and D, intensities may thus be computed, with the aid of the calculations in Table 11.2, for the individual hyperfine groups. T h e results for an angle of solar depression of p = 6P5 are shown in Fig. 11.7; we shall now discuss the application of this figure to the interpretation of measurements of the D lines.

TABLE 11.4

COMPONENTS OF THE D-LINES FOR T = 220' K

Component

Total D, + D, Intensity.-The interpretation of observations of the intensity is not always straightforward, as there may be considerable difficulty in determining what portion of the observed signal arises from resonance radiation scattered in the sodium layer and what part is unwanted background light (Section 9.2.2).

Measurements with a scanning spectrometer, as obtained by Hunten [ 19564, lend themselves readily to a correction for the background

11.3. PHOTON SCATTERING BY ATMOSPHERIC SODIUM 46 1

I I I I I I I I

0 2 4 6 8 10 12 14 16 18 20

“lo9 Na atomUcme(wrtical column)]

FIG. 11.7. Absolute intensity and Dz/D1 ratio as a function of Na abundance, A”, for a solar depression of /J = 6:5 and a kinetic temperature of 2200 K in the scattering layer. The D1 + D, ordinate gives intensities “reduced to the zenith.” Solid curves should be used for observations near the zenith; dashed curves near the horizon. The dotted curve gives the intensity without scattering in the first passage through the Na layer and without any secondary scatterings. Similar curves for other .angles /J may be readily computed from the data in Table 1 1.2.

From Chamberlain, Hunten, and Mack [1958u] ; courtesy Pergamon Press.

Month

FIG. 1 1.8. Abundances over Saskatoon (latitude 520) derived from the measurements of Hunten [19566; also, more recent data]. The “average” and “extreme” curves were drawn from eye-estimates. From Chamberlain, Hunten, and Mack

[1958a]; courtesy Pergamon Press.

462 11. THEORY OF THE TWILIGHT A N D DAY AIRGLOW

intensity. Hunten's data have been calibrated on an absolute intensity scale and can thus be converted to abundances,M, with the aid of the above theory. Figure 11.8 shows the seasonal variation in abundance determined for Saskatoon over a period of several years. The data were obtained at /3 w 6" to 6 3 .

The average curve for Saskatoon varies between 6.5 x lo9 atom/cm2 at the end of February and 1.3 x lo9 near the end of June, a ratio of 5 to 1. The extremes of the curves are in the ratio 10 to 1 and the extreme points about 12 to 1. Blamont and Donahue [1958a] have reported on the seasonal variation over France; the amplitude of the variation seems to be larger than at the higher latitude, but measurements at different locations with similar equipment would be desirable.

2.0 - I

t FIG. 11.9. Total D, + D, intensity versus angle of solar depression, computed for observations near the horizon and T = 220° K. The total sodium abhdances Af are indicated on the curves. The figure does not include the effects of the Earth's

shadow, which will diminish the intensity at j3 > 70 or so.


At smaller angles of solar depression the intensity should be less than at /3 = 6” or 7”, as shown in Fig. 11.9. For small abundances the intensity forms a “plateau,” but for the larger wintertime abundances we should see a decrease in brightness toward the day side, as well as toward the night side, of the maximum. Such decreases have been observed by Blamont [1956a] (also see Blamont, Donahue, and Stull [1958a]). At very small angles ,B, direct comparisons of the theoretical intensity curves with Blamont’s are not informative, since the sodium- cell filter does not allow an accurate subtraction of the background light, owing primarily to the fact that the Fraunhofer D lines are not flat at the bottom. These instrumental effects have been discussed by Donahue [1956a], Hunten [1957a], and Donahue and Hunten [1958a].

Blamont, Donahue, and Stull [1958a] reported a peculiar asymmetry in the sodium abundance over southern France for over a year and a half, where on the average 1.43 times as much sodium appeared toward the west as to the east of the observatory.

D,/D1 Ratio.-In Fig. 11.7 the dotted curve for the D,/D, ratio may be obtained from Eqs. (1 1.46) and ( 1 1.47) with Hunten’s approximation of replacing T , with ~,,/1/2. [Compare these equations with Eqs. ( 1 1.59) and (1 1.51)]. Neglecting the small differences in the effective temperatures of the different hfs components and writing 710 = ~ ~ ( 0 , ~ ) and similarly for the other lines, we obtain for the ratio

Ratios have been measured by Galperin [1956a, b], Harrison and Vallance Jones [1956a], Lytle and Hunten [1959a], Montalbetti (reported in Paper IV), and Nguyen-huu-Doan [1959a]. Some of these results were collected in Paper IV and found to give about the same over-all seasonal variations as the absolute intensity. Additional ratio measurements, reported by Vallance Jones and McPherson [1958a], are also in good agreement with the abundances of Paper IV. Figure 11.10 gives the variation of the theoretical D,/D, ratio with angle of solar depression for various total abundances. This figure may be compared with Fig. 11.9 for the total intensity.

Donahue [ 1958~1 has emphasized that if the abundance is to be derived with high accuracy from D,/D, ratios, po must remain constant during the photographic exposure, since the ratio is quite sensitive to po. Hence, rather accurate guiding on the intersection of the Earth’s shadow


with the sodium layer is required. He also points out that the ratio must be obtained at small enough values of po (corresponding to, say, ,t? < 7") that extinction of the exciting sunlight is unimportant. If the Earth's shadow begins to enter the Na layer, the upper part of the layer will scatter a relatively larger amount of the D-line radiation than before.

Z X l d

6XI09 10x10~ 14x10. mxld

cb

d : .80

.20 7 3' 4' 5' 6' 7' 8" 9'

8. angle of solar depesrion

FIG. 11.10, The DJD, ratio versus angle of solar depression /3 for observations near the horizon and T = 2200 K. The total sodium abundances A' are indicated on the curves. Unlike the total intensities of Fig. 11.9 the Earth's shadow when present will not have a dominating effect on the ratio. For observations in the zenith the ratio is just slightly greater, and the difference can generally be ignored.

Since the ratio depends slightly on the path that the photon takes out of the Na layer, it can be affected. Finally, the ratio may be affected slightly by radiation scattered into the line of sight by the lower atmosphere. Since this radiation comes in general from other parts of the Na layer where po is different, it will not have the same ratio as the region observed directly. This effect is minimized, however, by making the observations as much as possible at fairly large zenith angles toward the sun, so that only in a small part of the sky is the Na layer brightly illuminated.

Na Abundance f r o m Absorption Studies.-Attempts have also been made to derive the sodium abundance from telluric D absorption lines in stellar spectra. Roach [1949a] computed a theoretical curve of growth (which relates the equivalent width of an absorption line with abundance) for an atmosphere at 300" K. Sanford [1950a] inspected several Mount Wilson coudC spectra; the most suitable was one of a Virginis made on a May night at a mean zenith distance of 68". The presence of a D, line was uncertain. (The stronger D, is too confused


by telluric water vapor lines to be of use.) The Na abundance was thus less than 10'" atom/cm2 (reduced to the zenith). Earlier measurements of interstellar lines by Dunham [1939a, 1940~1 were similarly interpreted by Bates and Nicolet [1950a]. I t should be possible to measure the telluric absorption line on coudt spectra if a bright, early-type star like LY Virginis is observed rising or setting in winter. The abundance of sodium in the daytime has been measured by the small telluric component in the D lines of the sun by Scrimger and Hunten [1956a, 1957~1; again the agreement is satisfactory.

11.3.4. Day Airglow

Observations of the sodium day airglow from balloons can supply important information on the sodium layer beyond what can be found from twilight data alone. If a photometer were placed above the lower atmosphere and scanned over the sky for several hours or longer, it could give a variety of results:

1 . Heights could be obtained from the van Rhijn type of analysis commonly used in nightglow photometry. The height should be ob- tainable with higher accuracy than with similar observations from the ground both because of the low amount of tropospheric extinction and because the height itself, as measured from a balloon, will be lower. On the other hand, it will be necessary to compare observed intensities with those computed from the radiative-transfer theory, wherein the intensity is not simply proportional to l /p ; however, the correct analysis offers no difficulty in principle.

2. Fluctuations in the abundance of sodium during the course of a day and even over a period of several days could be measured. A knowledge of these variations would be of enormous value to the theorist attempting to discuss the photochemistry and ionization of atmospheric sodium.

3. Geographic irregularities (patchiness) of Na in the upper atmosphere were first noticed by Swings and Nicolet [1949a] in twilight spectra taken in Texas. Observation of these patches over a period of hours or longer would not only be of use to studies of sodium but may provide an excellent means of tracing winds in the D region.

T o a first approximation the intensity of the dayglow will be about the same as that at twilight. The Na abundance does not appear to change much during the day or night, as judged from the small morning-to- evening twilight variations and from the agreement between abundances


as determined from the twilight theory and daytime absorption (Scrimger and Hunten [1957a]; Paper IV).

There are, however, two effects that tend to alter the daytime intensity from that in twilight. First, incidence occurs at an angle not necessarily as grazing as in twilight and does not have to pass through the layer once before reaching the scattering layer. Hence the extinction by the sodium layer itself is less. Second, the ground albedo plays a more important role in the day. In twilight, reflection of scattered D-line radiation between ground and the sodium layer may have a small effect on the observed intensity (Table 11.3), but in the daytime the incident solar flux, as well as the scattered radiation, will be reflected. With a high ground albedo, the incident sunlight (direct and reff ected) could thus be twice the twilight value.

Calculations of the D, intensity for three widely-spaced abundances, and with secondary scattering neglected, were made by Donahue [19566]. The problem has also been treated in Paper V of the series entitled Resonance Scattering by Atmospheric Sodium.I5

The problem has been treated both for observation from below the sodium layer and from above it. The latter situation would present the observational problem of eliminating background sunlight diffusely reflected by the ground and troposphere, which is not unlike the problem of trying to see the dayglow from the ground. The difficulties are not insuperable, but very narrow band detectors and high accuracy are necessary ; thus observations from balloon altitudes offer the greater immediate promise by far. Were the instrumental problem overcome, observations from an Earth satellite would be the ideal way to study geographic distributions.

The analytic solution of the problem offers nothing fundamentally different from the twilight problem, so the analysis need not be repeated here. I would mention, however, that the analytic integration over the line profile is simpler here than in the twilight problem, because of the absence of the extinction exponential introduced by the first passage of sunlight through the sodium layer [see Eq. (11.52)].

Sample calculations of the dayglow intensity against Na abundance have been made in Paper V; similar values can be calculated readily for any particular conditions (p, p0, and A,). I n this respect it should be noted that it is important to estimate the ground albedo at the time and place of dsyglow observations. Preferably, the photometer should scan the ground as well as the sky.

1 I .4. PHOTOCHEMISTRY AND IONIZATION 467

11.4. Photochemistry and Ionization of Atmospheric Sodium

Observations on the twilight and day airglow give abundances of Na atoms; in order to understand how Na is related to the total sodium abundance, we must examine both the photochemical and ionic equilibria. At low altitudes sodium will be incorporated in some compound; at higher levels it will become ionized. We shall bear in mind through the discussion that there is probably a small Na enhancement in the morning, compared with the evening, and definitely a large seasonal variation with maximum in winter (Section 9.2.2).

The photochemical and ionic reactions and equilibria have been discussed by Chapman [1939a], Bates [1947a], Bates and Seaton [1950a], Bates and Nicolet [1950a], and Hunten [1954a]. A brief review of the problem, with emphasis on the explanation of daily and yearly variations, has been published by Omholt [1957a].

11.4.1. Photochemistry

Free sodium is possibly formed by Chapman’s reduction mechanism,

NaO + 0 - N a + O,, (1 1.65)

and may be oxidized by one or more of the following:

Na + O,-tNaO + O,, (1 1.66)

N a + O + X - + N a O + X ,

and (1 1.67)

Na + 0, + X-tNaO, + X, (1 1.68)

where X is an unspecified third body. If the latter reaction is important, as seems likely, it may be followed by a partial reduction,

NaO, + 0 + NaO + 0,, (11.69)

and then by reaction (1 1.65) to complete the cycle. Bates and Nicolet suggested that alternative reactions might involve

H instead of 0. Thus instead of (or in addition to) reaction (11.65), we may have

NaH + 0 -t Na + OH. (1 1.70)


If oxidation occurs mainly by process (1 1.68), NaO, might be removed by

NaO, + H + NaH + 0, (1 1.71)

or

NaO, + H -+ NaO + OH. (1 1.72)

The cycle (11.68) and (11.71) might supply NaH for nightglow Na excitation by (11.70) (see Section 13.5.3). A quantitative discussion is hampered by poor information on reaction rates and even a lack of knowledge of dissociation energies. Indeed, if the energies available in the reactions were known, the reaction rates could be at least roughly estimated.

Let us suppose for illustrative purposes that the sodium concentration is governed by reactions (11.65), (11.68), and (11.69). Then writing concentrations per cm3 in square brackets, as N(Na0) = [NaO], we have

For the three-body reaction (1 1.68) around 250” K, s68 is about 5 x cm6/sec (Bates [19546]), and if the mesopause temperature is as

low as 150” K, the rate coefficient may be as high as cm6/sec (Dalgarno [1958a]). The most important temperature dependence is in the two-body reactions, where the rate coefficient has an exponential factor as in Eq. (1.11 2).

The ratio [NaO]/[NaO,] thus varies only with the temperature, while the [Na]/[NaO] ratio depends also on the density. Above the temperature minimum around 80 km, the relative abundance of Na compared with NaO will increase both because of the increase of [O] compared with [O,] and [XI and because s65/sB8 may increase rapidly with height.

If above 85 km or so most of the sodium is neutral, the maximum atomic concentration must appear at this height to explain twilight observations. On the other hand, should free Na constitute only a part of the total sodium in this region, it would have to become ionized rapidly at greater heights in order for the maximum Na to appear at 85 km. Hunten’s [1954a] theoretical discussion of the ionization, however, suggests that the height variation in the Na+/Na equilibrium is not steep near the “layer” maximum (see below). Therefore, sodium is probably mainly atomic at 85 km, although this conclusion is not certain.

The hypothesis that much of the sodium is in the molecular form even at the sodium “layer” might allow the possibility of large seasonal

1 1.4. PHOTOCHEMISTRY AND IONIZATION 469

variations by changes in the photochemical equilibrium. Should the temperature minimum move a few kilometers in winter, the amount of Na might vary considerably. Quantitative discussion is scarcely possible, not only for lack of knowledge on rate coefficients, but also because of our ignorance of the seasonal temperature variation in the region concerned and the precise position of the Na layer relative to the temperature minimum (Le., the mesopause).

In the upper atmosphere the total abundance of Na rarely exceeds 1Olo atom,/cm2. The density of Na is probably never greater than lo4 atom/cm3 or one atom in lolo. Moyerman and Shuler [1953a] find that inland air at the ground contains on the average about 1.5 x 10l1 atoms of sodium/cm3, mostly in the form of NaCl ; that is, approximately one atom in 5 x lo8 is sodium at sea level. Hence even if a considerable fraction of the total sodium is hidden in molecular compounds or ionized, the relative sodium abundance in the upper atmosphere probably does not exceed that at the ground. Earlier it was often thought that sodium in the high atmosphere must originate from extraterrestrial sources (Section 9.2.2). There is no longer any compelling reason to invoke such a hypothesis. In the absence of any correlations of Na intensity with meteors or solar activity, it seems likely that atmospheric sodium comes predominantly from the sea. Although salt particles may have an appreciably smaller scale height than atmospheric gases, it seems not unreasonable that enough sodium can be transported to the high atmosphere to explain the twilight observations (Chamberlain, Hunten, and Mack [ 1958~1).

If sodium is governed entirely by the reactions discussed above, an increase in the temperature at some height would mean an increase in the rates as given by Eq. ( I 1.73). Thus if reaction (11.65) produces Na in the 2P excited term, as Chapman [1939u] proposed, the nightglow would follow the twilight seasonal variations in a nearly constant ratio. There are objections to the Chapman excitation mechanism, however, even if reaction (1 1.65) is important in governing the Na equilibrium. It is not known whether the reaction can produce sufficient energy to excite the D lines; but if it can, the nightglow D lines should be produced below the maximum concentration of Na. The reaction rate given by Eq. (1 I .73) may be written as [NaO + NaO,] [O] sB5 sB9/(sB5 + s6J. In the region concerned, [O] varies slowly with height. If the total sodium abundance follows the density distribution of the atmosphere, the emission rate should increase toward lower altitudes, provided that the rate coefficients do not decrease. Collisional deactivation would not be expected to be important in the neighborhood of the temperature minimum; thus the lower boundary of the nightglow should be well


below the twilight “layer.”l8 However, the altitude measurements seem to place the nightglow in the same region as the free Na, or even slightly higher. Nightglow D,/D, ratios may help clarify this problem (Chamberlain and Negaard [1956a]).

11.4.2. Ionization

A discussion of the ionization equilibrium by Bates [1947a] has been modified by Bates and Seaton [1950a] and by Hunten [1954a] with more recent data on the flux of sunlight shortward of 2420 A. The rate of Na ionization in daytime is about q = [Na] ~ m - ~ sec-l. Radiative recombination probably has a coefficient less than 2 x lo-,, cm3/sec, but mutual neutralization of positive and negative ions [Eq. (1.107)] may have a coefficient as high as lo-* cm3/sec. The work of Bates and Massey [1946a] suggests that at 110 km the daytime ratio of negative- ions/electrons might reach 2 x Since Ne is about lo5 ~ m - ~ , the ratio [Na]/[Na+] may be of order unity in the 110-km region.

Hunten [1954a] has used the ionization of Na as the basis for a theory of the daily and seasonal variations. The time constant for the rate of change of Na+ is the order of a day, so that ionization equilibrium may never actually be reached. Hunten’s calculations give the relative intensity to be expected in the morning and in the evening twilights as a function of the fraction of the day that sunlight illuminates the sodium region and for various values of the product (charge-transfer coefficient) x (negative-ion density). Hunten concluded that the morning/evening ratio is unlikely to exceed 1.5 and this maximum ratio at any latitude would occur at the equinoxes.lS

The seasonal variation computed from ionization equilibrium seems to be considerably smaller than the observed amplitude. The computations, depending critically on the ratio of dark to sunlit hours, show a marked variation with latitude in the summer/winter ratio. We have little idea how the actual seasonal change depends on latitude, as the necessary absolute photometry has not been carried out.

In the polar regions there should be a strong seasonal variation, as

Bates [1947a] and Hunten [1956a] have similarly related the nightglow and twilight heights on the assumption of Chapman’s reactions (1 1.65), (1 1.66), and (1 1.67), neglecting any temperature dependence of the rate coefficients.

At a height of 85 km the equinoxes occur at appreciably different times than on the ground. At the latitude of Saskatoon (52”), they fall about the middle of February and the end of October. The ionizing radiation is absorbed by 0, in the Herzberg continuum. Hunten [19566] estimates the screening height, to be used in computing the time of sunset (Section 10.1.5), as 54 km.

1 1.4. PHOTOCHEMISTRY AND IONIZATION 471

Na has little chance to become ionized in winter but is maintained at the daytime equilibrium in summer. Hunten [1956b] has thus suggested that the large seasonal variation at lower latitudes may be due to mass motion of neutral sodium out of the arctic regions. The suggestion of winds in the high atmosphere affecting the sodium density seems appropriate also from the standpoint of the irregular day-to-day fluctuations observed in winter. Winds of the order of 50 meterfsec are required; the sodium clouds ejected from rockets indicate winds of this order (see below). One apparent difficulty pointed out by Hunten is that the large abundances are observed beyond early March (Fig. 11.8), when the polar night ends (for ionizing radiation at 85 km). Perhaps extended study of the dayglow will help resolve the problem.

The Na+ ionization has been considered as the source of the D layer (Jouaust and Vassy [1941u]). Bates and Seaton [1950a] have examined the rate of production of Na+ to be expected on the basis of known Na abundances, the relevant continuous-absorption coefficient, and the incident flux of sunlight. They found photoionization of Na to be inadequate to account for D layer ionization except, possibly, at the very base of the layer (near the 75-km level). The D layer may actually be formed by photoionization of NO (Nicolet [1949a, 1957u]), or x-ray ionization.

Ions of Na+ may, however, play an important role in the nighttime E layer, where the electron density is maintained around lo4 ~ m - ~ in the 100- to 105-km region. The effective recombination coefficient in the daytime (- 2 x lop8 cm3/sec as derived from radio observations) is too large to be compatible with the nighttime ionization (Nicolet [I 955~1). At least a large portion of the daytime recombination occurs by dissociative recombination [Eq. (1.106)] of molecular ions. One possible explanation for the residual ionization at night is that it exists in the form of atomic ions, which recombine by mutual neutralization [Eq. (1.107)] at best or radiative recombination [Eq. (1.94)] at worst.

Since the morning/evening ratio of the twilight is between 1 and 2 on the average, recombination of Na+ at night is evidently not too important. I t thus seems possible that sodium and perhaps other metallic atoms contribute significantly to the residual nighttime layer. If so, a theory (such as Hunten’s) of the daily and, more significantly, the yearly variation in Na+ ions should also explain annual variations in the ionospheric characteristics. Rocket observations have not, however, detected metallic ions as yet.

Another alternative, that ionization is produced throughout the night by meteor impact, has been discussed in some detail by Nicolet [1955a]. It seems that a nighttime recombination coefficient smaller than the day-


time value is still required; otherwise meteor impact is not important enough to maintain the ionization.20 I t is possible that not only do meteors provide ionization at the time of impact but also that they are an important source of the metallic atoms that are later ionized by sunlight and provide the low nighttime recombination coefficient. It appears that calcium is more likely than sodium to give us observational information on the effect of meteors on ionospheric composition (Section l l .6.3).

11.4.3. Sodium Ejected from Rockets

Bates [ 1950~1 suggested that sodium artificially introduced into the upper atmosphere would provide a means of testing hypotheses on its excitation, photochemistry, and ionization. A team at the Air Force Cambridge Research Center,21 has since flown several rockets to perform the Bates experiment. These flights have raised interesting new problems, but thus far have not been especially helpful in elucidating the airglow.

In the twilight experiment, for example, the problems are not entirely the same as in the airglow. In one flight, about 5 x atoms of sodium were ejected between 75 and 110 km. The mean density, as estimated from the dimensions of the trail, was about lo9 Na atom/cm3. Through the diameter (about one kilometer) there were therefore about 1014 atom/cm2. The optical thickness for incident sunlight in this shortest dimension was thus some lo3 times the maximum value likely to be encountered in twilight. (Over most of the line profile, 7, would exceed lo2.) I t is thus meaningless to use the g-value of Table 11.1 ; it would be a closer approximation to suppose that all the incident sunlight (over an effective line width corresponding, say, to 7, 2 1 along the direction of incident sunlight) striking the sodium trail is absorbed and re-emitted.

Below 90 km or so the sodium trail failed to show the D-lines, and it is thus a matter of some speculation as to how much free Na was in the trail at these altitudes a short time after ejection.

At the higher altitudes where the D lines appear, the intensity of A3302 (from the second transition of the Na principal series, 3 2S - 4 "') could in principle be used as a check on the correctness of resonance

2o The ionization of meteor atoms themselves will be much more important than ionization of atmospheric molecules by the meteors.

21 Edwards, Bedinger, Manring, and Cooper [1956a]; Bedinger and Manring [1957a]; Bedinger, Ghosh, and Manring [1957a]; Bedinger, Manring, and Ghosh [1958a]; Cooper, Manring, and Bedinger 11958~1, Manring, Bedinger, Pettit, and Moore [1959a]. A number of other experiments on ion clouds produced with the alkali metals sodium, cesium, and potassium have been reported in a separate series of papers. The program is summarized in Paper I by Marmo, Aschenbrand, and Pressman [1959a].

1 1 -5. THEORY OF T H E OXYGEN RED LINES 473

scattering. However, in computing this ratio it is necessary to allow not only for the difference in attenuation or screening of incident sunlight but also for differences in the radiative-transfer problem. While the D lines may be scattered many times, all the radiation absorbed will eventually escape (in the absence of collisional deactivation). But A3302 will be degraded, after a large number of scatterings, through the emission cycle of 4 2S - 4 2Po, 3 2Po - 4 ?S, and 3 2S - 3 nPo (D lines), or, more rarely, through 3 2D - 4 2P0, 3 ‘ P O - 3 2D, and 3 2S - 3 zPO. From sodium ejection experiments performed under the French rocket program Vassy and Vassy [1959a, b] detected a weak h3302, but its intensity was not always in a constant ratio to the yellow lines.

Computation of the amount of Na ionization in the ejected cloud is made somewhat difficult by the time dependence in the problem. With the relatively high Na densities produced in the rocket experiments, a large density of Na+ ions would be expected in daytime equilibrium, since Na + will recombine rather inefficiently. However, the ionization approaches a daytime equilibrium very slowly, and a calculation based on equilibrium is not valid for predicting the critical frequency of a radio reflection from a freshly expelled sodium cloud.

In the nighttime flights there are also difficulties of interpretation. The D-line emission was found with maxima near 65, 100, and 140 km. While some of this emission perhaps arises from the same photochemical process that is responsible for the nightglow, none of the excitation is satisfactorily explained.

Possibly the most valuable contribution of these rocket experiments lies in the use of sodium in twilight as a tracer for winds in the 80- to 100-km regions and higher. Speeds up to 150 meter/sec have been observed, with large differences in direction and magnitude found over a vertical distance of 10 km. Blamont [1959a] has obtained especially interesting results on winds and turbulence. Other artificially induced airglows are discussed in Section 13.4.4.

11.5. Theory of the Oxygen Red Lines

11 S.1. Resonance Scattering and Ultraviolet Dissociation Excitation of [OI],, by resonance scattering with allowance for deactivation has been treated in Section 11.1.1. In the event that the deactivating substance follows a scale height of one half that of 0 (so that Hx = H0/2), we have b = 1/2. Then Eq. (11.11) gives


Calculations have been made (Chamberlain [1958a]) with Eqs. (1 1.6) and (1 1.74) for A6300 on the assumption that 0, is the deactivating substance X. The condition H , = Ho/2 may therefore be approximately correct. For numerical values I have taken H , = 13 km, H, = 6.5 km, N ( 0 I 110 km) = 5.3 x loll ~ m - ~ , and N ( X = 0, I 110 km) = 6.2 x loll ~ m - ~ . Figure 11.11 shows the results for various values of the deactivation

- coefficient, sD.

320 I

280

240

200

I60

I20

80

40

0 -110 120 130 140 150 160 170 180

Height zo (kml

FIG. 1 1 . I 1. Computed scattering for A6300 in the zenith ( p = 1) for various values of the rate coefficient for deactivation, sg (which is in units of cm8 sec-l). To obtain 4773 in an arbitrary direction (where 9 is the brightness in lo6 photon/ cm2 sec sterad) divide the values in the graph by p = cos 8, where 8 is the angle of emergence of a ray at the mean height of the scattering region. From Chamberlain

[1958a] ; courtesy University of Chicago Press.

The theoretical intensities in Fig. 11.1 1 may be compared with the observed intensities of Robley shown in Fig. 10.10, p. 397. Not only is the observed absolute intensity throughout twilight much greater than can be justified theoretically, but the rate of decrease after sunset is much slower than the computed curves, except for the larger values of s,. For these values, however, the discrepancy in the intensities is even worse. Resonance scattering is apparently responsible for only a small portion of the [OI],, twilight. Further evidence against resonance scattering is given by the great disparity in the various curves in Fig.lO.10 for observations in different directions. The failure of these observa-

11.5. TIIEORY OF THE OXYGEN RED LINES 475

tional curves to overlap suggest that the basic assumption involved in the plot-instantaneous scattering of red light-is incorrect.22

Another possible mechanism involving the direct and immediate action of sunlight is dissociation of 0, in the Schumann-Runge region (Bates [1948a]). Some approximate calculations were made (Chamberlain [1958a]) that indicate the mechanism is more important than resonance scattering, in spite of the large screening height (h, m 135 km), when observations are made in the azimuth of the sun and at large zenith distances. Although the mechanism does not explain the observed intensity and the slow decrease with time after sunset, observations indicate that it provides some of the early twilight enhan~ement . ,~

11.5.2. Collisional Deactivation

It has been pointed out by Bates and Dalgarno [1953a] that the reaction

2) (11.75)

is within 0.004 ev of resonance for v' = 2. There is some doubt, however, as to how important near-resonance will be in a reaction of this type. If resonance is very important, so that l,Y; invariably appears in v' = 2, then the reverse reaction to (1 1.75) must be considered.

Seaton [1958a] has treated the situation where reaction (11.75) is in exact resonance. The ratio of forward to reverse rate coefficients is then given by detailed-balancing considerations, and the importance of reaction (1 1.75) can be estimated as a function of the probability that 0, will escape from the b '2: state by some other mechanism. One such process is, of course, radiative cascades to X 3 Z ; and to a ld,. The transition to the former state, yielding the Atmospheric system, is known to have a probability of A - lo-' sec-l. But if this were the only

O(l0) + O,(X 3z;, v" = 0) -+ O(3P2) + O,(b 'z;, v'

1z The lifetime of the 'D term, about 2 minutes, is short compared with the duration of twilight. Hence the assumption that resonance scattering is instantaneous is appropriate enough.

23 The excitation arises from the fact that Schumann-Runge dissociation leaves one atom in the excited term:

0 2 + hv+ OPP) + O(1D). (11.74a)

Barbier [1958a, 1959~1 finds that this component of the twilight is restricted to regions of the sky at large zenith angles near the solar azimuth.

Bates [1948a] also drew attention to photodetachment,

0- + hv+ O(lD) + e (1 1.74b)

as a possible source of the morning twilight, when negative ions have had an opportunity to form. About 1 photodetachment in 16 will produce an atom in the ' D term.


alternate escape mechanism, the resonance reaction ( 1 1.75) would not be an important source of deactivation. Seaton suggested that the transition b lL': --t a Idy, which has never been observed, may have A - 1 sec-l; the resonance collision could then be important.

Alternative means of deactivating an excited molecule include electron transfer [see Eq. (7.95), Section 7.4.21 and possibly atom-atom interchange, as was first suggested by Bates [1955a]. In the present case the latter reaction might be

o(3q + o,(b 1~';) -+ o , (~ id,) + o(3q (11.76)

which would conserve electron spin. These reactions would thus compete with the reverse of (1 1.75).

Reaction (11.75) appears to be responsible for producing the 0, Atmospheric bands in the aurora(Section 7.4.2). Wallace and ChamberIain [1959a], in an analysis of the auroral emissions, concluded that actually resonance was not an important factor and that v' = 2 was not preferentially excited. They derived an empirical rate coefficient for (1 1.75) of sD * lo-" cm3/sec (see also Section 13.4.2).

11 -5.3. Dissociative Recombination

Dissociative recombination, such as

NO+ + e + O * + N*, (11.77)

was first invoked by Bates and Massey [1947a] (for an unspecified ion) to explain the large recombination coefficient in the ionosphere. Bates [1948a] later suggested that some of the post-twilight enhancement might arise from such a process. The mechanism for 0; is energetically capable of exciting the nightglow [01],, green line as well (Nicolet [1954a]). But since the excitation would occur in the F region and the green line is now known to arise predominantly from the 100-km neighborhood, other processes are apparently more important for X5577. With NO+ only the red [OI],, lines could be excited.

The NO+, which recombines by reaction (1 I .77), is presumably formed in the F region by ion-atom interchange:

O+ + N, + NO+ + N, (1 1.78)

with 0' produced by solar radiation. Nicolet and Mange's [1954a] work on diffusion first showed that there should be an adequate amount of 0, in the F region for it to be important in reactions of this type, but it now appears that the reaction with N, is more important.

11.5. THEORY OF THE OXYGEN RED LINES 477

The excitation of the red lines in evening post-twilight by reactions of the types (1 1.77) and (1 1.78) has been advocated by Bates [1948u], St. Amand [1955u], and Barbier [1957c], and has been investigated in detail by Chamberlain [1958u, 1959~1.

While in the original paper it was supposed that 0, and 0: were the molecules in reaction (1 1.78), the theory is appropriate as well for the reactions treated here, which now seem to be the dominant ones. The basic simplifying assumptions of the theory are that (1) N, remains in diffusive equilibrium, (2) all ionization is in the form of either O+ or NO+, (3) the above reactions provide the only recombination mechanism, (4) each recombination produces on the order of one atom in the 'D term, ( 5 ) diffusion of ions is negligible, and (6) at sunset the electron density N f ) , is a constant with height. The theory does include, however, recombination in both the Fl and F2 regions, where (1 1.77) and (11.78) are, respectively, the limiting processes.

Figure 11.12 shows the computations of the intensity decay compared

500

400

300

200

I00

0

t: time after sum& in the bnosphen. hccl

FIG. 11.12. Variation, with time after sunset in the F region, of total A6300 emission from dissociative recombination for two values of N p ) . Absolute value; of the observed points have an estimated uncertainty of a factor of 2. After

Chamberlain [1958a] ; courtesy University of Chicago Press.


with the brightness variation measured by Robley (see Fig. 10.10, p. 397). Computations for two values of the initial electron density are shown. Although the height of emission is rather sensitive to N(N,) sV8, the total intensity is almost independent of the coefficients after a short time after sunset, with the simplifying assumptions stated above. The altitude of maximum emission probably rises from about 225 km, at 15 to 20 minutes past the time ionizing radiation disappears from the F region, to around 300 km, after 2& or 3 hours. At these altitudes collisional deactivation is negligible.

The mechanism of dissociative recombination thus appears to provide a reasonable explanation for much of the ordinary twilight [OI],, effect, the so-called post-twilight enhancement, and at least a portion of the nightglow as well. The mechanism is consistent with the most reliable estimates of nightglow height (Sections 12.2 and 12.3) and with correlations of the red-line brightness with ionospheric data (St. Amand [ 1955~1; Barbier [ 1957~1).

The evidence is also greatly in favor of dissociative recombination (1 1.77) as the principal means of recombination in the ionosphere, according to theory (Bates and Massey [1947u]) and an analysis of radio-reflection data by Ratcliffe, Schmerling, Setty, and Thomas [1955u] (see also Bates [1954u, 1956~1). In this connection Barbier [1957c] has found a nearly linear relationship between the observed red-line intensity and a semiempirical formula involving the critical frequency and the virtual height of radio reflection (see Section 12.3.3). Barbier [1956u, 1957u, b, 1958u, 1959~1 has observed enhancements in the middle and second half of the night that are not so simply explained. These additional problems are treated in Section 13.2.3. For nighttime production of the red lines in the F, region by dissociative reconibina- tion, vertical diffusion of ions becomes important; the theory is extended to the nightglow in Section 13.2.2.

11.5.4. Dayglow in t he Red Lines

Estimates of the brightness to be expected in the dayglow have been made by Brandt [ 195863 on the basis of dissociative recombination (1 1.77) and Schumann-Runge dissociation. Resonance scattering is even less important, relative to the other processes, than it is in the twilight.

I t is clear that the dayglow will be much brighter than the twilight. Dissociative recombination proceeds so rapidly that in a very short time after the ionizing radiation leaves the emitting regions, most of the NO+ disappears. The emission then comes only from the higher altitudes where most of the ionization is in the form of O+ and where

I I .6. EXCITATION OF OTHER EMISSIONS 479

the limiting reaction is charge transfer ( 1 1.78). But in the daytime, recombination in the F, region is also important. Collisional deactivation greatly affects the daytime brightness from dissociative recombination by governing the low-altitude emission.

Similarly, ultraviolet dissociation [see Eq. (1 1.74a)l is much more important in the dayglow than in twilight. The twilight screening height is of the order of 135 km, and hence an enormous advantage is associated with incidence of the light from above the high atmosphere, rather than from below, as in twilight.

The incident sunlight is greatly attenuated below 105 km for vertical incidence. Above this height deactivation becomes important, but probably does not entirely suppress the radiation. The rate of deactivation has been assumed throughout to be proportional to the 0, abundance. If this is the case the emission rate at low altitudes becomes independent of 0, density, since the 0, dependence of the rates of excitation and deactivation effectively cancel. Thus it is the attenuation that eventually cuts off the profile of Schumann-Runge excitation.

Brandt’s calculations of the dayglow brightness depend rather strongly on the values of atmospheric parameters as well as on the relevant reaction rates. Accurate measurements of emissions may thus eventually allow, for example, direct measurement of the rate of recombination of 0; or NO+. The dayglow in general may someday assume an important role in the study of the ionosphere. In the table in Appendix 11, Brandt’s estimates of the dayglow in [OI],,, X6300, are given along with representative other data.

11.6. Excitation of Other Emissions

11.6.1. The [Nl]z, Lines

The main hypotheses that have been offered for excitation of the weak nitrogen doublet (4S0 - 2Do) are resonance scattering and fluorescence (M. Dufay [1951a]),

N + h v - + N * , (1 1.79)

and dissociative recombination (Bates [ 19524 ,

N: + e - N* + N*. (1 1.80)

Absorption of sunlight at A3466 (4S0 - ,Po) followed by cascading to ,Do with emission of X10,400 (see Appendix VI) is a more important way of populating ,Do than direct absorption at X5199. Nevertheless the

480 11. THEORY OF THE TWILIGHT A N D DAY AIRGLOW

g-value of Table 11.1 is only 7.5 x 1O-I' photon/sec atom, as calculated by Nicolet [1952b].

An average zenith emission rate of 10 R would then require some 10'' fully illuminated N atom/cm2 (column), were the lifetime short compared with the time scale involved in twilight and in the absence of deactivation. Actually the radiative lifetime of zDo is of the order of one day (Garstang [1952a]). Thus the effective value of g at sunset would be slightly less than the computed value (depending on the length of the day) and it would decrease very slowly after sunset. Complete dissociation of N, above 140 km would provide an adequate amount of atomic nitrogen. However, not only is such extensive dissociation improbable, but we have thus far neglected collisional deactivation.

If there were no deactivation the intensity during the night would be nearly as high as in twilight. But superelastic electron collisions, with a rate coefficient as low as s w cm3/sec in the F region and a probability of deactivation of Nes, would lead to a fairly rapid disappearance of the line after sunset (Bates [1952b], Seaton [1955a]), whereas actually the emission persists in the nightglow. Further, the amount of atomic nitrogen required is increased, of course, when deactivation is important. It therefore seems unlikely that resonance scattering and fluorescence can contribute much to the intensity of h5199.

Excitation by reaction (11.80) may be adequate to account for the emission. This reaction proceeds with a high rate coefficient and will subtract N,+ from theF region soon after the ionizing radiation disappears. To explain the persistence of the line at night (Section 9.1.4), it appears necessary to invoke nocturnal ionization of N: (as in Section 11.2.2), if dissociative recombination is the correct mechanism. The matter is discussed in detail in Section 13.2.4.

Dufay [1953a] found no correlation of [NI],, with magnetic activity, although NZ is apparently so correlated. It would appear at first sight that with this interpretation N: and [NI],, should be closely related, but the explanation may be that the increased N: ionization associated with magnetic activity persists for a short time compared with the lifetime of the (excited) ,Do term of NI. The increased number of photons from [NI],, would thus be emitted over a longer period than are the N l photons, so that the relative enhancement during the twilight period would be less for the former.

11.6.2. 0 2 Infrared Atmospheric Band

Vallance Jones and Harrison [ 19584 (also see Vallance Jones [ 1958~1) have discussed their twilight observations (Section 9.2.4) in terms of the

11.6. EXCITATION OF OTHER EMISSIONS 48 1

following mechanisms of excitation: three-body association into an excited state,

0 + 0 + x -0; + x; (11.81)

fluorescence,

O,(X 3 2 3 + hv - OZ(u Idg); (1 1.82)

and the photochemical reaction,

0 + 0,+20;. (1 1.83)

Three-body association can be eliminated immediately because of the time dependence. The reaction would predominate between 80 and 90 km, where the product [O]2[X] is a maximum.24 But at this level the concentration [O] remains nearly constant all night.

I t is not entirely clear, however, whether reaction (1 1.82) or (1 1.83) is more important. The transition probability has been estimated by Vallance Jones and Harrison as A(0-0) = 1.9 x lop4 sec-l from the equivalent width of a weak rotational line in the Fraunhofer spectrum. Calculation of the relative band strengths gave A(0-O)/A(O-1) 10. Fluorescence is thus not easily proved because the radiative lifetime is of the order of 1 hour. This long life could account for the absence of a morning enhancement by reaction (1 1.82).

For fluorescence a mean screening height, caused by 0, absorption, is h, = 40 km. In computing the rate of decay in the evening it is necessary to allow both for the time dependence of the shadow sweeping across the emitting region and for the finite lifetime of the excited state. Collisional deactivation influences the height of emission, the absolute brightness, and the rate of decay. They find that both the brightness and the rate of decay are satisfactorily explained with a probability of deactivation of 8 x 10-l1 per gas-kinetic collision. The emission then arises from the region between 50 and 100 km.

Thus while fluorescence appears to give an adequate explanation, it does depend on the postulated value of the deactivation rate, and it seems also that the ozone-oxygen reaction (1 I .83) may be important. After sunset both 0 and 0, are destroyed by this reaction. In addition the abundances are affected by the three-body reaction,

0 +o, +x+o,+x. (1 1.84)

*( Brackets [ ] are used here to denote concentrations of the constituents.


Vallance Jones and Harrison adopted rough estimates of the rate coefficients and computed the approximate rate of intensity decrease. The time of sunset in the Herzberg continuum (2000-2400 A) is governed by a screening height estimated as h, = 57 km.

If the reaction (1 1.83) always gave two 0, molecules in the ' A , state, the mechanism would produce about four times the emission produced by fluorescence in early twilight. The true efficiency of the reaction is unknown, but it is quite possible that it gives an amount of excitation comparable to (1 1.82). Also, because the rate coefficients are not known with precision, accurate calculations of the absolute intensity are uncertain. Similarly, the rate of decay as computed seems reconcilable with the observed data, but precise computations are not now possible.

Whatever the primary means of excitation, some additional emission might be expected in the 0-1 band through successive scatterings in the 0-0 band. According to the relative transition probabilities, about one time in ten or so the upper level, v' = 0, will emit the 0-1 band; otherwise it will emit 0-0 which is reabsorbed by 0,, thereby repopulating the excited state. Eventually, in the absence of deactivation, the 0-0 radiation is partially degraded to 0-1 and partially scattered out of the atmosphere. This mechanism was first suggested by Bates [19543] as contributing to the nightglow Atmospheric-system band at 8645 A. A quantitative discussion has been given for that band (Chamberlain [1954a]) with the theory of radiative transfer. For the Infrared Atmos- pheric system the f-value is, however, much lower, which means that the conversion of 0-0 to 0-1 emission would tend to occur quite low in the atmosphere where it will be suppressed by collisional deactivation.

11.6.3. Ca II H and K Lines

In Section 9.2.4 the observation of these lines has been discussed. For permitted resonance lines the mechanism of scattering is rather efficient and seems quite reasonable (although not definitely established as for the case of the N a D lines). There is some evidence, based on this assumption for the excitation mechanism, that the emission is predominantly concentrated in the E layer between 100 and 120 km. With resonance scattering the abundances of Ca+ may be readily computed. Vallance Jones [1958a] finds abundances as high as 5 x lo8 ion/cm2 (column). His discussion makes it reasonable to suppose that this calcium is deposited in the upper atmosphere by meteors. The lifetime for meteor ions such as Ca+ will be the order of a month if only radiative recombination is important in destroying the ions. In the D layer, however, mutual neutralization in collisions with negative ions at night may

. 11.6. EXCITATION OF OTHER EMISSIONS 483

drastically shorten this time. The lifetime in the E layer may be appreciably reduced by mixing and diffusion, which will carry Ca+ to the lower altitudes (see Nicolet [1955a]). Of course, Ca+ may be continually reformed by photoionization. In any case the evidence for a cosmic origin of atmospheric calcium is stronger than is the case for sodium.

11.6.4. Li I Resonance Lines

Obse,rvations of the resonance lines at 6708 A (see Section 9.2.4) have been discussed in terms of the abundance of Li on the basis of resonance scattering by Barbier, Delannoy, and Weill [1958a] and Gadsden and Salmon [1958a]. The former authors conclude that the g-value for the lithium resonance lines is 8.34 times that for Na D, + D, (see Table 11.1). In addition they make a rough allowance for the fact that the screening layer is lower for lithium than for sodium, which means, in effect, that during the twilight exposure the 6708 A radiation is excited longer than that at 5893 A. Equal abundances of Li and Na would then give A6708 about 17 times as strong as the D lines, in the absence of radiative- transfer effects.

Their approximate measurements indicate an abundance ratio of [Li]/[Na] = 0.006. The ratio applies only to free neutral atoms of the two metals, but seems consistent with abundance ratios in meteors. Barbier et al. suggest that if both elements arose from the sea, the abundance of lithium would be far less. Gadsden and Salmon have obtained similar results and note in addition that the intensity ratio of X6708/A5893 seems to vary at different times and/or locations between 0.1 and 1 .O. (These observations were made in the southern hemisphere.)

Donahue [1959a] has pointed out, however, that the intensity ratio of Li/Na may not be proportional to the abundance ratio if radiative- transfer effects are important for either. When the Na intensity is fairly high, there may even be an ambiguity in the abundance (see Fig. 11.7). At extremely high abundances (off the scale of the figure) the intensity curve goes through a maximum so that a given intensity does not correspond to a unique abundance. Measurements of the D,/D, ratio could help resolve any uncertainty, however.

In the northern hemisphere Vallance Jones 11959~1 has obtained the lithium lines at Saskatoon, and Kvifte [1959a] at As, near Oslo. From calibrated plates Vallance Jones obtained a zenith emission rate of 30 R when the solid-Earth shadow was at 80 km. Were the atmosphere fully illuminated by sunlight, the brightness would possibly be as great as 150 R, corresponding to about 2 x lo7 Li atom/cm2 (column) or [Li]/[Na] - and in sea water In meteors this ratio is 2 x


it is 2.3 x The abundance uncertainties are appreciable and it is even possible that much of the lithium that was observed in twilight was introduced into the atmosphere by a high-altitude explosion of a hydrogen bomb (Barber [1959a] ; see Section 8.2.1 for further discussion of high-altitude explosions).

11 -6.5. Additional Emissions to be Expected

The question of the origin of atmospheric sodium may be clarified by examination of the resonance lines of potassium. Lytle and Hunten [1959a] have attempted to observe the resonance lines (4s 2S - 4p 2Po) at 7665 and 7699 A. They estimate that they would detect the lines on some occasions if the abundance ratio were [K]/[Na] > 1/30. In sea water the ratio is 1/47 and in meteors, 1/7. The absence of potassium from the twilight is thus partial support for the view that sodium arises from the sea rather than meteors. The discovery and measurement of the brightness of K lines would clearly be important.

Shklovskii [1957a] has suggested the presence of other lines in twilight as a result of BowenZ5 fluorescence from the Lyman ,8 line in the solar spectrum. Atomic oxygen has a term, 3d3D0, at 97488.1 cm-l above ground (2p4 "p), whereas Lyman /I (at 1025.71 7 A) supplies 97492.3 cm-'. With 3D0 populated by absorption, the following cascade may occur,

3d 3D'J + 3p 3P -+ 3s 3S'J + 2p4 3P. (1 1.85)

Infrared lines at 11,294 and 11,287 A arise from the first cascade, while the well-known auroral line 8446 A arises from 3s 3S0 - 3p 3P. Actually these lines will not appear in the twilight (p47r4 - 1 R) because of the severe screening height applicable to Ly ,8. But Brandt [1959a] has shown by a radiative-transfer treatment that detection of the lines in the dayglow may well be possible, since the emission rate will be p 4 n 4 rn 500 R.

Nicolet [1955b] has discussed the role of nitrogen oxides in the airglow, and concludes that the daytime continuum due to

NO + 0 +NO, + hv (1 1.86)

may be some 20 times as bright as in the nightglow (Sections 12.3.1 and 13.4.3). Many other enhancements will undoubtedly occur. A systematic listing of dayglow features is not likely to be very successful

2 6 The fluorescence mechanism proposed by Shklovskii for the twilight was first invoked by Bowen [1947a] to explain the enhanced (compared with 3s 'So - 3p 'P, X7774) 0 1 line A8446 in certain emission-line Rstars.

11.6. EXCITATION OF OTHER EMISSIONS 485

at the moment; mention is made here only of those emissions for which quantitative estimates have been made.

PROBLEMS

1. (a) Use Eq. (11.23) to show that P = 0 for the D, line of Na. (b) Show that the green line [OI],, is also unpolarized for resonance scattering. What is the maximum twilight polarization for A6300 [OI],, ? (See Chamberlain [ 195933 .)

2. Show by Eq. (1 1.42) that when the incident flux in D, is in the ratio = 2, the scattered intensity in the a and b hyperfine groups is 516 and 14/9, respectively, times the values computed by the resonance approximation, but that the total line intensity is the same. Then show that strict resonance scattering will overestimate the intensity of the second scattering by 6 percent of the accurate secondary component. The relative strengths may be read from the tables in White’s book [1934a; see p. 356 and Appendix] or in the original paper by White and Eliason [1933a].

3. Neglect the intensity alternation and compare the profile for h3914, N,+ First Negative 0-0, for excitation by continuous radiation with no absorption lines (FK independent of K ) with Tkin = 250 OK as computed by (a) the exact formula and (b) the approximate formulation with no change in angular momentum during excitation. What is the effect on the two profiles of a 2 : 1 alternation in statistical weights in which levels with even K are more heavily populated than those with odd K ?

Chapter 12. Spectral Photometry of the Nightglow

12.1. Methods of Height Determinations

12.1.1. Fundamentals of the van Rhijn Method

In connection with his attempts to separate the terrestrial from the astronomical component of the night sky by photometric means, van Rhijn [1921a] derived an expression for the dependence of airglow

intensity on zenith angle when the emitting layer is optically and linearly thin, homogeneous, and spherically symmetric, but with no extinction in the lower atmosphere. Although these conditions are never fulfilled in reality, the simple expression resulting from these assumptions forms the basis of what has come to be called the van Rhijn method of height measurements. The method makes use of the fact that the precise manner in which the intensity changes with zenith angle depends on the height of the emitting layer.

If the emitting layer is thin and homoge- FIG. 12.1. Geometry of the neous, the intensity emitted in any direction 6, van Rhijn method of height measured from the perpendicular to the layer

measurements. (see Fig. 12.1), is proportional to sec 6. And from the triangle in Fig. 12.1 we see that

c

(12.1)

where 5 is the observer’s zenith angle, a is the Earth’s radius, and z is the height of the layer. Writing9, for the intensity from the zenith, we have for the intensity in direction 5,

yc = y o V(Z I 51, where the van Rhzjn function, V(= sec 6), is

(12.2)

(12.3)

486

TABLE 12.1

VAN RHIJN FUNCTIONS, V(z I 5)

1 (km) (degrees)

60 80 100 125 150 175 200 250 300 350 400 lo00

0 5

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

1.oooo 1.0000 1.0037 1.0037 1.0151 1.0150 1 .0345 1 ,0343 1 .0628 1 .0624 I . 1011 1.1004 1.1511 1.1499 1.2152 1.2134 1.2969 1.2942 1.4012 1.3971 1.5356 1.5291 1.7113 1.7012 1 .9465 1 .9299 2.2711 2.2425 2.7381 2.6846 3.4438 3.3336 4.5565 4.3009 6.1985 5.5852 7.3378 6.3695

1 . o m 1.0037 1.0149 I .034l I .0620 I .0997 1. I488 1.2116 1.2915 1 .3930 I .5229 1.6913 1.9138 2.2151 2.6347 3.2342 4.0860 5.1278 5.7103

1 .oooo 1 ,0036 1.0148 1.0338 I .0615 1.0988 1.1474 I .2095 1.2882 I .3880 1.5152 1.6793 1.8946 2.1826 2.5765 3.1227 3.8599 4.6921 5.1222

1 .woo 1 .0036 1.0147 1.0335 1 ,0609 1 .0979 1.1460 1.2073 1 .2849 1.3831 I .5077 1.6678 1 ,8761 2.1518 2.5227 3.0231 3.6697 4.3550 4.6893

1 .oooo 1 ,0036 1.0145 1.0333 1.0604 1.0971 1.1446 I .2052 I .2818 1 ,3783 1 ,5005 1 ,6566 1 .8583 2.1226 2.4726 2.9335 3.5068 4.0842 4.3539

1.000 1.004 1.014 1.033 1.060 1.096 1.143 1.203 1.279 1.374 1.493 I .646 1.841 2.095 2.426 2.852 3.365 3.861 4.084

1 .Ooo 1.004 1.014 1.033 1.059 1.095 1.141 1 . I99 1.273 1.365 1.480 1 ,625 1.809 2.004 2.341 2.710 3.130 3.511 3.672

1 .Ooo 1.003 1.014 1.032 I ,058 1.093 I . I38 1.195 I .267 1.356 I ,467 I .606 1.779 1.997 2.267 2.590 2.943 3.247 3.372

1 .Ooo 1.003 1.014 1.032 1.057 1.090 1.136 1.192 1.261 1.348 1.454 1.587 1.751 1.954 2.200 2.487 2.789 3.039 3.040

1 .Ooo 1.003 1.014 1.031 1.056 I .090 I . 133 1.188 1.256 1.340 1.443 I .570 I .725 1.915 2.141 2.398 2.660 2.870 2.953

1 .000 1.003 I .011 1.026 1.047 1.074 1.109 1 . I52 1.203 I .263 1.334 1.416 I . 508 1.609 1.714 1.816 1.905 1.966 1.988

488 12. SPECTRAL PHOTOMETRY OF THE NIGHTGLOW

In Table 12.1 are collected some previously unpublished V-functions computed by Roach, Megill, and Marovich for a range of heights between 60 and 175 km and for 5-degree intervals in <; the values for 200 < z _< 1000 km are taken from Roach and Meinel [1955a].

If the rate of emission is constant over a wide height interval with lower boundary at z1 and upper boundary at z2, the relative intensity is (see Problem 1)

which reduces to Eq. (12.2) as z2 and z1 approach z. For a more complicated distribution of emission through a thick layer, a solution might be obtained by a method introduced by Barbier [1934a] in connection with the study of absorption by atmospheric ozone. However, very precise data and analysis would be required before the observed intensity variation could yield a reliable emission profile. Fesenkov [1935a] has modified the van Rhijn formula to allow for a systematic azimuth dependence in the event of a latitude variation, but again, the airglow is unfortunately not sufficiently well behaved to make such extensions to the theory of practical value.

The above discussion has neglected absorption and scattering in the lower atmosphere. To correct for these factors it is not sufficient merely to diminish the theoretical intensities by an exponential factor involving the atmospheric extinction coefficient, as though radiation were absorbed in passing through the atmosphere. There is true absorption in the ozone layer and an exponential attenuation is appropriate for that part of the atmosphere. But in the troposphere Rayleigh scattering is the dominant process for a clear, dry atmosphere, and a proper treatment of observations must allow for radiation scattered into as well as out of the line of sight. Scattering by dust and haze will not follow the Rayleigh phase functions, however, and their presence introduces an appreciable uncertainty in the results. Diffuse reflection at the ground will also modify the observed intensities.

The radiative-transfer problem applicable to photometric corrections of the nightglow is treated in Section 2.5. In Fig. 12.2 are some illustrative examples. In allowing for the lower atmosphere two approaches are possible; one may compute theoretical curves allowing for scattering and absorption and then compare these curves directly with the observations (as in Fig. 12.2); alternatively, one may choose to reduce the observations to “outside the atmosphere” and make the comparison with the van Rhijn functions of Eq. (12.3).

p 100

200

300

400

1000

in zoo

2.0 -

1.0 .. .-

C I I I I I I I l l 1 I 1 ( 1 I

20 40 60 80 20 40 60 00

,

489

ZEHITH DISTANCE

FIG. 12.2. Theoretical curves .f5/y0 versus 1 for various emission heights (noted in km) and for four wavelengths. The calculated curves allow for absorption by 0.25 atm-cm of ozone and (from Ashburn's [1954a] computations), Rayleigh scattering appropriate to the atmosphere above Cactus Peak, California (elevation 5415 feet), and for a ground albedo of 0.25. The effect of the lower atmosphere is seen most clearly on the curves for an emitting layer at infinity, which would be a horizontal line if there were no extinction. The black circles represent mean intensities based on numerous measurements in different azimuths. These data do not correspond to any single height of emission and were interpreted as representing a combination of airglow emission and astronomical (infinity)

light. From Roach and Meinel [1955a]; courtesy University of Chicago press.


12.1.2. Results of the van Rh i jn Method

The van Rhijn method is notorious for the wide variations in heights it has produced. There are several reasons why these discrepancies enter, which we shall discuss in the next section. I n Table 12.2, which is an extension of an earlier compilation by Chamberlain and Meinel [1954a], are summarized most of the height determinations that have been published in the years after World War 11. Earlier measurements are summarized in a review by Barbier [19523).

TABLE 12.2 VAN RHIJN HEIGHTS OF NIGHTGLOW-EMITTING LAYERS

Emission Reference

A6300 [OII,,

A5893 Na I

Meinel OH

100 85

100 90

195

250 403 260 200 21 5 110

400- 1000

62- 104

280

170 260 275

116-143

400- 1000

200 108-129

356 125 275 310 150

160- 180 306-335

70 900

Roach, Megill, Rees, .and Marovich [1958a] Manring and Pettit [1958a, b] Barbier and Glaume [ 1957~1 Elsasser and Siedentopf [ 1956a, b] J. Dufay and Tcheng [1955a] Roach and Meinel [1955a] J. Dufay, Berthier, and Morignat [1953a] Huruhata [1953a] Karimov [1947a, 1952~1 Roach and Pettit [1952a] Barbier, Dufay, and Williams [1951a, 1954~1 Roach and Barbier [1950a] Abadie, Vassy, and Vassy [1949a]

J. Dufay and Tcheng [1955a] Roach and Meinel [1955a] Huruhata [1953a] Karimov [1952a] Roach and Pettit [1952a] Abadie, Vassy, and Vassy [1949a]

J. Dufay and Tcheng [1955a] Roach and Meinel [1955a] Huruhata [1953a] Karimov [ 1952~1 Roach and Pettit [ 1952~1 Roach and Barbier [1950a] Barbier [1944a]

Berthier [1956a] Huruhata [1953a] Roach, Pettit, and Williams [1950a] Pavlova, Rodionov, Sominskii, and Fishkova

[ 1950al

Notes

7

9

5 6

10

11 12

12.1. METHODS OF HEIGHT DETERMINATIONS 49 1

TABLE 12.2 ( con t . )

Emission Height (km)

Reference Notes

~~

Atmospheric 150-200 Berthier [1956a] 0,

Herzberg 0, 200 Barbier [1953a, b] 13

Blue-green 900 Barbier [19476] 14 region

“Continuum” A5300 43-78 Roach and Meinel [1955a] 6 A5180 460 Barbier, Dufay, and Williams [1951a, 1954~1

NOTES

1.

2.

3.

4.

5 .

6.

7.

8. 9:

10. 11 . 12.

13.

14.

Height depends critically on, and was determined by, the assumed extinction coefficients. The probable error of a height deduced for a single night would be & 15 km, if the extinction coefficient, ground albedo, etc. were known exactly. This paper gives a detailed discussion of height uncertainties introduced by these parameters. Variation of zenithihorizon ratios for different observations is important. Standard deviation of 488 hourly means corresponds to a height variation of +68 km, if the data are all reduced with a constant extinction coefficient. Also see Manring and Pettit [1956a]. Uncertainties in extinction coefficient and ground albedo make precise measurement impossible. A height as high as 300 km seems definitely excluded, however. Extinction coefficient measured nightly with a stellar photometer. The northern sky gives slightly lower height, the southern sky a greater height, owing to a gradual increase in brightness from south to north. This analysis replaces earlier ones by Dufay and Tcheng [1946a, 39473, 1948a, 1954~1. These heights may be reduced slightly if a thin haze is postulated in the lower atmosphere during the observations. Values quoted are believed to be lower and upper limits of height, with the uncertainty due mainly to the extinction coefficient. Earlier, Roach and Pettit [I95161 estimated 250 km for A5577 and, at the same laboratory, D. N. Davis [1951a] deduced 200 km for a single night. Replaces Roach and Barbier [1949a]. Emission indicated two broad layers, with the relative importance of the two varying with time. See also Abadie, Vassy, and Vassy [1945a] and Vassy and Vassy [1948a, 1952~1. Roach and Meinel [1955b] reinterpreted the data in terms of a single airglow layer (1 30 km for h5577; 150 km for h6300) and an astronomical (infinity) component. Based on observational data of Garrigue [1936a]. Replaces earlier analysis by Berthier [1953c] which gave 130-150 km. Values apply to measurements in two different wavelength bands. Replaces earlier measurements by Huruhata [195Ou]. Uncertainties in ground albedo and scattering corrections lead to great uncertainty in the height. This analysis replaces an earlier one by Barbier [19476]. Formerly this emission was thought to be due to N, Vegard-Kaplan bands.


12.1.3. Difficulties with the van Rhi jn Method

Although fundamentally quite simple, the van Rhijn method is filled with practical difficulties that are manifested in the wide discordance among the various measurements reported in Table 12.2. The magnitude of these difficulties has been recognized only gradually by photometric observers, but it now appears that the necessary corrections are sufficiently uncertain and serious to render the technique extremely hazardous.

With few exceptions the van Rhijn measurements formerly indicated heights above 200 km. That these altitudes might be seriously in error, at least insofar as sodium D was concerned, was suggested on the basis of theoretical considerations regarding the excitation by Bates and Nicolet [1950u]. Nicolet [1952c] and Bates and Dalgarno [1953u] also reviewed the theoretical expectations for the maximum allowable heights of the various airglow emissions. The latter authors concluded, for example, that the argument was apodictic against sodium being emitted as high as the observations indicated, and, indeed, if a chemical reaction gave rise to the D lines, the altitude could “scarcely be much above 70 km.”

The basic difficulty with the method is that the accuracy in the ratio of zenith to horizon intensities, corrected to outside the atmosphere, must be very good in order to give a reasonable height accuracy. Thus D4jardin and Bernard [1938a] pointed out that Garrigue’s early measurements (which showed that the ratio of intensity at 80” zenith distance to that in the zenith varies between 2 and 3) would correspond to height fluctuations between about 400 and 90 km. Hence the observations must not only be accurate, but corrections to the data for comparisons with Eq. (12.2) must be made carefully. These corrections may be considered under the following three general headings.

Radiative Transfer i n the Troposphere.-The problem of making these corrections is treated in some detail in Section 2.5. For a known ground albedo, intensity corrections for Rayleigh scattering may be read from tables published by Ashburn [ 1954~1. A practical difficulty, however, lies in obtaining the extinction coefficient for the atmosphere and in ascertaining what fraction of a star’s extinction should be ascribed to true absorption by ozone, say, and what part to scattering. Further, the scattering is not all due to Rayleigh scattering; haze and dust will scatter according to quite different phase functions, and to the extent that these substances are in the atmosphere additional uncertainties are

12.1. METHODS OF HEIGHT DETERMINATIONS 493

introduced (Seaton [ 195663). Ordinarily there is also considerable uncertainty in the ground a1bedo.l

Usually the extinction coefficient has not actually been measured simultaneously with the airglow photometry, a procedure that led Ashburn [ 1955~1 to suggest that were the radiative-transfer corrections properly made, the observed heights would be systematically lower, consistent with theoretical expectations.2

Instrumental Errors.-The most important source of error due to imperfections in the equipment has been spectral purity. Errors may arise in photometric measurements of an airglow emission line due to background continuous radiation or neighboring discrete emissions that are not eliminated by the photometer. Corrections for these contamina- tions may be quite difficult to evaluate. Each of the three strong atomic emissions of the nightglow, hh5577, 5893, and 6300, has an OH band nearby, and the green airglow continuum may also contribute to the measurements with a wide band-pass photometer. Of course, if these emissions all originate from about the same height in the atmosphere, no great systematic error is introduced.

A more important source of error to the van Rhijn method has been the astronomical component. Roach and Barbier [1950a], Barbier, Dufay, and Williams [1951a, 1954~1, and Roach and Meinel [1955a] have tried various ways to correct their observations for this radiation ; but since the correction must depend on the position of the Milky Way and zodiacal light, it is difficult to accomplish accurately.

T o a large extent this problem has been eliminated by photometers equipped with birefringent filters (Blamont and Kastler [1951a], Dunn and Manring [1955a]). The filter (see Evans [1949a]) is used to modulate the signal produced by a sharp emission line. The alternating component of the photomultiplier current is then proportional to the line intensity, while a background continuum gives a d.c. component, which is readily eliminated electronically.

The birefringent filter may itself introduce a different type of error,

Typical albedos for various ground conditions have been measured by Krinov [1947a] and quoted by Penndorf [1956a] and Roach, Megill, Rees, and Marovich [1958a].

is difficult to make a realistic correction for dust and haze, however. Ashburn objects to the common procedure of computing the extinction coefficient for ozone absorption (for an assumed ozone thickness) plus Rayleigh scattering and ignoring the component due to dust and haze. If dust and haze only absorbed light, their omission might produce a large error; however, since they actually scatter light with a high albedo, the error introduced is evidently not so great as Ashburn suggested. The matter has been discussed further by Barbier [19566] and Feygelson [1958a].


since it is a polarizing device. Light that has undergone Rayleigh scattering in the troposphere will be partially polarized and hence incorrectly measured by the photometer.

If the field of view of the photometer is several degrees, observations at large zenith angles will require a correction (Roach and Meinel 11955~1). Finally, even errors in measuring the zenith angle at which the instrument is pointed can introduce uncertainties (and have done so).

Departures from a van Rhijn Layer.-The van Rhijn method postulates that the emitting layer is thin (both linearly and optically), homogeneous, and at a uniform height. The main deviation from this simplified layer is probably in the homogeneity. In X5577, which has been studied more thoroughly than other radiations, the airglow is quite patchy, so that individual measurements with a photometer may be relied on to give nonsensical results when interpreted by Eq. (12.2). The general procedure has been to make a large number of readings at various azimuths but at a constant zenith distance, and to average these measurements before applying the van Rhijn formula. Never- theless, systematic errors might arise because of departures from the ideal geometry (Barbier [ 19564).

For the sodium lines the airglow layer may at times (especially in winter) have an appreciable optical thickness. I n this case D-line quanta may be scattered one or more times by atmospheric sodium before escaping from the upper atmosphere, which could affect height determinations, as Donahue and Foderaro [1955a] first pointed out. The degree to which the van Rhijn height is affected depends not only on the atmospheric Na abundance, but on the Na model (position of the majority of Na atoms in the atmosphere relative to the nightglow excitation layer) and on the temperature of the Na atoms.3 The DJD, ratio is also altered significantly by the resonance scattering ; careful measurements of the ratio in the zenith and near the horizon may be of importance in ascertaining the correct Na model.4

a The excited atoms may have a higher kinetic temperature than the remainder of the Na, since kinetic energy may be acquired in the excitation process.

* Calculations with radiative-transfer theory have been made for three models by Chamberlain and Negaard [1956u], but require a small correction for hyperfine structure in the manner indicated by Chamberlain, Hunten, and Mack [1958a, p. 1541.

12.1. METHODS OF HEIGHT DETERMINATIONS 495

12.1.4. Height Measurements by Triangulation

Although the patchiness of the airglow often frustrates attempts to derive heights by the van Rhijn method, this structure can be exploited to give heights by triangulation. Table 12.3 summarizes the measurements for the green line that have utilized some variation of triangulating.

TABLE 12.3

HEIGHTS FOR A5577 BASED ON OBSERVATIONS OF THE IRREGULARITIES IN THE EXCITATION PATTERN (PATCHINESS)

Reference Notes

80-100 Manring and Pettit [1958a, b] 1 270-300 Huruhata, Tanabe, and Nakamura [1955a, 1956~1 2 80-100 St. Amand, Pettit, Roach, and Williams [1955a] 3

100 Roach, Williams, St. Amand, Pettit, and Weldon [1954a] 4 180 Roach, Williams, and Pettit [1953a] 5 3 00 Davis [1951a] 6

NOTES

1. Triangulation on regions showing the same relative change of brightness with time. 2. Triangulation on a discrete patch and on regions of the same mean intensity as measured

3. Triangulation on regions showing the same relative change of brightness with time. 4. Triangulation on regions of the same mean intensity. Lack of good agreement for

any assumed height, during the early part of the night examined, raised the question of whether the emitting layer is uniformly thick at a constant height.

from two stations.

5. Triangulation on discrete patches. 6 . Single-station height derived from the time required for excitation patterns to move

from east to west, on the assumption that the pattern is approximately fixed relative to the sun, the apparent motion being set by the rate of the Earth's rotation.

The most straightforward technique involves ordinary triangulation from two stations on a discrete patch. Since the contrast of bright regions to the general background may involve only a factor of two or less, and since the scale of the patches may cover a sizeable fraction of the sky, it is not always easy to pick out corresponding points on the photometer scans from the two stations. Insofar as the emission is not


contained in a plane-parallel layer, the irregularities may appear quite different when viewed from one direction than from another.

A modification of this simple procedure, then, is to compare photometer records from two stations over a fairly large area of sky and to triangulate on regions that show the same mean intensity as seen by the two photometers. In this way one attempts to smooth out the sharp irregularities that might lead to spurious heights while maintaining the advantage of a nonuniform layer.

St. Amand, Pettit, Roach, and Williams [1955a] introduced a further modification of the method by triangulating on regions showing the same relative change of brightness with time as observed from two stations. This technique minimizes errors due to inaccurate calibration of the two photometers and also further diminishes the likelihood of error due to the different appearance of a particular area when viewed from two directions. Manring and Pettit [1958a] have pointed out, however, that the changes in brightness could conceivably arise from a different height than the bulk of the emission.

Still another method makes use of the fact that the excitation pattern moves in the sky and maintains more or less the same appearance for some time. If one knew the linear velocity of one of these patches, it would be possible to measure its position at two times and compute the height. This technique would be, essentially, triangulation from a single observing point. The method is effectively the same if one supposes that the patches remain in the same position relative to the center of the Earth and the sun, and that the Earth rotates under them. We can consider the observer as making measurements from two points in space, because of the rotation, while the emission pattern remains fixed. Davis (see Table 12.3) obtained a height for A5577 by this method for a single night. Barbier [1957a] has also used the method on X6300, where the assumption of an excitation pattern fixed relative to the sun is somewhat better justified, and obtained a height of 300 km.

12.1.5. Height Measurements by Rockets

Rockets equipped with photometers and flown directly into the emitting region are certainly the most reliable means of obtaining nightglow heights, but this technique is still not without its. difficulties. The main problem in the interpretation has been the lack of spectral purity (see the discussion under Section 12.1.3, above). The various measurements that have been reported are summarized in Table 12.4.

12.1. METHODS OF HEIGHT DETERMINATIONS

TABLE 12.4 ROCKET HEIGHTS OF NIGHTGLOW-EMITTING LAYERS

497

Emission Height (km)

Reference Notes

A5517 90-118 P I I S 2 80- 120

A6300 > 163 roIlz1 2 146

A5893 85-1 10 Na I 80-115

70-100

Meinel OH 56-100

Herzberg 0, 90-100 (2600-2900 A)

“Continuum” 5335 A 90-110 5200-5500 A 85-1 10

A1215 85-120 LY

~

Heppner and Meredith [1958a] Tousey [1958u]

Heppner and Meredith [1958a] Tousey [ 1958~1

Heppner and Meredith [1958a] Tousey [ 1958~1 Koomen, Scolnik, and Tousey [1957u]

Heppner and Meredith [1958a]

Tousey [1958a]

Heppner and Meredith [1958a] Tousey [1958a]

Kupperian, Byram, Chubb, and Friedman [1958a]

9 10

11

NOTES 1. Sharp lower boundary. Maximum emission at 94 km. 2. Some variation in boundaries among the results of four flights, including that reported

by Heppner and Meredith. Maximum emission around 95-100 km. Preliminary reports on two of these flights were published by Berg, Koomen, Meredith, and Scolnik [1956a] and Koomen, Scolnik, and Tousey [1956n]. An earlier but unsuccessful attempt was reported by Koomen, Lock, Packer, Scolnik, and Tousey [1956a]. A more detailed analysis of the two flights was given by Koomen, Scolnik, and Tousey [1957a].

3. Majority of A6300 probably arises from above the maximum height reached by the rocket, but the A6300 photometer also showed an emitting region from below 56 to 100 km. This is probably due largely to the 9-3 OH band, which overlaps A6300. The tabulated height for OH should be regarded with some scepticism.

4. Emission detected in the region 80-100 km may be due to A6300, OH, or to continuum. Above peak of flight at 146 km there is still airglow.

5. Flight of 5 July 1955. Upper boundary especially uncertain. Maximum at 93 km. 6. Flight of 28 March 1957. Maximum at 95 km. 7. Flight of 12 December 1955. Maximum at 85 km. Considerable uncertainty is involved

8. Maximum near 100 km; height distribution resembles that for A5577. 9. Maximum near 105 km.

in the subtraction of background continuum and OH from the measurements.

10. Some variation for different filters and flights. Maxima are usually near 100 km. 11. Probably due to Ly OL radiation from the interplanetary medium scattered by atmos-

pheric hydrogen. See Sections 9.1.3 and 13.5.2.


12.1.6. Indirect Means of Deriving Heights Because of the contradictions of van Rhijn measurements among each other and with the theoretical expectations, many upper-air physicists sought indirect means of obtaining some information on airglow heights, even though such information might be inconclusive. One technique has been to seek correlations of airglow brightness or activity with ionospheric phenomena. Correlations that are good may indicate the region where the excitation takes place (and something about the excitation mechanism as well). The most successful application of this method is the relationship that St. Amand [1955a] and Barbier [1957c] have noted between A6300 and F-layer ionization. If the height of one emission is definitely established, one may then use photometric correlations between different wavelengths to establish heights for other radiations. (For further discussion of correlations see Section 12.3.3.)

Another indirect means of height determination lies in temperature measurements (Section 12.2). Formerly it was the hope that airglow studies could be used to obtain data on the temperature structure of the atmosphere, but the unsatisfactory nature of height measurements has occasionally caused the procedure to be reversed. The variation of temperature with height is treated in Appendix IV.

The low rotational temperature of 0, (both the Atmospheric and Herzberg systems) places the emitting height below 100 km. Similarly, OH cannot be excited in the F region as some of the van Rhijn measurements implied. Doppler temperatures for the forbidden lines are also useful in placing the general height region. Temperatures of 700” to 1000” K for the twilight and nightglow red line (h6300) are consistent with F-layer excitation, while measurements of 150” to 250” K for the green line (h5577) are indicative of the lower ionosphere (see Section 12.2.2). One must bear in mind, however, that the “temperature” of the excited atoms may be higher than for the surrounding gas, if excess kinetic energy acquired in the excitation process is not dissipated by collisions before the atoms radiate.

12.2. Spectroscopic Temperatures

Airglow temperatures have in the past been useful as a means of indicating emission heights, as discussed in the preceding section. Since these heights are now becoming known with some accuracy by independent means, the spectroscopic temperatures should become more useful as measures of the kinetic temperature and its variations or as indicators of the excitation mechanism.

12.2. SPECTROSCOPIC TEMPERATURES 499

12.2.1. Rotational Temperatures

When the rotational structure is well resolved the rotational temperature is obtained directly from the relative line intensities as discussed in Section 1.4.2. I t is often the case in airglow spectra, however, that the individual lines are not resolved. In this situation the calculation of synthetic profiles offers the best means of deriving a temperature. Let $(A) be the actual distribution of intensity in a band (i.e., as observed with infinite resolving power) and .Ymeas(A) the measured distribution. Because of the finite resolving power a very sharp line at A, will appear in the spectrum with an intensity profile K(X - A,), which we shall call the smearing function. This instrumental profile, which can be obtained directly from the profile of a sharp line on the plate, may be normalized:

W I K(A - A,)d(A - A,) = 1. (12.5) -W

Thus we have

W

9m,,,(A) = J 9 ( A ' ) K(A - A ' ) dX'. (12.6) 0

A synthetic profile may be computed from the right side of Eq. (12.6) for various assumed temperature distributions, and these calculations may be compared with the measured profile to obtain the temperature.

Temperatures have been estimated from the unresolved 0, Atmos- pheric 0-1 band at 8645 A. Meinel [1950fl found Trot rn 160" K with a variation of about 20" K for different spectra. (Wallace and Chamberlain [1959a] pointed out that Meinel's value 150" K should have been 160" K.) On one occasion, when the band was abnormally strong, the temperature was about 200" K. Dufay and Dufay [1951a] similarly obtained a low temperature (130" K) from low-dispersion spectra. Figure 12.3 shows synthetic profiles for several temperatures for the 0, band as observed with the 9-in. Meinel spectrograph (70 A/mm) at Yerkes Observatory; Wallace and Chamberlain [1959a] obtained a mean temperature of 183" f 7" K. This uncertainty is the mean error from the scatter of the various determinations. The uncertainty in a single measurement was probably 10" or 20" K. Branscomb [1952aj investigated the band system in the laboratory and concluded that collisions are frequent enough in the upper atmosphere to establish a thermal distribution among the rotational levels of the excited molecule before spontaneous emission occurs.


Rotational temperatures of the 0, Herzberg bands are also quite low. Chamberlain [1955a] concluded that Trot 5 200" K. Because of the uncertainties in photographic photometry with extremely long exposures and in the theoretical line strengths for this system, a more precise estimate was not possible ; the line with maximum intensity appears to

I I I I I I A

+ P +

WAVELENGTH

FIG. 12.3. Observed and model intensity profiles of the 0-1 band in the airglow From Wallace and Chamberlain [ 1959~1; courtesy Pergamon Press.

be in the unresolved band head. From lower dispersion spectra, Swings [1943u] and Barbier [1947b, 4 estimated temperatures in the range 150"-220" K, but again high accuracy cannot be claimed.

The most accurate rotational temperatures obtained from airglow spectra are from the Meinel bands of OH. These bands arise from levels that probably have rather long lifetimes and, although this conclusion is not definitely established, i t is reasonable to suppose that the rotational temperatures are indicative of the gas-kinetic temperatures. Meinel [1950e] found some evidence that this is the case: temperatures derived from several OH bands agreed best when the rotational constants B, of the excited levels were used, which suggests that rotational redistribution does occur after excitation and before emission. While the relative intensities in the open P branch give the rotational temperature in the

12.2. SPECTROSCOPIC TEMPERATURES 50 I

most straightforward way, alternative methods involve comparing the total intensities in the P, Q, and R branches and comparing the relative intensities from the two components of the 217 state. This method gives about the same results (Meinel [1950e]). Wallace [1961u] has emphasized that vibrational cascading tends to alter the rotational temperature of a vibrational level and that the value of Trot derived from several different bands on a single spectrogram could not agree as well as they do (e.g., Kvifte [19596]), if rotational redistribution did not occur.

Various determinations of the temperature in middle latitudes indicate values scattered around 250" K ; there may be some dispersion in the measurements for different nights. The available measurements are summarized in Table 12.5, which is based on a table previously published by Wallace [ 1960~1.

TABLE 12.5 SUMMARY OF OH TEMPERATURE DETERMINATIONS~

Meinel [195Oe] Cabannes, Dufay, and Dufay [1950a] Dufay and Dufay [19510] Chamberlain and Oliver [1953u] Gush and Vallance Jones [1955a] Mironov, Prokudina, and Shefov [ 1958~1

Prokudina [1959b]

Fedorova [1959a, b] Shuyskaya [ 195901 M. Dufay [1959a] Kvifte [1959b] Blackwell, Ingham, and Rundle [1960a] McPherson and Vallance Jones [1960u]

+ 4236 45. 45. 16.6 52.1 55.1 68.6 55.7 68.3 40.4 60.2 45. 59.1

- 16.3 + 52.1

58.8 14 .1

240 * 5 185 3= 46b 242 & l b .v 300 200 & 20 213 & 19b 282 19b 222 & 19 280 to 460 216 & 15 250 &- 11 231b 215 f 8 294 216 + 27 227 214 & 35

a Small corrections have been made by Wallace [1960a] to all the above determinations except those by Gush and Vallance Jones, Kvifte, and Blackwell, Ingham, and Rundle, for the use of the mean rotational constants rather than exact energy levels. Some of the station latitudes were incorrectly tabulated in the original paper, but have been corrected by Wallace for inclusion here.

In the case of these results, it is not clear whether the P, branch or a blend of the PI and P2 branches should be used in the correction process. Consequently, the corrected values in these cases may be as much as 7 percent too low.


A variation of the temperature with latitude was first disclosed by Chamberlain and Oliver [1953a], who found Trot to be around 300" K in northern Greenland (near the geomagnetic pole). Krassovskii's associates (Mironov, Prokudina, and Shefov [ 1958a1, Fedorova [ 1959a, b], Prokudina [1959b]) have investigated this latitude effect by means of a chain of several stations equipped with identical spectrographs, and they find a systematic increase of temperature toward higher latitudes. Similar results were obtained from Canadian stations by McPherson and Vallance Jones [ 1960~1. However, Blackwell, Ingham, and Rundle [ 1960al have also found a high temperature, nearly 300" K, in the tropics. Rocket measurements have now confirmed the airglow result that the 75-km region is hotter in the Arctic than at temperate latitudes (Jones, Peterson, Schaefer, and Schulte [1959a]). If there is a strong latitude variation of Trot, it seems plausible that there might be a strong seasonal variation also. If so, data obtained at different latitudes should not be compared indiscriminately to derive the precise latitude profile. At Yerkes Observatory ( A = 42") Wallace [1961u] found only a small yearly variation, with an amplitude of less than 30" K, which is also consistent with the rocket experiments of Jones, et al. But at Yakutsk ( A = 62") Krassovskii, Shefov, and Yarin [1961n] observed a yearly variation with an amplitude at least twice as great as that at the lower latitude. The two sets of airglow data show about the same phase, with the maxima occurring in winter.

Krassovskii et al. also reported an interesting correlation between Trot and the absolute OH intensity at Yakutsk. Such a relationship appears to be absent at Zvenigorod ( A = 55?7), which has been interpreted by Krassovskii [ 1958bI as evidence against the ozone-hydrogen excitation process-at least, at that latitude (see, however, further discussion in Section 13.5.1).

A higher temperature in the Arctic would not be expected if the upper atmosphere were heated entirely by local absorption of solar radiation. If conduction of heat from the solar corona and interplanetary medium were important, as proposed by Chapman [1957a, h ] , or if particle bombardment is an important heat source (Section7.3. l), it is not unreasonable to expect greater heating in the Arctic, where the magnetic field has less inhibiting effect on the vertical motion of ionized particles and therefore on the inward flow of heat. Meridional circulation at high altitude may also be important in governing the temperature of the polar mesosphere. Investigation of airglow spectroscopic temperatures can thus provide critical data on the heating of the upper atmosphere. However, the latitude temperature variation could be partly an indication of a latitude difference in the height of formation of OH molecules.

12.3. INTENSITIES, POLARIZATION, AND VARIATIONS 503

12.2.2. Doppler Temperatures

The profile of an emission line formed in the upper atmosphere is usually governed only by the motions of the atoms and by the Doppler effect. (Radiative-transfer effects can produce some distortion ; see Fig. 11.6.) This line-broadening serves to define a Doppler temperature (Section 1.1.4). Babcock [I 923~1 first demonstrated that the line widths could be ascertained through interferometric measurements. But just as there may be some uncertainty in interpreting a rotational temperature in terms of the gas-kinetic temperature, the explanation of the Doppler width is not always straightforward. Since the excited atoms may have acquired an excess of kinetic energy in the process of becoming excited, they may give Doppler widths much greater than would be characteristic of the local kinetic temperature^.^ Indeed, in some cases the excited atoms may not even approximate a Maxwellian distribution (e.g., see Gauzit [1945a]).

Measurements of Doppler temperatures have been made on the nightglow [OI],, green line, h5577, by Wark and Stone [1955a] (also see Phillips [1956a]), Armstrong [19566], Karandikar [1956a, 61, and Wark [1960a]. These measurements did not give definitive values for the temperature, partly because of the uncertain correction of the instrumental profile, which is of the same order as the Doppler profile. However, it appears that TDop is probably in the range 200" 50" K. Later observations by Armstrong [1959a] give results in the range 180" to 220" K.

Measurements of [OIlzl, h6300, have been made in twilight (Phillips [1956a], Wark [1960a]), where TDop = 710" 50" K . In the nightglow Cabannes and Dufay [19566], found TDop probably less than 500" K, but Wark [1960a] obtained 980" & 120" K.

12.3. Intensities, Polarization, and Geographic and Time Variations

The pioneering investigations of Rayleigh, Dufay, McLennan and several others (see Section 9.1.2) opened the field of photometry of individual airglow radiations, and in more recent times important advances in instrumentation have accelerated progress in this subject. These advances have been concerned with improving the spectral purity by

For example, the lack of excess broadening of the twilight Na D lines tends to substantiate resonance scattering as the excitation mechanism. See the discussion under Section 9.2.2.


the use of interferometers6 and by new filtering techniques ;’ by improvements in the mechanical and electronic aspects of low intensity photometers and in their calibration;S and in the utilization and development of new infrared detector^.^

12.3.1. Absolute Intensities and Polarization

Separation of Airglow and Astronomical Light.-In the spectral regions where astronomical light contributes appreciably to the night sky, such light must be subtracted in some manner from the total, if absolute airglow intensities are to be obtained. The existence of an airglow was first suspected partly on the grounds that the absolute intensity of the night sky and the distribution of this radiation over the celestial sphere were not compatible with starlight being the sole source. The early investigations are summarized in Section 9.1.2. Dufay [ 1929~1 and, somewhat later, Fesenkov [1935a] made attempts to sort out observationally the starlight, zodiacal light, and airglow, by utilizing starcounts and expected time variations and distributions over the sky for the different components. Divari [1951a] extended Fesenkov’s analysis, and Barbier [1947b, 1954a, 1955~1 has derived photometrically the terrestrial component in the blue (3900-4800 A). On the average Barbier finds the airglow in the direction of the celestial pole ( 5 = 45”) is 40 percent of the total night-sky radiation, with extreme values ranging from 24 to 54 percent. In the zenith the airglow may be relatively weaker if the Milky Way passes near that point, while at large zenith angles almost all the radiation may arise from airglow if the zodiacal

See especially Blamont and Court& [1955a], Armstrong [1956a], Karandikar [1956a,b], Cabannes and Dufay [19566], and Phillips [1956a].

‘I Birefringent filters have been developed and applied to the airglow by Blamont and Kastler [1951a], Koomen, Packer, and Tousey [1956a], and Dunn and Manring [1955a]. For the N a D lines Blamont [1953a, 1956~1 has developed a sodium-vapor filter that employs the Zeeman effect produced by a strong magnetic field to make the “filter” alternately absorbing and transparent; this filter is appropriate for twilight but too insensitive for the nightglow.

Elvey and Roach [1937a], Grandmontagne [1941a], Abadie, Vassy and Vassy [1945a], Marlow and Pemberton [1949a], Roach and Pettit [1951a], Baillet, Barbier, Bosson, Lallemand, and Maguery [1953a], Baillet [1955a], Barbier [1955b], St. Amand 1195561, J. Dufay, Berthier, M. Dufay, and Morignat [1956a], Link, Neuiil, and Zacharov 11957~1, Barbier and Lkveque [1957a], Onaka and Nakamura [1958a].

@ Elvey 11943~1, Stebbins, Whitford, and Swings [1945a], Kron [1950a], Osherovich and Rodionov [1954a], Gush and Vallance Jones 11955~1, Ogawa, Nakamura, and Hashizume [1956a], Krassovskii [1956a] (and earlier references listed in Section 9.1.4), Harrison and Vallance Jones [1957a], M. Dufay [1958a, c], Bolshakova, Georgiyevskii, Otto, and Rodionov [1958a].


light and Milky Way are not nearby. Roach and Meinel [1955u] and Tohmatsu [1958u] find about 60-70 percent of the continuum at 5300 A is due to astronomical light. In other regions of the spectrum the airglow contributes relatively more than in the blue-green.

A somewhat different aspect to the problem of separation of astronomical and airglow radiation lies in the question of the spectral composition of the zodiacal light and gegenschein. A number of investigationslO have concluded that these sources emit the atomic lines seen in the airglow. This enhancement has been considered as evidence that part of the zodiacal light arises from the upper atmosphere and that the Earth’s atmosphere is stretched out in the direction away from the sun in a manner similar to comet tails. This gaseous tail of the Earth has been associated with the gegenschein (Fesenkov [1950u], Divari [1950u], Astapovich [ 1950~1). The most accurate (photoelectric) work seems to indicate, however, that there is no detectable enhancement of emission lines in these sources.11

Absolute Intensities.12-Since most of the emissions are variable, only orders of magnitude can be given for the mean intensities. In the blue region (3900-4800A), which is filled with numerous weak bands, generally so close together that they give the appearance of a continuum13 under low resolution, the emission rate, ~ 4 7 ~ 1 , averages about 0.5 R/A according to Barbier [1954a]. The observable Herzberg bands of 0, in the near ultraviolet have an integrated emission intensity, p47r.9, of about 430 R or an average specific intensity of p4rI = 0.80 R/A.14 In the green region the emission continuum is of the order of 1 to 3 R/A (Barbier, Dufay, and Williams [1951u], Chuvayev [1952u], Shefov [1959a]; also cf. Fig. 9.6).

lo Tikhov [1950a], Rozhkovskii [1950a], Karimov [19526, 1957~1 and observations by Karimov and Z. V. Kariaguina reported by Fesenkov [1956a]; also see the photometric study by Divari [1949a] and a general review by Swings [1952a].

l1 Roach, Pettit, Tandberg-Hanssen, and Davis [1954a], Roach and Rees [1956a], Divari and Asaad [1959a]; see also the early work by Eropkin and Kozyrev [1935a].

l2 Measurements quoted here are referred to the zenith in all cases. For this reason the emission rate in rayleighs is expressed as p4?r$, where p is the cosine of the angle of emergence of the radiation from a plane-parallel layer. See Appendix I1 for further explanation. Also, measurements discussed here in detail are collected in a table for easy comparison and reference in Appendix 11.

I3 Toward the long wavelength end of this region the (true) green continuum contributes; see Section 9. I .4.

I4 The measurements of Barbier [1953a] must be multiplied by a factor 2.89, as corrected in a later paper (Barbier [ 1956a]), which also contains additional measurements. Rodionov and Pavlova [1951a] obtained similar results over roughly the same wavelength interval.


Numerous measurements have been made on the [OI],, green line,15 h5577. The average intensity corresponds to about 250 R ; the first such measurement by Rayleigh [1930a] gave 181 R. The [OI],, red lines have a theoretical photon intensity ratio of h6300/h6364 = 3/1. Although the red lines have a pronounced post-twilight decrease, and in some instances a pre-dawn rise, the intensity in the middle of the night probably averages around 50 to 100 R.16

The Na D lines go through a pronounced seasonal variation and in the summer especially the intensity is difficult to measure accurately, because of an overlying OH band. Manring and Pettit’s [1957a] observations with a birefringent filter suggested that the Na emission rate may be around 100 R in winter. Winter values of 200-300 R are quoted by various other observers. The D lines are much fainter, however, in summer months (Section 12.3.2). Prokudina [ 1959~1 (also see Shklovskii [1959a]) reported Ha in the airglow, which varies between 5 and 20 R, while rocket measurements by Friedman et al. (Section 9.1.3) give 2500 R for Ly a.

M. Dufay [1958a] has estimated the emission rate of the 0-1 Atmos- pheric band of 0, at 8645 A by comparing it with the green line. He finds ~ 4 7 7 9 - 1500 R, corrected for extinction by the lower atmosphere. Barbier [1956c] has quoted a value of 2000 R; these measurements may be considered to be in good agreement.

A number of measurements have been made in the infrared region where the radiation is due predominantly to OH. Some care is required in applying or interpreting these data. Measurements with a wide band- pass filter will give a value of the total radiation detected; but if several OH bands contribute, one must know the relative intensities of these different bands in order to weight them properly against the photometer curve of sentitivity versus wavelength, and to allow for differential atmospheric extinction. The relative intensities depend on the vibrational transition probabilities and on the relative rates at which different levels are populated directly by the excitation mechanism. As this

l 5 Some of the more recent ones, utilizing photoelectric photometers, are by Rodionov, Pavlova, and Rdultovskaya [1949u], Barbier, Dufay, and Williams [1951a, 1954~1, Roach [1955a], Barbier [1956a], and Manring and Pettit [1957a]. Others are listed by Roach, Williams, and Pettit [1953u, Table 21.

l6 Berthier and Morignat [1956u] find the intensity ratio for A6300/A5577 to be about 0.2; Roach [1955a] quotes 0.56. Also, A6300 intensities have been measured directly by Barbier [1956a] and Manring and Pettit [1957u]. With disturbed magnetic activity at low auroral latitudes, however, the red/green line ratio may increase considerably. At the moment it is largely a matter of semantics as to whether some of these red-line enhancements should be termed “auroral” (Barbier [39576, 195861, Sandford [1958a]; see discussion in Section 9.1 .I).


information is not known with much accuracy, corrections based on theoretical band intensities may be greatly in error. For the same reason estimates of the total OH emission that have been made on the basis of the intensity of one or a few bands could easily be in error by an order of magnitude.

Photometric measurements over wide spectral regionsli give mean intensities at the ground corresponding to p4nI - 10 R/A between 7500 and 9000 A and about 30 R/A in the 9000-1 1,000 A region. Harrison and Vallance Jones [1957a] have recorded the region from 1.1 to 2 . 0 ~ with a scanning spectrometer with 100 A resolution; Noxon, Harrison, and Vallance Jones [ 1959~1 later extended the measurements to 4 . 0 ~ . Between 1.5 and 1 . 7 ~ the average emission rate is about 200 R/A; longward of this wavelength water-vapor absorption becomes very serious, and beginning at 2 . 5 ~ the thermal emission of the lower atmosphere is important.

Estimates for the emission rates for individual bands are about 2.5 kR for 7-3 at 8824 A (Onaka and Nakamura); 33 kR for the three bands 9-5,4-l,and 5-2 between 1 .O and I.lp(Roach,Pettit and Williams); and 175 kR for 4-2 at 1 . 5 8 ~ (Harrison and Vallance Jones). The latter measurement was obtained with fairly good resolution and the band is almost unaffected by atmospheric extinction. Several other bands between 1 and 2 p have been measured by Moroz [1959a]. Fedorova has obtained good measurements on 6 bands in the near infrared. The relative intensities of 8 bands (including some for which absolute intensities have been measured) between 7000 and 11,000 A have been obtained by M. Dufay [1957a, 1959~1. In the visible region intensities have been measured by Kvifte [1959b, c] and Blackwell, Ingham, and Rundle [1960a]. And Shefov [1959a] has related the intensities of 4 bands in the visible to the 6-2 band. Moreover, the total emission rates of several blended bands may be obtained from the measurements of Roach et al. and Noxon et al. With these intensities, and Heaps and Herzberg's [ 19524 transition probabilities, we may estimate population ratios of the different levels, the rates of population by the excitation mechanism, the emission rate for additional bands, and (extrapolating the population rates) the total rate of emission for O H (4500 kR; see Section 13.5.1).

Polarization.-The early work on the polarization of the light of the night sky is summarized in Section 9.1.2. More recent investigations

'' Roach, Pettit, and Williams [1950a], 6400-1 1,600 A; Pavlova, Rodionov, and Sholokhova [1954a], 7500-9000 A and 9000-10,750 A; Osherovich and Rodionov [1954a], 1-3p; Onaka and Nakamura [1957a], 6500-12,000 A; Fedorova [1958a], 8000-1 1,000 A. Revised and considerably larger values have been given by Fedorova [1959a, b].


have dealt with polarization of the atomic lines. Khvostikov [1938a, 1940~1 reported polarizations up to 17 percent for these lines, but the results were questioned by Ginzburg [1943a], who pointed out that the green line should not become polarized (see Chapter 11, Problem 1 b).

Bricard and Kastler [1947a, 6 , 1948a, 1950~1 found virtually no polarization (less than 1.5 percent) in the red and green lines with a Savart-Lyot polariscope. They also concluded that the yellow sodium lines cannot have more than a weak polarization, if any.

12.3.2. Geographic and Periodic Variations of the Intensities

Not so many years ago a faith, mostly blind, persisted among atmospheric physicists that the airglow was a reasonably well-behaved phenomenon. One hopefully assumed that a particular emission would arise from a fairly narrow range of altitude and be distributed homogeneously over a spherical shell. Because such a layer is postulated in the conventional height analysis, we may for simplicity refer to it as a van Rhijn layer.

1 I I I I I I I I

AURORA I-

-

-

-

-

-

-

-

-

200 400 600 800 1000 1200 1400 1600 I800 2000

INTENSITY IN RAYLEIGHS

FIG. 12.4. Frequency distribution of airglow and weak auroral brightnesses near the geomagnetic pole (Thule) and at a subauroral station (Fritz Peak). After Roach, McCaulley, and Purdy [ 1959~1; courtesy National Bureau of Standards.


Further, one expected that with the heights derived for these van Rhijn layers and with spectroscopic temperatures, the airglow would contribute to the general knowledge of the temperature structure of the atmosphere. We have seen in previous sections why the faithful may well have turned into cynics!

Still another disappointment lay in store. If general variations in the airglow intensities could be found, perhaps a clue to the excitation mechanism would suggest itself. If systematic variations with latitude during the night, through the year, or over a sunspot cycle could be established, one might then have important evidence toward elucidation of part of the airglow riddle. With precious few exceptions, any such systematic effects have remained well hidden. Before the International Geophysical Year, photometric observations were restricted to a few isolated stations. At best absolute photometry is a difficult business, and with the weak light source supplied by the airglow, the photometric corrections necessitated by the lower atmosphere (Section 2.5), and the patchiness of the airglow emission, important errors are not easily avoided. The injury is compounded by the strong fluctuations appearing in most of the emissions from one night to the next or even within one night, in a rather random fashion (see Fig. 12.4).

Latitude Dependence.-Studies of a latitude effect of various airglow emissions are hampered by the difficult photometric problem, by possible “auroral” enhancements, and by the time fluctuations in brightness at any one station. Several attempts to compare the green line, in particular, between different locations have given inconclusive results, but do suggest a general increasing brightness toward higher latitudes, possibly complicated with a bright belt at middle latitudes.18

l8 Fesenkov [1935b, 1941~1 and Divari [1955a] found an increase with latitude in integrated, visual light; Rayleigh and Spencer Jones [1935a] and Struve, Van Biesbroeck, and Elvey [1938a] also found a brighter airglow at their higher-latitude stations; Abadie, Vassy, and Vassy [1949a] compared the behavior of the green and red lines at two latitudes; Currie [1950a] reported the airglow to be brighter in Saskatoon than at lower latitudes; Garrigue [1939a] had reached similar conclusions in Greenland ; Barbier and Pettit [1952a] compared results between Alaska and middle latitudes; Roach, Williams, and Pettit [1953a, Table 21 have collected green-line intensities from various locations (and by different observers with different types of equipment), but no latitude effect is apparent; Nakamura [1957a, 1958~1, Huruhata and Nakarnura [1958a], and Tanabe and Tohmatsu [1957a] felt that a tendency exists for the airglow to have a minimum in equatorial regions, on the basis of observations aboard ship. Jorjio [1959n] finds the green and red lines nearly twice as bright at Loparskaya ( A = 68”) as at Zvenigorod ( A = 56”). Roach, McCaulley, and Purdy [1959a] find the airglow near the north geomagnetic pole to be about twice as bright as at Boulder, Colorado (see Fig. 12.4).


The airglow program for the IGY has been particularly concerned with the latitude effect, and preliminary results from the program are quite interesting. Barbier [1957d, 1958~1 found that there were several differences between l’observatoire de Haute-Provence, France (43’56’ N) and Tamanrasset, Algeria (22’47’ N). The green and red [OI] lines, Na D, and OH were all stronger at the higher latitude; the intensity variations during the night were quite different for the two stations; and the red line at Tamanrasset occasionally showed a remarkable increase, by possibly as much as a factor of 10, for two or three hours.

S 60 - 2 50 -

- a

SP CP FP HP - E L N 240- N -

- N

30 - u- 0

m 2 0 -

6 0, 0 - 10- - s a

32 33 34 35 36 37 38 39 40 41 42 43 44 45

North geographic latitude

FIG. 12.5. Histogram of the percentage of occurrence of the maximum airglow A5577 brightness toward the south, near the zenith, or toward the north. The four stations represented here-Sacramento Peak, Cactus Peak, Fritz Peak, and Haute- Provence-suggest a zone of maximum intensity at middle latitudes. From Roach

[1959a] ; courtesy Institute of Radio Engineers.

Roach [ 1959~1 and Barbier and Glaume [ 1959~1 have obtained evidence that the airglow green-line may have a seasonal-latitude effect, with the latitude of maximum brightness varying in a systematic way through the year. Figure 12.5 illustrates how the direction of maximum brightness (north or south) seems to be different at stations at slightly different latitudes. I t appears that this statistical preference for the maximum in the south at the two northernmost stations is due to the fact that at those stations southern maxima occur predominantly during a larger fraction of the year than do northern maxima (see Fig. 12.6).

12.3. INTENSITIES, POLARIZATION, AND VARIATIONS 51 1

DAY IN YEAR

FIG. 12.6. Mean ratio of intensity in the north to that in the south at Fritz Peak through the year for X5577. The southern tendency persists for the larger part of the year, as reflected by the histogram in Fig. 12.5. The apparent motion of the airglow zone of maximum intensity is reminiscent of the yearly motion of the

auroral zone. From Roach [1959a]; courtesy Institute of Radio Engineers.

Mean Daily Variations.-A large fraction of the research on the airglow brightness has investigated its variations with local time, i.e., with longitude relative to the sun. A daily maximum in the green-line intensity around local midnight was first reported by McLennan, McLeod, and Ireton [1928a] and by Rayleigh [1929a], and the possibility of a regular intensity variation has since been examined by many others.lg

Although an occasional dissenting voice was heard, the general opinion until roughly 1955 was that a midnight maximum in the [OI],, green-line intensity was a more or less regular feature of the daily variation. The more recent work has disclosed a far more complex pattern if, indeed, the daily variation can be said to follow a pattern at

la For example, Rayleigh and Spencer Jones [1935a], Eropkin and Kozyrev [1935a], Dobrotin, Frank, and Cerenkov [1935u], Lebedev and Khvostikov [1935u], Barber [1941a], Elvey, Swings, and Linke [1941a], Elvey and Farnsworth [1942a], Elvey [1948a], J . Dufay and Tcheng [1946a], Barbier, Dufay, and Williams [1951a, 1954~1, Roach and Pettit [1951b], Davis [1951a], Roach, Williams, and Pettit [1953a, b], Roach, Petitt, Williams, St. Amand, and Davis [1953a], Huruhata [1953a], Pettit, Roach, St. Amand, and Williams (1954~1, Roach [1954a, 1955~1, Pettit and Manring [1955a], St. Amand [1955a], Barbier [1956a, 1959b], Berthier and Morignat [1956u], and Manring and Pettit [1957a, 1958~1.


all. In fact, it seems that there is little tendency for the maximum to occur at any particular time, except possibly in the winter months (Barbier [ 195961).

Some of the earlier photoelectric work on the variations of the [OI],, red lines and the Na D lines did not completely exclude the overlying OH bands, and must therefore be discarded. Barbier [1956a] eliminated OH (6-1) from his A6300 data by observing alternately with two filters, one of considerably greater band pass than the other. Manring and Pettit [1957a] have employed a birefringent filter to suppress the other emissions.

Low-dispersion spectra obtained by Elvey and Farnsworth [1942a] and Dufay and Tcheng [1946a] showed a long, slow decrease after sunset and a corresponding increase before sunrise. These variations were termed the post-twilight and pre-dawn eflects by the latter authors, and have since been confirmed by several investigators.20 Near the middle of the night the red line emission tends to be rather stable and the nightly variation is more regular from night to night than in the other atomic lines.

Barbier finds that the pre-dawn enhancement is quite unsymmetrical to the post-twilight effect. In the evening the intensity pattern moves from east to west, corresponding to a height of about 275 or 300 km when interpreted as an excitation pattern fixed relative to the sun. But in the morning hours the enhancement seems to appear first in the (geomagnetic) north, whence it spreads over the sky, propagating along the geomagnetic meridian. The morning enhancement seems to have a height of 230 km and is more pronounced in winter ; it would seem as though the effect has insufficient time to develop completely in the short summer nights. The above applies only to middle latitudes. Barbier's [1957d, 1958a, 1959~1 observations at Tamanrasset (23" N) frequently show more erratic enhancements. Also, St. Amand [1955a] and Barbier [1957c] have obtained striking correlations between the brightness of A6300 and the characteristics of the nighttime F layer (Section 12.3.3).

The N a D lines do not appear to experience any pronounced daily variations. There may be a very small post-twilight and pre-dawn effect, but it is difficult to be certain that these enhancements do not result simply from multiple scattering of sunlight by free Na atoms. Some investigators have reported a slight and gradual increase of Na

2o Berthier [1953a], Pettit, Roach, St. Amand, and JVVilliams [1954a], Berthier and Morignat [1956a], Barbier [1956a, 1957a, 1958a, 1959~1, and Robley [1956a]. See Fig. 9.13.


brightness through the night, but it is not well established that such a variation is regular in its occurrence.z1

From photometric observations in the infrared by a number of workersz2 it appears that there is no strong, regular daily variation in the OH emission. Through a given night the mean intensity may change systematically in either direction by 50 percent or more, or it may fluctuate several times. As with the green line, localized irregularities (patchiness) may be an important feature of OH emission, with the patches moving across the sky during the night. Berthier [1955b, 1956~1 similarly finds no systematic variation for the 0, Atmospheric band, but slow changes of intensity by a factor of two through the night are not uncommon. In the ultraviolet Barbier’s [1953a] observations do not -show a definite trend in the daily variation.

Yearly Variations.-The [OI],, green line, h5577, fluctuates from night to night over a range of mean intensities from below 100 R to above 500 R. Indeed, St. Amand and Ashburn [1955a] suggested that if there were no qualitative distinction between the aurora and the green-line a i r g l o ~ , ~ , the auroral occurrences at low latitudes might be represented by the tail of the frequency distribution curve for airglow intensities. An analysis by Roach, McCaulley, and Marovich [1959a] suggests that the aurora and airglow can actually be fitted to the same distribution curve, with no abrupt change between airglow and aurora (see Fig. 12.4).

Such strong night-to-night fluctuations make the establishment of a yearly variation for the green line most difficult. Further, the extensive data of different investigatorsz4 suggests that any yearly variation may be a sensitive function of latitude. If there exists a zone of maximum airglow intensity in the middle latitudes, which shifts north and south with the seasons, then the yearly variations observed at different locations could vary widely (see Figs. 12.5 and 12.6).

21 See Dufay and Tcheng [1946a], Roach and Pettit [1951a], Pettit, Roach, St. Amand, and Williams [1954a], Pettit and Manring [1955a], Berthier and Morignat [1956a], and Barbier [1956a].

22 Infrared-sensitive photoelectric photometers have been used by Elvey [1943a], Rodionov and Pavlova [1949a], Rodionov [1950a], Huruhata [1950a], and Armstrong [1956a]. Spectrographic photometry has been pursued by Berthier [1955b, 19.56~1.

23 Readers who feel the distinction is obvious are referred to Section 9.1 . l . Incidentally, frequency distribution curves of green-line brightness were previously drawn by Dufay and Tcheng [1947a] and St. Amand and Pettit [1954n].

24 Especially, Rayleigh and Spencer Jones [1935a], J. Dufay and Tcheng [1947a], J. Dufay [1948a], Barbier, Dufay, and Williams [1951a, 1954~1, Roach, Pettit, Williams, St. Amand, and Davis [1953a], Pettit, Roach, St. Amand, and Williams [1954a], Pettit and Manring [1955a], Manring and Pettit [1958a], Barbier [19596].


According to Barbier [1956a], the [OI],, red line, h6300, probably possesses very little regular seasonal variation in the mean nighttime intensity (after post-twilight and pre-dawn effects are eliminated), although the nightly behavior varies somewhat through the year, as discussed above. I t seems likely that earlier results,25 which reported a maximum in winter and minimum in summer, were contaminated in various degrees by OH.

The most pronounced seasonal variation is in the Na D lines. Several observers26 found a large amplitude, with a maximum in winter and a minimum in summer, similar to the seasonal variation of Na D in the twilight airglow. Still, with the band pass afforded by interference filters, appreciable OH is also recorded and usually is incompletely allowed for by a “control” filter at a neighboring position in the spectrum. Manring and Pettit [1957a], observing with a birefringent filter, estimate that in midsummer the D lines may be fainter than 3 R but their filter may well have overcorrected the OH. In winter they find the emission rate to be of the order of 100 R.

Barbier [19596] reports a seasonal variation in OH (with a maximum in winter and a minimum in summer, similar to Na D) as suggested by some previous observations ;27 however, Berthier’s [ 1955a, 1956~1 extensive spectrographic program showed very little variation in monthly means. The observations by Harrison and Vallance Jones [ 19574 with an infrared-sensitive spectrometer also disclose no systematic seasonal variation, but the night-to-night intensity fluctuations may cover a range of a factor of two. Also see Section 12.1.1.

Meinel [1950fl found that the 0, Atmospheric band at 8645 A on one occasion showed a large enhancement accompanied by an increase in the rotational temperature (Section 12.2.1). Berthier’s [1955a, 1956~1 spectra show monthly mean intensities nearly twice as great in June to November as in January through April. Still, the erratic fluctuations from night to night raise some doubt as to the statistical significance of this apparent seasonal variation.

The 0, Herzberg bands, in the ultraviolet and blue, and some bands of unknown origin in the blue have been thought to have some seasonal

2 5 Dufay and Tcheng [1947a], J. Dufay [1948a], Huruhata [1953a], Pettit, Roach, St. Amand, and Williams [1954a].

2e Elvey, Swings, and Linke [1941a], Dufay and Tcheng [1947a], J. Dufay [1948a], Roach and Pettit [1951a], Pettit, Roach, St. Amand, and Williams [1954a], Pettit and Manring [1955a], and Barbier [1956a, 195961.

2’ Cabannes, Dufay, and Dufay [195Oa], J. and M. Dufay [1951a], and Huruhata [1953a]. The spectral correlations discussed below would also lead one to suspect a similar seasonal behavior between OH and Na.


effects, amounting perhaps to factors of two in the intensity. These results have been based on fewer data than have been used in trying to establish a regular variation for the green line (where the seasonal effect is still rather uncertain). Therefore, in view of the Iarge daily fluctuations that appear, the validity of systematic yearly changes remains questionable.28

12.3.3. Spectral Correlations

Correlations with Geophysical and Solar Phenomena.-But for one notable exception, attempts to find a definite positive correlation of airglow emissions with other geophysical phenomena or with solar events have been singularly unsuccessful. However, St. Amand [1955a] found rather good correlations between ionization at the peak (and below) of the nocturnal F layer and the red [OI],, intensity. There were certainly departures from perfect correlations and St. Amand concluded that if a definite relation exists between the two phenomena, it is complex. Nevertheless, the apparent association between the ionosphere and the red lines was strong enough to suggest a physical relationship. Barbier [1957c] provided further evidence in this direction: he showed that the observed intensity correlates with a semi-empirical formula involving the critical frequency and the virtual height of radio reflection. Barbier’s formula is essentially an expression for the rate of dissociative recombination at the peak of the F layer, where the rate coefficient is an empirical function derived from the radio work of Ratcliffe, Schmerling, Setty, and Thomas [1955a].

Similarities between the reported seasonal and daily variations of the green-line intensity and characteristics of the F layer have been interpreted in terms of excitation in the upper ionosphere (Martyn and Pulley [1936a], Martyn [1952a]; also see Mitra [1945a] and Huruhata

28 Cabannes and Dufay [1935a] measured three unresolved Herzberg bands near 4420 A and an emission at 4173 A, which arises from the Herzberg 1-8 band and several additional features of unknown origin. The two groups showed the same variations. Barbier [1953a] used a photoelectric photometer to observe the ultraviolet, which arises almost entirely from 02. Robley [1957a] observed the same two groups as Cabannes and Dufay plus a third at 4070 A, arising from a blend of a Herzberg band and another feature possibly in the 34, +- ld, system of 0,. These various authors do not agree too well on the occurrence of maxima and minima. In addition, M. Dufay [1954a] reported that the Herzberg bands in the ultraviolet followed the same type of variation reported by Cabannes and Dufay, but did not give details. Barbier [1953a, 195963 especially comments on the similarity between the Herzberg 0, annual variation and that for the [OI],, green line and the emission continuum around 5200 A, as measured by Barbier, Dufay, and Williams [1951a, 1954al.


[1953u]). The older van Rhijn heights seemed to substantiate such conclusions, but the evidence has never been very compelling. Bradbury and Sumerlin [1940u] could find no relation between the nocturnal E layer and the night-sky light in the blue; Elvey [1943u] found no such correlation with infrared radiation. However, McCaulley and Hough [1959u] have noted some evidence for variations in the green line with ionospheric variations in the E region.

Although Barber [ 1941~1 found some similarity between magnetic activity and the green line intensity, no such relationship was found in investigations by Dufay [1946u] and Roach, Pettit, Williams, St. Amand, and Davis [1953u]. In the IGY program Sandford [1958u, 1959~1 found a correlation of both A5577 and A6300 with magnetic activity at h, =

51” S; he suggests that these “airglow” enhancements are basically auroral in origin.

A long-period variation in the green line was suspected by Rayleigh and Spencer Jones [1935u], who suggested that it arose from a dependence on the sunspot cycle. A correlation of the green line with solar activity could not be established by Dufay [1946u] or Roach [1955u], although the intensity does seem to increase, Barbier [19596] reports, with increasing sunspots.

Correlations Between Different Emissions.-The study of correlations between different airglow emissions has been slightly more re- warding than attempts to correlate the airglow with other phenomena. I hasten to add that thus far the positive correlations obtained for some emissions have not been of immense value in explaining or helping one understand the airglow. Nevertheless, a positive result is far more satisfying than a negative one, and the physicist at least finds it easier to maintain his patience and sanity if the future seems to hold some promise of clarification.

Numerous investigations have sought correlations for the intensities of the three atomic lines h5577, X5893, and h6300. Photographic photometry provided only a crude means of making comparisons, however, and for weaker emissions little more could be done than to try to compare daily or yearly trends. The advent of photoelectric photometers with various color filters made comparisons of different emissions possible on a more elaborate and precise scale (Grandmontagne and Delestrade [1949u], Huruhata [1953u], and Barbier 1195463).

In particular, the observations with an eight-color photometer by Barbier [19546, 1956~1 have been valuable in establishing three coaariunce groups. The emissions within each group are well correlated with one another, both through one night and in night-to-night fluctua-


tions through the whole of a moonless observation period. These groups are:

(u) The green-line group, including A5577 [OI],,, 0, Herzberg bands, the blue bands, the green continuum, and the 0, Atmospheric band.29

(b ) The sodium group, including A5893 Na D and OH.30 ( c ) The red-line, A6300 [OI],,. The behavior of this radiation seems

usually to be unrelated to any other component of the airglow. At a particular time of year a nearly linear relationship exists between

the intensities of any two emissions within groups (a) or (b). During another month the two emissions will still fluctuate by proportional amounts, but possibly with a different proportionality constant. Barbier finds that whereas the two groups (u ) and (b ) tend to vary independently, they may also appear to become coupled and vary in a parallel way for several hours.

12.3.4. Structure and Motion of Excitation Patterns

We have seen in the previous sections that the nonuniformity or patchiness of airglow emissions has caused a great deal of grief in photometric studies of the airglow. The departures from what we may call a van Rhijn layer have all but made van Rhijn height determinations impossible. Moving patches of brightness cause the mean intensity at any one station to change constantly in a somewhat random fashion, and if these changes are the same order of magnitude or larger than systematic daily, yearly, or latitude changes, then the latter can be most elusive and difficult to establish.

But if my discussion above has seemed pessimistic, the present section may be regarded as the silver-lining department. For all the

2 8 The blue bands include some Herzberg 0,, possibly the $A,+ l A g system of 0,, and some unidentified bands. Barbier's blue filter has an effective width of 570 A peaked at 4400A, and thus it probably transmits a small amount of green continuum also. The correlation of A5577 with the O2 Atmospheric band was not covered in Barbier's work but has been added on the basis of M. Dufay's [1958a, 1959~1 observations with an infrared photoelectric spectrometer. Actually the green line was reported earlier to be similar in general behavior to the continuum by Barbier,~Dufay, and Williams [1951a, 1954~1; to the Herzberg bands by Barbier [1953a]; and to the blue bands by Barbier

su The correlation of Na and O H was found independently by Berthier LlY54al. Earlier, Barbier [1954a] included A6300 in this group also, but the contamination from O H (9-3) through the A6300 filter had been incompletely corrected. Contamination by OH probably is responsible also for the good correlation between A6300 and Na D found by Dufay and Tcheng [1947a].

[ 1 954al.


difficulty that the patchiness has caused, it remains an object of interest in its own right. Indeed, the patchy excitation patterns present an exciting challenge both to the observer (who must discover any systematic behavior that may be present and, in any case, find a way of summarizing concisely whatever behavior there is), and to the theorist (who must learn to think in terms of a dynamic airglow).

Although Elvey, Swings, and Linke [1941a] and others occasionally found some patches of the sky to be brighter than others, it remained for automatic photoelectric programs to map the sky at intervals of a few minutes and disclose details of the structure and apparent motions of the luminous clouds. From Fig. 4.5 we see that for a useful range of zenith angles up to 80°, an emitting layer 100 km high can be observed for a radius of about 470 km from a single station. By scanning the sky in a systematic fashion, one can construct an isophotal map for this area. Comparison of a series of such maps shows how the pattern changes through the night. Several stations that overlap one another’s regions may operate cooperatively to extend the geographic coverage. The green [OI],, line has received the most attention but the other bright emissions also show changing s t r ~ c t u r e . ~ ~

Figure 12.7 illustrates the changing pattern for one night. All intensities have been referred to the zenith with the assumption of an emitting height of 100 km.

Some of the earlier work on the green line by Roach and Pettit [1951b, 1952~1, Davis [1951a], and Roach [1954a] suggested that the excitation pattern remained nearly constant relative to the sun and that the Earth rotated under this pattern. This concept seemed compatible also with a daily variation ; evidently the excitation pattern, being brightest opposite the sun, would explain a maximum intensity near midnight.

Subsequent studies32 have modified this simplified picture. On a given night the excitation pattern may appear to move uniformly from east to west, as though it were fixed at some height in space, but it may also move in any other direction during the night; this superficial resemblance to common auroral motions has inevitably sired speculations on a physical similarity of the two phenomena. At times the whole

s1 For example, Roach and Pettit [1951a] studied meridional scans on the Na D lines; Huruhata [1950a, 1 9 5 2 ~ 1 has discussed drift motions observed for the infrared OH emission; and Barbier [1957a, b,c , 1958~1 has reported on the inhomogeneities in the red lines of [OI],,.

Barbier, Dufay, and Williams [1951a, 1954~1, Roach, Pettit, Williams, St. Amand, and Davis [1953a], Roach, Williams, and Pettit [1953a, b), Vassy and Vassy [1953a], Pettit, Roach, St. Amand, and Williams [1954a], Huruhata, Tanabe, and Nakamura [1955a], and Manring and Pettit [1958a].


pattern may change its brightness almost uniformly, without becoming distorted, or localized changes of brightness may completely alter the appearance of the pattern within an hour or so. Any systematic effects that might be present are difficult to establish because of the magnitude of what seem to be irregular and random fluctuations and motions.

FIG. 12.7. Circular plots of the sky for h5577, 1-2 October 1956. The radius is 470 km. The heavier shading represents greater brightness, with all intensities referred to the zenith before being plotted. Times are hours, local zone time. The intense patch present in the beginning has moved southward by the middle of

the night. A brightening in the north at 0200 failed to develop. Courtesy F. E. Roach.

However, Manring and Pettit find evidence of an excitation pattern fixed relative to the sun and the center of the Earth (upon which sporadic features are superimposed), a pattern that changes in a regular fashion through the year. If so, the pattern almost certainly depends critically on latitude as well.

Statistical studies (Roach, Tandberg-Hanssen, and Megill [ 1958a, b ] ) on the sizes and motions of the green-line patches indicate that typical diameters are larger than 1000 km (and may be as large as 2500 km), and that typical speeds are around 75-100 meter/sec (270-360 km/hr). These estimates are based on measurements from a single station, where the field of view of the layer at 100 km height is about the same size as or smaller than the patches; no really satisfactory means of obtaining characteristic diameters could be used. Of additional interest would be the distribution function for different cell diameters. The velocity of motion was obtained by dividing the characteristic diameter by the average semiperiod for major intensity fluctuations in a fixed direction


(about 10 hr). About the same apparent velocity was obtained from the motion of isophotes of various brightnesses (see Fig. 12.8).

I t is to be emphasized that these motions do not necessarily imply winds ; nevertheless, the speeds deduced are consistent with those found

N

W E

S

of 31 October 1956. Courtesy F. E. Roach.

for the same altitude region from sodium ejected from rockets in twilight (see Section 11.4.3) and from meteor trains (Goody [1958a, Chap. 51, Elford [ 1959~1). A possible physical relationship between airglow motions and the patchiness itself is discussed in Section 13.4.6.

FIG. 12.8. Southward movement of the 300 R isophote during the early morning

PROBLEMS

1. Show that for a thick but uniform emitting layer, the intensity is given by Eq. (12.4). Compare the relative intensities at 5 = 40” and 5 = 80” for a thin layer at 100 km with those for a homogeneous emitting layer between 80 km and 120 km.

2. Estimate the ratio of emission-line “signal” to background “noise” (including continuum and OH emission) for interference filters of 20 A band width centered on h5577, 25893, and A6300 and transmitting the light of the night sky. For A5893 consider both summer and winter values.

Chapter 13. Excitation of the Nightglow

13.1. Introduction: Mechanisms of Nightglow Excitation

The nightglow is the least understood of the various types of radiation emanating from the upper atmosphere, a fact not surprising in view of the rarity of systematic geographic and time variations and correlations with other phenomena that might serve as vital clues. The two most obvious possibilities for the excitation energy are fast particles and solar electromagnetic radiation.

Excitation by particle impact is implied by the terms nonpolar aurora and permanent aurora, which is why airglow, a word more descriptive phenomenologically but less restrictive physically, was introduced into the language. The hypothetical fast particles are generally thought to originate outside the Earth’s atmosphere (Dauvillier [1932a, b, c], Elvey [1942a], Bates [1946a], Ginzburg [1952a], Swings [1954a], Barbier [1958a], Chamberlain and Sagan [ 1960~1). However, local acceleration of particles by electric fields has also been proposed (Wulf [1953a], Tandberg-Hanssen and Roach [1959a]), although it has never been developed into a satisfactory the0ry.l Meteoric dust falling into the upper atmosphere has been suggested as a source of airglow enhancements, not from direct impact but by providing particles to act as “third bodies” in ordinary reactions (Hoffmeister [1952a]); Kaiser and Seaton [1954a] have shown, however, that this dust will be an extremely rare constituent and is not likely to be of any importance.

The viewpoint that extraterrestrial particles (Section 13.3.2) might excite a major part of the airglow seemed more likely in former times, when it was commonly thought that the green line was emitted predominantly in the F layer and showed pronounced correlations with magnetic and solar activity (see Section 12.3.3). In Section 13.3.1 we shall also have occasion to investigate the excitation to be expected from impact by thermal electrons in the high atmosphere.

Wulf’s theory considers the potential difference that could be generated by zonal winds cutting across the geomagnetic field. In view of the comparatively high conductivity of the ionosphere, Wulf’s calculation gives no information on the electron velocities that could be produced by such a potential. Tandberg-Hanssen and Roach have postulated the existence of an accelerating field and have used Chamberlain’s discharge theory (Section 7.3.2) to compute green-line excitation rates.

52 1

522 13. EXCITATION OF THE NIGHTGLOW

Sunlight could produce delayed excitation either through chemical reactions that proceed throughout the night as a result of photodissociation (or possibly molecular excitation) during the day, or through electron-ion recombinations following photo-ionization. In this chapter we shall treat these photochemical and recombination reactionsseparately. It is conceivable that a small component of the night airglow also arises from solar Lyman a radiation that undergoes resonance scattering and fluorescence by extraterrestrial hydrogen. About 60 percent of the Ly (Y

that appears in the night sky (- 2.5 kR) as observed from rockets is absorbed in the 100 km region and may provide additional excitation (see Section 9.1.3 and references to the rocket work cited there). A number of review articles have dealt with the various reactions to be expected in the upper atmosphere and the consequent production of the airglow.2

A source of atmospheric energy, in addition to direct solar radiation and extra-fast particles, lies in mass motions of air (e.g., winds), which can dissipate energy through viscous interaction. For these motions to provide the radiant energy of the airglow, however, some mechanism is necessary to convert the translational energy into atomic excitation. The important role of mass motions probably lies not in providing the basic excitation energy, but rather in altering the rates at which absorbed solar energy is dissipated in airglow.

I t is not unreasonable, then, to look to these mass motions for explanations of some of the intensity variations discussed in Section 12.3. Diffusion and vertical (and perhaps even horizontal) mixing are important in altering the composition from that which would result in local photochemical equilibrium. Turbulent motions, which are probably important in the 100-km region (Section 13.4.6), may affect the temperature distribution as well as the composition. Temperature fluctuations may be especially important in two-body reactions where an activation energy is required (see Section 1.5.2). Also, density fluctuations produced by tidal motions could conceivably introduce periodic intensity variations (Section 13.4.5). In the following sections we shall examine questions of intensity fluctuations along with the principal sources of excitation energy.

For example, Bates [1948a, 1949c, 19523, 1954b, 1957~1, Nicolet [1948a, 1952~1, Bates and Dalgarno [1953a], Seaton [1955a], and Dalgarno [1958a].

13.2. EXCITATION BY RECOMBINATION IN THE IONOSPHERE 523

13.2. Excitation by Recombination in the Ionosphere3

13.2.1. Review of Red-Line Excitation

Quite a few processes probably contribute to the red [OI],, lines, A6300 and X6364. In early twilight (see Section 11.5) ultraviolet dissociation seems to be responsible for some of the enhancement (Barbier [ 1959a]), although resonance scattering provides a negligible portion. Another component of the twilight, most of the post-twilight (Section 11.5.3), and at least part of the nightglow (Section 13.2.3) arise from dissociative recombination,

0; + e + O * + O* (13.la)

or NO+ + e + N * + O*, (1 3.1 b)

where in general an asterisk (*) is used to denote an atom or molecule that may be in an excited state. Other red-line excitation in the nightglow might be furnished by several photochemical reactions (although deactivation at the lower altitudes where such processes flourish will probably suppress most of the excitation; see Section 13.4.2) and by inelastic electron collisions (Sections 13.3.1 and 13.3.2).

We have reviewed the evidence from height and temperature measurements and ionospheric correlations that place the red-line excitation in the F region, in part at least.* These observations do not in themselves eliminate the possibility that an appreciable part of the emission comes from lower altitudes, a topic discussed further in Section 13.4.

The theory of the post-twilight decay of the red lines (Chamberlain [1958a]) has been reviewed briefly in Section 11.5.3. Several hours after sunset the predicted emission is of the correct order for the nightglow (50-100 R) and originates from the 250- to 300-km region. Although

The emission of continuous radiation through electron recombination and attachment is discussed with photochemical reactions in Section 13.4. This section is concerned only with mechanisms of exciting discrete line emission.

*Formerly there seemed to be similar evidence in favor of the green-line (A5577 [OI],,) excitation being in the F region and since reaction (13.1~) is energetically capable of it and was thought to be the main recombination process for the F layer, Nicolet [1954u] suggested that it might produce the green line (excitation potential = 4.17 ev). It is not known what fraction of the reactions (13.la) will produce O(lS) or O('D), upper terms of the green and red lines respectively. Probably a small amount of green- line emission does arise from this reaction in the F layer, but the evidence, especially from rocket heights, is in favor of most of the emission coming from the 100-km region.


inevitably there are uncertainties in the reaction rates appearing in the theory, dissociative recombination may very well furnish enough excited atoms to explain the “normal” red-line intensity near the middle of the night. There is some question, however, as to how much of the intensity variations can be attributed to this mechanism (Section 13.2.3).

Barbier (see Section 12.3.2) has described the development of the morning enhancement, beginning near the middle of the night in winter in the geomagnetic north and spreading over the sky with an apparent velocity (for an emitting height of 230 km) that increases from about 340 km/hr (100 meter/sec) to 1500 km/hr (400 meter/sec) between the time the enhancement first appears in the north and its arrival in the south. T o explain this phenomenon Barbier [1958u] suggests bombardment by extraterrestrial particles. An entirely different type of over-all enhancement seems to appear at lower latitudes: every few nights in summer and even more frequently in winter a rather erratic brightening of A6300 occurs and lasts for a few hours, and then fades. This phenomenon has received no explanation.

13.2.2. Recombination and Diffusion of Ions in the Nighttime F Layer

The Differential Equation.-With a portion of the red-line emission being produced as a direct consequence of recombination in the F layer, we shall examine the behavior of the upper ionosphere at night in some detail. I n the next section we shall apply the results to a discussion of the red lines. Recombination will be assumed to occur predominantly through reaction (13.1~) or (13.lb) with the molecular ions formed by ion-atom exchange,

o+ + o,+o: + 0 (13.2a) or

Of + N, + NO+ + N. (13.2b)

The rate coefficient for these reactions, sex, may be the order of 10-1O cm3/sec, since the reactions proceed through ion-atom exchange, which is more efficient than simple charge exchange5 (Bates [1955b]).

At the lower altitudes of the Fl layer the large abundance of 0, and

Rocket measurements show NO+ to be the dominant molecular ion on the F, region, which favors (13.2b) (see Krassovskii [1957a], Hertzberg [1958a], and Nicolet [1959a]). But as 0, and N, are approximately in diffusive equilibrium in the F region, the variation of these constituents with height would be nearly identical. The discussion is then fundamentally the same for either case.


N, causes most of the ionization to take the form of 0; and NO+. These ions recombine soon after twilight so that the Fl layer disappears, leaving the F , layer, where atomic ions are dominant. For the present discussion we can therefore consider Of as providing most of the ions, and limit the present discussion to the F, region. (For the early part of the twilight decay, recombination in the Fl region must be considered as well-see Section 11.5.3.) The number density of O+ at height z then equals the electron density: N(O+ I z ) = N&). If recombination by reaction (13.1) proceeds with a rate coefficient of arec M lo-’ cm3/sec (Bates [1950b, 1951a]), the lifetime of an NO+ or 0: ion will be the order of 1/Ne arec M I minute. Therefore, the rate at which electrons recombine is essentially the rate at which reaction (13.2) proceeds. In the F, layer ion-atom interchange is the process limiting the rate of recombination, since the lifetime of an ion will be several hours or longer (depending, of course, on the height).

The ionization at a given height will change at night not only through recombination but by ambipolar dzffzision and other motions of ions and electrons. For simplicity we shall consider an isothermal atmosphere and neglect any nocturnal production of ionization (for example, by bombarding particles) and any motions other than vertical diffusion, e.g., motions resulting from turbulent mixing, tidal oscillations, or electromagnetic forces on the charged particles. We let z be the height measured from some arbitrary point; Hl = kT/plMog is the scale height in diffusive equilibrium for 0, which has molecular weight p1. The atmosphere is predominantly 0 in the F region and will therefore have a scale height of approximately HI.

We will take 0, or N, to be distributed according to a scale height H , = H,/p. Thus p = 0 corresponds to the molecule being distributed uniformly in the atmosphere; p = 1 gives perfect mixing of the molecule with 0 ; p = 2 gives diffusive equilibrium for 0, and is close to diffusive equilibrium for N,. If the ion-electron gas were in diffusive equilibrium, it would follow a scale height of about 2H,; in practice we expect to find such a distribution only at very great heights.

The electron density is thus governed by the equation (Ferraro [1945a])

(13.3)

The first term in parentheses represents diffusion from the pressure gradient, whereas the second term is introduced from the gravitational force. When the gas is in diffusive equilibrium, these terms are balanced and diffusion vanishes.

526 13. EXCITATION OF T H E N I G H T G L O W

Here p is the recombination rate; from the discussion above it is clear that reactions (13.1) and 13.2) must proceed at the same rate, and that j? = aex N ( 0 , or N, I z). Thus we write

/3 = sex N ( 0 2 or N, I z = 0) e - p z / H i = Po e-pz'H1, (13.4)

which defines Po. The fact that F-layer recombination depends on the first power of N,, rather than on Ng as it does in the E and (daytime) F, layers, has the important result of making the differential equation linear. (Ferraro's [1945a, 1946~1 early discussions of diffusion assumed that recombination depends on NE.)

In Eq. (13.3) D(z ) is the diffusion coefficient, which is mildly dependent upon the temperature and inversely proportional to the gas density. Earlier calculations ( e g . , Ferraro [ 1945u, 1957~1 and Cowling [1945u]) probably overestimated D by a factor of 3 to 6. Using the calculations by Dalgarno [19586] for the diffusion of O+ through 0 at a temperature near 1000" K, we may write

= Do ez lH1 cm2/sec, 2.3 x 101*sin2i N ( 0 14

D(z) = (13.5)

where Do = D(z = 0) and where the numerical value quoted assumes N is given in atom/cm3. Here i is the angle of inclination of the magnetic field to the horizontal; the sin2 i reduction factor is valid for low gas densities, but in any case is of small importance except in equatorial regions. From Eq. (3.12) we may write tan i = 2 tan I A,,, 1 , where A,, is the geomagnetic latitude.

The linearity of Eq. (13.3) allows one to eliminate the time dependence when p > 0 by writing

(13.6)

where N j is a function of x only. Substituting Eqs. (13.4)-(13.6) into (13.3) gives

which is an eigenvalue equation, possessing solutions only for discrete values of hj . Make the following changes of variable:

yi = N . ez14Hi . x = e-zlH1. (13.8)


Then we have finally

(13.9) dx2 DO D o x 16x2

One of the boundary conditions is supplied by the consideration that as z -+ a. the term in brackets in Eq. (13.3) (or the velocity of diffusion) cannot be infinite. This condition requires diffusive equilibrium at great heights and gives N , -+ const e-ziZH1 . At very low heights ( z +

- m), Ne cannot increase without limit. It will develop that imposing this simple condition leads to solutions where Ne + 0 at the bottom of the layer.

Solutions of the Differential Equation.-The case of p = 0 (0, distributed uniformly with height) is rather far from the actual case, but this problem has been treated by Yonezawa [1955a] and Ferraro and &dogan [1958a]. [The separation of variables by (13.6) is not valid in this case, as Eq. (13.9) would no longer be an eigenvalue equation.] The solution gives a layer that drops at night, contrary to the behavior of the observed layer, which normally rises during the first part of the night. Since j3 is made constant with height by setting p = 0, recombination is underestimated in the lower part of the layer, if j3 is properly chosen for, say, the layer maximum. Were diffusion ignored altogether, the shape and height of the layer would remain constant while recombination removed the ionization. The addition of diffusion allows for a flow of ionization upward as well as downward, but as the distribution above the maximum tends toward diffusive equilibrium, the downward flow becomes the more important. Hence, the layer falls.

A case much more instructive, because it is closer to reality but can still be solved analytically, is that for p = 1 (physically, 0, and 0 are assumed to be distributed in perfect mixing). The boundary conditions given above require that y j -+ const x1I4 as x -+ 0 and that y, + 0 as x -+ 03. Equation (1 3.9) is in the same form as the radial wave equation for the hydrogen atom and is discussed in many text books. By following through the solution we find the eigenfunctions in terms of the generalized Laguerre polynomials, L ~ ~ ' z ( v ) :

N . = A . v ~ / z p j 2 L.-IE 3 (v). (13.10) Here Aj is a constant to be fixed by the initial electron distribution and the independent variable is

(13.11)


The polynomial may be written in a power series,

where the coefficients are related by the recursion relation, Lj-”2(v) = 1 + a, z, + u2 212 + ... + uj vj , (13.12)

m - j %+, = a,; (m = 0, 1 ...; a. = 1). (13.13)

(m + 1) (m + 4) The eigenvalues are

hi = - ( j + t,; ( j = 0, 1, ...). HI

(13.14)

The solutions for large j represent, by Eqs. (13.6) and (13.14), short- lived fluctuations in the Ne distribution. A short time after sunset these higher-order solutions will vanish, and Ne can be expressed as a linear combination of the first two or three eigenfunctions. An illustrative calculation is shown in Fig. 13.1, where No, N,, and N , are plotted on

200 300 400 500 600 roo HEIGHT (km)

FIG. 13.1. Eigenfunctions for p = 1 computed from Eq. (1 3.10). Each component N j of the electron density N e decays with time exponentially with lifetimes l /hj given by Eq. (13.14). Each curve is plotted here on a scale of unity for the maximum value; the actual relative importance of each curve must be determined

by the observed N , distribution at a definite time.

13.2. EXCITATION BY RECOMBINATION I N THE IONOSPHERE 529

an arbitrary scale of unity for the major maximum of each curve. Since the real atmosphere probably is closer to p = 2, a solution fo rp = 1 may not be especially accurate, except possibly near the height for which the parameters are evaluated. Nevertheless the main features of a more precise solution are contained here. Some of the parameters are not known with suitable accuracy, but for definiteness these calculations assumed z = 0 at a height of 300 km, N ( 0 1 z = 0) = 3 x lo9 ~ m - ~ , H I = 50 km, Do = 7 x lo8 cm2/sec, and Po = sec-’. The latter value was indicated by the F-layer analysis of Ratcliffe, Schmerling, Setty, and Thomas [1955a] for the 300-km region.

The lifetimes l/A, for the various curves are given on the figure. As the component distributions N, and Nl decay, the peak altitude rises. Of course, the relative importance of the different components is governed by the initial Ne distribution. I t is possible that some of the curves N j would be given a negative weighting factor, provided Ne is everywhere and at all times positive.

After several hours, Ne = No & o f ; the height and shape of the electron distribution curve then no longer changes with time. The peak of Ne has risen to 365 km and Ne will decay with a lifetime of about 10 hr. The distribution at a given time is of the form

N , = const e-z/2Hi exp [ - H,(Bo/Do)1’2 e-zlHi],

which is the generalized expression for a Chapman layer [Eq. (3.63)]. At high altitudes the ions are in diffusive equilibrium, and over a considerable range below the peak the distribution may be closely approximated by a parabolic distribution.

When p = 2 the general equation (13.9) may be written in the convenient form

( 1 3.1 5 )

where

Numerical solutions for the eigenfunctions and eigenvalues can be obtained by application of a variational principle. Dungey [ 19564 has found in this fashion a solution for the smallest eigenvalue ( j = 0), which gives the distribution of electron density after a long time. He finds that (4p0 H,2/D0)2/3 Xo/,k?o = 1.06 gives this lowest eigenvalue. [Since D2(z) ,k?(z) is independent of height, it makes no difference at what height Po and Do are evaluated.]


At this point one may proceed in a variety of ways to compare theory and observation, depending on what parameters he wishes to adopt as known. Dungey's method is to assume the height to be 370 km. Numerical integration of Eq. (13.15) gives a value of X at the peak of N j , so that with Eqs. (13.16) and (13.8) one finds (4H,2&ax/Dmax). Again, radio observations of the F layer give an average lifetime suggesting 1/X, m 6.7 hours or A, - 4 x sec-l. Then the computed eigenvalue allows a determination of /3max (at z = Zmax). The scale height Hl may be estimated either from the observed variation of P(z) with height by Eq. (13.4) or from a comparison of the observed layer thickness with the distance below Zmax where the computed Ne drops to one half its maximum. The computed value depends on HI, which can thereby be ascertained; Dungey adopts H, = 70 km. In this fashion he finds pmax = 2 x sec-l, which is supposed to be appropriate for 370 km and does, in fact, appear compatible with values derived from ionospheric analysis by Ratcliffe, Schmerling, Setty, and Thomas [ 1955~1. Finally, we obtain Dma, = 1Oln cm2/sec; and for a geomagnetic latitude of 55" N (for Slough, England), Eq. (13.5) gives N ( 0 ) = 2 x lo8 ~ m - ~ , again for 370 km.6 This density appears reasonably compatible with models based on rocket and satellite measurements, suggesting that diffusion has been properly allowed for in the theory. Dungey's [1956u] paper also allows for uniform vertical motions of ions by other (unspecified) means than diffusion. But as the additional motions are not yet well understood it seems inappropriate to try to include them in numerical predictions with the theory.

13.2.3. Time Variations i n the Red Lines Arising from Dissociative Recombination

The rate of photon emission in A6300 + A6364 by dissociative recombination in the absence of collisional deactivation is

where is the fraction of atoms formed in the 1D term by reaction (13.1). At night it is necessary to consider Ne(z) according to the recombination-diffusion equation of the previous section, as diffusion is

a The density of 5 x lo8 quoted by Dungey was too large because of the errors mentioned above in earlier estimates of the diffusion coefficient. However, there also seems to be an error in overestimating the effect of the magnetic field, which when corrected makes Dungey's density 2.6 times larger still.


important in keeping the ions at a reasonably low altitude where recombination can proceed throughout the night.'

From Eq. (13.17), where we adopt 5D - 1, the emission profile can be estimated once Ne(z) is obtained from the solution of Eq. (13.3). For illustrative purposes let us consider the solution with p =. 1, whose eigenfunctions are plotted in Fig. 13.1 ; the adopted values of the atmospheric parameters are listed below Eq. (13.14).

After a few hours, Ne = No, and if at the layer peak Ne = lo5 electron/cm3 the maximum rate of emission is about 5 photon/cm3. The emission profile is peaked slightly below 300 km and has a half width of about 75 km. The emission, FZ1, at every height (and hence the total photon intensity,$) decays with a lifetime 1/X, =Z 10 hours. The total emission in the zenith is p4n9 - 50 R, which is about the observed value near the middle of the night.

There is one important feature of the middle-latitude observations that the theory of recombination and diffusion does not seem capable of coping with, and that is the enhancement that moves out of the north after the middle of the night (Section 12.3.2). One possibility for an explanation of this pre-dawn effect lies in semiregular daily motions of ions other than by diffusion. The nocturnal F layer does possess motions not well understood. Ionospheric analyses can give values of Ne(z) for various times throughout a night. It would be valuable to make a detailed comparison (perhaps from IGY data) of the airglow with the ionospheric densities by means of Eq. (13.17) for several nights through the year and at different latitudes.

13.2.4. Excitation of the [N1]21 lines

Bates [19526] suggested dissociative recombination

N , + + e + N * + N * (13.18)

as the mechanism for twilight excitation of the doublet at 5199 A from 4S0 - zDO (see Section 11.6.1). The mechanism would subtract N;

'I In the discussion of the post-twilight decay (Section 11.5.3) diffusion was not considered for two reasons: in the earlier stages of twilight, recombination is important in the Fl region, where N e f N(O+); however, Fl recombination is not allowed for in the present diffusion theory. Secondly, in the post-twilight the eigenfunctions in Eq. (13.6) with j = 1, 2, and 3 are quite important, and to determine the relative weights of these eigenfunctions, the N e distribution with z would have to be known quite accurately at some fixed time. Thus diffusion is best neglected in the early post-twilight.


ions from the ionosphere soon after sunset, as the rate coefficient arec is perhaps on the order of lo-' cm3/sec at F-layer temperatures and lop6 cm3/sec in the E layer where Ne is lower (Bialecke and Dougal [19586]). Thus in the absence of deactivation the intensity would decay with a lifetime governed by the radiative transition probability, A,, e

With electron collisions deactivating the term, however, the lifetime is considerably less at high altitudes. In Section 13.3.1 electron collisions are discussed in greater detail and the rate coefficient for deactivation, szl, is given by Eq. (13.23). Seaton [1956c] finds sZ1 w lo-' cm3/sec in the F region (for T w 1000" K), giving a lifetime for an excited atom of 1jNe s,, - 3 hours.

If the mechanism of dissociative recombination is responsible for the excitation, continuous formation of N,f through the night by particle impact may be important. The twilight observations of N: also can be explained by nocturnal production of ionization (Section 1 1.2.2) and we may estimate the rate of emission of [NIlZ1 that would be expected on this basis.

The twilight intensity of A3914 (Section 11.2.1) indicates a total N,f abundance of = 5 x lo9 ions/cm2 (column). If this abundance is maintained throughout the day and night the rate of emission in equilibrium would be

sec-l (Garstang [1952a, 1956~1).

(13.19)

If the denominator is large compared with unity, the total emission becomes

(13.20)

where we take 8, = 1 and assign values to the rate coefficients arec and s2, as quoted above. We thus find p4.rr.Pe 50 R. The twilight emission has been crudely estimated at 10 R (Section 9.2) and the nightglow seems to have about this same value. With the uncertainties involved, the predicted intensity seems to be of the desired order of magnitude. We conclude that [NI],, may well arise from dissociative recombination of N,f ions produced largely by incident particles as well as by sunlight. Interferometric measures of the relative intensities in the doublet would be useful (see Section 7.4.2).

13.3. EXCITATION BY PARTICLE COLLISIONS 533

13.3. Excitation by Particle Collisions

13.3.1. Thermal Electrons

In the F region and higher, where the temperature may exceed 1000" K, a few electrons, forming the tail of a near-Maxwellian distribution, may have sufficient energy to excite low atomic levels by inelastic collisions.

Oxygen Red Lines.-The rate of photon emission in A6300 + A6364 of [OI],, will be

(13.21)

where the denominator allows for deactivation by electron collisions, and cascading from higher terms is neglected. Here s12 is the rate coefficient for excitation and sZ1 the coefficient for deactivation. Writing the cross section Q in terms of the collision strength SZ, we have [Eq. (1.99)]

(13.22)

When SZ is independent of v and the electrons are in a Maxwellian distribution f(v), the rate coefficient is [see Eq. (1 .lOl)]

where we use the relation SZ,, == Q,,, imposed by detailed-balancing considerations in thermal equilibrium.

For the excitation coefficient the analysis is similar except that the integral in Eq. (13.23) has a lower limit of v,,, where E , , = ~ r n vt, is the excitation energy of ID. Then

1

s12 = (G~,&~) sZ1 c F 1 2 ' k T . (13.24)

Seaton [19533, 1956~1 has made detailed calculations of SZ,, and sI2. At T = lo3 he finds s2, m 2 x cm3/sec. Then with A,, m loe2 sec-l (Appendix VI) we see that deactivation is not very important for the nighttime F region, where N , does not greatly exceed lo5 ~ m - ~ .

Because of the exponential in Eq. (13.24) the red-line emission is very sensitive to temperature-so much so that it is not possible to make a realistic prediction of the intensity to be expected from this


mechanism. The total emission in a vertical square-centimeter column is p47r9, where p = cos 0 and 0 is the angle of emergence from a plane- parallel layer (see Appendix 11). If T = 1000" K over most of the F layer, p47r9 - lo-* R, compared with an observed value around 50 to 100 R. Pikelner [1954a], for example, considered the mechanism and concluded that electron impact was of negligible importance. If, however, the temperature were as high as 3000" K, the F region would contribute more than the entire amount observed near the middle of the night.

The observed red-line intensity therefore puts a limitation on the temperature gradient in any atmospheric model. With a model atmosphere and some estimates about the nocturnal distribution of ionization from the preceding section, one can readily compute the red-line emission. If the model temperature is too high in the F region or even above, the predicted emission may wellexceedtheobserved (Section 3.5.3).

"I],, Lines.-For the A5199 [NI],, doublet the analysis is quite similar to that above. As s,, w cm3/sec and A,, rn sec-', the denominator in the expression for F,, [see Eq. (13.21)] is greater than unity in the F region. Then with Eq. (13.24), we have

(13.25) F,, = N(N) A,, 4 e-Elg'kT.

Even for a temperature as high as 2000" K, over lo1' N atoms would be required to explain the nightglow. This abundance would require complete N, dissociation above 140 km, which is quite unrealistic (and in any case the temperature above 140 km is well below 2000" K). Thus the mechanism is of no importance for [NI],,.

B

W1

13.3.2. Extraterrestrial Particles and Other Nonthermal Collisions

First Negative Bands.-A bombardment of extraterrestrial particles on the upper atmosphere has been suggested as one explanation of the twilight airglow of N i (Section 11.2.2), and it seems plausible to explain these particles as having escaped from the radiation belt first detected in satellite experiments by Van Allen, McIlwain, and Ludwig [1959a]. In the nighttime ionosphere we may adopt arec Ne - lo-, sec-l, where mrec is the rate coefficient for dissociative recombination of N; [reaction (13.18)]. This coefficient decreases with increasing temperature in a way that tends to compensate for the increase of Ne with height.

If the N,f abundance in a square centimeter column,M(N,+), inferred from twilight observations (Section 1 1.2. I), is an equilibrium nocturnal

13.3. EXCITATION BY PARTICLE COLLISIONS 535

abundance governed by partide bombardment and dissociative recombination, then the rate of ionization in the entire column is

arec N e X (Ni) w 5 x lo7 ion/cm2 sec. (13.26)

If one ionization in 50 produces a quantum of h3914, we would expect a zenith emission rate of ~ 4 7 r . a ~ ~ ~ ~ - 1 R. The predicted brightness is thus quite low and would not be noticed over the background radiation. This estimate is in the nature of a lower limit, however, since during disturbed magnetic conditions the N l abundance is several times greater than the 5 x lo9 ion/cm2 adopted here. Hence it seems not impossible that A3914 may appear faint in the nightglow as a result of particle bombardment, perhaps constituting a weak permanent aurora emanating primarily from the E region.

In Section 13.2.4 the excitation of the [NI],, lines at 5199 A is discussed. It appears that ionization of N l by particle impact would also explain A5199 and its persistence through the night.

Oxygen Red Lines.-Particle bombardment could produce excitation of the red lines in several different ways including (a) collisional excitation by a fast incident electron, (b) ionization of an atom or molecule with the ejected electron then collisionally exciting the red lines, and (c) ionization followed by dissociative recombination by reactions (1 3.1) and (if 0 is ionized) reactions (13.2).

It seems likely that process (c) will produce the order of one excitation to the 'D term for every oxygen ionization, at least at the higher altitudes where negative ions are not abundant. Hence process (a) can be neglected; the cross section for electron excitation of 'D is important only at low electron energies, since it requires electron exchange. For example, at 500 ev the ionization cross section is some lo3 times that for excitation.

The contribution from process (b) is difficult to evaluate precisely. If an electron is ejected with several ev of energy in a pure 0 atmosphere, we would expect one or more excitations of the lD term before the electron slows down. At energies just above 2 ev there would be nothing for the electron to spend its energy on but the metastable terms and elastic collisions; the latter take only about (= 2m/M) of the total energy per collision, although the cross section may be very large. With an appreciable molecular population the energy may be degraded through inelastic collisions that excite vibrational levels in the ground electronic state as well as in higher electronic states. Again the twilight observations of N,f provide an estimate of the rate of ionization. Normally, above 200 km the N,f density is probably well below 10 ion/cm3 at night,


which implies an equilibrium rate of ionization of arec N , N(N;) - 10-1 ion/cm3 sec. Since in the F region 0 is an order of magnitude more abundant than N,, the oxygen ionization rate will lead to perhaps one red-line quantum/cm3 sec or a total emission from the F region of p47r.Y - 10 R. This calculation is extremely rough. But it does serve to point out that some of the red-line variations that are observed in the nightglow may arise from particle bombardment (also see Section 7.4.1). An effort should be made to correlate twilight enhancement in the N; First Negative bands (which directly indicate ionization) with the [OI],, intensity at night. The comparison should allow for the fact that enhanced recombination may persist for a long period after the excess ionization production ceases.

Fast electrons that can produce inelastic collisions, Bates [19543, 1957~1 proposed, might also be liberated by associative detachment,

0 + 0- + 0, + e (5 3.7 ev), ( 1 3.27)

which would occur mainly in the E layer and below. There is considerable uncertainty in estimating the photon yield in the [OI] lines from this mechanism. Bates suggests that it might be of appreciable importance in the absence of deactivation, but at low altitudes a large portion of O(l0) atoms are undoubtedly deactivated (Section 13.4.2).

‘41

13.3.3. Atomic and Molecular Thermal Collisions

Bates [1951a] noted that an important factor in cooling the F region would be radiation emitted from excited levels within the ground 3P term of 0. These levels are populated by ordinary atomic collisions. In the extreme case of very low density every excitation would lead to an emitted photon. But the problem in the F region is closer to the oppobite extreme, wherein collisions are frequent compared with the lifetime of the excited levels, so that the populations are in nearly a Boltzmann distribution [Eq. (1.7)].

The so-called “coronal transition” 3P, - 3P, gives a line at 62p and has a transition probabilitys of A,, = 8.9 x sec-l according to Pasternack [1940a] and Garstang [1951a]. Transitions from the upper level 3P,, may be neglected both because of the lower population and transition probability involved. The photon emission rate is then

3, exp (- e l /kT) 1 rn 3 A,, N(0 ) .

(13.28) F12 = A,,N(O) 9, + G , exp (- EJKT) + 6, exp (- E$KT)

In this section the subscripts refer to the J values of the levels involved in a transition.

13.4. PHOTOCHEMICAL REACTIONS 537

From the lower part of the nocturnal F region (say, 250 km, where N ( 0 ) = 7 x lo8 ~ m - ~ ) , the photon emission is quite large by normal airglow standards: F,, w 2 x lo4 photon/cm3 sec, and the total emission above that point probably exceeds 100 kR or 3 x erg/cm2 (column) sec, an important loss of energy in the F region.

This radiation could only be observed from above the E region, however, because of reabsorption of the 62p line by 0 in the ground level, ",. At the center of the line the absorption coefficient will be a0 - 5 x cm2; thus in the E region the optical thickness T~ will become unity within a few kilometer^.^

Bates [ 1951~1 has considered thermal excitation of molecular vibrational levels as well. The relatively abundant homonuclear molecules, 0, and N,, are prohibited from producing much radiation, since vibrational electric-dipole transitions are forbidden. Molecules such as CO, NO, etc., on the other hand, are too rare in the high atmosphere to be of much importance in this respect.

The thermal radiation from the region below 100 km becomes most complicated because of the dominating importance of radiative-transfer effects. The subject matter here has been aptly summarized in the book by Goody [1958a, Chap. 61.

13.4. Photochemical Reactions in a n Oxygen-Nitrogen Atmos- phere

A multitude of photochemical reactions, ionization and recombination processes, etc., is possible in an atmosphere consisting only of oxygen and nitrogen. A rather extensive list of such reactions has been given by Harteck [1957u], but because the rate coefficients are so poorly known it is not feasible to make an exhaustive study of equilibrium abundances or even to sort out all the important processes.

Theoretical discussions of the various reactions have been given by several authors.1° Here I shall be primarily concerned with indicating

Bauer and Wu [1954u] have treated the radiative transfer problem in an approximate way. They neglected reabsorption, however, in making numerical calculations regarding the cooling of the E region by the radiation at night. But because the optical thickness is so large, any loss of heat must be considerably less than in a transparent atmosphere. Indeed, because of the dependence of the problem on N(0) and T as a function of height, one can not even be certain a priovi that this radiation will not tend to increase the net energy content at a particular height.

lo Rather general treatments with application to the airglow have been published by Bates [1952b], Nicolet [19556, c, 1957~1, Barth and Kaplan [19576], Harteck [1957u], and Kaplan and Barth [1958u]. Similarities between active nitrogen in laboratory after-


the reactions that seem likely to be responsible for airglow emissions, and the discussion of more general problems of aeronomy will be secondary to that purpose.

13.4.1. Excitation of 0 2 Band Systems

Expected Rate of Emission.-The main problem with 0, has been not so much in finding a suitable reaction to account for its excitation but in explaining why the emission, from some states at least, is not stronger than it actually is. Bates [19546, 19.57~1 has pointed out that oxygen molecules may be formed in the upper states to emit the various nightglow band systems (as well as in the ground X 3 2 ; state-see Fig. 5.33) by three-body association of normal 0 atoms:

o(3q + o(3q + x -, 0; + x. (13.29)

This is probably the excitation process responsible for the Herzberg and Atmospheric bands observed in laboratory oxygen afterglows (Rroida and Gaydon [1954a], Kurzweg, Bass, and Broida [1957a], Barth and Kaplan [ 1957a, 1959~1). Differences between the laboratory and airglow vibrational distribution in the Herzberg bands can probably be attributed to greater vibrational deactivation at the higher laboratory densities. In the region near 100 km where photodissociation,

0, + hv 3 0 + 0, (1 3.30)

is important, reaction (13.29) is the dominant means of molecular association. Equating the average rates of the two reactions over a 24-hour period, Bates finds that the mean rate of formation of 0, in each of these states should be about 101o-lO1l molecule/cm2 (coiumn) sec. There is no apparent reason why the ground state should be especially favored, so that we might expect a total emission rate as high as 100 kR. The observed intensity is considerably less than this value (Appendix I1 and Section 12.3.1), but a large fraction of the total emission is not observable from the ground.

glows and the airglow have been discussed by Oldenberg [1953a, 1958~1 and Tanaka, Jursa, LeBlanc, and Inn [1959a]. Krassovskii [1957a] and Hertzberg [1958a] have given particular attention to nitrogen-oxygen ions and the problem of ionospheric recombination. Recent laboratory work has been concerned with determining rate coefficients of the reactions in oxygen-nitrogen mixtures; see Ford and Endow [1957a], Kistiakowsky and volpi [1957a].


Total 0, Emission.-In the observable range the Herzberg bands ( A 32J -+ X 3Z;) emit about 0.5 kR. Additional emission shortward of the ozone cutoff is expected (and has evidently been detected by rockets -see Table 12.4) but probably does not contribute an order of magnitude more radiation than lies within the observable range.

Strictly, the tentatively identified B 34, + a ld, bands in the blue should not be counted. Since they do not emit to the ground state, the photon count will appear in the a ---f X (Infrared Atmospheric) bands. But in any case these bands contribute probably less than 0.1 kR.

The Atmospheric system (b IZ; --t X ”;) is represented only by the 0-1 band, h8645, with about 1.5 kR. There is some question as to how much additional emission should be attributed to the 0-0 band, h7619, which is not observed because of absorption or scattering by 0, below the emitting region. Bates [1954b] suggested that the 0-0 emission would undergo resonance scattering by 0, until it is converted to 0-1 radiation by fluorescence. An approximate solution of the radiative-transfer problem (Chamberlain [1954a]) indicates that in the limiting case of no collisional deactivation only about 25 percent of the observed A8645 emission i s initially emitted in the 0-1 transition. On the other hand, the resonance scatterings occur mainly in the region around 50 km. The rotational temperature of the Atmospheric band is generally below 200” K (Section 12.2.1) and may be close to the temperature of the Herzberg bands. The kinetic temperature in the 50-km region is considerably higher than 200” K, suggesting that the fluorescence mechanism does not actually contribute much of the total 0-1 band. There is some additional evidence (see below) that collisional deactivation of 0, is important at considerably higher altitudes than this. The fluorescence mechanism may therefore be of no practical importance, with virtually all the emitted 0-0 radiation absorbed at lower levels and not re-emitted.

The relative photon emission in the two bands is proportional to q(v’v”)/A3, where q is the Franck-Condon factor [Eqs. (1.72) and (1.74)]. With the calculations of q by Fraser, Jarmain, and Nicholls [1954a], we find that the photon ratio for h7619Ih8645 is 21. Hence without resonance scattering and fluorescence the total Atmospheric system gives approximately 30 kR. With the 0-1 band enhanced by Bates’ mechanism, the total radiation may be as low as 8 kR.

An upper limit can be placed on the nightglow emission in the a ld, + X 3Z; (Infrared Atmospheric) system from the twilight measurements by Vallance Jones and Harrison [1958a]. The 0-1 band at 1 . 5 8 ~ evidently emits less than 5 kR at night. The 0-0 band is reabsorbed in the lower atmosphere, as with the Atmospheric system discussed above, but should emit about 10 times as strongly as 0-1.


Hence the upper limit to the nightglow Infrared Atmospheric bands is about 50 kR. The difficulty in measuring the 0-1 band is that it is blended with the Q branch of the O H 4-2 band. Observation of 0-0 at 1 . 2 7 ~ from rockets may be the most suitable means of obtaining an accurate nightglow intensity for this system.

Deactivation of O,.-The total emission from 0, is thus probably in the range 10 to 80 kR, mostly from the lower states (see Fig. 5.33). There is probably considerable deactivation from the upper states A "Z ;+ (for the ordinary Herzberg I bands), B 34, (for the weak inter- combination system in the blue and the Herzberg [1953a] I11 bands, which are probably absent) and c12; (for the Herzberg [1953a] I1 system, which seems to be absent). Deactivation by electron collisions should be quite inappreciable, and Bates [1955a] has emphasized that direct conversion of excitation to kinetic energy by ordinary superelastic collisions between heavy particles is very inefficient. Bates proposed that a more important deactivation process for the airglow would be atom-atom interchange:

which effectively deactivates a molecule from state 01 to ,8. The process is essentially an ordinary chemical one of the type (1.109) and may occur rapidly, especially for the A 32U+, B 34u, and c lL'; states, which have small binding energies and therefore, probably, large rate coefficients.

Although the Herzberg bands and probably the 34, -+ ld, blue bands are populated to rather high vibrational levels, as would be expected for excitation by association, the Atmospheric system shows emission only from V' = 0. Bates [1954b] has proposed that the vibrational deactivation of the upper, b lZbf, state might proceed rapidly through an interchange of electronic energy between an excited molecule and one in the ground level:

O , ( m ; , 0' > 0) + O2(X3Z;, 0'' = 0)

The mechanism is probably facilitated by the approximate equality of the equilibrium internuclear distance re and the vibrational quantum we in the two states.

13.4. PHOTOCHEMICAL REACTIONS 54 1

Other Excitation Mechanisms.-Of course, the great intensity of the Atmospheric bands compared with the emission from the higher states may be due to additional mechanisms populating the b lZ; state. Kaplan [1952a] and Nicolet [1955b] have proposed the reaction

NO, + 0 + NO + O,(b '2;). (13.33)

Partial support for the mechanism is provided by Kaplan's [1952a] afterglow experiments," where the Atmospheric bands were more intense when small amounts of nitrogen were present than they were in pure oxygen. In addition, strong bands of NO, were present in the visible and photographic infrared. Identification of NO, bands in the airglow would be further support for the reaction by demonstrating that N0,is continually reformed in sizeable quantities(see Section 13.4.3).

Barth and Kaplan [1957a, b] have found evidence that the Herzberg bands in air afterglows in the laboratory are produced in part by

N + 0, -+ NO + O,(A ":). (1 3.34)

Kaplan [1952a] had suggested earlier that the reaction may contribute to the afterglow excitation of the Atmospheric system.

13.4.2. Photochemical Excitation of [OI]

GreenLine [OI],,.-Although a portion of the green line, A5577 ( lD - 'S), may arise from dissociative recombination (13.1) in the F region, most of the excitation seems to be limited to the 100-km region. Before the 0, bands had been identified in the airglow, Chapman [1931a] proposed that the green line might arise from

0 + 0 + o-to, + O(lS), (1 3.35)

which is reaction (13.29) where the third body, 0, is excited by some of the energy liberated in association. The location of the emission around 100 km is in conformity with this mechanism, as dissociation of 0, places the maximum 0 concentration in that region. The 0, emission formed by means of (1 3.29) might arise from a slightly different altitude, since the reaction can presumably use any constituent as a

l1 The Atmospheric system in emission was first observed in afterglows by Kaplan [1947n, b] . See also Kvifte [1951b], Branscomb [1952u], Kurzweg, Bass, and Broida [ 1957al.

542 13. EXCITATION OF T H E NIGHTGLOW

third body. The temperature dependence of these processes is not known.

Kaplan's [ 1932a, 1934a, 1936~1 afterglow studies suggested that metastable ( A ,Z$) N, molecules might excite the green line, but the absence of the Vegard-Kaplan bands ( A ---t X ) in the nightglow spectrum makes the process now seem unlikely. The Chapman process is thus the only mechanism thus far proposed that seems capable of producing the green line. The intensity correlation with the 0, bands (Section 12.3.3) and the approximate height coincidence of [OI],, and 0, (Section 12.1.5) tend to support the mechanism.

Little is known about deactivation processes for the ' S term. Kvifte and Vegard [1947a] investigated

O(lS) + 0, -+ O(3P or lD) + 0; (13.36)

in the laboratory and found that only one collision in 3 x lo5 is effective. The rate coefficient [see Eq. (1.95)] corresponding to a gas-kinetic collision in the upper atmosphere is about 3 x 1O-lo cm3/sec. Hence for reaction (13.36), we have sg6 e cm3/sec. As the radiative lifetime of lS is the order of 1 sec, deactivation by this reaction will be inappreciable above 75 km. Seaton [ 19584 has suggested that

O(U) + N, 3 O(l0) + NZ (13.37)

might be the most effective deactivation process. In this case N,* would be vibrationally (not electronically) excited ; the final 0 term has therefore been written as lD, since 3P would involve a violation of the Wigner spin-conservation rule (see Massey and Burhop [1952a, p. 4271).

Red Lines [OI]21.-The main problem with regard to photochemical excitation of the red lines (,P - ID) lies in accounting for the faintness of the emission around 100 km. The rocket measurements show that most of the emission comes from the F region, and appropriate mechanisms for these altitudes have been discussed in Sections 13.2 and 13.3. Although some red-line radiation may come from the E region and below, it is clear that deactivation is nevertheless very important. First of all, were there no deactivation, the emission in A6300 + A6364 would be at least equivalent to the green-line emission because of cascading:

O(1S) 3 O(10) + A5577. (13.38)

In addition, the Chapman mechanism (13.35) probably excites the ID term directly. But the nightglow red lines have actually less than


half the brightness of the green emission (Section 12.3.1), and most of this comes from much higher than 100 km.

Other photochemical reactions have been proposed for the red lines in order to explain the different behavior of the red and green emissions (see Bates [1954b, 1957~1). But these processes would also occur at relatively low altitudes, where deactivation is evidently important. The predominance of F-region excitation for the red lines and 100-km excitation for the green line presumably accounts for the lack of correlation of these radiations.

The lifetime of lD is the order of 100 seconds. Electron collisions are ineffective in producing deactivation because the electron density is too low (Section 13.3.1). Deactivating collisions with molecules ordinarily have an extremely low probability. The reaction

o(1q + N, + o(3q + N; (13.39)

has insufficient energy to excite an electronic state of N,; here NZ represents vibrational excitation of the ground state. This reaction may be especially slow because it involves a change of total electron spin.

The most important deactivation process for O(lD) very likely involves a transfer of electronic energy, as in

o(1q + 0, .+ o(3~) + o* 2 ’ (13.40)

where 0: is in the a ld, or b ‘2; state. Bates and Dalgarno [1953a] and Seaton [1954a] proposed that this

reaction might be especially rapid if the energy exchange is very small. The reaction

ope) + o,(x 3z;, v t * = 01 -+ 0(3~,) + o,(b iz;, I 2) (13.41)

is within 0.004 ev of exact resonance for ZI’ = 2. The problem has already been discussed in Sections 7.4.2 and 1 1.5.2. The inverse reaction to (13.41) when v’ = 2 might be prohibited if the molecule is readily deactivated, either by radiative cascades or reactions (13.31) or (13.32). I t appears, however, that (13.41) does not populate v’ = 2 preferentially.

13.4.3. The Continuum a n d Unidentified Blue-Green Bands

Gaydon [1944a] first suggested that the yellow-green continuum commonly seen in air afterglows in the laboratory is produced by

NO + 0 .+ NO, + hv. (13.42)


Additional work by Tanaka and Shimazu [1949a], James and Sugden [1955a], Stewart [1957a], Tanaka, Jursa, and LeBlanc [1957a], and Kaufman and Kelso [1957a] tends to substantiate the identification. Referring to the afterglow experiments, Krassovskii [195 1 b], Bates [1954a], and Broida and Gaydon [1954a] independently proposed that the airglow continuum comes from this reaction. Bates [19546, p. 5861 estimates the rate coefficient to be less than 1O-l’ cm3/sec. The conclusion from laboratory work by Kistiakowsky and Volpi [1957a] that the reaction occurs at almost every gas-kinetic collision does not seem reasonable.

The spectrum in the laboratory may actually have a banded structure superimposed on the continuum. If so, a more detailed comparison of the afterglow with the airglow may reveal similarities in the “continuum structure.”

Kaplan [1952a] suggested that reaction (13.42) (but with the addition of a catalytic third body) occurred in his laboratory afterglow. The reaction may indeed reform NO,, which is converted into NO by reaction (13.33). These two processes together would associate 0 atoms into 0, molecules, thereby deriving energy for the Atmospheric bands, the continuum, and possibly NO, bands. Kaplan’s [1952a] afterglow showed NO, in the visible and near infrared; again, a detailed comparison of airglow and afterglow spectra in the visible may be most enlightening.

Nicolet [1955b, 1957~1 has estimated the NO photochemical equilibrium and concIuded that a total zenith emission rate exceeding 1000 R might result from (13.42), but the atmospheric NO abundance is uncertain. The reaction would have to give about this rate of emission to account for the 1 RIA or more observed in the green continuum (Section 12.3.1). The maximum emission probably occurs in the 80-90 km range. Jursa, Tanaka, and LeBlanc [1959a] obtained an upper limit to the NO concentration of los ~ m - ~ in the 63-87 km region from a rocket flight. For reaction (13.42) to produce the continuum, concentrations above lo7 ~ m - ~ would probably not be required.

Several other mechanisms for producing continuous radiation in the nightglow have been proposed. Bates [ 19544 has suggested association of two normal 0 atoms,

O + O - + O , + h v , ( 1 3.43)

might give a detectable contribution, which would appear mainly around 90-100 km.

Pikelner and Chuvayev [1953a, 1954~1 have proposed that radiative attachment,

0 + e -0- + hv (13.44)


would be sufficient to explain the airglow continuum. Attachment to 0,,

(1 3.45) 0, + e -+ 0; + hv,

may also be important. If electrons are not replenished these processes probably proceed at fairly steady rates throughout the night only in the region above 100 km, and therefore they would face the objections that the continuum appears to belong to the green-line covariance group (Section 12.3.3) and that rocket measurements (Section 12.1.5) favor a height near 100 km. And if the rate of reaction (13.44) or (13.45) were sufficiently rapid to produce the entire airglow continuum (probably the order of 1 kR), then attachment would subtract most of the F-layer electrons soon after sunset.

Hence a collisional mechanism such as

0 + 0- -+ 0, + e (1 3.46)

is necessary to maintain the free electron density (see Bates [19546, p. 6141). Persistence of strong radio absorption (Section 4.3.4) in the D region throughout the night in some instances also seems to require a collisional mechanism that destroys negative ions at a fairly rapid rate. From the measured rate coefficients12 it appears that the attachment continuum will be too weak. Dalgarno [1958a] points out that the mechanism may give an enhancement at twilight.

Radiative recombination of the type

O+ + e -+ 0 + hv (13.47)

has a rate coefficient of lo-', to 10-l1 cm3/sec and thus produces a negligible contribution (Bates, Buckingham, Massey, and Unwin [1939a]).

13.4.4. Artificially Induced Airglow

Although much can be learned about the airglow and atmospheric photochemistry through laboratory studies of flames, discharges, and afterglows, the dimensions and boundaries of the experiment are often too restrictive. Rocket exploration makes it feasible to use the high atmosphere as the laboratory, either for the study of atmospheric physics

l2 For photodetachment and attachment cross sections see Branscomb [1957a], Branscomb, Burch, Smith, and Geltman [1958a], Smith, Burch, and Branscomb [1958a], Burch, Smith, and Branscomb [1958a], Chanin and Biondi [1958a], Chanin, Phelps, and Biondi [1959a], Hurst and Bortner [1959a]. For a general review of negative ions see Branscomb [19576].


itself or for more fundamental studies of atomic and molecular processes that cannot be appropriately investigated on the ordinary laboratory scale.

A few preliminary flights, carrying experiments designed to elucidate the oxygen-nitrogen reactions in the atmosphere, have been made with Aerobee rockets by a group at the Air Force Cambridge Research Center.13 One experiment was concerned with detecting ionization produced by photoionization of a cloud of NO ejected at 95 km. The rough agreement between the total ion content inferred from radio reflections and that expected (from the known solar flux in Ly a, the photoionization cross section, and the recombination coefficient) was cited as evidence that the D layer is due to Ly a ionization of NO, first proposed by Nicolet [1949a]. The main uncertainty, however, is still the normal abundance of NO in the atmosphere.

In a second flight NO was seeded at night and caused a visible glow composed mostly of continuous radiation. Presumably reaction (13.42) was responsible. Knowing the total intensity and the 0 concentration, one can estimate the reaction rate. A crude estimate of this rate was made, but again whether (13.42) is important in the natural airglow depends critically on the nocturnal equilibrium of NO.

A third flight released C,H, (ethylene) at night at 105 and 143 km. Although the glow was photographed from the ground with blue- sensitive and panchromatic film, the lack of satisfactory spectra makes any conclusions regarding the dominant chemical reactions rather nebulous.

These artificial airglows may also give data on atmospheric winds, convection, and turbulence at different levels. This is possible as well for the experiments with sodium and other metals discussed in Section 1 1.4.3. Seeding can give information on atmospheric densities or mean free paths (from the observed time of outward diffusion of a cloud), but the apparent rate of diffusion might also be affected by the gradual chemical disappearance of the seeding substance and, possibly, by reabsorption of emitted radiation within the cloud itself. (The latter is a hazard with sodium experiments, for example.)

High altitude experiments need not necessarily be limited to artificial seeding, which affects the local composition. Other techniques may alter the temperature, ionization, or dissociation, or induce dynamic effects (Section 8.2.1). Of course, rocket and satellite experiments are

lS Marmo, Pressman, Aschenbrand, Jursa, and Zelikoff [1957u], Pressman, Aschenbrand, Marmo, Jursa, and Zelikoff [1956u, 1957~1, and Zelikoff, Marmo, Pressman, Manring, Aschenbrand, and Jursa [1958u].


extremely expensive and one feels that any experiment he proposes should hold considerable promise. The subject is one open to ingenuity.

13.4.5. Regular Variations in Intensity

It appears (Section 12.3.2) that any latitude or seasonal effects in the green-line covariance group (which probably arises predominantly from oxygen and nitrogen photochemical reactions) are slight (perhaps involving factors of two or three) and possibly rather complex. The daily variations are also somewhat complicated and not fully understood. I t would not be unreasonable to look for variations correlated with solar activity, which might well affect, for example, the degree of dissociation of some substance, but no such relationship has been established.

Intensity changes might be produced by variations in the chemical abundances, pressure, or temperature. Little is known of the latitude and seasonal variations of the properties of the upper atmosphere, and accurate predictions of even the daily variations are hampered by poorly determined reaction rates and abundances. The 0, bands and the green line, as formed by three-body association [(13.29) and (13.35)], could conceivably change appreciably through the night due to variation of the 0 abundance. However, no general decay of these radiations has been established, which indicates that the 0 abundance in the emitting region is not seriously depleted overnight. Reactions involving the oxides of nitrogen (producing, perhaps, the continuum, some of the weak blue-green bands, and the Atmospheric 0, system) may, on the other hand, exhibit important post-twilight effects, but again the relevant abundances and reaction rates are so poorly determined that quantitative prediction is scarcely possible (see Nicolet [1955b, 1957~1). Similarly, little drop in temperature is expected as a result of radiative cooling.

On the other hand, composition, pressure, and temperature may be altered by dynamical processes such as diffusion, mixing, and tidal oscillations (see Nicolet [19553], Krassovskii [1956b, 195761, Tohmatsu [19583]). As Krassovskii has pointed out, covariance in the intensities of different emissions may be a consequence of simultaneous changes of temperature or pressure, even if these emissions are caused by different reactions. Hence we would expect the members of a covariant group to be emitted from the same general height region, but they do not necessarily have to arise from similar reactions.

The general circulation properties of the upper atmosphere are poorly understood. Perhaps large scale circulation patterns play a central role in governing latitude and seasonal variations (e.g., Hikosaka, SaitB, and Yano [1958a]), but again no such effect has yet been estab-


lished. Conceivably, the circulation could affect the airglow by altering either the composition or temperature or indirectly through the turbulent or diffusive dynamics.

Tidal Oscillations.-It seems likely that tidal oscillations of the upper atmosphere could be responsible for some daily variations. Liszka [1956a] has compared a few published data on the time of maximum intensity of the green line with the lunar phase (that is to say, with the moon’s angular distance from the sun). If the tidal action of the moon is important (and there is reason to suppose that it is about as large as or larger than the solar effect at high altitudes) a correlation would be expected. Liszka does indeed find some evidence for such a relationship, but a more extensive statistical study is required. The mahimum nightly intensity will be governed largely by the patchiness, which is probably related to atmospheric winds and turbulence (Sec- tion 13.4.6), and small changes due to the direct action of tides will become obscured.

Direct evidence of tides in the region of interest was obtained by Appleton and Weekes [1939a], who found a semi-diurnal lunar oscillation in the daytime height of the E layer. (A diurnal lunar tide has not been found from barometric observations as the ground, although a semidiurnal lunar tide was established by Chapman [1935a].) The interpretation placed on the height oscillation was that it indicated a change in the height corresponding to a fixed pressure: individual ions in the E region should have a lifetime of a few minutes at most. In a Chapman layer (Section 3.4.1) the recombination coefficient is independent of height; hence the height of maximum ionization will change as the number of atoms attenuating the ionizing radiation from above (that is to say, the partial pressure of the “active” constituent) changes,

The solar tide (which involves thermal as well as gravitational effects) is less easily established because solar radiation produces the layer. The observed solar oscillation was 12 km, with minimum height near noon; this result is about what would be expected from ionosphere theory without any solar tide (Wilkes [1949a]). At the ground the semidiurnal solar tide is many times more important than the lunar, although the gravitational effect of the moon is twice that of the sun.

Indirect evidence of ionospheric tides is also furnished by the daily variations of the geomagnetic field. Chapman [1919a] showed that the dynamo action of ionization being transported across magnetic-field lines will satisfactorily explain the solar and lunar components of the variation (Chapman and Bartels [1940a]). There is some difficulty in


reconciling these interpretations with the resonance theory of tides (see Wilkes [1949a]). Pekeris' [1937a] theory seemed to account for Chapman's [1919a] semiempirical result that pressure oscillations in the upper atmosphere are out of phase with those in the troposphere, but quantitative difficulties remain (Bates [19543, p. 6181). The Appleton and Weekes [1939a] radio experiments suggest a pressure fluctuation in phase with that near the ground.

At any rate, interpretation of the radio work seems straightforward, and it indicates a semidiurnal lunar oscillation with an amplitude of about 1 km, the maximum heights being attained approximately 3/4 hour before the upper and lower lunar transits.14 The solar tide may well be of the same order of magnitude. For our purposes it is more instructive to consider the pressure variation, produced by the tidal wave, at a fixed height. From the barometric equation,

p ( z ) = p o e-(z-zo)lH, ( 1 3.48)

where po = p(.zo), we have for the pressure change corresponding to a Sz change in height,

(1 3.49)

In the 100-km region H is the order of 7 or 8 km. Thus a height variation of 1 km corresponds to roughly 10 percent pressure variation. The height differential in Eq. (13.49) should be measured from the height where the pressure is p,. If the altitude of constant pressure increases by 1 km, the pressure at constant height increases by 10 percent.

If the green line is formed by the Chapman mechanism (13.35) with no deactivation, it may vary asp3. Hence we might expect systematic fluctuations in the green-line intensity of the order of & 30 percent from the mean, arising from lunar tides alone. Near new moon the solar tide, if appreciable, will tend to reinforce the lunar. It appears on this basis that the oft-reported midnight maximum (Section 12.3.2) may have some theoretical justification statistically, and the fact that photometric observations are usually made near new moon may have increased this tendency. Tohmatsu [19586] has emphasized that if the pressure change is adiabatic, the change in temperature may also cause variations in the rate coefficient for excitation. If the tidal forces on the upper

l4 Sporadic E has a mean tidal oscillation of 0.22 km amplitude, with the maximum occurring 7.0 hours after lunar transit, according to Wright and Skinner [1959a]. There seem to be considerable variations from month to month, especially in the average phase.

5 50 13. EXCITATION OF THE NIGHTGLOW

atmosphere are significant in the daily variations, they may also be responsible for some seasonal effects, such as those indicated by the work of Manring and Pettit [1958a].

13.4.6. T~rbu lence '~ and Green-Line Patchiness

Dynamical effects in the upper atmosphere are undoubtedly important in determining the height of oxygen association (Section 3.5.2), and if the green-line emission is due to photochemical processes, as seems to be the case, atmospheric motions are probably responsible for the patchiness (Section 12.3.4). There is some reason to suppose that the patchiness is directly related to turbulent motions in the 100-km region. I t is plausible that turbulence, with the enormously increased rate of mixing that accompanies it, could sufficiently modify the degree of dissociation at a given level to affect the rate of emission. That turbulence does in fact exist is suggested by shearing motions observed in the winds at 100 km (see below) and by the Reynolds number. The Reynolds number at which laminar flow breaks into disordered, turbulent motion is

(13.50) V L

R = - > 103, V

where TI is the characteristic velocity, L the characteristic length of the system, and v the kinematic viscosity (v = p/p, where p is the coefficient of viscosity and p the mass density).

I t is convenient in the analysis of turbulent flow to consider the Fourier components of the motion with wavelength 2n-/k; k is then a wavenumber. The kinetic energy in turbulence is said to be distributed over the wavenumber spectrum according to a function F(k), the turbulence spectrum, such that in isotropic, homogeneous turbulence

m - u2 = F ( k ) d k ,

0 (13.51)

where 2 is the mean square velocity of all eddies.

that the rate of dissipation into thermal energy per unit volume is Further, it may be shown from the Stokes-Navrnquation of motion

m

0 b = 2 p v F(k) k2 dk. (13.52)

lS A general elementary review of turbulence theory and references to the literature have been given by Chandrasekhar [1949a]. Some of the more recent developments have been summarized in another article by Chandrasekhar [ 1957~1.

13.4. PHOTOCHEMICAL REACTIONS 55 1

The Kolmogorov spectrum, valid in the intermediate range of wave- numbers in three-dimensional, isotropic turbulence, is F(k) = A kk5j3, where A is a constant. It is apparent that this distribution of energy cannot be valid over all k, as both Eq. (13.51) and (13.52) would become infinite. We shall adopt the Kolmogorov spectrum, therefore, in the range k, < k < kg, where now k, pertains to the largest components of the motion (the largest eddy sizes) and ks indicates the smallest eddies present. We may thus consider 2rr/ko to be the wavelength at which energy is fed into the system and 2n/ks the eddy size at which energy dissipation through viscosity becomes dominant. (At larger eddy sizes the energy is primarily degraded to smaller eddies rather than dissipated into heat.) Chandrasekhar [19493] has shown that ks and KO are then related by

Equation (13.51) becomes

(13.53)

( 1 3.54)

and Eq. (13.52) is

(13.55) E = 2pv i,”” F(k) k2 dk = - 3 pv A k:/3.

2

For a numerical value of the characteristic speed at 100 km we take lo4 cmjsec (360 km/hr). This value is indicated by the motion of green- line patches (Section 12.3.4), by the sodium clouds ejected from rockets (Section 11.4.3), and by meteor trains (Goody [1958a, Chap. 5, Elford

gm/cm3; then Y w 1.5 x lo5 cm2/sec. The appropriate scale length is the most uncertain quantity. If in the horizontal direction it is given by the size of the airglow patches (Section 12.3.4) and is the order of lo8 cm (1000 km), then R = lo7 and is well above the critical value required for wind motions to become turbulent.

If the diameter of the airglow cells is also taken to be 277/k0, then Eq. (13.54) gives A = 5.7 x lo2 and Eq. (13.53) gives ks = 1.6 x

cm-l (or 2rrikg = 4 x lo3 cm). Finally, Eq. (13.55) yields an energy dissipation of i. = 2.5 x erg/cm3 sec.

This rate of energy dissipation is far greater than can be accounted for by airglow radiation. This point was appreciated by de Jager [1952a],

[ 1959a1). w e take p rn 1.5 x lo-* gm/cm sec and p =


who was the first to apply the theory of turbulence to the airglow. For example, in the green line the 100-km region probably emits 5 x erg/cm3 sec and the 0, Atmospheric system about 3 x lo-* erg/cm3 sec. If there were no reabsorption of the “coronal” line of [OI] at 62p (Section 13.3.3), it would dissipate 5 x lo-’ erg/cm3 sec, but even this value must be greatly diminished by radiative-transfer effects.

Thus de Jager suggested that turbulence should be considered as an energy reservoir, along with atmospheric ionization and dissociation. However, the analysis given above, which predicts such a fabulous rate of energy decay, must be re-examined. In the analysis we take as observed the kinetic energy in the large eddies (ko), Application of the theory of isotropic turbulence tells us that this energy is degraded to smaller eddies until it is finally dissipated by viscous friction. The theory is thus used to extrapolate the energy distribution to the region of small eddies. But if the theory is incorrect, the amount of energy in the small eddies may be grossly overestimated, and there is reason to believe this is the case.

We found above that dissipation appears to become important at scale lengths less than about 40 meter. This is considerably less than the vertical scale height (say, 10 km) so that turbulence may well be three- dimensional in eddies of this size. On the other hand, the largest sizes (277/ko), from which we extrapolated to the dissipation region, are some 100 times the vertical scale height and for these clouds the turbulence is essentially two-dimensional.

Unfortunately there is no complete two-dimensional theory of turbulence. But Lee [1951a] has demonstrated that the existence of a Kolmogorov range (k, < k < k,) in two dimensions is inconsistent with dynamical constraints on the vorticity. And Reid [1959a] has proposed that energy initially put into turbulence in one wavelength may become degraded toward larger as well as toward smaller eddy sizes. Reid suggests that in tropospheric turbulence, energy is fed from small-scale vertical motions, at a wavelength appropriate to the vertical scale, into horizontal motion and thence to larger and smaller eddies in the horizontal motion. Investigating the peculiarities of the turbulence spectrum in an atmosphere where the density changes with height, Bolgiano [1959a] also concludes that the inertial transfer is much greater and dissipation into heat much less than in the isotropic, homogeneous situation.

It is not unreasonable to suppose that the rapid mixing produced by turbulent motions is responsible for appreciably altering local composi- tions and thereby affecting the rates of airglow emission. Tohmatsu [19588] has also investigated the composition changes resulting form

13.5. EXCITATION OF EMISSIONS FROM MINOR CONSTITUENTS 553

diffusion and has contrasted them with the changes resulting from photodissociation and association.

There are still many questions to be answered regarding the rate at which turbulent energy is actually dissipated, the origin of the turbulent motion, and the precise manner in which turbulence causes an enhancement of airglow emissions. As a final word of caution I should emphasize that there is even considerable disagreement over whether the observed air motions at 100 km do indicate a predominance of turbulence rather than simple winds or drift motions. The matter depends essentially on the scale length L over which there is a significant change in the characteristic velocity.

13.5 Excitation of Emissions From Minor Constituents

13.5.1. Photochemical Or ig in of the Meinel OH Bands

Excitation Rate.-From measurements of the absolute intensities of a number of bands and computations of the transition probabilities, it is possible to estimate the rate of excitation in the various vibrational levels of the OH bands. (For a discussion of the structure of these vibration-rotation bands, see Section 9.1.4.) In his original analysis, Meinel [1950d, el (also see Shklovskii [1950b, 1951~1) suggested that the intensity distribution of the bands might be explained by excitation from the photochemical reaction into u = 9 only, with lower levels being populated by cascading from above. The idea seemed consistent at the time with the ozone-hydrogen reaction (see below) which has just enough energy to excite o = 9 but not higher levels. In the absence of a detailed theory for the distribution of the energy produced in a chemical reaction, it is impossible to predict how the various levels will be excited. But the idea that resonance would be important-that is, that a chemical reaction would proceed with a high rate coefficient because nearly all the excess chemical energy could be picked up by a particular molecular level-has been largely discredited by Oldenberg [1952a]. There seems to be no valid reason to expect highly preferential excitation of the ninth or any other level.

Nevertheless it is of some interest to obtain the excitation rates of the various levels, not only because it may someday be of assistance in providing an understanding of the chemistry, but for the practical reason of predicting emission rates in the far-infrared bands that are unobservable from the ground. For this purpose we must examine the


status of our knowledge of the transition probabilities, A , ...., as obtained from Eq. (1.66).

Independent calculations of the relative values of A wuI w , l have been made by Shklovskii [19506, 195761 and by Heaps and Herzberg [1952a]. In both these papers a Morse potential, Eq. (1.76), was assumed for the OH molecule. Heaps and Herzberg expanded the nuclear dipole moment in a power series

p , = po + p,(v - re) + p,(r - + * * * + I (13.56)

where r is the nuclear separation and re is the equilibrium position, and made complete calculations for all bands with the linear term and calculations for only a few bands with the quadratic term. Shklovskii’s computations included only the linear term and his relative Av,v,, are in good agreement with those of Heaps and Herzberg based on only the linear term.

Near r = re the expansion (13.56) is appropriate since the effective nuclear dipole moment is not simply proportional to the separation of the nuclei from their equilibrium positions, because of the influence of molecular binding forces. At infinite separation, for example, the moment tends to zero. The high-order terms thus allow for an electrical anhavmonicity, which should be distinguished from the usual mechanical anharmonicity in the vibration of the nuclei, which is accounted for by the Morse (or other) potential function. In this regard see the further improvements in calculations of the matrix elements introduced by Herman and Rubin [1955a].

The use of a Morse potential in deriving the vibrational wave functions is itself a rather crude approximation, especially where the higher vibrational levels are concerned. (See Section 1.4.1 ; also, for a historical review of the problem of the determination of the vibrational constants of OH, see Andrillat [1956a].)

With Heaps and Herzberg’s calculations and measurements of various bands (obtained, to be sure, at different times and different locations) as discussed in Section 12.3.1, Chamberlain and Smith [1959a] have used equations of statistical equilibrium to derive effective rates of excitation (that is, with collisiona1 deactivation ignored) of the OH vibrational levels. Each of these levels seems to be populated directly by the chemical reaction at about the same rate. Bands originating from the few lowest levels have not yet been measured, so we have assumed that they are populated initially at the same rate as the higher ones. The lower levels are also populated by cascading so that in general the population decreases with increasing 0. It is possible to characterize


these populations with Eq. (1.78) by a vibrational temperature of 10,000’ K for v between 4 and 9 ; for the population ratio of v = 1 and 2 this value decreases to 7200” K. Needless to add, such a “temperature” is merely a parameter in an exponential and has no physical significance as far as the gas temperature is concerned. With a knowledge of the

WAVE LENGTH (MICRONS)

FIG. 13.2. Predicted photon emission rates in rayleighs and energy emission rates in erg/cm2 (column) sec for the OH Meinel bands. Within each sequence (dw = const) the band with v’ = 9 is on the right. From Chamberlain and

Smith [ 1959~1; courtesy Journal of Geophysical Research.

relative populations the intensities of all bands in the system can be predicted. The results are given in Fig. 13.2; in the original paper a table of intensities is given. The total rate of emission is about 4500 kR or 3.2 erg/cm2 (column) sec.

An estimate of the absolute intensity of a single branch or line may be obtained with the aid of Table 13.1, which gives the relative intensities (in energy units, not photons) within a band. These intensities depend on the line strengths, the rotational-level populations, and on a v4 factor [Section 1.4.2, Eq. (1 .SO)] and therefore vary with the temperature and with the band, being especially sensitive to its sequence (dv = constant).

TABLE RELATIVE INTENSITIES OF

556

Band zl’ - zl” - __

9-8 8-7 7-6 6-5 5-4 4-3 3-2 2- 1 1-0 9-7 8-6 7-5 6-4 5-3 4-2 3- 1 2-0 9-6 8-5 7-4 6-3 5-2 4- 1 9-5 3-0 8-4 7-3 6-2 5- 1 9-4 4-0 8-3 7-2 6- 1 9-3 5-0 8-2 7- 1 6-0 9-2 8- 1 7-0 9- 1 8-0 9-0

0.0273 0.0284 0.0298 0.0310 0.0322 0.0335 0.0349 0.0361 0.0375 0.0275 0.0285 0.0298 0.0311 0.0324 0.0336 0.0349 0.0361 0.0278 0.0288 0.0302 0.0314 0.0326 0.0339 0.0279 0.0352 0.0289 0.0302 0.0314 0.0327 0.0277 0.0340 0.0288 0.0301 0.0313 0.0279 0.0325 0.0289 0.0303 0.0315 0.0278 0.0289 0.0302 0.0279 0,0290 0.0278

PI(2)

0.0727 0.0761 0.0796 0.0827 0.0861 0.0892 0.0926 0.0960 0.0991 0.0739 0.0773 0.0807 0.0840 0.0874 0.0905 0.0938 0.0970 0.0753 0.0785 0.0820 0.0853 0.0888 0.0920 0.0763 0.0953 0.0795 0.0831 0.0864 0.0898 0.0757 0.0930 0.0792 0.0828 0.0859 0.0763 0.0895 0.0797 0.0833 0.0865 0.0761 0.0797 0.0831 0.0764 0.0798 0.0762

0.0366 0.0376 0’.0387 0.0397 0.0407 0.0418 0.0427 0.0436 0.0445 0.0375 0.0385 0.0394 0.0408 0.0416 0.0426 0.0435 0.0443 0.0380 0.0390 0.0400 0.0411 0.0421 0.0432 0.0383 0.0442 0.0392 0.0402 0.0414 0.0423 0.0386 0.0434 0.0397 0.0408 0.0418 0.0390 0.0428 0.0400 0.0410 0.0421 0.0389 0.0400 0.0409 0.0383 0.0393 0.0389

0.0860 0.0886 0.0908 0.0928 0.0947 0.0965 0.0981 0.0996 0.1009 0.0895 0.0921 0.0942 0.0965 0.0984 0.1002 0.1017 0.1030 0.0913 0.0937 0.0959 0.0982 0.1001 0.1020 0.0927 0.1035 0.0952 0.0974 0.0997 0.1014 0.0912 0.1034 0.0939 0.0962 0.0981 0.0922 0,1002 0.0948 0.0970 0.0991 0.0922 0.0949 0.0970 0.0927 0.0953 0.0928

0.0324 0.0325 0.0327 0.0326 0.0327 0.0327 0.0326 0.0324 0.0323 0.0339 0.0340 0.0341 0.0342 0.0342 0.0342 0.0341 0.0338 0.0349 0.0349 0.0350 0.0350 0.0350 0.0350 0.0353 0.0349 0.0354 0.0354 0.0355 0.0354 0.0353 0.0354 0.0355 0.0355 0.0355 0.0357 0,0355 0.0358 0.0359 0.0358 0.0357 0.0359 0.0359 0.0359 0.0360 0.0359

0.0691 0.0692 0.0692 0.0688 0.0684 0.0678 0.0672 0.0663 0.0653 0.0729 0.0730 0.0728 0.0725 0.0721 0.0714 0.0707 0.0695 0.0747 0.0747 0.0745 0.0741 0.0737 0.0730 0.0764 0.0722 0.0763 0.0762 0.0758 0.0752 0.0764 0.0746 0.0765 0.0764 0.0759 0.0772 0.0754 0.0772 0.0771 0.0766 0.0772 0.0773 0.0771 0.0764 0.0764 0.0777

0.0221 0.0214 0.0208 0.0201 0.0195 0.0188 0.0181 0.0175 0.0167 0.0238 0.0231 0.0223 0.0217 0.0209 0.0202 0.0195 0.0186 0.0246 0.0238 0.0231 0.0224 0.0216 0.0209 0.0250 0.0201 0.0242 0.0234 0.0227 0.0219 0.0247 0.0212 0.0240 0.0233 0.0225 0.0252 0.0218 0.0244 0.0237 0.0228 0.0253 0.0246 0.0238 0.0255 0.0247 0.0255

0.0429 0.0414 0.0401 0.0384 0.0368 0.0353 0.0337 0.0322 0.0305 0.0465 0.0449 0.0433 0.0416 0.0399 0.0382 0.0364 0.0346 0.0482 0.0465 0.0448 0.0430 0.0412 0.0394 0.0489 0.0377 0.0471 0.0454 0.0436 0.0417 0.0488 0.0400 0.0470 0.0454 0.0436 0.0497 0.0418 0.0478 0.0461 0.0443 0.0498 0.0481 0.0463 0.0502 0.0484 0.0503

Relative energy intensities of lines in the individual branches were computed with a Boltzmann distribution of levels for T = 2250 K and the line strengths from the Honl-London formulae, as quoted by Herzberg [1950a, p. 2081, where the quantum number s1= A + 2 (and B = & 8) has been substituted for A . While the numbers are tabulated to three significant figures, the simplified theory for the line strengths is not that accurate. For more accurate relative intensities it is necessary to use line strengths for intermediate coupling (see Benedict, Plyler, and Humphreys [1953a], Wallace [1960a]).

557 13.1 OH LINB AND BRANCH==

0.0121 0.0113 0.0105 0.0097 0.0090 0.0083 0.0076 0.0071 0.0015 0.0134 0.0125 0.0116 0.0108 0.0100 0.0092 0.0085 0.0078 0.0139 0.0130 0.0120 0.0112 0.0104 0.0095 0.0141 0.0088 0.0131 0.0122 0.0113 0.0104 0.0144 0.0096 0.0134 0.0125 0.0115 0.0143 0.0107 0.0133 0.0123 0.0114 0.0144 0.0134 0.0124 0.0146 0.0136 0.0146

0.0217 0.0201 0.0186 0.0171 0.0157 0.0143 0.0132 0.0120 0.0109 0.0241 0.0223 0.0206 0.0190 0.0174 0.0159 0.0146 0.0132 0.0252 0.0233 0.0215 0.0197 0.0181 0.0166 0.0257 0.0152 0.0237 0.0219 0.0202 0.0185 0.0262 0.0169 0.0243 0.0223 0.0205 0.0260 0.0189 0.0241 0.0222 0.0204 0.0262 0.0243 0.0224 0.0265 0.0245 0.0266

0.0054 0.0048 0.0043 0.0038 0.0033 0.0029 0.0025 0.0022 0.0015 0.0062 0.0054 0.0048 0.0042 0.0037 0.0033 0.0028 0.0025 0.0065 0.0057 0.0050 0.0045 0.0039 0.0034 0.0066 0.0030 0.0058 0.0052 0.0045 0.0040 0.0066 0.0035 0.0059 0.0052 0.0046 0.0068 0.0040 0.0060 0.0053 0.0047 0.0069 0.0061 0.0054 0.0068 0.0060 0.0069

0.0093 0.0082 0.0072 0.0063 0.0055 0.0048 0.0041 0.0036 0.0031 0.0105 0.0092 0.0081 0.0071 0.0061 0.0053 0.0046 0.0040 0.0110 0.0097 0.0084 0.0074 0.0064 0.0056 0.0113 0.0048 0.0099 0.0087 0.0076 0.0066 0.0114 0.0057 0.0100 0.0087 0.0077 0.0117 0.0067 0.0102 0.0090 0.0079 0.0115 0.0101 0.0088 0.0117 0.0102 0.0117

0.0021 0.0017 0.0014 0.0012 0.0009 0.0008 0.0007 0.0006 0.0004 0.0024 0.0020 0.0017 0.0014 0.0011 0.0009 0.0007 0.0006 0.0025 0.0021 0.0018 0.0014 0.0012 0.0010 0.0003 0.0008 0.0022 0.0018 0.0015 0.0012 0.0027 0.0007 0.0022 0.0018 0.0016 0.0027 0.0012 0.0022 0.0019 0.0015 0.0027 0.0022 0.0018 0.0027 0.0022 0.0027

0.0033 0.0027 0,0023 0.0018 0.0015 0.0013 0.0010 0.0008 0.0007 0.0039 0.0032 0.0026 0.0021 0.0018 0.0015 0.0012 0.0010 0.0041 0.0033 0.0028 0.0023 0.0019 0.0015 0.0042 0.0013 0.0035 0.0029 0,0024 0.0019 0.0043 0.0016 0.0036 0.0030 0.0025 0.0043 0.0020 0.0036 0.0029 0.0024 0.0043 0.0035 0.0029 0.0044 0.0036 0.0044

0.443 0.444 0.446 0.446 0.447 0.448 0.449 0.450 0.450 0.466 0.466 0.466 0.467 0.467 0.467 0.467 0.466 0.478 0.477 0.477 0.477 0.477 0.477 0.483 0.477 0.484 0.484 0.484 0.483 0.484 0.483 0.484 0.484 0.483 0,489 0.483 0.488 0.488 0.487 0.489 0.489 0.488 0.490 0.489 0.492

0.219 0.226 0.232 0.239 0.245 0.250 0.256 0.262 0.268 0.229 0.236 0.243 0.249 0.255 0.261 0.267 0.273 0.227 0.234 0.241 0.247 0.253 0.258 0.225 0.264 0.231 0.238 0.244 0.250 0.228 0.256 0.234 0.241 0.247 0.227 0.253 0.233 0.240 0.246 0.227 0.234 0.240 0.227 0.234 0.226

0.338 0.330 0.322 0.315 0.308 0.302 0.295 0.288 0.282 0.305 0.298 0.291 0.284 0.278 0.272 0.266 0.261 0.295 0.289 0.282 0.276 0.270 0.265 0.292 0.259 0.285 0.278 0.272 0.267 0.288 0.261 0.282 0.275 0.270 0.284 0.264 0.279 0.272 0.267 0.284 0.277 0.272 0.283 0.277 0.282

The intensities are normalized so that they add up to unity for each band. Absolute intensities of the individual lines or branches in the nightglow may be obtained by multiplying the relative intensity in this table by the absolute intensity in Fig. 13.2. Relative photon intensities of the lines differ very little from the intensities in energy units. Wavelengths of the lines are given in Table 9.1. The energies corresponding to these wavelengths (and not energies derived from a mean B, for the 2Z71/z and z17,/z states) were used in the Boltzmann distribution.


In Table 9.1 are listed the wavelengths of the band origins and P and R lines.

An estimate of the absolute number of molecules in excited levels at any time requires a knowledge of the absolute values of A...... With Heaps and Herzberg’s assumption that A,, a lo2, Chamberlain and Smith computed these populations, but the precise values obtained are not important. The absolute rate at which the vibrational levels are populated directly by the excitation reaction is about 1.2 x 1011 O H molecule/cm2 (column) sec in each vibrational level. With the assumption that this rate applies to all v, we obtain a total rate of excitation of some 10 times this value; if the emission is distributed over a height range of 20 to 30 km the mean rate of O H formation is roughly 5 x lo5 molecule/cm3 sec.

The Ozone Mechanism.-Soon after the identification of the O H bands by Meinel [1950b] the ozone mechanism was suggested independently by Bates and Nicolet [1950c, d ] and Herzberg [1951a]. The most complete discussion available is an exhaustive survey of the photochemistry of an oxygen-hydrogen atmosphere by Bates and Nicolet 11 950b1.

The primary reaction is H + 0, -+ OH* + 0; (+ 3.32 ev). (13.57)

The excitation energy of v = 9 in the ground (”) state of OH is 3.23 ev, whereas for v = 10 the energy is 3.49 ev. The activation energy for reaction (13.57) will also be available for excitation, but as it is probably around 0.10 or 0.12 ev, only levels with v 2 9 could be produced. Formerly the fact that only bands originating from v I 9 were observed seemed strong evidence in favor of the mechanism., Krassovskii [1952a, 1954b, 1956d] has pointed out, however, that O H with v 2 10 could react with 0, toward the left in (13.57), thereby eliminating highly excited OH molecules before they could radiate. There is some question, however, as to whether the mean free time for such a collision is short enough compared with the radiative lifetime of v 2 10 (Bates and Moiseiwitsch [1956a]). The matter depends critically on the height of O H formation.

The H destroyed and the OH produced by reaction (13.57) may be recycled by the reaction

OH + 0 -+H + 0,. (1 3.58)

Prediction of the OH intensity produced by this combination of reactions is hampered by uncertainties in the relevant rate coefficients. Not only


do we lack definite information on the activation energies of these two processes [which by Eq. ( I . 1 12) greatly affect the rate coefficients] but the concentrations of H and OH in the high atmosphere can be guessed only crudely because of uncertainties in the rates of the various reactions producing and destroying these substances.

However, Bates and Nicolet have noted that both (13.57) and (13.58) destroy what Chapman has aptly called odd oxygen atoms. The total number of both reactions cannot therefore exceed the rate at which odd atoms are created by photodissociation of 0,. On this basis they estimate that the rate of excitation near 65 km (where the product of the H and 0, concentrations probably reaches a maximum) could be as high as 3 x lo5 OH molecule/cm3 sec, if indeed (13.57) and (13.58) are the main reactions destroying odd atoms. This maximum rate of production is roughly what is required (see above) to explain the observed intensities, so the question is whether other reactions might not be more important to the oxygen equilibrium around 65 km. Reactions between the allotropes of oxygen, especially

0 2 + 0 + x-03 + x, (13.59)

and 0 + 0 3 + 0 2 + 0 2 , (1 3.60)

may well be important in this regard, but again the lack of knowledge on rate coefficients hinders quantitative discussion. Daily variations in the concentrations are probably important.

Evidence in favor of the ozone-hydrogen mechanism was obtained by McKinley, Garvin, and Boudart [1955u, 1956~1, who produced the Meinel bands with zl’ 5 9 in the laboratory by mixing 0, and H. Measurements by Garvin and McKinley [1956a] also suggest that the rate coefficient of (13.57) is fairly high.

The chief critic of the ozone-hydrogen mechanism has been Krassovskii [1951u, 1952u, 1954a, b, 1956d, 1957~1, but Bates and Moiseiwitsch [1956u, 1957~1 have shown that his criticisms are not in fact serious objections to the theory.16

l6 The main objections dealt with the importance of (13.59) in removing 0 atoms after sunset, thereby rendering (13.58) ineffective at night, and with the rate of photodissociation of 0,. There also were some disagreements as to the energy, available for (13.57), as to the upper limit to the OH abundance, set by the absence in stellar spectra of telluric absorption in the near ultraviolet from OH electronic bands, and as to the height of OH as suggested by some early rocket flights. The interpretation by Mironov and Prokudina [1957a] that these rocket data around 5300 A applied to weak OH bands seems to be incorrect, because of the rather strong green continuum. See Table 12.4.


Again because of the great uncertainties in concentrations and rate coefficients, the photochemical theory is not able to predict reliably the time variations in OH intensity. Krassovskii [1958b] has reported that the increase of rotational temperature with latitude (Section 12.2.1) and the temperature variations from night to night do not seem to be accompanied by large changes in OH intensity, as would be expected at first if the rate coefficient of (13.57) is temperature-sensitive, as in Eq. (1.112). But neither is this objection to the ozone mechanism necessarily valid, since the concentrations of 0, and H are also probably strongly dependent on the temperature. In fact, to the extent that 0, is governed by reactions (13.59), (13.60), and ultraviolet sunlight, its main temperature dependence in the 55-65 km region lies in the fact that the nighttime equilibrium of O3 is there nearly proportional to s60-1’2, where sso is the rate coefficient for (13.60). This conclusion is reached because the nighttime equilibrium abundance of 0, is essentially the daytime abundance of 0, since 0, cannot increase after sunset to more than the 0 + 0, ( m 0) daytime value (see Bates [19543, p. 5801). I t is not inconceivable that the net yield of (13.57) is therefore only mildly dependent on T , since sG0 also follows the form of Eq. (1.112) and probably has an activation energy exceeding that of either (13.57) or (13.58). (See also Problem 4.)

These considerations do not, of course, argue in favor of the ozone reaction ; they merely point out the enormous complexity of the problem. The OH theory will eventually require a thorough re-examination of the photochemistry of an oxygen-hydrogen atmosphere, when sufficient abundances and rate coefficients become available. Nighttime diffusion or mixing of some of the constituents, previously neglected in the theory, is also likely to be an important parameter.

The 0; Mechanisrn.-Krasso~skii~~ considers the formation of 0, molecules in excited vibrational levels in the ground ,Z; state (denoted by 0:) to occur through a variety of association processes including

1 0, + 0 + x-to,. + x 0,. + 0-0,. + 0,. (13.61)

l’ In an early note on the subject of OH excitation Krassovskii [1951a] objected to the ozone mechanism and proposed in its place a mechanism involving metastable electronic states of 0,. This idea was soon discarded by Krassovskii and Lukashenia [1951a] in favor of vibrationally excited 02. Detailed discussions (Krassovskii [1952a, 195461) as well as shorter notes and reviews (Krassovskii [ I9544 1956c, d , e , 1957c, 1958~1) have since been published.


and 0 + 0 + x-to,. + x. (13.62)

He considers the precise mechanism of 0: formation unimportant, but once these vibrationally excited molecules exist they react with H:

0,. + H-+OH* + 0. (13.63)

Atomic hydrogen is reformed as in the ozone mechanism by reaction (13.58). Since 0, in the ground level is more tightly bound (De = 5.08 ev) than O H (De FZ 4.4 ev), reaction (13.63) could not proceed at atmospheric temperatures unless 0, does contain an excess of internal energy.

Excitation by (13.63) to OH* (v 2 10) is thought by Krassovskiil* to be negligible because it requires 0: with v 2 26. The absence of such highly excited 0, is supposed to result from collisions of the type

0; (v 2 26) + 0, --f 0 + 0,. ( 1 3.64)

However, Bates and Moiseiwitsch [1956a, 1957~1 suggest that the activation energy and perhaps steric hindrance will render (13.64) rather ineffective. Moreover, at the 100-km level, where the 0: process should be most important, deactivation of O H (v 2 10) by (13.57) reacting to the left is also likely to be ineffective.

The basic question of whether vibrationally excited molecules and perhaps even metastable atoms can be important in the airglow is one of considerable interest. Laboratory investigations relating to this problem have been conducted by Lipscomb, Norrish, and Thrush [1956a] and Porter [1957a].

Bates and Moiseiwitsch have maintained that vibrational deactivation of 0; will proceed quite rapidly when free 0 atoms are present (which may not be the case in the laboratory) through the direct process

0 + 0; (0 = vl) + 0 + 0: (w < w l ) (13.65)

and through atom-atom interchange,

0 + 0; (v = vl) + 0: (v < vl) + 0. (1 3.66)

With a total rate coefficient of the order of 10-lo cm3/sec, these processes would deactivate 0: molecules so rapidly that Krassovskii's mechanism (13.63) would be quite ineffective.

18Here we adopt the calculations of this threshold energy level by Bates and Moiseiwitsch [1956a, 1957~1; Krassovskii quotes w 2 27.


13.5.2. Hydrogen Lines in the Night-Sky Spectrum

Rocket observations have disclosed nocturnal radiation in Ly a (1215 A) of about 2.5 kR, with a slight minimum of intensity in the direction opposite the sun (Sections 9.1.3 and 12.3.1). Similarly Ha seems to show feebly in the night sky with an emission rate of 5 to 20 R (Sections 9.1.4 and 12.3.1). Part of this radiation may arise in the interplanetary medium and should not be classified as part of the airglow. The upper atmosphere also radiates Ly 01 upward with a flux of about 42 percent of the incident flux. Most of this is probably due to diffuse reflection by the upper atmosphere of the incident extraterrestrial component, although the possibility remains that part of it is excited locally within the atmosphere.

Shklovskii [ 1959~1 and Brandt and Chamberlain [1959a] have made some estimates of the density of neutral hydrogen in the interplanetary medium implied by these results, and have suggested that both Ly 01

and Ha might result from scattering of sunlight. The calculations are straightforward with the equations derived in Chapter 1 1, which deals with the theory of the twilight airglow. With Eq. (1 1.6) and g ( L y a) =

photon/sec atom from Table 1 l . i , we find that 47.9 = 2.5 kR for Ly a implies a total number of H atoms along the line of sight of A‘- =

2.5 x 1012/cm2. An astronomical unit is 1.5 x 1013 cm. If these atoms are distributed in the interplanetary medium, their average density near the Earth is thus probably in the range 0.1 to 0.3 atom/cm3. This density appears to be higher, however, than can be reconciled with the temperature and electron density near Earth (Section 8.1.1).

An alternate interpretation of the night-sky hydrogen emission is that it is sunlight scattered by H atoms in the Earth’s outer atmosphere or geocorona. Johnson and Fish [1960u] have advocated this solution and the observed intensity does seem to be in general accord with the expected abundance of H over distances out to several Earth radii, provided direct sunlight illuminates these atoms. The minimum of intensity in the antisolar direction would then be merely an effect produced by the Earth’s shadow, whereas with the interplanetary interpretation the minimum would appear entirely as a result of the fewer H atoms in the radial direction from the sun. [In the latter case, a van Rhijn type of analysis (Section 12.1.1) gives an effective distance of 0.3 AU beyond the Earth’s orbit.] The main difficulty with Johnson and Fish’s interpretation lies in accounting quantitatively for the intensity in the shadow zone. They assume secondary scatterings to play an important role, a conclusion that appears doubtful in view of the absolute intensity observed in the shadow and the low optical thickness of terrestrial


H. Perhaps the correct explanation depends on an asymmetrical outer atmosphere, highly distended in the direction away from the sun (Brandt).

The ratio of intensities of Ha/Ly a should then be just the ratio of their g-values. From Table I 1. I we find g(Ha)/g(Ly a) = 2.3 x the observed emission rate for Ly a thus implies that Ha should be 6 R, which is near the lower limit reported for the observed emission.

All these rough estimates suppose that the solar system is optically thin to Ly 01 radiation. To verify whether that may indeed be the case, we use Eq. (1.12) to relate the f-value to the absorption coefficient at the line center:

(1 3.67)

Substituting numerical values (transition probabilities and f-values for H are tabulated by Allen [1955a] and Bethe and Salpeter [1957a]), we find that the hydrogen detected in the night sky would have an optical thickness T, = Na, - 1/4, with a temperature of 4000" K. Unless the density of neutral hydrogen between the Earth and sun exceeds that near the Earth, there should be no appreciable attenuation of solar Ly a by interplanetary gas. And high-resolution spectra of the solar Ly a line (Purcell and Tousey [1960a]) show that the self reversal produced by the solar atmosphere in the center of the emission lowers its intensity only a few tenths of the maximum intensity.

The assumption of resonance scattering of Ly 01 by an optically thin gas might be checked through observations of the polarization. With the theory of Section 1 1 . I .2, we find that the component 1s 2S1,z - 2p2P,,, will be unpolarized. But the 1s 2Sl,z - 2p 2P3,z line will be polarized in an amount depending on the hyperfine structure. First, consider the polarization that would result with completely separated hyperfine levels. With a nuclear spin of I = 1/2, we obtain from Eqs. (11.16) and (1 1 .l7) the ratio 2 /3(F')/Z a(F ' ) = 0.203. For incident unpolarized

light, the maximum polarization of the scattered radiation, at a scattering angle 0 = 90°, is given by Eq. (1 1.23) and is 25.4 percent. The contribution of the component from 2Pli2 would cause the net polarization to be diminished by a factor of approximately 2/3; or, more accurately, the 2Pljz component contributes one-half times the mean intensity from 2P3jz, as given by Eq. (1 1.26), since the polarized component is not scattered isotropically. The polarization of the combined line is then P,(Ly a I ~ / 2 ) = 16.0 percent.

Actually, however, the ZP,,, level has a hyperfine splitting of dv =

0.24 x lo* sec-l (Bethe and Salpeter [1957a, p. l lO]) , whereas the

F J F ,


natural broadening of the level is of the order of du = A2p--ls/277 =

1 x lo8 sec-l [see Eqs. (1.25) and (1.45)]. The upper hyperfine levels are thus quite indistinct, being blurred into one level by the natural width. (On the other hand, the Lamb-shift splitting between 2 2S1,2 and 2 2Pl,2 is 10.58 x 108 sec-l, so that these two levels are well separated.)

In the complete absence of hfs splitting of the upper level, the theory predicts 42.9 percent polarization for the component from 2P3i2 and 27.3 percent for the total Ly a line, when viewed at 90" from the sun. Thus rocket measurements should disclose a polarization somewhere in the range 16 to 27 percent, probably closer to the larger value.

I t is interesting to note that since the polarization depends on the scattering angle, it can be used to obtain an effective distance of the H from the Earth, in a manner similar to the use of total intensity in a van Rhijn analysis. Incidentally, there is a slight anisotropy for resonance scattering, which should be considered in an accurate van Rhijn treatment of the intensities. The relevant formulae are given in the paper by Brandt and Chamberlain [1959a].

The Balmer emission may similarly show large polarization, but as Ha is extremely weak, it would be most difficult to detect. The term and level structure involved in Ly p absorption followed by Ha emission appears at first to be the same as for Ly a scattering, so that the same polarization would be expected. Actually, however, the Lamb-shift splitting between 3 2D312 and 3 2PsiZ is less than the natural width of the levels, so some fluorescence of Ha might occur in 2 2P - 3 2D3,2, as well as in 2 2S - 3 2P; the polarization would then be somewhat altered.

13.5.3. Photochemical Excitation of Sodium D Lines

The twilightglow and dayglow offer much more direct means of studying atmospheric sodium, especially its abundance, height, and patchiness, than the nightglow. There seems little question but that the Na nightglow originates from photochemical processes, so the main problem here lies in relating the nightglow excitation mechanism to the more general aspects of sodium photochemistry and ionization, which are more appropriately treated in Section 11 .4.19

In the past there has been considerable doubt that the excitation was photochemical and that the twilight sodium was directly related to the nightglow D lines. The great heights (above 200 km) indicated by van Rhijn analyses (Table 12.2) were shown to be incompatible with photochemical excitation by Bates and Nicolet [195Ou] and Bates and Dalgarno [1954a]. One explanation tentatively put forth was that Na atoms continually bombarded the atmosphere from interplanetary space ( e .g . , Saha [1951a, 1952~1).


Chapman [1939a] proposed that the upper term (") for the D lines would be excited by

NaO + 0 + Na(,P) + 0,, (13.68)

which could be followed by one of several oxidation processes [see reactions (1 1.66)-( 1 1.68)]. Whether (1 3.68) is exothermic or not is doubtful (see Bawn and Evans [1937a], Ogawa [1954a]). Bates and Nicolet [1950a] suggested an alternative mechanism,

NaH + 0 --+ Na(2P) + OH (1 3.69)

and Bates [1954b] proposed

NaH + H - Na(2P) + H,, (1 3.70)

both of which are known to be exothermic. Bates [1957a] suggests that the NaH in these reactions might be formed by

Na + 0, + X -+ NaO, + X (13.71)

followed by

NaO, + H - NaH -t 0,. (13.72)

Continued laboratory studies (see, e.g., Tanaka and Ogawa [1956a]) are necessary in order to sort out the relevant processes and determine reaction rates.

Of some importance to the nightglow theory is the altitude relationship between the nightglow layer and the main Na (twilightglow) layer. Although the two regions are evidently close, height measurements that could distinguish them would be valuable. In Section 11.4 it is pointed out that with the Chapman mechanism (13.68), the nightglow would be expected well below the 85-km level where Na appears to be concentrated ; rocket heights (Table 12.4) favor slightly higher altitudes for the nightglow.

I t may be possible to ascertain whether the nightglow is above, below, or coincident with the Na layer from D,/D, ratios in nightglow spectra. Rather high accuracy (- 5 percent) would be required, even with wintertime abundances. The types of zenith-horizon variation to be expected in the ratio have been given in some illustrative radiative- transfer calculations by Chamberlain and Negaard [1956a].


PROBLEMS

1. Choose a model atmosphere with a temperature increasing at great heights, such as one derived by Nicolet [1959a], and compute the emission in the red [OI],, lines due to thermal electrons.

2. Consider the characteristic length of the airglow at 100 km to be given by the scale height, rather than by the horizontal diameters of the patchiness, and compute the rate of energy dissipation by the theory of isotropic, homogeneous turbulence.

3. Adopting winds of the order of 100 meter/sec, estimate the Reynolds number in the F region. Would you expect turbulent mixing to alter greatly the ion distribution expected from diffusion theory ?

4. Adopt the daytime concentrations and the reaction rates for (13.57) through (13.60) quoted by Bates and Nicolet [1950b], Bates [19546], and Nicolet [1954b]. (a) See whether the OH cycle is a relatively important means of destruction of odd oxygen atoms in the 65-70 km region. (b) Locate the daytime height of maximum production of OH emission, and estimate, neglecting diffusion, the rate of change of the H, O! and 0, concentrations and the OH emission at this height at sunset. (c) Neglect the effect that (13.57) and (13.58) might have on the abundances of 0 and 0,. Then show that the nighttime OH emission rate at 60 km is relatively insensitive to temperature, provided that the abundances are governed by local photochemical processes without diffusion. Obtain the “initial” or daytime oxygen abundances from the equations for an oxygen atmosphere given by Bates [19546].

APPENDIX I

A Table of Physical Constants"

Fundamental Constants

Velocity of light Gravitational constant Planck's constant Mass of unit atomic weight Mass of hydrogen atom Mass of electron Electronic charge

Avogadro's number Loschmidt's number (gas density at

273" K and 1 atmosphere pressure) Boltzmann constant (gas constant per

atom) Gas constant per mole

c

G = 6.668 x dyne cm2/gm2 h = 6.624 x erg sec Mo = 1.660 x gm MH = 1.673 x gm rn = 9.1066 x gm e = 4.8025 x 10-lo esu

= 1.602 x emu l/Mo = 6.025 x molecule/mole

= 2.998 x 1O1O cm/sec

No = 2.687 x molecule/cm3

K R = 1.987 cal/deg mole

= RM, = 1.380 x 10-l6 erg/deg

= 8.314 x lo7 erg/deg mole

Atomic and Radiation Constants

Radius of first Bohr orbit = 0.529 x lo-* cm Area of first Bohr orbit = 0.880 x 1O-l6 cmz Rydberg constant for hydrogen R, = 109,677.58 cm-l Rydberg constant for infinite mass = 2n2rne4/ch3 = 109,737.31 cm-l Energy per unit wave number = 1.986 x 10-l6 erg cm Integrated absorption coefficient per

atom for unit f-value ne2/rnc = 2.647 x cm2/sec Fine structure constant ct = 2re2/hc = 7.297 x First radiation constant (specific in-

uo

nu;

R, hc

tensity, X units) c1 = 2 hc2 = 1.191 x erg cm2/ sec sterad

Second radiation constant c2 = hc/k = 1.439 cm deg Wien displacement-law constant h,,,T = 0.2898 cm deg

"For more complete tables, see Allen [1955a].

567

568 APPENDIX I

The Earth

Radius (mean) a = 6.37 x lo8 cm Surface area 4.rra2 = 5.10 x 10l8 cm2 Mass A = 5.98 x gm Acceleration of gravity (at the surface) g = 9.807 x LO2 cm/sec2 Magnetic moment of the dipole M = 8.1 x gauss cm3 Velocity (mean) about the sun = 3.0 x lo6 cmjsec Distance (mean) from sun 1 AU = 1.496 x 1013 cm

The Sun

Radius (mean) Surface area Mass Acceleration of gravity (at the surface) Acceleration of gravity (at 1 AU from

Magnitude, absolute photovisual Magnitude, apparent photovisual Effective temperature (total energy

radiated is equivalent to a black body with T = T,,,)

the sun)

Flux at sun's surface

= 6.96 x 1O1O cm = 6.09 x cm2 = 1.99 x gm = 2.740 x lo4 cm/sec2

= 0.593 cm/sec2 = f 4.84 = - 26.73

T,,, = 5710" K = 6.25 x 1O1O erg/cm2 sec

Conversion Factors

1 day = 8.64 x 104 sgc 1 year -- 3.1557 x lo7 sec 1 electron volt == 1.602 x 10-l2 erg

= 8.067 x lo3 cm-l 1 erg = 5.035 x 1015 cm-l

= 6.242 x lo1' ev 1 cm-I (kayser) = 1.986 x erg

= 1.240 x ev 1 ev/molecule = 23.1 kcal/mole Speed of 1 ev electron = 5.93 x lo7 cm/sec Speed of 1 ev proton = 1.38 x loe cm/sec Wavelength equivalent of 1 ev = 12,396 x lo-* cm Temperature associated with 1 ev Elk = 11,606' K

APPENDIX I1

The Rayleigh: A Photometric Unit for the Aurora and Airglow

In photometry of an extended source the quantity measured is the integrated intensity or surface brightness9 (see Section 2.1.2 for definitions). Normally a surface brightness is expressed in such units as erg/cm2 sec sterad, although in aurora-airglow work it is usual to replace the energy unit with number of photons.

The quantity of importance insofar as physical processes are concerned is ordinarily the volume emission rate in photon/cm3 sec. T o derive the emission rate requires some knowledge of the distribution of emission along the line of sight. Even if this distribution is poorly known, it is useful to know the integrated emission rate over an entire column along the line of sight. This quantity is directly related to the surface brightness.

Suppose that the rate of emission in a single line or a specified wavelength interval at distance r and in an arbitrary direction from the observer is F(r) photon/cm3 sec. The photometer has a “sensitive” area A and thus subtends a solid angle A/r2 steradian as seen from the source. The effective clear field of view (without vignetting) of the photometer is 52 steradian. We suppose that 52 is small compared with the angular size of irregularities in the source and is sufficiently small that the sensitive surface of the photometer is effectively perpendicular to the entire field of view.

The number of photons falling on the photometer from an element of volume of length dr and area 1 cm2 perpendicular to the line of sight is (A/4nr2) F(r) dr. The total number of photons emitted at distance r to r + dr and intercepted by the photometer is (A/4nr2) r2 .QF(r) dr. Integrating over the length of the column we find the total radiation striking the photometer to be(AQ/h) JrF(r)dr photon/sec. The surface brightness is obtained by dividing these measurements by the area of the photometer and its angular field of view. Then

47r9 = 1; F(r) dr (11.1)

is the emission rate integrated over the whole column along the line of sight. I f 9 is obtained from the measurements in units of photon/cm2 sec sterad, the emission rate (4779) is in photon/cm2 (column) set.' I t was common in the

The word “column” is generally written in the units to emphasize that the quantity is an integrated emission rate, not a flux. Here the column is oriented along the line of sight, but the same unit is often used when only a vertical column is meant (i.e., when the measurements are referred to the zenith).

5 69

570 APPENDIX I1

past for measurements to be reported in the latter units. Because of a lack of general understanding of the units, however, there was some confusion and misuse of observational data.

Also, in the derivation of Eq. (11.1) we have tacitly assumed that the radiation is emitted isotropically and that photons once emitted are not subsequently absorbed or scattered in the source. These assumptions are not always justifiable in an accurate analysis. Therefore, 4wY represents in general only an apparent emission rate.

For this reason, and to have a less cumbersome unit, the rayleigh (R) was introduced (Hunten, Roach and Chamberlain [1956a]). If 3 is measured in units of lo6 photon/cm2 sec sterad, then 4n.Y is in rayleighs.2 Thus

1 R = an apparent emission rate of 1 megaphoton/cm2 (column) sec. (11.2)

In the event of isotropic emission and in the absence of any radiative-transfer complications, the rayleigh gives a true rate of emission. On the other hand, the rayleigh can be used as defined without any commitment as to its physical interpretation, even though it has been chosen to make interpretation convenient. Basically, the apparent emission rate in rayleighs is the measured brightness (corrected if necessary for scattering and extinction in the lower atmosphere) multiplied by 4 ~ .

When the radiation is emitted isotropically and with no reabsorption from a plane-parallel, homogeneous layer, the intensity is proportional to sec 8, where B is the angle of emergence, measured from the normal to the layer. In such cases it is common to refer measurements to the zenith by multiplying them by p = cos 0. [The angle B is related to the observer’s zenith angle by Eq. (12.1)]. Hence, the quantity p4wX is the apparent emission rate referred to the zenith.

The accompanying table compares the approximate rates of emission for various airglow and auroral lines. The sections referred to in the footnotes should be consulted for further details. Note that for the airglow all results are given for the zenith rather than for the larger zenith angles where observations are usually made.

The unit is named after the fourth Lord Rayleigh (R. J . Strutt). who made the first measurement of the absolute intensity of the night airglow (Rayleigh [19300]).

APPENDIX I1 571

TABLE 11.1 COMPARISON OF AURORA AND AIRCLOW PHOTON EMISSION RATES

Source Emission 4H9

Auroraa, IBC I I1

I11 IV

Night airglowb (in the zenith)

Twilight airglowc (referred to the zenith)

[OI],, 5577 A

[ 0 1 ] 3 2 5577 A [OI],, 6300 A Na 5893 A

summer winter

Ha 6563 A Ly a 1215 A 0, Atmospheric (0-1) 8645 A 0, Herzberg (observable range)

OH (estimated total)

N2 3914 A (quiet magnetic conditions)

Na I 5893 A summer winter

[OI],, 6300 A Ca I1 3933 A Li I 6708 A

OH (4-2) 1 . 5 8 ~

[NI],, 5199 A 0, I.R. AtmosL..eric (O-

Day airglowd Na 5893 A (referred to the zenith) summer

winter

01 8446 A 01 11,290 A

N: 3914 A

[OI],, 6300 A

1 kR 10 kR

100 kR 1000 kR

250 R 50-100 R

< 3 0 R 200 R

2.5 kR 1.5 kR

430 R 175 kR

4500 kR

1 kR

5-20 R

1 kR 5 kR 1 kR

150 R 200 R

10 R 20 kR

2 kR 15 kR 50 kR

0.5 kR 0.5 kR

< 70 kR > 1 k R

a Recommended as definitions of the International Brightness Coefficients (IBC) by Hunten [1955u] on the basis of a study by Seaton [1954u]. For emission rates of other features in the auroral spectrum, see Table 5.5.

Average values. See Section 12.3.1. Approximate values of the maximum emission rates that are observed during twilight.

These values are often governed by the time after sunset when observations first become possible. See detailed discussions in Section 9.2.

Values predicted from theory by Brandt and Chamberlain [1958a], Brandt [19586, 1959~1, Chamberlain and Sagan [1960u]; see Sections 11.3.4, 11.5.4, and 11.6.5.

APPENDIX 111

A SHORT LIST OF AIRGLOW-AURORA OBSERVING STATIONS"

Country Station

Algeria Tamanrasset Argentina San Juan Antarctica Ellsworth

Little America Marie Byrd Land South Polar

P 1 ate a u Australia Macquarie Is.

Melbourne Canada Churchill

Meanook Resolute Bay Saskatoon

Chile Santiago France Observatoire de

Haute Provence (St. Michel)

Greenland Thule India Mt. Abu Japan Maruyama Mexico Tonanzintla New Zealand Campbell Is.

Christchurch Northern Belfast

Ireland

Geographic coordinates Geomagnetic coordinates Dipole-field Dipole-field Latitude Longitude Latitude Longitude declination inclination

x 4 Am +m 4 1

-

22O 47' N 0 5 O 32' E 25O 21' N 31 37 S 68 32 W 20 09 S 77 43 s 41 08 W 66 51 S 78 34 S 163 56 W 74 22 s 80 00 S 120 00 w 70 35 S 90 00 S - 78 30 S

54 30 S 158 57 E 61 12 S 37 52 S 144 46 E 47 10 s 58 46 N 94 10 w 68 48 N 54 37 N 113 20 W 61 55 N 74 41 N 94 55 w 82 50 N 52 08 N 106 40 W 60 30 N 33 27 S 70 20 W 21 55 s 43 55 N 05 43 E 45 55 N

76 34 N 68 50 W 88 03 N 24 36 E 72 43 E 15 22 N 35 01 N 139 38 E 24 47 N 19 02 N 98 18 W 28 57 N 52 32 S 168 59 E 57 23 S 42 32 S 172 37 E 41 05 S 54 38 N 06 09 W 58 28 N

790 2 6 E 12O 19' W 430 2 9 36 17

14 38 E 13 44 W 77 56 47 05 W 47 45 E 82 02

80 00 24 02 W

0 07 w 0 25 E

22 25 E 0 0 - 84 11 $

hi

116 139 31 59 66 49 01 89

20 45 36 20 58 40 10 49

W 18 0 E 74 38 $ W 9 24 E 65 08 W 13 36 E 79 01 W 17 17 E 15 04 W 44 08 E 86 24 W 14 22 E 74 13 W 0 18 E 38 48 E 16 05 W 64 10

F?

01 08 E 01 02 w 89 01 144 10 E 07 25 W 28 49 154 23 W 06 06 E 42 45 31 54 W 06 27 E 46 40

106 50 W 18 22 E 72 16 107 35 W 14 58 E 65 05 79 30 E 19 54 W 12 56

Norway Oslo 59 58 N I1 06 E 60 0 N 99 36 E 23 13 W 73 53

Peru Huancayo 12 03 S 75 20 w 0 39 s 06 13 W 0 08 E 01 17 Sweden Uppsala 59 48 N 17 36 E 58 35 N 105 20 E 22 36 W 73 01

Tromso 69 40 N 18 57 E 67 06 N 116 53 E 30 57 W 78 04

U.S.A. College, Alaska 64 5 1 N 147 50 W 64 35 N 103 34 W 27 13 E 76 38 Fritz Peak 39 52 N 105 31 W 48 42 N 43 44 w 10 23 E 66 17

Ithaca, N. Y. 42 27 N 76 31 W 53 56 N 09 31 W 02 32 E 69 59 Lick Obs. (Mt. 37 20 N 121 39 W 43 44 N 60 56 W 12 44 E 62 25

McDonald Obs. 30 40 N 104 01 W 39 52 N 40 01 W 08 39 E 59 06

(Boulder), Colo.

Hamilton), Calif.

(Fort Davis), Texas

Point Barrow, 71 20 N 156 46 W 68 30 N 119 16 W 33 03 E 78 51

Rapid City, S. Dak. 44 02 N 103 03 W 53 10 N 42 19 W 10 48 E 69 30 cd

Sacramento Peak 32 43 N 105 45 W 41 40 N 42 22 W 09 16 E 60 40

Alaska %

E Obs. (Sunspot), x N. Mex. c(

Shingleton, Mich. 46 21 N 86 28 W 57 21 N 22 31 W 06 23 E 72 14 =I Yerkes Obs. 42 34 N 88 33 w 53 15 N 24 25 W 06 26 E 69 31

(Williams Bay), Wis.

U.S.S.R. Alma Ata 43 15 N 76 55 E 33 39 N 149 20 E 07 56 W 52 04 Loparskaya 68 15 N 33 05 E 63 30 N 125 30 E 26 03 W 76 0

Roshchino 60 12 N 29 34 E 56 43 N 116 38 E 21 06 W 71 50 Zvenigorod 55 43 N 36 51 E 51 05 N 120 20 E 17 50 W 68 02

(Murmansk)

0 Geomagnetic quantities were computed with the equations in Section 3.1.1 and with the axis of the (centered) geomagnetic dipole at geographic latitude A, = 78” 30’ N and longitude+, = 69” 0 W. A complete list of stations operated during the International Geophysical 2 Year is given in ‘‘Annals of the International Geophysical Year,” Vol. 8. Pergamon Press, London, 1959. w

APPENDIX IV

Temperature, Density, and Composition of the Upper Atmosphere

Table IV.l gives a model for the atmosphere between 50 and 300 km from Nicolet [1958a, 1959aJ. The thermosphere model is based on conductive heat flow from high altitudes. It is quite likely, however, that there is an important source of heating from solar radiation between 100 and 200 km. In this event

FIG. IV.1. Temperature profile of the atmosphere at temperate latitudes. The dashed portion is uncertain.

the model may require severe modifications (see Nicolet [19593]). The methods used in developing models are summarized in Section 3.5.2; also see Nicolet [ 1960~1.

Successive columns give the height, z ; acceleration of gravity, g ; temperature, T ; concentrations of N,, 0,, and 0 in particle/cm3, N . For 100 km and above we list also the scale height for 0 in diffusive equilibrium, H ( 0 ) ; the total number of JV each constituent in a square-centimeter column above height z [see Eq. (3.76)]; and finally the equivalent depth, f , in atmo-centimeters as defined by Eq. (3.78), where we consider atoms of all species as equivalent

574

APPENDIX IV 575

and where N8(z = 0) = 5.37 x lOle ~ r n - ~ (twice the density of diatomic molecules at the ground).]

Figure IV.1 shows the temperature structure of the atmosphere (Section 3.5.3) and Fig. IV.2 plots the equivalent depth.

3(

2t

?

3 2( N

I- I

w I

P

15

I

FIG. IV.2. Height versus equivalent depth in atm-cm, from Table IV.l.

The unit atmo-centimeter (atm-cm), introduced by Chapman [1943a], refers to the length of an air column with unit cross section at standard temperature and pressure that would contain A’ atoms. Whereas the physical unit is one of length, use of the prefix removes the possibility of confusion with pressures as expressed in terms of the length of a column of Hg.

TABLE IV.1 A MODEL FOR THE UPPER ATMOSPHERE'

50 60 70 80 90

100 110 120 I30 140 150 160 170 180 190 200 210 220 240 260 280 300

964 96 1 958 955 952 950 947 944 941 938 935 932 929 926 924 92 I 918 915 910 905 899 894

274 253 210 156 153 200 290 380 470 560 630 700 763 824 884 94 1 996

1051 1156 1256 1352 1445

1.84(16) 5.71(15) 1.61(15) 3.47( 14) 3.53(13) 4.25( 12) 8.08( 11) 2.40( 1 I ) 9.12(10) 4.15(10) 2.17(10) 1.22(10) 7.25 (9) 4.54 (9) 2.93 (9) 1.96 (9) 1.34 (9) 9.45 (8) 4.94 (8) 2.68 (8) 1.61 (8) 9.81 (7)

5 . 1 (15) 1.60(15) 4.5 (14) 9.8 (13) 9.2 (12) 8.50(11) 1.52(11) 3.95(10) 1 .36( 1 0) 5.69 (9) 2.76 (9) 1.45 (9) 8.10 (8) 4.69 (8) 2.93 (8) 1.87 (8) 1.22 (8) 8.26 (7) 3.99 (7) 2.01 (7) 1.13 (7) 6.49 (6)

3.5 (10) 9.0 (10) 1.7 (11) 1.9 (11) 5.3 (11) 1.70(12) 4.04( 1 1) 1.80(11) 9.44(10) 5.60( 10) 3.66( 10) 2.52(10) 1.80(10) 1.34(10)

7.80 (9) 6.12 (9) 4.92 (9) 3.25 (9) 2.22 (9) 1.60 (9) 1.17 (9)

l.OO(10)

10.9 15.8 20.8 25.8 30.8 34.8 38.8 42.4 45.9 49.4 52.8 56.0 59.3 64.9 71.7 77.6 83.5

2.64( 18) 7.30(17) 2.86( 17) 1.34(17) 7.30( 16) 4.32( 16) 2.71 (1 6) 1.75(16) 1.19(16) 8.26(15) 5.92( 15) 4.29(15) 3.20( 15) 1.85(15) 1.10(15) 7.15(14) 4.68( 14)

4.62( 17) 1.20(17) 4.11(16) 1.75(16) 8.76(15) 4.80( 15) 2.8 1 ( I 5) 1.72(15) 1.08(15) 7.24( 14)

3.42(14) 2.45( 14) 1.31(14) 7.22(13) 4.38(13) 2.71( 13)

4.9q 14)

1.85(18) 6.38(17) 3.74(17) 2.44( 17) 1.72(17) 1.27(17) 9.78( 16) 7.63(16) 6.15(16) 4.94( 16) 4.12(16) 3.43(16) 2.92( 16) 2.11(16) 1.59(16) 1.24(16) 9.77( 15)

1 . 5 (-1) 4.36(-2) 1.92(-2) 3 1 .02(-2) 6.26(-3) 4.16(-3) 2.94(-3) 2

3

2.14(-3) 1 .63(-3) I .26(-3) 1.01(-3) 8.13(-4) 6.74(-4) 4.68(-4)

2.59(-4) 2 . 0 0 4 )

3.41(-4)

In this table a number q x 109 is written &).

APPENDIX V

The Ionosphere"

Region Height of layer peak N ( F ) oreft

(W ( ~ m - ~ ) (cm3/sec) Ion production

~

Recombination

D 90 1.5 x 104 3 x lo-" Ionization by solar x-rays, or Ly-or ionization Lower following (noon); absent of NO. Enhanced ionization following solar

flares, due to x-ray ionization of all species. Electron attachment to 0 and 0, forms negative ions; ratio of negative ions to electrons increases with depth and at night

solar flare at night

E 110 1.5 x lo5 (noon); 10-8 < 1 X 104(night)

Ionization of 0, may occur directly by absorption in the first ionization continuum (hv > 12.0 ev). Coronal x-rays may also contribute, ionizing 0, O,, and N,. Nighttime E and sporadic E (thin patches of extra ionization) are perhaps due to meteor or charged-particle bombardment. Some E, radio reflections may be due to turbulence in normal E layer. Main E, ion seems to be N:

Electrons form negative ions, which are destroyed by photodetachment (daytime only), associative de- + cd

tachment(0 + 0-4 cd

0, + e), and mutual neutralization i (0- + X'+O+X)

4

Dissociative recombination 0: + e - + 0 4 0 and NO' + e - 0 + 0

~~

VI 4 4

For a summary of ionization and recombination processes, see Section 3.4.2.

Region Height of layer peak NLrnm) (W ( ~ m - ~ )

Fl 200 2.5 x 106(noon); absent at night

300 1 OB (noon) lo5 (midnight)

Height and electron density highly variable. Large daily, seasonal, and sunspot-cycle variations are combined with general erratic behavior

aeff

(cm3/sec) Ion production Recombination

7 x Ionization of 0 by Lyman “continuum” or by 0’ ions readily trans- emission lines of He. This ionization probably fer charge to NO+ accompanied by N, ionization, which dis- and perhaps to 0:. appears rapidly after sunset Most of the ioniza-

tion is thus in molecular form and disappears by dissociative recombination z

4

- lo-% Ionization of 0 by same process producing Recombination of Variable; molecular ions as in probably creasing height; F2 region produces little F,; but limiting pro- decreases attenuation of radiation. Additional ionization cess is here charge

with processes may contribute in F2 that are atten- transfer, giving an increasing uated in F, attachment-like re-

F,; F, formed because were decreases with in-

height combination law

APPENDIX VI

Forbidden Atomic Oxygen and Nitrogen Lines

The spectroscopic nomenclature adopted in this book is summarized in Sec- tion 1.1 2. The ground configurations of 01,011, NI, and NII are each composed of three terms. Numbering these terms I , 2, and 3 for the lowest, middle, and highest in each case, we may denote the multiplets occurring within the ground configuration by, for example, [OI],,, which signifies the so-called auroral transition, from the third to the second term of [OI]. Similarly, [OI],, indicates a nebular transition and [OI],, a transauroral transition.

All the terms in the ground configurations have rather low excitation energies (5 ev or less) as shown in Fig. VI.1. Consequently these terms are more readily

e.v. J Term e.v. J Term 01 2p4 on 2p3

0.00 u lb

O.9Osec. IS

ID

3P

Frc. VI.1. Level structure and multiplets of the ground configurations of 01, 011, NI, and NII. For the meaning of the transition probabilities given in paren-

theses and the term lifetimes, see the text.

519

580 APPENDIX VI

excited by chemical reactions and by collisions with fair!y slow electrons than are the other configurations, at much higher energies. Since the extremely low transition probabilities associated with transitions within one configuration are not always detrimental at the low densities prevailing in the upper atmosphere, these radiative transitions often occur and play a central role in auroral and airglow physics.

All these transitions are strictly forbidden by electric-dipole radiation, and the transition probabilities, A , are finite (but small) only through the existence of electric-quadrupole (denoted by q) and magnetic-dipole ( m ) radiation. Table VI.1 gives these values of A for [OI] and [NII] from Garstang [1951a]; those for [OII] and "I] are also from Garstang's [1952a, 1956~1 calculations, part of which are simply modified from earlier results by Pasternack [1940a]. Occasionally both kinds of transition (q and m) are allowed for a line, but if one dominates over the other, only the important one is listed.

TABLE VI.1 TRANSITION PROBABILITIES A FOR FORBIDDEN LINES

Transition Kind 0 1 NII

Multiplet of line h (A) A (sec-') h (A) A (sec-l) type Linea

3-2 'DZ - 'S, 3- 1 3P1 - 'So 2 + l 3P2 - 'DZ

'PI - 'D2

4 m

m

m

5577.345 1.28 5754.8 1.08 2972.325 0.078 3063.0 0.034 6300.308 0.0069 6583.6 0.0030 6363.790 0.0022 6548.1 0.0010

NI 011

10,395.4 0.031 7318.6 0.057 10,395.4 0.054 7319.4 0.11 10,404.1 0.048 7329.9 0.093 10,404.1 0.025 7330.7 0.058

3466.4 0.0027 2470.3 0.023 3466.4 0.0067 2470.4 0.057 5198.5 1.6 x lo-' 3726.16 1.3 X

5200.7 7.0 x lo-' 3728.91 4.1 x lo-'

a Note that in accordance with conventional notation of atomic spectra, the lower level is specified first.

APPENDIX VI 58 1

Figure VI.1 gives the term and level structure and excitation potentials for the ground configurations of 01, 011, NI, and NII and indicates the transitions listed in the table. In addition, the effective transition probabilities for the multiplets (Amult) are listed in parentheses. These values are computed from the A’s for the individual lines (Aii) on the assumption that the level populations are proportional to their statistical weights, G j . Then we find

(VI.1)

It is conceivable that in a specific situation the populations would not be in the assumed ratio, in which case the value of Amult would be altered from that listed. The radiative lifetimes given for the excited terms in the figure are T~~~~ = l/ZAmult, where the summation is carried over all multiplets (here, either one or two) originating from the excited term.

APPENDIX VII

Glossary of Symbols

This list contains the principal symbols used in the book. Those used on only one or two pages are mostly omitted. Subscripts x, y , z, 8, 4, and r refer to components of a vector (see Fig. 3.1). Bold face is used to represent a vector, and A = 1 A 1. Cgs and Gaussian units are adopted for use throughout the book.

radius of the earth radius of first Bohr orbit Einstein coefficient magnetic vector potential transition probability of a 7r polarization component transition probability of a D polarization component

parameter characterizing a line of force, Eq. (3.10) Einstein coefficient magnetic induction (equivalent to the magnetic field in free space) rotational constant

speed of light function defined by Eq. (7.15)

diffusion coefficient dissociation energy rotational constant function defined by Eq. (7.20)

base for natural logarithms charge on electron (esu); in chemical reactions, etc., an electron equation of time electric field amplitude wave function of electric vector exponential integral: Eq. (2.23) emission efficiency in aurora

oscillator strength (f-value) velocity distribution function force hyperfine quantum number, giving total (electronic and nuclear)

angular momentum 582

APPENDIX VII 583

5

I0

rotational energy in cm-l hydrogen emission rate per incident proton per unit velocity interval photon emission rate per unit volume at height z number of transitions per cm3 per sec from level 01 to level /3 or

photon emission rate per unit volume at depth 5 in a homogeneous

for particles: the flux across an area normal to magnetic lines of force for light: equivalent mean intensity; T? is net photon flux per

unit frequency interval across an area normal to the incident beam fraction of atoms formed from dissociative recombination that appear

in an excited term

acceleration of gravity number of solar photons scattered per second by one atmospheric

atom if there were no deactivation or attenuation of incident sunlight imaginary part of the complex index of refraction is gi total photon emission or ionization produced by a single proton vibrational energy in cm-1

Planck’s constant closest approach to the Earth’s surface of an incident light ray screening height for incident solar radiation scale height magnetic field

angle of inclination (to the horizontal) of the magnetic field

nuclear-spin quantum number electron intensity, defined above Eq. (7.66) equivalent specific intensity for horizon hydrogen profiles, Eq. (7.1 1) in Section 2.5.2 and Ashburn’s tables, the extra intensity of the

sky when the ground reflects with an albedo A,, beyond its intensity when A, = 0

intensity incident from the zenith [= Iinc(- l)] (in discussions of airglow photometry)

specific intensity at the line center (in discussions of line profiles) intensity that is diffusely reflected upward at the ground incident intensity above the atmosphere specific intensity; I,(t, 1 p, 4) is intensity at depth t , and toward

integrated intensity or surface brightness integrated intensity incident from zenith angle 5

photon emission rate per unit volume

atmosphere

4-1

direction B = cos-l p and 4

584 APPENDIX VII

J

J 1 0

Jv- I

k k

K k"

K(h -

1 L

m M M Mo

scattered intensity polarized with the electric vector perpendicular

scattered intensity polarized with the electric vector parallel to the

equivalent integrated intensity for horizon hydrogen profiles,

to the plane of scattering

plane of scattering

Eq. (7.13)

inner quantum number (for atoms), giving total angular momentum

rotational quantum number (molecules), giving total angular

current density approximate (first-order) value of J , mean intensity energy dissipation by electrons source function

of orbital electrons

momentum including electron spin

Boltzmann's constant wave number in turbulent flow absorption coefficient per unit volume molecular quantum number of total angular momentum apart

A,) smearing function, which describes the finite resolving power of a from spin

spectrograph

longitude (in chap. 10) atomic quantum number of orbital angular momentum of electrons

mass of a particle; usually the mass of an electron specifically mass of a particle magnetic moment of Earth's dipole mass of unit atomic weight

ordinary index of refraction complex index of refraction number density of particles number density of electrons eigenfunction in diffusion problem: Eq. (13.6) number of atoms in a vertical square-centimeter column equivalent number of fully illuminated atoms without deactivation

total number of particles per cmz along the path of a beam of light in a vertical square-centimeter column

grazing the Earth at height h

APPENDIX VII 585

PO

4 4 8 r r Y

Y

1 0

R R R R R R w

pressure ratio of scale heights of two constituents dipole moment scattering phase function electric polarization per unit volume associated Legendre functions degree of polarization of scattered light when the incident light is

plane polarized with the electric vector perpendicular to the plane of scattering

degree of polarization for unpolarized incident light

Franck-Condon factor rate of ionization or excitation per unit volume cross section

residual range radial spherical coordinate internuclear distance in a molecule central intensity in a Fraunhofer line, relative to the continuum residual range outside the atmosphere rayleigh, unit of rate of emission (see Appendix 11) radial cylindrical coordinate gas constant per mole Reynolds number reflection coefficient matrix element radius of curvature

rate coefficient for a reaction involving a change of state from a to j3 radiative-transfer function defined by Eq. (2.56) radiative-transfer function defined by Eq. (2.61) radiative-transfer scattering function, Eq. (2.35) electron-spin quantum number for atoms line strength electron scattering function, defined above Eq. (7.66)

time retarded time time of sunset (or sunrise) vertical optical thickness to a specific height (depth) in the atmosphere temperature radiative-transfer transmission function, Eq. (2.36) transmission function for atmospheric transparency, Eq. (10.38)

586 APPENDIX VII

U

x 20

,eff 0

(yex

%ec

%r

ff”

most probable velocity

velocity vibrational quantum number potential van Rhijn function, Eq. (12.3)

equivalent width

particle velocity in units of thermal “most probable velocity;”

Cartesian coordinates radiative-transfer X-function, Eq. (2.43) unspecified atoms

radiative-transfer Y-function, Eq. (2.44)

depth or height in atmosphere actual height = height of intersection of actual shadow line (as

produced by atmospheric screening) with the line of sight, with allowance for atmospheric refraction of the incident sunlight

see Eq. (1 1.49)

actual height zo for an observation in the zenith height of intersection of unrefracted shadow line, produced by an

height z1 for an observation in the zenith apparent height (i,e,, height of solid-Earth shadow) in the direction

apparent height for an observation in the zenith apparent height for an observation in the azimuth plane of the sun apparent height of shadow on the horizon [= xb([ = ~ / 2 ) ] atomic number

atmospheric screening layer, with the line of sight

of observation

fine-structure constant rate coefficient angle of solar depression measured at the observer auxilliary quantity used in calculation of polarization ; defined by

effective absorption coefficient at the centroid of a hyperfine group rate coefficient for atom-ion exchange rate coefficient for recombination rate coefficient for charge transfer absorption coefficient or scattering coefficient per atom

Eq. (11.16)

APPENDIX VII 587

B

B” 8” Y

Y r 6 6

&

5

Q

K

K

recombination rate when electron loss depends on first power of N e ; sometimes called the effective attachment coefficient; see Eqs. (3.67), (13.3), and (13.4)

gradient of the scale height, Eq. (3.79) angle of solar depression measured at the observed point auxilliary quantity used in calculation of polarization; defined by

constant (in Morse potential function, Chapter 1) absorption coefficient

Eq. (11.17)

angular distance on the Earth’s surface between the observer and

classical damping constant damping constant

the observed point in the atmosphere

Dirac 6-function declination of the sun

energy; energy density

in Section 7.1.3 the angle between the yx-plane and the velocity

zenith distance atmospheric equivalent depth in units of initial residual range of

vector

an electron: [ / ro

intensity of auroral primaries, measured across an area perpendicular to the trajectories

polar angle in spherical coordinates (in airglow problems Q is measured from the perpendicular to the emitting layer; in auroral problems it is usually measured from the magnetic field direction)

polar angle of direction of wave propagation, measured from the direction of the magnetic field

angle between incident and emergent rays or particles at a scattering center

dielectric constant or permittivity (= unity for empty space) as a subscript, to denote the continuum of energies for a free electron

latitude wavelength geomagnetic latitude ground albedo

588 APPENDIX VII

P P P P P

V

V

VC

YO

t 77

3

GO

P P P Po

U

U

Y

magnetic moment molecular weight permeability (= unity for empty space) cos 8 coefficient of viscosity

kinematic viscosity frequency collision frequency frequency at the center of a line; natural frequency of an oscillator

equivalent depth, Eq. (3.78)

ratio of circumference to diameter of a circle

statistical weight albedo for single scattering

mass density radius of gyration collision diameter classical radius of electron

conductivity fraction of atoms (molecules) in an excited level that is collisionally

electron residual range in units of initial residual range: r/ro volume lifetime hour angle of the sun hour angle of the sun at sunset (or sunrise) optical thickness of ozone layer 7, at the center of a line total vertical optical thickness of an atmosphere at frequency v

longitude azimuth; azimuthal angle in spherical or cylindrical coordinates azimuth of the sun geomagnetic longitude bremsstrahlung cross section

magnetic declination Schrodinger wave function in Section 7.1.3, the angle between the z-axis and the projection

of the velocity vector onto the yz-plane energy spectrum of primary auroral particles

deactivated before radiating

APPENDIX VII 589

angular or circular frequency gyrofrequency or cyclotron frequency vibrational constants of a molecule natural angular frequency of an oscillator plasma frequency, Eq. (3.54) solid angle magnetic scalar potential collision strength

APPENDIX VIII

A List of Books and Review Articles on the Aurora and Airglow

Titles are quoted here for convenience; for complete references, see the bibliography.

The main historical works on the aurora are Mairan [ 1733~1 “Trait6 Physique et Historique de 1’Aurore BorCale” Capron [1879a] “Aurorae: Their Characters and Spectra” Fritz [1881a] “Das Polarlicht” Tromholt [1885a] “Under the Rays of the Aurora Borealis” Lemstrom [1886a] “L’Aurore BorCale” Angot [ 1896~1 “The Aurora Borealis”

Harang [ 195 la] “The Aurorae” Stormer [ 1955~1 “The Polar Aurora”

Kayser [ 1910~1 Spectrum des Nordlichtes Vegard [ 1928~1 Das Nordlicht Hulburt [ 1937~1 Terrestrial magnetic variations and aurorae Hewson [1937a] A survey of the facts and the theories of the aurora Vegard [1939a] The aurora polaris and the upper atmosphere Chapman and Bartels [1940a, Chaps, 14 and 251 The aurora polaris and

Swings [1949a] The spectra of the night sky and the aurora Meinel [1951a] The spectrum of the airglow and the aurora Mitra [1952a, Chaps. 8 and 91 Aurora polaris and Theories of magnetic

Swings and Meinel [1952a] The spectra of the night sky and the aurora Ferraro [1953a] The aurorae Chamberlain and Meinel [ 1954~1 Emission spectra of twilight, night sky,

Vassy [ 1956a, Chap. 11 Les aurores polaires (in “Physique de 1’Atmosphkre”) Elvey [ 1957~1 Aurora borealis Chamberlain [1958c] Theories of the aurora Heathcote and Armitage [1959a] The First International Polar Year Paton [1959a] The study of the aurora during the Second International

Recent books on the aurora have been published by

Major review articles on the aurora have been written by

Theories of magnetic storms and aurorae (in “Geomagnetism”)

storms and auroras (in “The Upper Atmosphere”)

and aurorae

Polar Year 590

APPENDIX VIII 59 1

Mariani, F. and Molina, F. [ 1959al Perturbazioni geomagnetiche, aurorali, ionosferiche e dei raggi cosmici: interdipendenze e relazioni con l’attivith solare

Bates [1960a] General character of auroras Bates [1960b] The auroral spectrum and its interpretation Booker [1960a] Radar studies of the aurora

Books dealing principally with the airglow are Dufay [1928u] “Recherches sur la Lumikre du Ciel Nocturne” Khvostikov [ 19484 ‘I Luminescence of the Night Sky” (translated title)

Fabry, Dufay, and Cojan [1934a] Gtude de la lumihe du fond du ciel

Dijardin [1936u] The light of the night sky Elvey [1942a] Light of the night sky Swings [1949a] The spectra of the night sky and the aurora Meinel [1951u] The spectrum of the airglow and the aurora Mitra [1952a, Chap. 101 Lights from the night sky (in “The Upper

Swings and Meinel [1952a] The spectra of the night sky and the aurora Chamberlain and Meinel [1954a] Emission spectra of twilight, night sky,

Vassy [1956u, Chaps. 2 and 31 La lumikre du ciel nocturne andPhCnomknes

Bates [1906c] The airglow

The major articles and reviews concerned with the airglow are

nocturne

Atmosphere”)

and aurorae

crCpusculaires d‘hmission (in “Physique de l’btmosphkre”)

Several conferences held in recent years on the aurora and airglow have been instrumental in furthering interest in these topics. Papers read at these meetings have in some cases been collected and issued as a symposium volume. Books of this nature include

“The Emission Spectra of the Night Sky and Aurorae” (Papers read at an International Conference held under the auspices of the Gassiot Commit- tee of the Royal Society in London in July, 1947), London: The Physical Society [ 19481 ;

“Relations Entre les PhCnomknes Solaires et Gkophysique” (Colloques Internationaux du Centre National de la Recherche Scientifique, IX, Lyon, Septembre 1947),Paris: C.N.R.S. (13,Quai Anatole-France) [1949];

“L’gtude Optique de 1’Atmosphkre Terrestre” (Communications prC- sentees au colloque international tenu i 1’Institut d’Astrophysique de 1’UniversitC de Liege les 3 et 4 Septembre 1951), Louvain: Imprimerie Ceuterick [1952] (Extrait des MCmoires in-8” de la SociktC Royale des Sciences de Likge, SCrie 4, 12, Fasc. 1-11);

“Proceedings of the Conference on Auroral Physics” (held at London, Ontario, 23-26 July 1951), ed. N. C. Gerson, T. J. Keneshea, and

592 APPENDIX VIII

R. J. Donaldson, Jr., Geophysics Research Papers No. 30, Air Force Cambridge Research Center, TR-54-203, [ 19541 (for copies apply to U. S. Dept. of Commerce, Office of Technical Services, Washington 25, D. C.); and

“The Airglow and Aurorae” (A symposium held in Belfast in September, 1955) ed. E. B. Armstrong and A. Dalgarno, London: Pergamon Press [1956].

From time to time reports are issued by the various international scientific unions that contain both original research articles and reviews of recent progress. Examples of these reports are

“ Conseil International des Union Scientifiques: Neuvikme Rapport de la Commission pour 1’Etude des Relations entre les PhCnomhes Solaire et Terrestres” [1957], Paris: Imprimerie J. et R. Sennac (address correspondence to the President of the Commission, Prof. C. W. Allen, London Univ. Obs., Mill Hill Park, London, N. W. 7, England);

“International Council of Scientific Unions, Mixed Commission on the Ionosphere, Proceedings of the Fifth Meeting held at New York Univer- sity, 14-16 August 1957; published in Vol. 15, j? Atm. Terr. Phys. [ 19591,” (address correspondence to the Secretary of the Commission, Dr. W. J. G. Beynon, Dept. of Physics, University College of Swansea, Shingleton Park, Swansea, Great Britain) ; and

“Transactions of the International Astronomical Union,” Vol. 10, 1958” [ 19601, Cambridge: University Press (address correspondence to Dr. D. H. Sadler, General Secretary, Royal Greenwich Observatory, Herstmon- ceux Castle, Hailsham, Sussex, England).

A bibliography of research on the airglow and aurora conducted in the Soviet Union prior to 1958, along with evaluations of the individual papers, is given in

“A Review of Soviet Airglow and Auroral Literature” [1961] (for copies apply to U. S. Dept. of Commerce, Office of Technical Services, Wash- ington 25, D. C., for I. D. No. 61-11121).

A few of the less technical summaries on the aurora and airglow to appear in recent years are by

Gartlein [1947a] Unlocking secrets of the northern lights Elvey [1950b] Progress in studies of the airglow in upper air research Harang [1951b] Aurorae and magnetic storms Hulburt [ 1954~1 Magnetic storms, aurorae, ionosphere, and zodiacal light Isaev [1955a] Polar aurorae (translated title) Godoli 11957~1 Le aurore polari Bates 1195733 The airglow Elvey and Roach [1957a] Aurora and airglow Ferraro [ 19574 Aurorae and magnetic stornis Chamberlain [1958e] Origin of the aurora

Bi bl iog rap h y

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ABBOTT, W. N. [1951a]. The aurora of August 19, 1950, photographed in Greece.

__ [1958a]. Displacements of the radiant point during the auroral disturbance

ABBOTT, W. N. and CHAPMAN, S. [1959a]. On the aurora of 19 August 1950,

ABOUD, A.; BEHRINC, W. E.; and RENSE, W. E. [1959a]. Emission-line intensities

AGY, V. [1960u]. Spiral patterns in geophysics. J . Atm. Terr. Phys. 19, 136-140. AKASOFU, SYUN-ICHI [ 1960~1. The ring current and the outer atmosphere. J.

_- [ 19604. On the ionospheric heating by hydromagnetic waves connected

ALFVQN, H. 119391~1. A theory of magnetic storms and aurorae. I. Kungl. Sv. Veten-

__ [1940a]. A theory of magnetic storms and aurorae. I1 and 111. Kzmgl. Sv.

-- [ 1950~1. “Cosmical Electrodynamics.” Clarendon Press, Oxford. __ [ 1955~1. On the electric field theory of magnetic storms and aurora. Tellus

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- [1959a]. Momentum spectrum of cosmic radiation. Tellus 11, 106-1 15. - [19596]. Momentum spectrum of the Van Allen radiation. Phys. Rev. Letters

ALLCOCK, G. McK. [1957a]. A study of the audio-frequency radio phenomenon known as “dawn chorus.” Australian J. Phys. 10, 286-298.

ALLEN, C. W. [1944a]. Relation between magnetic storms and solar activity. Monthly No. Roy. Ast. SOC. 104, 13-21.

~ [ 1955~1. “Astrophysical Quantities.” Athlone Press, London. ALLEN, L., Jr.; BEAVERS, J. L., 11; WHITAKER, W. A.; WELCH, J. A., Jr.; and

WALTON, R. B. [1959a]. Projet Jason measurement of trapped electrons from a nuclear device by sounding rockets. J. Geophys. Res. 64, 893-905.

ALLER, L. H. [1953a]. “Astrophysics: The Atmospheres of the Sun and Stars.” Ronald Press, New York.

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J . Atm. Terr. Phys. 1, 343-344.

of September 22, 1957. Can. J . Phys. 36, 643-648.

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Geophys. Res. 65, 535-543.

with geomagnetic micropulsations. J. Atm. Terr. Phys. 18, 160-173.

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ZHURAVLEV, S. S. [1955a]. Intensity of bright lines in spectra of aurora borealis (translated title). Trudy Nauchno-Issledovatel’skogo Institutu Zemnogo Magne- tizma [21], No. 11, 174-177. - [ 195563. Spectrophotometry of rapidly changing forms of aurora borealis

(translated title). Trudy Nauchno-Issledovatel’skogo Instituta Zemnogo Magne- tizma [21], No. 11 , 178-183.

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Author Index

Boldface pages refer to the bibliography.

A Bagariatskii, B. A., 158, 186, 190, 194, 256, 257, 341, 342, 366, 595

Bailey, D. K., 143, 595 Baillet, A,, 504, 595, 596 Barber, D. R., 382, 383,484, 511, 516, 596 Barbier, D., 40, 41, 43, 44, 45, 46, 48, 57,

125, 132, 186, 187, 200, 201, 315, 346, 351, 352, 358, 360, 385, 386, 415, 416, 425, 442, 415, 477, 478, 483, 488, 490, 491, 493, 494, 496, 497, 500, 504, 505, 506, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 521, 523, 524, 596, 597, 598, 653

Abadie, P., 490, 491, 504, 509, 593 Abbott, W. N., 104, 133, 593 Aboud, A., 294, 593 Aden, A. L., 441, 620 Agy, V., 115, 593 Akasofu, Syun-Ichi, 303, 326, 593 A l f v h H., 76, 79, 302, 325, 339, 3409 593 Allcock, G. McK., 145, 593 Allen, C. W., 17, 330, 563, 567, 593 Allen, L., Jr., 148, 149, 150, 426, 593 Aller, L. H., 12, 17, 18, 20, 28, 593 Ambarzumian, V. A., 49, 594 Anderson, K. A., 141, 146, 271, 594 Andrillat, Y., 554, 594 Angot, A., 590, 594 Angstrom, A. J., 151, 185, 348, 594 Appleton, E. v-, 80, 142, 218,548, 549, 594 Aristotle, 104, 117, 594 Armitage, A., 590, 627

Arnoldy, R., 141, 146, 147, 272, 594, 669 Arnott, G. F., 215, 658 Asaad, A. S., 505, 615

Barnard, E. E., 109 Barnett, C. F., 247, 248, 598, 659 Bartels, J., 64, 66, 73, 111, 116, 138, 148,

Barth, C. A., 352, 537, 538, 541, 598, 633 Baschin, O., 128, 598 B ~ ~ ~ , A. M., 538, 541, 636 Bates, D. R., 22, 30, 31, 32, 33, 35, 87,

88, 92, 93, 96, 98, 187, 214, 215, 216,

294, 296, 298, 309, 312, 313, 314, 317, 318, 361, 378, 390, 414, 418, 423, 425, 426, 437, 438, 439, 440, 441, 442, 465, 467, 468, 470, 471, 472, 475, 416, 477, 478, 479, 480, 482, 492, 521, 522, 524, 525, 531, 536, 537, 538, 539, 540, 543, 544, 545, 549, 558, 559, 560, 561, 564, 565, 566, 591, 592, 598, 599, 600, 629

149, 548, 590, 598, 611

Armstrong, E. B., 212, 5037 504, 513, 594 244, 247, 248, 253, 255, 256, 285, 293,

L. M*, 4723 546, 639, 651,

Ashburn$ E. v., 57p 59* 6op 619 1259 2057

Ashkin, J., 270, 271, 284, 603 Aspinall, A., 218, 224, 228, 595 Astapovich, I. S., 505, 595 Astrom, E., 325, 595 Auberger, L., 358, 595

670

489, 492, 493, 513, 594, 655, 656

Bauer, E., 537, 600 Bauer, W., 128, 132, 627 Bawn, C. E. H., 565, 600 Beavers, J. L., II., 330, 593 Bedinger, J. F., 390, 472, 600, 601, 612, 618, 639, 643

Behr, A., 321, 601 Behring, W. E., 294, 593 Beiser, A., 70, 323, 325, 601 Belon, A. E., 142, 187, 210, 215, 601, 611,

B

Babcock, H. D., 150, 185, 348, 349, 503,

Babcock H. W., 150, 595, 658 595, 658

628

67 1

672 AUTHOR INDEX

Benedict, W. S., 556, 601 Bennett, W. H., 325, 601 Berg, M. R., 220, 221, 222, 225, 226, 227,

Berg, 0. E., 268, 283, 391, 497, 601, 642 Bernard, R., 152, 186, 192, 203, 314, 352,

379, 380, 382, 415, 492, 601, 602, 614 Berthier, P., 359, 377, 385, 490, 491, 504,

506, 511, 512, 513, 514, 517, 602, 616

636, 651, 655

Bethe, H., 270, 271, 284, 426, 563, 603 Bialecke, E. P., 441, 532, 603 Biermann, L., 324, 603 Biondi, M. A., 441, 545, 603, 609, 610 Birfeld, J . G., 220, 230, 603 Birkeland, Kr., 325, 603 Birkhoff, R. D., 271, 284, 603 Blackett, P. M. S., 346, 603 Blackwell, D. E., 321, 359, 361, 362, 368,

Blamont, J. E., 383, 384, 416, 450, 458,

Blaton, J., 434, 655 Bless, R. C., 136, 139, 203, 604 Blevis, B. C., 225, 604 Block, L., 68, 325, 604 Bohm, D., 304, 604 Bolgiano, R., Jr., 552, 604 Boller, W., 104, 110, 604 Bolshakova, L. C., 504, 604 Bonner, T. W., 208, 215, 254, 605 Booker, H. G., 218, 222, 223, 225, 228,

Bornstein, R., 250, 636 Bortner, T. E., 545, 630 Bosson, F., 504, 596 Boudart, M. J., 559, 640 Bowen, I. S., 318,350,484,605 Bowles, K. L., 225, 230, 605 Brackmann, R. T., 248, 312, 621 Bradbury, N. E., 86, 87, 516, 605 Bramhall, E. H., 114, 128, 623 Brandt, J. C., 97, 323, 391, 450, 454, 455,

478, 484, 562, 563, 564, 571, 605 Branscomb, L. M., 208, 215, 254, 499,

541, 545, 605, 606, 658 Breit, G., 428, 430, 435, 605 Brewer, A. W., 392, 663 Bricard, J., 381, 382, 383, 384, 408, 415,

501, 502, 507, 603

462, 463, 473, 493, 504, 603, 604

230, 235, 239, 241, 591, 604, 605

Broida, H. P., 352, 358, 538, 541, 544, 606,

Briick, H. A., 323, 606 Brunner, W., 350, 606 Buckingham, R. A., 545, 599 Builder, G., 142, 594 Bullough, K., 218, 219, 222, 223, 224, 226,

228, 231, 606, 632 Burch, D. E., 376, 606 Burch, D. S., 545, 605, 658 Burhop, E. H. S., 250, 319, 542, 639 Burns, G. J., 347, 606 Byard, P. L., 116, 631 Byram, E. T., 93, 358, 497, 606, 636 Byran, R. B., 314, 606 Byrne, E. C., 142, 628

636

C

Cabannes, J., 185, 345, 349, 350, 351, 352, 358, 359, 363, 379, 380, 385, 399, 418, 501, 503, 504, 514, 515, 607

Cain, J. C., 233, 607 Campbell, W. W., 348, 607 Capron, J. R., 590, 607 Cario, G., 190, 378, 379, 381, 408, 415, 607 Carleton, N. P., 208, 252, 254, 313, 608 Cerenkov, P. A., 272, 511, 608, 615 Chandrasekhar, S., 34, 46, 47, 49, 50, 51,

53, 54, 57, 58, 428, 433, 450, 454, 550, 551, 609

Chanin, L. M., 545, 609, 610 Chapman, R. P., 144, 610 Chapman, S., 64, 66, 67, 68, 69, 72, 84,

95, 98, 100, 101, 104, 106, 111, 116, 118, 128, 138, 139, 147, 232, 233, 234, 264, 293, 321, 322, 325, 344, 350, 379, 380, 415, 467, 469, 502, 541, 548, 549, 559, 565, 575, 590, 593, 598, 610, 611, 643

Cherniaev, V. I., 379, 611 Chivers, H. J. A., 144, 611 Christofilos, N. C., 330, 611 Chubb, T. A., 88, 93, 358, 497, 606, 611,

Chudakov, A. E., 326, 667 Chuvayev, K., 360, 505, 544, 611, 650 Cialdea, R., 101, 611 Clark, K. C.. 187. 210. 215, 601, 611

636

. _ . 436, 450, 508, 606 Clayton, H. H., 110, 611

AUTHOR INDEX 673

Cleary, J., 70, 648 Clegg, J. A., 218, 229, 235, 638 Cojan, J., 591, 620 Cole, K. D., 340, 611 Collins, C., 143, 217, 220, 222, 223, 226,

227, 229, 230, 242, 612, 652 Condon, E. U., 4, 13, 15, 612 Constantine, G., 40, 612 Cook, C. J., 247, 249, 612 Cooper, C. D., 472, 612, 618 Coroniti, S. C., 332, 646 Cortie, A. L., 112, 612 Costello, M., 378, 612 Court&, G., 388, 504, 604, 612 Cavington, A. E., 144, 612 Cowling, T. G., 526, 612 Crawford, J. A., 339, 340, 612 Crone, W. R., 324, 635 Cronin, H. E., 383, 384, 416, 612 Cullington, A. L., 331, 612 Cullington, E., 390, 643 Curran, S. C., 253, 283, 663 Currie, B. W., 114, 128, 132, 134, 135,

136, 138, 144, 220, 222, 226, 227, 230, 235, 304, 305, 306, 379, 384, 509, 610, 612, 613, 621, 631, 634, 641

D

Dahlstrom, C. E., 125, 140, 196, 203, 205,

Dalby, F. W, 194, 613 Dalgarno, A., 33, 248, 249, 292, 390, 423,

468, 475, 492, 522, 526, 543, 545, 564, 599, 613

613

Daniels, F. B. J., 98, 613 Danielson, R. E., 70, 613 Das Gupta, N. N., 285, 613 Dauvillier, A., 380, 521, 613 Davidson, T. W., 231, 606 Davies, F. T., 104, 108, 113, 114, 613 Davis, D. N., 491, 495, 496, 505, 511, 513,

Davis, L. R., 268, 283, 323, 339, 613, 642 Davis, T. N., 100 de Jager, C., 551, 552, 614 Dbjardin, G., 346, 350, 352, 358, 367, 368,

379, 492, 591, 614, 616

516, 518, 613, 653

Delestrade, C., 516, 625 Deming, L. S., 437, 669 Denise, J. F., 148, 614 Dessler, A. J., 98, 303, 326, 327, 614 Dieke, G. H., 152, 614 Dieterich, E. J., 254, 614 Dirac, P. A. M., 428, 614 Divari, N. B., 504, 505, 509, 614, 615 Dixon, F. E., 113, 615 Dobrotin, N., 511, 615 Dodson, H. W., 149, 615 Dogniaux, R., 195, 646 Dollfus, A., 206, 615 Dolphin, L. T., 221, 618, 655 Donahue, T. M., 359, 384, 416, 417, 448,

450, 458, 459, 462, 463, 466, 483, 494, 604, 615

Dorum, K. G., 209, 666 Dougal, A. A., 441, 532, 603 Douglas, A. E., 152, 194, 613, 615 Dowden, R. L., 145, 615 Dufay, J., 185, 200, 345, 348, 349, 350,

351, 352, 358, 359, 360, 363, 377, 378, 379, 380, 385, 408, 414, 415, 418, 421, 490, 491, 493, 499, 501, 503, 504, 505, 506, 511, 512, 513, 514, 515, 516, 517, 518, 541, 597, 607, 614, 616, 617, 620

Dufay, M., 186, 187, 200, 358, 359, 363, 367, 377, 378, 388, 389, 414, 479, 480, 499, 501, 504, 506, 507, 514, 515, 517, 607, 616, 617

Duffendack, 0. S., 208, 617 Dunbar, D. N. F., 247, 249, 652 Duncan, R.A., 145,201,202,206,617,618 Dungey, J. W., 333, 529, 530, 618 Dunham, T., Jr., 465, 618 Dunn, R. B., 206, 493, 504, 618 Dyce, R., 220, 221, 222, 225, 226, 227,

329, 618, 636, 651, 655

E

Eccles, W. H., 81, 618 Edwards, H. D., 472, 618 Edwards, H. W., 114, 379, 384, 612 Egedal, J., 110, 128. 618 Einstein, A., 13, 14, 618 Elbert, D. D.. 54, 57, 59. 454. 609

Delannoy, J., 390, 425, 483, 597, 614 Elford; W. G.; 520, 551, 618

674 AUTHOR INDEX

Eliason, A. Y., 485, 669 Ellett, A., 434, 618, 629 Elliot, H., 331, 618 Ellis, G. R., 145, 146, 276, 277, 281, 618 Ellyett, C. D., 218, 221, 229, 235, 638, 656 Elsasser, H., 321, 490, 601, 619 Elsasser, W. M., 35, 619 Elvey, C. T., 100, 108, 114, 140, 147, 203,

345, 347, 351, 352, 358, 363, 378, 385, 415, 418, 504, 509, 511, 512, 513, 514, 516, 518, 521, 590, 591, 592, 619, 654, 66 1

Emde, F., 264, 631 Emelkus, K. G., 185, 310, 655. 659 Endow, N., 538, 621 Eropkin, D. I., 505, 511, 619 Evans, A. G., 565, 600 Evans, J. W., 493, 619 Evans, S., 106, 136, 619 Eyring, H., 32, 625

F

Fabry, C., 347, 348, 380, 591, 620 Faire, A. C., 441, 620 Fan, C. Y., 139, 152, 192, 194, 199, 203,

208, 213, 215, 254, 339, 609, 620, 642, 654

Farnsworth, A. H., 385, 415, 418, 511, 512, 619

Fath, E. A., 348, 351, 620 Fediakina, N. I., 139, 142, 670 Fedorova, N. I., 158, 186, 194, 366, 501,

502, 507, 595, 620 Fenton, K. B., 70, 658 Fermi, E., 338, 620 Ferraro, V. C. A., 325, 344, 525, 526, 527,

592, 611, 620, 621 Fesenkov, V. G., 40,488, 504, 505,509,621 Feshbach, H., 237, 287, 644 Feygelson, Ye. M., 493, 621 Finch, J. F., 64, 621 Fish, R. A., 97, 562, 632 Fishkova, L. M., 202, 490, 621, 649 Fite, W. L., 248, 312, 621 Foderaro, A., 359, 494, 615 Forbush, S. E., 621 Ford, H. W., 538, 621 Forsyth, P. A., 144, 217, 220, 222, 223,

226, 227, 228, 229, 230, 233, 234, 235, 239, 242, 304, 305, 306, 612, 613, 621, 622

Foss, H., 622 Fowler, P. H., 331, 622 Francis, G., 304, 622 Franck, J., 381, 622 Frank, I., 272, 511, 615, 622 Frank, L. A., 326, 664 Franklin, A,, 54, 609 Fraser, P. A., 23, 199, 252, 439, 539, 622,

Freden, S. C., 339, 622 Freier, P. S., 146, 147, 622, 645 Frerichs, R., 185, 350, 622 Fricker, S. J., 220, 226, 622 Friedman, H., 88, 94, 358, 497, 506, 606,

Frish, M. S., 377, 657 Frishman, I. G., 205, 622 Fritz, H., 104, 590, 622 Fukushima, N., 139, 622 Fuller, V. R., 114, 128, 622, 623 Fundingsland, 0. T., 441, 620

63 1

611, 636

G

Gadsden, M., 220, 230, 231, 390,483, 623,

Galbraith, W., 346, 631 Gallagher, P. B., 221, 649 Gallet, R. M., 145, 278, 282, 623 Galperin, Iu. I., 199, 203, 204, 207, 230,

Garrnire, 'G., 149, 640 Garner, D. M., 110, 623 Garrigue, H., 384, 385, 399, 418, 491, 509,

Garriott, 0. K., 278, 623 Garstang, R. H., 480, 532, 536, 580, 623 Gartlein, C. W., 100, 108, 127, 136, 139,

140, 186, 192, 196, 199, 203, 212, 222, 223, 225, 228, 230, 235, 335, 592, 604, 605, 624

663

256, 326, 463, 623, 657

607, 623

Garvin, D., 559, 624, 640 Gauss, C. F., 64 Gauzit, J., 359, 378, 379, 380, 503, 607,624 Gaydon, A. G., 152, 352, 358, 538, 543,

544, 606, 624, 649

AUTHOR INDEX 675

Geddes, M., 104, 107, 125, 128, 624, 669 Gellibrand, H., 71 Geltman, S., 545, 605 Georgiyevskii, Yu. N., 504, 604 Gerson, N. C., 91, 222, 624 Getmantsev, G., 144, 624 Ghosh, S. K., 285, 613 Ghosh, S. N., 314, 472, 600, 601, 624 Ginzburg, V. L., 205, 206, 508, 521, 624 Glass, D. G., 226, 227, 633 Glasstone, S., 625 Glaume, J., 490, 510, 598 Gnevyshev, M. N., 324, 625 Godoli, G., 592, 625 Gold, E., 264, 625 Gold, T., 323, 325, 341, 625 Goldanskii, V. I., 346, 625 Goldberg, L., 16, 625 Goldstein, S., 80, 625 Goody, R. M., 35, 95, 520, 537, 551, 625 Gorchakov, E. V., 326, 667 Gordon, W. E., 239, 605 Gottlieb, M. B., 140, 642 Gotz, F. W. P., 186, 352, 625, 646 Grandmontagne, R., 504, 516, 625 Greaves, W. M. H., 148, 625 Greenhow, J. S., 144, 611 Greenstein, J. L., 101 Gribbon, P. W. F., 310, 313, 625, 659 Griffing, G. W., 247, 248, 249, 255, 256,

292, 600, 613, 625 Gross, E. P., 304, 604 Guirguis, G. K., 40, 626 Gush, H. P., 101, 366, 367, 388, 501, 504,

626, 663

H

Hakura, Y., 142, 626 Hale, D. P., 114, 136, 626 Halley, E., 138, 626 Halliday, I., 316, 626 Hamilton, D. R., 428, 626 Hammad, A., 40, 612, 626 Hansen, R. T., 149, 150, 626, 668 Harang, L., 101, 125, 128, 129, 132, 134,

135, 142, 143, 144, 202, 205, 206, 218, 220, 224, 226, 227, 235, 255, 267, 290, 590, 592, 626, 627, 647

Harris, D. L., III . , 20 Harrison, A. W., 174, 175, 186, 193, 194,

198, 199, 209, 210, 221, 367, 388, 425, 463, 480, 481, 482, 504, 507, 514, 539, 627, 646, 663

Harrison, D. P., 627 Harteck, P., 537, 627 Hartree, D. R., 80, 627 Hartz, T. R., 144, 276, 306, 627 Hashizume, A., 504, 647 Hasted, J. B., 248, 659 Hawkins, G. S., 218, 224, 228, 595 Heaps, H. S., 507, 554, 627 Heath, D. F., 152, 614 Heathcote, N. H. de V., 590, 627 Hebb, M. H., 29, 627 Hector, F. S., 139, 641 Hedeman, E. R., 149, 615 Heisenberg, W., 430, 432, 627 Heitler, W., 270, 271, 603, 627 Hellgren, G., 222, 628 Helliwell, R. A., 145, 278, 282, 623, 628 Henyey, L. G., 101 Heppner, J. P., 88, 139, 142, 268, 283,

Herlofson, N., 68, 128, 191, 228, 237, 238,

Herman, L., 203, 316, 363, 628 Herman, R., 152, 194, 316, 363, 628 Herman, R. C., 367, 368, 554, 628 Hertzberg, M., 524, 538, 628 Herzberg, G., 20, 21, 22, 23, 25, 26, 152,

352, 358, 442, 443, 507, 540, 554, 556, 558: 627, 628

497, 628, 632, 642

604, 628

Hessler, J., 108, 114, 619 Hessler, V.P., 118, 119, 120, 121, 122, 123,

Hewson, E. W., 590, 629 Heydenburg, N. P., 434, 435, 436, 629 Hikosaka, T., 202, 547, 629 Hines, C. O., 326, 629 Hirschfelder, J. O., 32, 629 Hoffman, R., 141, 146, 147, 272, 594, 669 Hoffmeister, C., 521, 629 Holmes, J. C., 87, 88, 632 Holt, R. B., 314, 606 Hope, E. R., 70, 629 Hornbeck, G. A., 367, 368, 628 Hough, W. S., 516, 640 Hoyle, F., 88, 323, 324, 340, 629

139, 628

676 AUTHOR INDEX

Hulburt, E. O., 114, 325, 391, 590, 592, 601, 629, 652

Hultqvist, B., 143, 334, 335, 336, 629 Humphreys, C. J., 556, 601 Hunaerts, J., 358, 629 Hunten, D. M., 67, 101, 124, 125, 140,

173, 190, 193, 194, 196, 198, 199, 203, 205, 209, 210, 211, 214, 215, 317, 379, 380, 383, 384, 401, 408, 409, 410, 411, 413, 416, 417, 418, 425, 426, 436, 445, 450, 453, 455, 460, 461, 462, 465, 466, 467, 468, 469, 470, 471, 484, 494, 570, 571, 609, 613, 615, 629, 630, 638, 655, 656, 657, 663

Hurst, G. S., 545, 630 Huruhata, M., 48, 202, 490, 491, 495, 509, 511, 513, 514, 515, 516, 518, 630, 631

I

Ingalls, R. P., 220, 226, 622 Ingham, M. F., 359, 361, 362, 368, 501,

Ingraham, R., 70, 631 Ingram, L. J., 142, 218, 594 Inn, E. C. Y., 538, 662 Ireton, H. J. C., 128, 350, 511, 640, 641 Isaev, S. I., 592, 631 Ishikawa, G., 299, 631

502, 507, 603

1

Jacka, F., 108, 114, 631 Jackson, W., 148, 644 Ja_cobs, J. A., 326, 646 Jaeger, J. C., 304, 631 Jahnke, E., 264, 631 James, C. G., 544, 631 James, J. F., 391, 631 Jamnick, P. M., 124, 125, 653 Janin, J., 152, 316, 367, 368, 614, 631 Janossy, L., 343, 631 Jarmain, W. R., 23, 199, 252, 439, 539,

Jarrett, A. H., 116, 631 Jastrow, R., 299, 631 Jelley, J. V., 273, 346, 631 Jensen, R. E., 134, 135, 631

622, 631

Jesse, W. P., 247, 249, 631 Johnson, C. Y., 87, 88, 632 Johnson, F. S., 97, 562, 632 Jones, C. K., 134, 613 Jones, E., Jr., 247, 249, 612 Jones, L. M., 502, 632 Jorgensen, T., Jr., 247, 249, 612 Jorjio, N. V., 202, 205, 509, 632 Jouaust, R., 471, 632 Jursa, A. S., 538, 544, 546, 632, 639, 651,

662, 670

K

Kahn, F. D., 382, 632 Kaiser, T. R., 218, 219, 222, 223, 224, 226,

228, 230, 231, 233, 234, 391, 521, 606, 632

Kanner, H., 247, 248, 632 Kaplan, J., 186, 193, 314, 352, 360, 537,

Karandikar, R. V., 503, 504, 633 Kariaguina, 2. V., 505 Karimov, M. G., 490, 505, 633 Karplus, R., 327, 614 Kastler, A., 351, 381, 382, 384, 408, 415,

416, 436, 450, 493, 504, 508, 604, 606, 633

538, 541, 542, 544, 598, 632, 633

Katterbach, K., 264, 633 Katzman, J., 70, 658 Kaufman, F., 544, 633 Kavadas, A., 224, 226, 227, 633, 638 Kayser, H., 151, 590, 633 Kellogg, P. J., 331, 340, 633 Kelso, J. R., 544, 633 Kern, J., 337, 609 Khvostikov, I. A., 386, 508, 511, 591, 633,

Kiepenheuer, K. O., 149, 634 Kim, J. S., 135, 136, 634 Kimball, D. S., 136, 139, 604 King, E. S., 151 King, J. I. F., 35, 634 Kistiakowsky, G. B., 538, 544, 634 Kleinschmidt, K., 11 3 Knecht, R. W., 142, 634 Koenig, H. J., 210, 630 Koomen, M., 497, 504, 601, 634 Kourganoff, V., 264, 634

634, 636

AUTHOR INDEX 677

Kozyrev, N. A., 347, 505, 511, 619, 634 Krassovskii, V. I., 98, 312, 326, 359, 361,

363, 366, 502, 504, 524, 538, 544, 547, 558, 559, 560, 561, 595, 634, 635, 638, 657

Kraus, J. D., 264, 324, 635 Krause, H., 633 Kreplin, R. W., 88, 611 Krinov, E. L., 493, 635 Krogness, O., 128, 132, 133, 134, 136, 635,

Kron, G. E., 366, 504, 636 Kupperian, J. E., 88, 358, 497, 606, 611,

Kurzweg, U. H., 538, 541, 636 Kvifte, G., 186, 187, 188, 190, 194, 199,

201, 204, 205, 209, 316, 359, 368, 408, 415, 416, 417, 483, 501, 507, 541, 542, 636, 667

666

636

L

La Cour, D., 117, 636 Laidler, K. J., 625 Lallemand, A., 504, 596 Landau, L., 79, 270, 280, 636 Landmark; B., 144, 224, 226, 227, 235,

Landolt (H. H.)-Bornstein (R.), 250, 636 Landseer-Jones, B. C., 325, 340, 636 Langmuir, I., 304, 662 Larmor, J., 81, 636 Larrick, L., 434, 629 Larsen, S., 415, 667 Lawrence, T. R., 252, 254, 313, 608 Leadabrand, R. L., 220,221,222,225, 226,

Leaton, B. R., 64, 621 Lebedev, A., 511, 636 Lebedinskii, A. I., 101, 302, 637 LeBlanc, F., 538, 544, 632, 662 Lee, T. D., 552, 637 Lehnert, B., 98, 637 Leinbach, H., 108, 114, 142, 143, 146, 203,

Lemstrom, K. S., 300, 590, 637 LCvOque, P., 504, 598 Lewis, H. W., 285, 286, 637 Lichten, W., 194, 315, 637

627

227, 618, 636, 649, 651, 655

619, 628, 637

Lifshitz, E., 79, 270, 286, 636 Liller, W., 203, 604 Lindemann, F. A., 325, 637 Link, F., 413, 504, 637 Linke, W., 351, 352, 358, 511, 514, 518,

Lipscomb, F. J., 561, 637 Liszka, L., 548, 637 Little, C. G., 142, 143, 144, 217, 218, 293,

Little, D. E., 138, 637 Lock, C., 497, 634 Logachev, Yu. I (also J. L.), 326, 667 Long, R. A., 221, 618 Longmire, C. L., 335, 654 Loomis, E., 104, 110, 638 Lovell, A. C. B., 144, 218, 229, 235, 637,

Lowry, R. A., 253, 638 Ludwig, G. H., 326, 330, 534, 664, 670 Lugeon, J., 397, 398, 638 Lukashenia, V. T., 366, 560, 635, 638 Lust, R., 323, 638 Lyon, G. F., 224, 638 Lytle, E. A., 194, 210, 426, 463, 484, 638

619

611, 637

638

M

MacArthur, J. W., 145, 281, 282, 638 Mack, J. E., 380, 425, 445, 450, 461, 469,

Maeda, H., 332, 638 Maeda, Ken-Ichi, 70, 638 Maguery, J., 504, 596 Mairan, J. J. D., 110, 112, 128, 590, 638 Malmfors, K. G., 325, 638 Malville, J. M., 114, 136, 203, 207, 314,

Mange, P., 88, 94, 476, 638, 646 Manring, E. R., 202, 206, 472, 490, 491,

493, 495, 496, 504, 506, 511, 512, 513, 514, 518, 519, 546, 550, 600, 601, 612, 618, 639, 650, 670

Mariani, F., 591, 639 Markova, G. V., 202, 621 Marlow, D., 504, 639 Marmo, F. F., 472, 546, 639, 651, 670 Marovich, E., 125, 200, 201, 345, 346, 488,

494, 609

331, 638

490, 493, 513, 653

678 AUTHOR INDEX

Marshall, L., 276, 639 Martvel, F. E., 220, 639 Martyn, D. F., 302, 325, 340, 515, 639 Massey, H. S. W., 87, 187, 250, 292, 312,

313, 314, 319, 438, 470, 476, 478, 542, 545, 599, 600, 639, 644

Mathews, W. G., 212, 639 Matsushita, S., 104. 141, 142, 331, 332,

Mawson, D., 135, 640 Maxwell, A., 144, 149, 637, 640 Mayaud, P. N., 384, 640 McCaulley, J. W., 125, 345, 346, 508, 509,

McDowell, M. R. C., 92, 293, 600 McEwen, D. J., 128, 135, 640 McIlwain, C. E., 268, 326, 330, 534, 640,

McKinley, D. W. R., 640 McKinley, J. D., Jr., 224, 559, 624, 640 McLennan, J. C., 128, 185, 186, 349, 350,

McLeod, J. H., 349, 350, 511, 640 McNamara, A. G., 142, 225, 226, 227, 231,

McNish, A. G., 67, 332, 641 McPherson, D. H., 380, 463, 501, 502,

McQuarrie, W. C., 349, 640 Meadows, E. B., 87, 88, 632 Meek, J. H., 115, 136, 139, 142, 231, 641 Megill, L. R., 317, 396, 488, 490, 493,

Megrelishvili, T. G., 386, 634 Meinel, A. B., 61, 104, 105, 109, 110, 111,

113, 136, 140, 152, 159, 160, 165, 166, 167, 168, 169, 187, 192, 194, 199, 202, 203, 213, 215, 226, 254, 256, 351, 358, 360, 363, 367, 377, 488, 489, 490, 491, 493, 494, 499, 500, 501, 505, 514, 553, 558, 590, 591, 609, 620, 641, 642, 653, 661

639, 659

513, 516, 640, 653

654, 664

503, 511, 640, 641

235, 641

641, 663

519, 641, 653, 654

Menzel, D. H., 29, 627 Meos, J., 222, 235, 628, 642 Meredith, L. H., 140, 268, 283, 284, 497,

Meyer, P., 146, 148, 323, 642 Mian, A. M., 264, 643 Miley, H., 390, 391, 643 Miller, G. H., 253, 638

601, 628, 642

Millman, P. M., 224, 640 Minneart, M., 455, 643 Mironov, A. V., 190, 192, 361, 363, 501,

Mitchell, A. C. G., 381, 382, 428, 643 Mitra, S. K., 80, 86, 226, 238, 275, 277,

Mohler, F. L., 86, 643 Moiseiwitsch, B. L., 558, 559, 561, 600 Molina, F., 591, 639 Montalbetti, R., 128, 135, 204, 207, 209,

Moore, C. B., 472, 639 Moore, C. E., 151, 643 Moore, R. K., 108. 218, 224, 624, 643 Mordukhovich, M. I., 366, 595 Moreau, G., 200, 617 Morel, J., 316, 628 Morel-Viard, J., 256, 643 Morgan, M. G., 145, 628 Morignat, B., 490, 504, 506, 5 1 1, 5 1 2, 5 1 3,

Morosov, V. M., 391, 643 Moroz, V. I., 367, 507, 643 Morse, P. M., 23, 237, 287, 644 Mott, N. F., 292, 644 Motz, J. W., 270, 644 Moyerman, R. M., 469, 644 Mularchik, T. M., 188, 212, 644 Muncke, G. W., 104, 644 Murcray, W. B., 36, 114, 147, 644 Mustel, E. R., 324, 644

502, 559, 643

314, 515, 590, 591, 643

253, 268, 378, 463, 612, 640, 643

602, 616

N

Naismith, R., 142, 218, 594 Nakada, M. P., 329, 618 Nakamura, J., 509, 630, 644 Nakamura, M., 504, 507, 509, 647 Nakamura, T., 495, 518, 630 Nakata, Y., 221, 644 Negaard, B. J., 109, 110, 111, 113, 359

Neuiil, L., 504, 637 Newcomb, S., 347, 644 Newkirk, G., Jr., 347, 644 Newman, P., 330, 644 Newton, H. W., 148, 625, 644 Ney, E. P., 146, 147, 331, 622, 633, 645

470, 494, 565, 609, 642

AUTHOR INDEX 679

Nguyen-huu-Doan, 359, 463, 645 Nicholls, R. W., 23, 199, 216, 252, 254,

439, 539, 622, 631, 645, 663, 668 Nichols, B., 21 8, 222, 223, 225, 228, 230,

231, 235, 605, 645 Nicolet, M., 31, 32, 88, 92, 93, 94, 95, 98,

186, 187, 195, 314, 352, 358, 378, 384, 387, 388, 414, 425, 441, 465, 467, 471, 476, 480, 483, 484, 492, 522, 523, 524, 537, 541, 544, 546, 547, 558, 559, 564, 565, 566, 574, 600, 629, 645, 646, 661

Nikolskii, A. P., 115, 646 Noelke, C. L., 383, 384, 416, 612 Norrish, R. G. W., 561, 637 Northover, F. H., 145, 646 Northrop, T. G., 335, 646 Noxon, J. F., 108, 114, 367, 507, 619, 646

0

Obayashi, T., 141, 326, 332, 334, 646 Ogawa, M., 504, 565, 646, 647, 662 01, A. I., 324, 625 Oldenberg, O., 213, 314, 315, 316, 538,

553, 606, 647 Oliver, N. J., 151, 186, 187, 189, 351, 358,

501, 502, 609, 647 Olving, S., 235, 642 Omholt, A., 186, 198, 199, 202, 203, 204,

205, 215, 250, 253, 256, 257, 259, 260, 262, 293, 294, 295, 296, 297, 312, 316, 317, 318, 342, 415, 467, 600, 647, 667

Onaka, R., 504, 507, 647 t)pik, E. J., 97, 648 Ortner, J., 143, 629 Osherovich, A. L., 504, 507, 648 Osterbrock, D. E., 101, 199, 203, 315,

Otsuki, T., 142, 626 Otto, A. N., 504, 604 Bzdoean, I., 527, 621

648, 656

P

Packer, D. M., 497, 504, 634 Panofsky, W. K. H., 8, 12, 236, 270, 273,

274, 215, 307, 648 Park, F. R., 101, 648

Parker, E. N., 146, 148, 321, 323, 324, 325, 326, 338, 339, 340, 614, 629, 642, 648

Parkinson, W. D., 70, 326, 648 Paschen, F., 350, 648 Pasternack, S., 536, 580, 648 Pastiels, R., 388, 646 Paton, J., 590, 648 Paulsen, A,, 151, 648 Pavlova, E. N., 363, 490, 505, 506, 507,

Pearse, R. W. B., 152, 187, 312, 313, 314,

Pecker, J. C., 150, 654 Pekeris, C. L., 549, 649 Pemberton, J. C., 504, 639 Penndorf, R., 382, 408, 493, 649 Percival, I. C., 313, 649 Peterson, A. M., 220, 221, 222, 226, 227,

Peterson, J. W., 502, 632 Peterson, L., 141, 146, 147, 272, 594, 669 Petrie, W., 144, 153, 155, 186, 187, 189,

198, 199, 209, 211, 214, 215, 304, 305, 306, 378, 612, 621, 649, 650

Pettit, H., 43, 44, 45, 202, 347, 472, 490, 491, 495, 496, 504, 505, 506, 507, 509, 511, 512, 513, 514, 516, 518, 519, 550, 598, 639, 650, 653, 654, 655

513, 649, 654

358, 600, 649

330, 649, 651

Peyron, M., 314, 367, 368, 602, 614 Phelps, A. V., 545, 610 Phillips, J. G., 503, 504, 650 Phillips, M., 8, 12, 236, 270, 273, 274,

Pickering, E. C., 151, 650 Piddington, J. H., 323, 325, 326, 341, 650 Pierce, E. T., 332, 646 Pierce, J. R., 278, 650 Pikelner, S. B., 534, 544, 650 Piotrowski, S. L., 40, 650 Placious, R. C., 270, 644 Placzek, G., 264, 650 Plass, G. N., 35, 650, 661 Pleiter, D., 254, 645 Pliny the Elder, 104, 117, 650 Plyler, R. K., 556, 601 Pogorelov, V. I., 220, 228, 639, 650 PoincarC, H., 325, 651 Pope, J. H., 145, 651 Porter, G., 561, 651

275, 307, 648

680 AUTHOR INDEX

Presnell, R. I., 220, 222, 223, 225, 226,

Pressman, J., 472, 546, 639, 651, 670 Priester, W., 455, 651 Prokudina, V. S., 192, 358, 359, 361, 363,

Pulley, 0. O., 515, 639 Purcell, J. D., 563, 651 Purdy, C. M., 346, 508, 509, 653

227, 636, 651

501, 502, 506, 559, 643, 651

Q

Quenby, J. J., 71, 331, 333, 334, 618, 651

R

Raasted, H., 215, 667 Ratcliffe, J. A., 84, 239, 478, 515, 529, 530,

651 Rayleigh, Lord (Strutt, R. J.), 194, 215,

346, 348, 349, 350, 351, 503, 506, 509, 511, 513, 516, 570, 651, 652, 661

Rayton, W. M., 144, 217, 218, 637 Rdultovskaya, Y e . V., 506, 654 Rees, M. H., 108, 125, 199, 205, 317, 490,

Reid, G. C., 143, 144, 146, 302, 627, 637,

Reid, W. H., 552, 652 Rense, W. E., 294, 593 Resnick, R., 417, 450, 458, 615 Revans, R. W., 208, 617 Reynolds, H. K., 247, 248, 249, 598, 652 Ribe, F. L., 248, 652 Richardson, R. A., 391, 652 Richardson, R. S., 323, 652 Rieke, C. A., 381, 622 Roach, F. E., 61, 124, 125, 200, 201, 345,

346, 347, 380, 415, 416, 464, 488, 489, 490, 491, 493, 494, 495, 496, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 516, 518, 519, 521, 570, 592, 598, 619, 630, 650, 653, 654, 655, 662

493, 505, 652, 653, 654

652

Roberts, J. A., 280, 281, 663 Roberts W. O., 150, 654 Robinson, B. J., 88, 654 Robley, R., 382, 384, 385, 419, 420, 436,

474, 478, 512, 515, 606, 640, 654

Rodionov, S. F., 363, 490, 504, 505, 506,

Roesler, F. L., 208, 365, 367, 368, 609, 654 Romick, G. J., 140, 203, 654 Roof, R. B., 144, 217, 218, 637 Rose, D. C., 70, 658 Rosenbluth, M. N., 335, 654 Rothwell, P., 326, 334, 654 Roy, A. S., 208, 617 Rozhkovskii, D. A., 505, 655 Rubin, R. J., 554, 628 Rubinowicz, A,, 434, 655 Ruedy, R., 349, 640 Runcorn, S. K., 72, 655 Rundle, H. N., 359, 361, 362, 368, 409,

Rutllant, F., 323, 606 Rypdal, B., 310, 655

507, 513, 604, 648, 649, 654

418, 450, 501, 502, 507, 603, 655

S

Sadauskis, J., 247, 249, 631 Sagan, C., 441, 521, 571, 609 Saha, A. K., 564, 655 Saha, M. N., 437, 438, 655 St. Amand, P., 125, 477, 478 495, 496,

498, 504, 511, 512, 513, 514, 515, 516, 518, 650, 653, 654, 655

SaitB, B., 547, 629 Salmon, K., 390, 483, 623 Salpeter, E. E., 426, 563, 603 Sandford, B. P., 201, 506, 516, 655 Sanford, R. F., 464, 655 Sayers, N. D., 185, 194, 655 Scanlon, J. C., 186, 647 Schaefer, E. J., 502, 632 Schiff, L. I., 273, 655 Schlobohm, J. C., 220, 221, 222, 226 227,

Schmerling, E. R., 478, 515, 529, 530, 651 Schove, D. J., 104, 655 Schulte, D. H., 105, 136, 140, 203, 226,

Schulte, H. F., 502, 632 Schwinger, J., 280, 656 Scolnik, R., 497, 601, 634 Scrimger, J. A., 380, 436, 455, 465, 466,

Seaton, M. J., 29, 60, 88, 215, 294, 302,

651, 655

620, 642

656 .

AUTHOR INDEX 68 1

310, 311, 312, 313, 314, 315, 317, 319, 391, 467, 470, 471, 475, 480, 493, 521, 522, 532, 533, 542, 543, 571, 600, 632, 649, 656

Seed, T. J., 144, 221, 656 Sekera, Z., 58, 59, 60, 656 Seneca, L. C., 104, 117, 657 Serson, H., 378, 612 Setty, C. S. G. K., 478, 515, 529, 530, 651 Shalek, R. J., 208, 215, 254, 605 Shane, C. D., 455, 657 Sharpless, S., 101, 648 Shaw, J. E., 337, 657 Shaw, J. H., 376, 606, 658 Shefov, N. N., 190, 192, 317, 360, 361,

363, 501, 502, 505, 507, 635, 643, 657 Shepherd, G. G., 209, 215, 379, 383, 413,

416, 418, 630, 657, 663 Sherman, D. F., 186, 196, 624 Shimazu, M., 544, 662 Shklovskii, I. S., 92, 251, 255, 256, 322,

326, 367, 391, 484, 506, 553, 554, 562, 643, 657

Sholokhova, E. D., 377, 507, 649, 657 Shortley, G. H., 4, 13, 15, 612 Shrum, G. M., 138, 185, 349, 637, 641 Shuler, K. E., 469, 644 Shull, H., 426, 439, 657 Shuyskayai F. K., 501, 658 Sibley, W. L., 68, 335, 336, 668 Siedentopf, H., 321, 490, 601, 619 Silsbee, H. C., 226, 658 Simpson, J. A., 70, 146, 148, 150, 323,

Singer, S. F., 97, 325, 338, 648, 658 Skinner, N. J., 549, 669 Slater, J. C., 1 , 2, 278, 658 Slipher, V. M., 186, 348, 349, 350, 378,658 Sloan, R., 376, 658 Small, R., 153, 155, 186, 187, 189, 190,

Smith, C. A., 368, 554, 555, 556, 609 Smith, E. K., 88, 662 Smith, F. G., 144, 637 Smith, J. W., 224, 669 Smith, S. J., 545, 605, 606, 658 Smyth, H. D., 215, 658 Smyth, M. F., 323, 658 Snow, W. R., 248, 621 Snyder, E. J., 104, 668

638, 642, 658

198, 199, 214, 215, 650

Sominskii, M. S., 490, 649 Sommer, L. A., 186, 349, 350, 658 Sommerfeld, A., 270, 658 Spencer, L. V., 285, 286, 288, 289, 658 Spencer Jones, H., 350, 509, 51 1, 513, 516,

Spitzer, L., 91, 92, 96, 97, 659 Sprague, G., 139, 199, 212, 604, 624 Stebbins, J., 363, 504, 659 Stedeford, J. B. H., 248, 659 Steiger, W. R., 331, 332, 659 Stetson, H. T., 110, 659 Stewart, A. L., 255, 625 Stewart, D. T. , 251, 310, 313,544, 625,659 Stibbs, D. W. N., 116, 611 Stier, P. M., 247, 248, 659 Stille, U., 190, 379, 381, 408, 415, 607 Stoffregen, W., 100, 142,218,619,627,659 Stone, J., 503, 668 Stone, M. L., 220, 226, 622 Storey, L. R. O., 145, 278, 326, 329, 629,

659 Stormer, C., 70, 79, 110, 114, 117, 118,

125, 128, 129, 130, 131, 132, 133, 135, 147, 191, 214, 324, 325, 333, 334, 590, 659

652, 659

Stratton, J . A., 63, 64, 80, 81, 661 Strong, J., 35, 661 Strutt, R. J., see Rayleigh, Lord Struve, 0. (The Elder), 185, 661 Struve, 0. (The Younger), 101, 347, 509,

Stull, V. R., 384, 417, 450, 458, 463, 604,

Sugden, T. M., 544, 631 Sugiura, M., 67, 611 Sullivan, F. R., 109 Sumerlin, W. T., 516, 605 Sverdrup, H. V., 114, 661 Swings, P., 191, 318, 351, 352, 358, 363,

378, 384, 414, 441, 442, 465, 500, 504, 505, 511, 514, 518, 521, 590, 591, 619, 659, 661

66 1

615

T

Tamm, I., 272, 622 Tanabe, H., 495, 509, 518, 662 Tanaka, Y., 538, 544, 565, 632, 662

682 AUTHOR INDEX

Tandberg-Hanssen, E., 141, 148, 505, 519, 521, 653, 654, 662

Tcheng Mao-Lin, 186, 187, 200, 385, 418, 490, 491, 511, 512, 513, 514, 517, 616

Teller, E., 335, 646 Thomas, G. M., 106, 619 Thomas, J. A., 88, 662 Thomas, J. O., 478, 515, 529, 530, 651 Thompson, A. R., 149, 640 Thompson, N., 314, 662 Thomson, E., 300, 662 Thorson, H. M., 114, 125, 609 Thrush, B. A., 561, 637 Tikhov, G. A., 505, 662 Tohmatsu, T., 48, 505, 509, 547, 549, 552,

Tonks, L., 304, 662 Tonsberg, E., 125, 128, 136, 187, 191, 209,

Tousey, R., 497, 504, 563, 634, 651, 662 Townley, S. D., 347, 662 Troim, J., 143, 220, 627 Trornholt, S., 110, 113, 590, 662 Turner, R. G., 199, 663 Twiss, R. Q., 280, 281, 663

631, 662

380, 408, 415, 627, 635, 667

U

Unwin, J. J., 545, 599 Unwin, R. S., 220, 222, 224, 226, 228, 231,

Urey, H. C., 392, 663 233, 663

V

Vakulov, P. V., 326, 667 Valentine, J. M., 253, 283, 663 Vallance Jones, A., 101, 151, 157, 161, 171,

172, 174, 175, 186, 190, 193, 194, 198, 199, 204, 209, 210, 211, 214, 215, 366, 367, 368, 380, 388, 389, 425, 463, 480, 481, 482, 483, 501, 502, 504, 507, 514, 539, 626, 627, 630, 641, 643, 646, 663

Van Allen, J. A., 140, 141, 299, 326, 327, 328, 330, 534, 642, 664, 670

Van Biesbroeck, G., 509, 661 van de Hulst, H. C., 240, 421, 664 van Rhijn, P. J., 348, 486, 664

Van Vleck, J. H., 428, 664 Vassy, A., 104, 473, 490, 491, 504, 509,

518, 590, 591, 593, 664 Vassy, E., 104, 471, 473, 490, 491, 504,

509, 518, 593, 632, 664 Vawter, F. E., 220, 222, 227, 230, 235, 613 Vegard, L., 67, 101, 114, 125, 128, 132,

133, 134, 138, 140, 151, 186, 187, 190, 191, 192, 193, 194, 195, 196, 199, 200, 201, 202, 203, 204, 205, 208, 209, 215, 253, 255, 310, 313, 316, 349, 380, 404, 408, 415, 416, 542, 590, 622, 636, 655, 664, 666, 667

Veksler, V. I., 340, 667 Veller, A. E., 203, 667 Vernov, S. N., 326, 661 Vestine, E. H., 68, 71, 104, 106, 110, 139,

226, 326, 335, 336, 337, 609, 658, 668 Villard, 0. G., 221, 649 Vogan, E. L., 144, 227, 229, 234, 622, 627 Vogel, H., 348, 668 Volpi, G. G., 538, 544, 634 Vuks, M. F., 379, 611

w

Waddington, C. J., 331, 622 Waldrneier, M., 149, 668 Wallace, L., 151, 162, 163, 186, 187, 189,

190, 198, 199, 210, 211, 212, 213, 316, 368, 439, 476, 499, 500, 501, 502, 556, 639, 668

Walton, R. B., 330, 593 Wang, S. C., 220, 226, 622 Wark, D. Q., 212, 396, 503, 668 Warwick, C., 149, 150, 668 Warwick, J. W., 143, 325, 668 Watkins, C. D., 221, 231, 606, 627 Watts, J. M., 145, 669 Weaver, J. T., 132, 613 Webber, W. R., 71, 333, 334, 651 Weber, W., 416, 604 Weekes, K., 84, 548, 549, 594, 651 Weill, G. M., 135, 390, 425, 483, 597, 614,

Weiss, A. A., 224, 669 Weisskopf, V., 428, 669 Welch, J. A., Jr., 330, 593, 669 Weldon, R. G., 495, 654

669

AUTHOR INDEX 683

Wells, H. W., 142, 144, 611, 669 Wenzel, W. A,, 247, 249, 652 Wescott, E. M., 139, 628 Westfold, K. C., 304, 631 Whaling, W., 247, 249, 652 Whitaker, W. A., 330, 593, 669 White, F. W. G., 104, 107, 669 White, H. E., 16, 434, 485, 669 White, R. S., 339, 622 Whitford, A. E., 363, 504, 659 Wiechert, E., 348, 669 Wilcke, J. C., 133, 669 Wilkes, M. V., 548, 549, 669 Wilkinson, P. G., 193, 194, 211, 669 Williams, D. R., 125, 186, 187, 360, 376,

490, 491, 493, 495, 496, 505, 506, 507, 509, 511, 512, 513, 514, 515, 516, 517, 518, 597, 598, 650, 653, 654, 655, 658

Williams, S. E., 314, 662 Winckler, J. R., 141, 146, 147, 272, 331,

Wolnik, S. J., 186, 647 Wood, M. B., 150, 669 Wright, R. W., 549, 669 Wu, Ta-You, 537, 600

594, 622, 633, 645, 669

Wulf, 0. R., 302, 437, 521, 669 Wurm, K., 191, 669 Wynne-Edwards, H. S., 128, 641

Y

Yadav, H. N., 248, 613 Yano, K., 547, 629 Yarin, V. I., 502, 635 Yntema, L., 347, 348, 670 Yonezawa, T., 527, 670 Yoshida, S., 326, 670 Yugoro, T., 142, 626

Z

Zaborshchikov, F. Va., 139, 142, 670 Zacharov, I., 504, 637 Zelikoff, M., 546, 639, 651, 670 Zemansky, M. W., 381, 428, 643 Zhdanov, G. B., 346, 625 Zhuravlev, S. S., 199, 205, 670 Zollner, F., 185, 670

Subject Index

Boldface pages refer to definitions of terms or defining equations. Atoms and molecules are listed under their full names; thus OH appears under Hydroxyl. Band systems are listed under the molecule.

A

Absorption, 34; also see Radiation Absorption cross section, 7; also see Ab-

Absorption, scattering, or extinction coeffi-

ionization (ionospheric theory), 84, 88 ozone absorption, 61 radiative-transfer theory, in, 38, 84 radio waves in ionized atmosphere, 83 Rayleigh scattering, 61 spectral line, Doppler broadening, 7 spectral line, Doppler plus natural

spectral line, natural broadening, 12,

sorption coefficient

cients

broadening, 20

17-18 Activation energy, 31, 32 Active electrons, auroral, 296 Adiabatic invariants

flux or third, 335 longitudinal or second, 79, 335, 336f. transverse or first, 77, 78-79, 335f.

Airglow, 345; also see Dayglow; Spectrum, nightglow; Spectrum, twilightglow

discovery, 347-50 distinguished from aurora, 104, 345-47

ground reflection, 38 single scattering, 34, 38

Albedo

Ampkres law; see Maxwell’s equations Angle of solar depression, 394

computation of, 400-402 Angular dispersion, auroral particles ; see

Auroral particles in geomagnetic field ; Electron bombardment in aurora; Proton bombardment in aurora

Anomalous dispersion, 12-13 Appleton-Hartree formula, 275

Argus experiment, 330 Arrhenius equation, 31 Artificial airglows, 472-73, 545-47 Artificial aurora, 331-32 Astronomical component of light of night

Astronomical twilight, 401 Atlas of auroral spectrum; see Spectrum,

aurora Atmospheric properties; also see Dynamics

of upper atmosphere; and under each ionospheric region (D , E, Sporadic E, F)

sky, 351-52, 360, 504-05

acceleration of gravity, 576 airglow, obtained from, 98, 376,498, 502 aurora, obtained from, 209-213, 299 composition, 92, 576 density, 576 equivalent depth, 90, 575-76 exopheric temperature, 91, 97 heat balance, 35, 36, 95-99 molecular weight, mean, 91f. outer atmosphere, 96-97, 329 scale heights, 89f., 91, 576 temperature profile, 35, 95-96, 574, 576 thermal radiation, 367, 376

Atom exchange, 31 Atom-ion interchange, 30

Aurora, 217; also see Characteristics of aurora; Motions of aurora; Occurrence of aurora

rate coefficient, 30

artificial, 33 1-32 distinguished from airglow, 104, 345-47 distinguished from radio-aurora, 217 subvisual, 217

absolute intensity, 202, 300 bremsstrahlung, 141 excitation, 300, 31 1

Aurora of I t February 1958

684

SUBJECT INDEX 685

Forbush decrease of cosmic rays, 147 ionospheric absorption, 143 spectrum, 154, 171-72, 202, 211

Auroral caps, 101 Auroral particles in geomagnetic field

adiabatic invariance, 334-38 angular distribution, 341-43 artificial injection, 330-32 Cerenkov radiation, 272-79, 329 energy spectra, 338-43 geographic location of bombardment,

gyro-radiation, 279-82, 329 local acceleration, 338-41 trapped particles, 326-29

Auroral region, 68-69, 101 Auroral theory; see Auroral particles in

geomagnetic field; Solar particles and streams

332-38

Auroral transition; see Forbidden lines Auroral zones, 101f., 113

blanketing of F layer in, 142 departure from parallels of geomagnetic

explanations, 114-15, 332-38 locations of, 104, 106-07, 332f. periodic shifts in positions, 112-13 width, 108f. x-radiation in, 140-41

latitude, 71, 334f.

B

Balloon experiments airglow, 376, 465 bremsstrahlung, auroral, 141 cosmic rays, solar, low-energy, 146 daytime aurora, 116

Band, molecular, 5 ; also see under each molecule

branches of a, 5 origin, 5 system, 5

Barometric law, 90 Betatron acceleration, 339 Blackouts; see Ionospheric absorption Boltzmann excitation equation, 6, 24, 25,

Boltzmann-Saha equation, 28 Born approximation, 238, 270-71

26, 28, 208, 211

Bowen fluorescence mechanism, 318, 391,

Bragg curve, 249-50 Breakup, auroral, 138

485

bremsstrahlung, association with, 141 dependence on magnetic time, 139 hydrogen emission, 140, 203f. magnetic variations, association with, 140

aurora, association with, 141 auroral zone, in, 141, 299 breakup, association with, 141 ionospheric absorption, association with,

magnetic Gariations, association with, 141 primary electrons in air, as due to, 141,

primary electrons striking rocket appa-

production of thermal emission, 306f. secondary ionization produced by, 293 theory, high energies, 269-72 theory, low energies, 270

Bremsstrahlung, auroral

141, 293-94

269

ratus, 269

C

Calcium (Ca+) resonance lines abundance of atmospheric calcium, 482 origin of atmospheric calcium, 472, 482 twilight excitation, 425, 482-83 twilightglow height, 390, 482 twilightglow intensity and variations,

377, 389-90, 571 Cameras, wide-angle and all-sky

Davis-Elvey-Stoffregen, 101, 102 Greenstein-Henyey, 101, 105 Lebedinskii, 101

Cerenkov condition, 275 Cerenkov radiation

optical frequencies, airglow, 346 radio frequencies, auroral particles, 145,

solar radio bursts, 276 272-79

Chapman-Ferraro theory, 325 Chapman layer; see Ionosphere Characteristics of aurora; also see Forms

and structure of aurorae; Intensity distribution with height in aurora;

686 SUBJECT INDEX

Motions of aurora; Occurrence of aurora

activity, 124, 135f. brightness, 124f., 345, 508, 571 color, 124f. dimensions, 124, 128f., 255 duration, 124f. heights, 128f. orientations, 133f. simultaneity of aurorae borealis and

australis, 138 synoptic view, 136f.

Charge transfer, 30, 87 Chorus; see under Radio emission, auroral

Civil twilight, 401 Classical theory of radiation; see Radiation,

theory of Coherent scattering, 447 Collision frequency, 81 f. Collision strength, 29-30, 533; also see

Electron collision Collisional excitation, 28 ; also see Electron

collisions ; Hydrogen collisions; Ther- mal collisions

Color of aurorae; see Characteristics of aurora

Configuration, electron, 4 Conduction

and related

electric; see Current density thermal, 91, 98, 321, 502

Conductivity, electric 63, 80, 83 complex, 82

Conjugate points, see Lines of force, geomagnetic

Continental drifts, 72 Coptinuurn, dayglow, 484 Continuum, nightglow

absolute intensity, 360, 505 astronomical component of night-sky

blue, 350-52, 360 correlation with green line, 517 excitation and identification of source,

green, 351, 359-60 height, 489, 491, 497 intensity distribution, 360, 505

Corona, solar, 321-23, 502 Coronal transition of [O], 96, 536-37

continuum, 351-52, 360, 504-05

543-45

Coronas, auroral, 117f. occurrence in magnetic zenith, 67, 117-

18, 123 Correspondence principle, I5 Cortie effect, 112, 324 Cosmic noise, 142; also see Ionospheric

Cosmic rays; also see Forbush decrease absorption

airglow produced by, 217 auroral and magnetic activity, association

effective geomagnetic dipole, 70-71 effective geomagnetic equator, 70 eleven-year variations, 147, 324 ionospheric absorption produced by, 143 low energy, solar, 143, 146, 148, 323 secular variations, 71

Covariance groups, 5 16- 17 theory of, 547f.

Cross section, 28; also see Absorption coefficient per atom; Electron collisions; Hydrogen collisions; Thermal collisions

with, 146-47

Critical level, 91, 97, 99 Critical reflection of radio waves, 83

ionosphere, 83 radio-aurora, 235-36, 242-43 sporadic E, 88

conduction, 11, 63, 80, 82 polarization, 11, 82

Current density

Curve of growth, 18 Cyclotron frequency ; see Gyro-frequency

D

Daily variations, aurora; see under Occur-

Damping constant classical, 9, 13 quantum mechanical, 15, 17

rence of aurora

Dawn chorus; see under Radio emission, auroral and related

Dayglow (Day airglow), 376; also see Continuum, dayglow; and under each atom and molecule

balloon observations, 465 eclipse observations, 391 rocket experiments, 358, 390-91

SUBJECT INDEX 687

theoretical estimates, 390, 466, 478-79,

Daytime aurora; see Occurrence of

Deactivation, auroral, 315-17, 319 Deactivation probability, 427 Declination

484, 571

aurora

astronomical, of the sun, 403 geomagnetic; see Geomagnetic field

Density; see Atmospheric properties; Electron density

Detailed balancing, 14, 28 Dielectric constant, 80f. Diffuse aurora, I 17f.

42, 202, 209

Diffusion, atmospheric

detection of faint background emission,

magnetic activity, relation to, 140

atmospheric constituents, 90f., 522, 547 ions in F region, 87, 478, 524-31

Diffusive equilibrium, 90, 97 Dipole, classical oscillating absorption by, 10-13

damping of; see Line broadening, natural emission from, 8-10 natural frequency of, 9-13

intensity rules for Zeeman component, 434

Dipole, magnetic; see Forbidden transitions and lines; Geomagnetic field; Magnetic field; Magnetic moment

Dipole (electric) radiation, 9, 15

Dipole moment, 9, 15, 20-21 Dirac &function, 51, 243, 274 Dirac’s theory of radiation, 15 Discharges, atmospheric

airglow, 521 auroral, 217, 292, 300-302

Dissociation energy, 23, 32 Dissociative recombination, 30, 87

airglow excitation, 313-14, 420, 476-80,

auroral excitation, 313-14 523-32

Doppler broadening, 4, 7, 19-20, 32, 213; also see Hydrogen emission in aurora; Temperature, Doppler

radio-aurora reflections, 225-26 sodium D lines, 445, 455-56, 460 width at half intensity, 7

Doppler shift, relativistic, 280

Drapery, auroral; see Forms and structure

D region; also see Ionospheric absorption of aurorae

electron density, 577 ion production, 88-89, 577 radio reflections during aurora, 142 recombination, 87, 577

centrifugal force, 77 crossed electric and magnetic fields, 75 dipole field, 99, 343 perpendicular gradient in magnetic

field, 76 total for inhomogeneous magnetic field,

77 Dynamics of upper atmosphere; see

Diffusion, atmospheric; Tides, atmospheric; Turbulence; Winds and circulation, upper-atmospheric

Drift velocity

E

Earth currents, 72

tions, 138-39 Earthlight, 347-48 Efficiency of auroral emission, 297f. Einstein coefficients, 13-14; also see

Einstein correction (for relative intensities),

Electron attachment, 86-87 Electron bombardment in aurora; also see

Auroral particles in geomagnetic field; Electron collisions

angular dispersion, 291, 338f. back-scatter aurora, 290-9 1 bremsstrahlung production, 269-72, 282 Cerenkov radiation, 272-79 energy deposition with height, 285,

energy spectrum, initial, 272, 282-83,

relation to aurora and magnetic varia-

Transition probability

16

288-92

320, 338f. flux, 272, 282-83 gyro radiation, 279-82 ionization yield, 283, 290, 293 laboratory experiments associated with,

254

688 SUBJECT INDEX

monoenergetic, monodirectional beam, theory for, 286-92

photon yield, 251, 283 secondary electrons from, 292-300

Electron collisions, 29; also see Electron

airglow excitation, 98, 475, 523, 533-36,

auroral excitation, 207-16, 292-300, 31 9 cross sections, collision strengths, 310,

deactivation, 316, 319, 532-33 energy loss, fast particles, 271, 292 photon yield, 251 rotational temperatures for excitation by,

thermal emission from, 304-08

bombardment in aurora

566

315, 532-33

26, 208

Electron density; also see Atmospheric properties

auroral, 294-97, 300 effect on absorption coefficient, 11 effect on index pf refraction, 11

Electrons in space; see Auroral particles in geomagnetic field; Interplanetary gas; Solar particles and streams

Emission, theory of; see Radiation Energy deposition in aurora; also see

Electron bombardment in aurora; Intensity distribution with height in aurora; Proton bombardment in aurora

total, 197f., 283

atomic configurations, 188-91, 579 atomic levels, metastable, 579 molecular, 193, 195

Energy-level diagrams

Energy spectra, auroral particles; , see Auroral particles in geomagnetic field; Electron bombardment in aurora; Proton bombardment in aurora

Equation of time, 401

Equivalent depth, 90; also see Atmospheric

Equivalent width, 19 E region; also see Sporadic E

table of, 403

properties

electron density, 577 ion production, 87-88, 440-41, 577 recombination, 87, 577

Escape, atmospheric; see Exosphere Evaporation of atmosphere; see Exosphere

Excitation function, 310 Excitation mechanisms, airglow, 521 -22;

also see Dissociative recombination ; Electron collisions; Particle bombardment, airglow ; Photochemical reactions ; Resonant and fluorescent scattering; Thermal collisions; and under each emitting atom and molecule

Excitation mechanisms, auroral; also see Electron bombardment in aurora; Proton bombardment in aurora; Secondary electrons, auroral

particle impact, fast, 308-313 radiative excitation, 317-18 thermal collisions, 299-300, 313-17

Excitation mechanisms, general, 27-32 Exosphere, 91

solar, 322 terrestrial, 96-97, 99

Exponential integral, 46, 263f. Extinction, 34, 393

coefficient, 38, 61, 421 ; also see Absorp- tion, scattering, or extinction coefficient

Extraordinary wave, 276

F

Faraday rotation, 227 Faraday’s law; see Maxwell’s equations Fermi mechanism, 338 Flaming aurorae, 118f., 135

ionospheric absorption, association with,

scintillation of radio stars, association

Flares, solar, 148-49 ; also see Solar activity

143

with, 144

aurora, association with, 147-50 cosmic rays from, 143, 146 delay time between flares and magnetic

factors affecting geophysical effective-

ionospheric absorption association with,

magnetic storms, association with, 147-50 x-radiation from, 88-89

Fluorescent scattering; see Bowen fluores-

storms, 148

ness. 148

143

SUBJECT INDEX 689

cent mechanism; Resonant and fluorescent scattering

monochromatic, 36 net outward, 36

Flux

Forbidden transitions and lines, 5, 18, 579-81 ; also see Transition probability; and under each atom

electric quadrupole, 19, 434 magnetic dipole, 19 nomenclature for, 5, 6, 579-81

Forbush decrease, 147, 324 magnetic storms, association with, 146-47

Forms and structure of aurorae, 116-24, 343; also see Breakup; Coronas; Diffuse aurora; Flaming aurora; Homogeneous arcs and bands; Pul- sating aurora; Ray structure

Fossil magnetism, 71 Fourier analysis of radiation, 10-1 2,224-25,

Franck-Condon factor, 22; also see under 273-74

each molecular band system relation to strength, 22-23

Franck-Condon principle, 22 Free-free transition, 269, 306 F region

airglow emission from, 87, 441, 476-79 bifurcation of, 87, 578 blanketing of, 142 cooling by conduction, 96 cooling by thermal radiation, 96 formation and ion production, 30, 87,

heating mechanisms, 96-99 recombination in, 87, 441, 578 rising associated with magnetic disturb-

vertical diffusion of ions, 87, 478, 524-31 Frequency of auroral occurrences ; see

Occurrence of aurora f-value; see Oscillator strength

96, 440-41, 578

ances, 141

G

Gegenschein, 505 Geocorona, 358, 562f. Geomagnetic coordinates, 65, 66; also see

Geomagnetic time

maps in, 68, 69 pole positions, 64, 66 relation to geographic coordinates, 66

Geomagnetic field; also see Auroral particles in geomagnetic field; Geo- magnetic coordinates ; Geomagnetic variations; Magnetic zenith and horizon

centered dipole, 64-71 cosmic-ray dipole, 70 declination, 67 eccentric dipole, 69-71 external part, 63 geomagnetic poles, 64 harmonic analysis of, 64 inclination, 66 lines of force, 65-68, 150 magnetic or dip poles, 70 magnetic meridian, 67 magnetic moment of centered dipole, 64 propagation of radio waves through

ionosphere, 80 Geomagnetic shell, 330 Geomagnetic time, 67

magnetic midnight, 67, 114 magnetic noon, 67

Magnetic storms disturbance daily variation, 72 disturbance field, 72 internal origin, 71-72 lunar, 72 magnetic bays, 73 micropulsations, 73 secular, 71 storm-time, 72 sudden commencements, 73

Atmospheric properties

forbidden transitions and lines

571

132, 202

Geomagnetic variations, 63, 71f.; also see

Gravity, acceleration of, 89-90; also see

Green line; also see Oxygen (0 and Of)

auroral intensities, 101, 124f., 197, 508,

auroral intensity distribution with height,

auroral temperatures, 212 excitation by electron collisions, 3 10-12,

excitation in nightglow, 523, 541-42 identification, 349-50

319

690 SUBJECT INDEX

nightglow association with ionospheric

nightglow association with magnetic

nightglow correlations with other emis-

nightglow height, 489-91, 495 497, 498 nightglow mean intensity, 506, 571 nightglow patchiness, 517-20 nightglow temperatures, 349, 503 nightglow variations, daily, 350, 5 1 1-12,

nightglow variations, latitudinal, 509-1 1,

nightglow variations, sunspot-cycle, 516 nightglow variations, yearly, 510-1 1,

night sky, contribution to total visual brightness of the, 350

occurrence frequency of brightness, airglow and aurora, 124-25, 345,

variations, 516

activity, 516

sions, 516-17

548-50

519

513-15, 519

508-09 polarization, 206, 485, 508 thermal-electron collisions, 3 I 1 twilight enhancement, 377, 379

Green’s function, 237, 273 Greenstein-Henyey camera; see Cameras,

wide-angle and all-sky Guiding center, 77 g-value, 424

Gyrofrequency, 74 Gyro radiation, 145, 279-82, 319, 329

table of, 425

H

Heating of atmosphere ionosphere during aurora, 36, 99, 297f. ozone layer during aurora, 147 rising of F layer, as cause of, 141

Heights of aurora; see Characteristics of

Heights of nightglow; also see under each aurora

atom and molecule indirect methods, 498 rockets, 496-97 triangulation, 495-96 van Rhijn method, 348, 486-94

Heights of twilightglow; also see Screening height and under each atom and molecule

actual, for known screening height,

apparent, closed solution, 396, 421 apparent, general solutions, 394-97, 421 apparent, horizon observations, 398-99 apparent, iteration solution, 394-97 apparent, vertical plane through the sun,

curve-fitting method, 416 tables, 397, 398 transmission function, method of, 416f. zenith-horizon comparisons, 398, 407-1 I zenith-horizon method, generalized, 417

atmospheric escape, 9 1-92 auroral bombardment, 244, 254, 3 18 auroral emission, 179, 192, 244, 254 auroral excitation, 3 17-1 8 source of atmospheric, 91-92

405-07

397-98, 421

Helium

Homogeneous arcs and bands, I17f.; also see Breakup, auroral

hydrogen emission, 140, 203f. motions toward low or high latitude,

occurrence with positive magnetic bays,

reappearance after breakup, 140 role in synoptic development, 136f.

135-40

139

Honl-London formulae, 26 Hour angle of the mean sun, 401 Hydrogen Balmer emission in night sky;

also see Lyman alpha broadening, 359 discovery, 359, 363 excitation, 425-26, 562-64 intensity, 359, 506, 571 polarization, 564

Hydrogen collisions ; also see Proton bombardment in aurora

cross sections, 247-49 excitation-ionization processes, 30, 245

Hydrogen emission in aurora; also see

altitude dependence, 253, 256, 266-68 breakup, relation to, 140, 203f. daily variation, 140, 203f. discovery, 191-92, 255

Proton bombardment in aurora

SUBJECT INDEX 69 1

Doppler broadening and shift, profiles,

homogeneous arcs, 140, 203f., 256 intensities, absolute, 197-99 intensity variations, 203-205 latitude dependence, 201 moments of profiles, 262 radio-aurora, association with, 230 rayed aurora, 140, 203f. ultraviolet, 197-99, 3 18 wavelengths and transitions, 179

geomagnetic disturbances, 325-26 ionospheric heating, 98, 99, 217, 302-03

Hydrostatic equilibrium, 89 Hydroxyl (OH) Meinel (vibration-rota-

tion) band system

170, 191-92, 206-07, 256, 262, 268

Hydromagnetic waves

band structure, 367, 556-57 discovery, 363 excitation mechanisms, nightglow, 558-

laboratory production, 367, 368, 559 molecular constants, 368 nightglow correlation with Na, 516-1 7 nightglow heights, 490-91, 497, 498, 566 nightglow intensity dependence on tem-

nightglow mean intensities, 506-07, 553-

nightglow patchiness, 518 nightglow spectra and tracings, 171-72,

nightglow temperatures, 500-02, 556-57 nightglow variations, 513, 514 nightglow vibrational populations, 24,

rotational line and branch intensities,

rotational lines, wavelengths, 368-75 transition probabilities, 554 twilight enhancement, 377 wavelength tables, 368-75

61

perature, 502, 560, 566

58, 571

361-66

554-55

556-57

Hyperfine groups, sodium D , 429, 446

I

Inclination; see Geomagnetic field Index of refraction

complex, 10-11, 81f., 275f.

real, 11-12, 82f., 275 f. Induced captures, 28 Induced emission, 13-14, 28 Intensity

equivalent mean, 36f. integrated, 36f. mean, 36f. specific, 36f.

Intensity distribution with height in aurora, 42, 128f., 132f., 202, 253, 255, 266-68, 298

Intensity rules hyperfine structure, LS coupling, 434,

Zeeman components, 434 485

International brightness coefficient, 124,

Interplanetary gas; also see Solar particles

conduction into the atmosphere, 91, 98,

density, 321 heating by conduction, 321-22 lifetime, 322 magnetic field, 147, 322-25 neutral hydrogen, 88, 322 outward expansion, 321-22 solar wind, 321 temperature, 321

57 1

and streams

502

Ionosphere; also see Ionospheric absorption; and each Region (D , E, Sporadic E, and F )

airglow, association with, 87-89, 440-41, 516

Chapman layer, 84-86 effective recombination coefficients, 577-

heating during aurora, 36 ion production, 86-89, 577-78 radio propagation through, 80-84 recombination mechanisms, 86-89, 577-

78

78 Ionospheric absorption

aurora, association with, 141-43, 294 auroral bremsstrahlung, association with,

magnetic activity, association with,

radio emission from aurora, association

141, 293-94

143

with, 144

692 SUBJECT INDEX

solar low-energy cosmic rays, caused by,

solar ultraviolet light, caused by, 148 theory, no magnetic field, 80-84

Ionospheric disturbances, 141f. ; also see

Ionospheric absorption International Geophysical Year, 100, 101,

106, 109, 114, 135, 136, 152, 157, 201, 268, 320, 326, 509, 510, 531

143, 146-47

Isoaurores, 107f. Isochasms, 104, 106, 334f. Isothermal region of atmosphere, 91, 97, 99

K

Kirchoff’s law, 305, 308, 319

L

Legendre function, associated, 64 Level

atomic, 4, 16 degenerate, 5 rotational, 5 vibrational, 5

Lifetime, atomic or molecular, 13, 17; also see Transition probability

Light of night sky; see Nightglow; Astro- nomical component of light of night sky

Line broadening collisional, 20 Doppler; see Doppler broadening instrumental, 499 natural, 9-10, 12-13, 17, 19-20, 32

Lines of force, geomagnetic, 65; aZso see

Geomagnetic field conjugate points, 68, 330 distortion from Earth’s rotation, 70-71 field strength along, 65 inclination to horizontal, 66, 150 intersection with Earth, 66 length, outside Earth, 67 numerical computations of, 67-68

atomic, 4; also see Forbidden and Permitted transitions and lines under each atom

Lines, spectral

classical theory of, 7-13

forbidden atomic; see Forbidden transi-

quantum theory of, 13-26 rotational, 5

Liouville’s theorem, 96-97, 343 Lithium (Li) resonance lines

tions and lines

abundance of atmospheric lithium, 483-

origin of atmospheric lithium, 483-84 twilight excitation, 425, 483-84 twilightglow height, 390 twilightglow intensity and variations,

377, 390, 483, 571 Lorentz force, 74 Lorentz transformation, 75 LS coupling, 16 Luminosity distribution; see intensity

distribution with height in aurora Lyman alpha

84

auroral, 197-99, 318 night sky, 88, 322-23, 358, 425-26, 497,

solar, 88, 323, 426 562-64, 571

M

Magnetic field, 63; also see Geomagnetic field

dipole, 64, 65f., 99 interplanetary, 147, 322-25 lines of force, 65f. motion of charged particle in, 73-79 scalar potential, 63, 99 solar, 150, 323 solar particle streams, 325, 338f.

Magnetic induction, 74; also see Magnetic

Magnetic midnight; see Geomagnetic time Magnetic moment

charged particle in external magnetic field, 78

dipole, 64 Earth’s centered dipole, 64

Magnetic mirror point, 79, 335 Magnetic reflection, 79 Magnetic rigidity or stiffness, 74 Magnetic storms, 72; also see Geomagnetic

field

variations airglow, association with, 516

SUBJECT INDEX 693

aurora, association with, 138-40 bays, 73 daily variations, 72, 115, 139, 226 earth currents, association with, 139 eleven-year variation, 1 10- 1 I 1, 138 extraterrestrial currents, 325 first phase, 73 Forbush decrease, association with, 146-

hydrogen emission in aurora, association


ionospheric currents, 134, 139, 326 main phase, 73 motions of magnetic zenith, 133 M-regions, association with, 73 radio-aurora, association with, 226, 231 -

radio emission, association with, 144-46 rising of F region, association with, 141 scintillations of radio stars, association

seasonal variation, 138 solar activity, association with, 73, 147-50 solar cosmic rays, association with, 146-

sporadic E , association with, 141-42 sudden commencements, 73 twilightglow, association with, 388, 441,

47

with, 140

142-43

32

with, 144

47

480 Magnetic time; see Geomagnetic time Magnetic zenith and horizon, 67

altitude and azimuth of zenith, 67 auroral zenith, relation to, 133, 150 occurrence of coronas near zenith, 67

Matrix element for dipole transitions, 15, 17, 20-23, 25; also see Strength; Transition probability

Maxwell-Boltzmann law, 2 Maxwellian distribution of velocities, 2, 3,

deviations from, 4, 212-13, 299-300,

exosphere, in the, 97 mean velocity in, 2, 3 most-probable velocity in, 2, 3 root-mean-square velocity in, 2, 3

24, 28, 29, 319

321-22, 503

Maxwell’s equations, 11, 80f. Mesosphere, 95

Milne relation, 28 Minauroral belt, 68-69, 101

aurorae observed in, 104 Mixing, atmospheric, 90, 92f. Model atmosphere, 89f. ; also see Atmos-

Molecular weight, mean atmospheric, 89,

Monochromatic equilibrium, 447 Morphology, auroral, 100; also see Charac-

teristics of aurora; Occurrence of aurora

pheric properties

92; also see Atmospheric properties

Morse potential function, 23, 24 Motions of aurora, 135-38, 226; also see

Occurrence of aurora auroral zenith, 133 daily variations, 139-40 east-west, 136 latitude, in, 135-40 magnetic variations, association with, I40 radio aurora, association with, 226 sporadic E, preceded by, 142

Motions of charged particles in fields, 73-79; also see Adiabatic invariants

converging magnetic field, 77-79 inhomogeneous magnetic field, 76-79 uniform electric and magnetic fields, 75 uniform magnetic field, 74

aurora, association with, 148 identification of, 73, 149-50 magnetic activity, association with, 73,

recurrence tendency, 27-day, 148

M-regions

148

Multiplet, 4 Mutual neutralization, 31, 86

N

Nebular transition; see Forbidden lines Nightglow, 347; also see Spectrum, night-

glow discovery, 347-50 distinguished from aurora, 104, 345-47

Nitric oxide (NO and NO+), atmospheric airglow continuum, 484, 543-44 formation, 94-95 ion production in D region, 88 recombination in E and F regions, 87

694 SUBJECT INDEX

Nitrogen (N and N+), atmospheric atomic

Nitrogen (N and N+) forbidden transitions relative abundance, 95

and lines auroral excitation, 310-1 3 auroral height and latitude variations,

auroral intensities, 197f. auroral occurrence, 176, 182f., 187 cross sections, collision strengths for

excitation, 310, 319 deactivation, 480, 532 nightglow excitation, 531-32, 534, 535 nightglow occurrence, 359 term and level structure, 176, 579-80 transition probabilities, 579-80 twilight excitation, 424, 425, 479-80 twilightglow intensity and variations,

wavelengths, 176, 579-80

200f.

377, 386-88, 480, 571

Nitrogen (N and N+) permitted transitions and lines

auroral excitation, 3 13 auroral intensities, 197f. auroral occurrence, 182f., 187, 189-90 term and level structure, 178-79, 190-91 wavelengths, 178-79

Nitrogen (N,) First Positive band system, 193

auroral excitation, 216 auroral intensities, 197f., 216 auroral occurrence, 180, 184f., 192-93 auroral rotational temperatures, 21 1-12 band heads and transitions, 180, 193 enhancement in type-B aurora, 125, 202 Franck-Condon factors, 199

Nitrogen (N,) Lyman-Birge-Hopfield band system, 193

auroral occurrence, 196 Nitrogen (N,) Second Positive band system,

193 auroral excitation, 215-16, 310 auroral intensities, 197f. auroral occurrence, 180, 182f., 192-93 band heads and transitions, 180, 193 Franck-Condon factors, 199 vibrational temperature in aurora, 21 5 ,

Nitrogen (N,) Vegard-Kaplan band system, 310

193

airglow occurrence, 352, 358, 491 auroral excitation, 216 auroral intensities, 197f., 216, 316 auroral occurrence, 181, 182f., 193-94 band heads and transitions, 181, 193 Franck-Condon factors, 199 height variation, 203 laboratory production, 193-94 rotational temperatures in aurora, 21 1 transition probability 194, 21 1

Nitrogen (N, and N,+), atmospheric molecular

dissociation 93-95 ion production in E and F regions, 87,

limitation on ionospheric N,+ from twi-

photoionization, 93 recombination, 94 sporadic E, constituent of, 88, 577

96, 440-41

light intensity, 440-41

Nitrogen (N,+)First Negative band system,

auroral excitation, 21 3-1 5, 309- 10, 3 17 auroral intensities, 1971. auroral occurrence, 181, 182f., 194 band heads and transitions, 181, 193-94 dayglow intensity, 571 Franck-Condon factors, 199,439 ion densities in sunlit aurora, 317 limitation on ionospheric N,+ from

twilight intensity, 87, 392, 440-41 nightglow excitation, 534-35 nightglow occurrence, 358 profile, twilightglow and sunlit aurora,

rotational structure, 161, 442-44 rotational temperatures in aurora, inter-

pretation of, 26, 208-1 1 transition probability, absolute, 439 twilightglow discovery, 378 twilightglow excitation, 392, 425-26,

twilightglow height, 413-14 twilightglow intensity, 376-78, 387, 392,

twilightglow variations with magnetic

vibrational development, auroral, 200-01,

194

442-44, 485

437-44

571

activity, 388, 441

213-16, 310 Nitrogen (Nz+) Meinel band system, 194

SUBJECT INDEX 69 5

auroral excitation, 309-10 auroral intensities, 197f. auroral occurrence, I8 I , 184f., I94 auroral rotational temperature, 2 I2 band heads and transitions, 181, 193-94 Franck-Condon factors, 199 interpretation of rotational temperatures

for excitation by electron impact, 26 Noise, audible auroral, 147 Nomogram for spherical triangles ; see

Spherical triangles Non-polar aurora, 347-48, 521 Nuclear explosions, 330-32, 484

V

Observing stations, aurora-airglow

Occurrence of aurora list of, 572-73

bremsstrahlung, association with, 140-41 daily variations, 114-16, 135, 136 daytime, 115-16 D-region radio reflections, association

Forbush decrease, association with, 146-

frequency distribution of brightness,

frequency of, 106, 109f., 124 geographic, 100-09 hydrogen emission, association with, 140 ionospheric disturbances, association

magnetic activity, association with, 133,

radio-aurora, association with, 217-18 radio emission, association with, 144-46 recurrence tendencies, 148 seasonal variations, 112-13, 134 solar activity, association with, 109-12,

solar cosmic rays, association with, 146-

yearly and 11-year variations, 109-12

with, 142

47

124-25, 345, 508

with, 141-44

138-40

147-50

47

O H ; see Hydroxyl Ohm’s law, 80, 82 Optical thickness

slant, 38

vertical, 38f. Ordinary wave, 276 Orientations of aurorae ; see Characteristics

Oscillator strength (f-value), 7, 13, 18-19; of aurora

also see Transition probability relation to strength, 18 relation to transition probability, 18

Overlap integral, 21-22 relation to strength, 22-23

Oxygen (0 and O+), atmospheric atomic ion production in F region, 87 principal photochemical reactions, 92-95

Oxygen (0 and OA) forbidden transitions and lines; also see Green line; Red lines

auroral excitation, 310-12, 319 auroral intensities, 197f. auroral occurrence, 176, 182f., 185-86 coronal transition, 62p, 96, 536-37 cross sections, collision strengths for

excitation, 3 10, 3 19 deactivation, 3 17 laboratory excitation, 349 nightglow, 349-50 term and level structure, 176, 349-50,

transition probabilities, 579-80 wavelengths, 176, 349-50, 579-80

579-80

Oxygen (0 and Of) permitted transitions and lines

auroral excitation, 3 13 auroral intensities, 197f. auroral occurrence, 177-78, 182f., 187-89 dayglow intensities, 484, 571 term and level structure, 177-78, 188-89 twilightglow intensities, 391, 484 wavelengths, 177-78

Oxygen (0,) Atmospheric band system,

auroral occurrence and intensities, 18 1 ,

auroral rotational temperatures, 21 2,

band heads and transitions, 181, 195 band origins, 152, 360 deactivation, 361, 540 excitation in aurorae, 312, 316, 318 excitation in nightglow, 538-41, 547 fluorescence excitation of 0-1 band, 35,

194-95

185, 194

317, 318

total, 38f. 318, 361, 377, 425, 539

696 SUBJECT INDEX

Franck-Condon factors, 199 nightglow correlation with greenline, 51 7 nightglow heights, 491, 498 nightglow intensity, 506, 539, 571 nightglow rotational temperatures, 499-

nightglow transitions, 360-61 nightglow variations, 513, 514 twilight enhancement, 377

500

Oxygen (0,) Chamberlain (blue-airglow) band system, 195

deactivation, 540 excitation in nightglow, 538-40 nightglow correlation with green line,

nightglow intensity, 539 nightglow transitions, 353-58 nightglow variations, 515 wavelength tables, nightglow features,

Oxygen (0,) Herzberg band system, 195

517

358

deactivation, 540 excitation in nightglow, 538-40 nightglow correlation with green line, 5 17 nightglow heights, 491, 497-98 nightglow intensity, 505, 539 nightglow rotational temperatures, 500 nightglow transitions, 352-57 nightglow variations, 5 13-1 5 nightglow vibrational populations, 24 wavelength tables, nightglow rotational

lines and band origins, 358 Oxygen (0,) Herzberg continuum, 92 Oxygen (0,) Infrared Atmospheric band

system, 194-95 auroral excitation, 31 8 auroral occurrence and intensity, 18 1,

band heads and transitions, 181, 195 band origin, 152 deactivation, 481 fluorescence excitation of 0- 1 band, 425,

Franck-Condon factors, 199, 481 nightglow intensity, upper limit, 539-40 transition probability, 481 twilight excitation, 480-82 twilightglow intensity and variations, 377

185, 194-95

481, 539

388, 571

Oxygen (0,) Schumann-Runge continuum,

Oxygen (O? and O,+), atmospheric molec- 92, 195, 318, 385, 421, 475

ular ion production in E region, 87-88 lifetime for dissociation, 93 photochemical reactions, 92f. photodissociation, 92f. recombination in E and F regions, 87

Oxygen (O,+) First Negative band system, 195

auroral excitation, 3 12, 3 14- 15 auroral occurrence and intensities, 18 1 ,

band heads and transitions, 181, 195 enhancement in type-B aurora, 125,

Franck-Condon factors, 199

absorption of auroral ultraviolet, 36 enhanced thermal emission in aurora, 147 extinction produced by, 43f., 57f., 61,

formation of, 92f. mesosphere heating by, 95 mechanism of OH excitation, 558-60

184, 195-96

202, 312, 314-15

Ozone (0,)

488

P

Parallactic photographs, aurora ; see Photo-

Partial reflection graphs, auroral

radio-aurora, 236-38, 242-43 reflection coefficient, 237 sporadic E, 88

Particle bombardment, airglow, 328, 346, 392, 441, 522, 534-36

secondary electrons, 535-36 Particles in space; see Auroral particles in

geomagnetic field ; Interplanetary gas ; Solar particles and streams

Partition function, 6 Passive electrons, auroral, 296 Perfect-gas law, 89 Permanent aurora, 347-48, 521 Permeability, 80f. Permitted transitions and lines, atomic;

see under each atom twilight screening height, 482 Phase velocity of light, 12

SUBJECT INDEX 697

Photochemical equilibrium, local, 93f. Photochemical reactions, 28-32; also see

under each atom and molecule airglow, 538-45, 553-61, 564-66 atmospheric composition, affect on, 92f. aurora, 314-15

Photadissociation, 27, 92f. Photoionization, 27, 94f.

Photometric corrections ionosphere, formation of, 87f.

airglow, absolute intensities and background corrections, 40, 46-49, 55-62,

airglow, height measurements, 40,46-49,

aurora, intensity distribution with height,

aurora, measurement of faint background

aurora, spectral corrections, 41 -45

504-07

55-62, 486, 492-94

41-45

emission, 41-45

Photographs, auroral, Frontispiece, 102-03, 104, 118, 119, 120, 121, 122, 123, 126-27, 137

first, 128 parallactic, 126f., 133 time lapse, 100-105

Pitch angle of particle in magnetic field, .79 Planck’s black-body radiation law, 14, 28,

Plane of scattering, 430 Plane-parallel atmosphere, 34, 55 Plasma frequency, 83, 275f. Plasma oscillations, 145, 303-04 Polar blackouts; see Ionospheric absorption Polarization, electric

current, 11, 82 per unit volume, 11, 82, 303

Polarization, electromagnetic aurora, optical, 205-06 daytime sky, 58 green line, 485, 508 gyro radiation, 279f. hydrogen, night sky, 358, 563-64 hyperfine structure, effect of, 428f.,

intensity rules, 434 light of night sky, 348, 507, 563-64 radiative transfer theory, 39, 58f. radio-aurora, 226-27 red lines, 206, 485, 508

304

563-64

sodium, twilight, 382, 434-37, 485 theory, resonance scattering, 206, 428-37 zodiacal light, 321

First, 114, 134 Second, 115, 117, 134, 379

Polar Years, International

Post-twilight enhancement, 376; also see

Potassium (K) resonance lines twilight excitation, 425, 484 wavelengths, 484

Potential energy, molecules, 32

Potential, magnetic; see Magnetic field Precipitation curve, aurora, 114f., 134,

333-34 Primary auroral particles, 292; also see

Auroral particles in geomagnetic field ; Electron bombardment in aurora; Proton bombardment in aurora

Principle of spectroscopic stability, 430 Principles of invariance; see Radiative

transfer theory Progression, spectral, 5 Profiles; also see Doppler broadening;

Hydrogen emission in aurora; Line broadening

Red lines

lines, spectral, 17, 19-20 Propagation of radio waves; see Radio

waves, propagation of Protons in space; see Auroral particles in

geomagnetic field ; Interplanetary gas ; Solar particles and streams

Proton bombardment in aurora, 244-69; also see Auroral particles in geomagnetic field; Cosmic rays; Hydrogen collisions; Hydrogen emission in aurora

altitude dependence of emissions, theory

angular dispersion, 258, 260f., 319, 320,

Balmer decrement, 249-50 collisional mechanisms of excitation-

energy spectrum, initial, 253, 262, 263-

Of, 256, 266-68, 290, 319

338f.

ionization, 245

69, 319, 320, 328f.

gyro iadiation, 281-82 historical review, 255-57

flux, 253-54, 258, 268, 284

698 SUBJECT INDEX

importance as source of auroral emis-

ionization yield, 249-54, 267, 290 laboratory experiments associated with,

moments of profiles, 260-62, 265-66 monoenergetic, theory, 245-54, 257-63 N2+/H intensity ratios, 250-55 photon yields, 249-54, 258, 262, 267-68,

profiles, theory of, 255-66, 319 ray structures, as source of, 253 residual range, 247, 250 rocket experiments, 268-69, 320 rotational temperatures, interpretation

secondary electrons from, 292-300 statistical equilibrium, 245-47


magnetic activity, association with, 140 scintillations of radio stars, association

sion, 250-55, 266, 268-69

254-55

319

of, 208-09

Pulsating aurora, 117f., 135

142

with, 144

Q

Quadrupole (electric) radiation; see For-

Quantum numbers bidden transitions and lines

atomic inner (J), 5 molecular rotation (J, K), 5, 25, 26 vibration, 5, 22-24

R

Radar reflections from aurora, see Radio-

Radiant point, see Magnetic zenith Radiation reaction, 8 Radiation, theory of

aurora

classical theory of absorption, 10-13 classical theory of emission, 8-10 excitation, 27-32 line absorption, 27 molecules, 20-27 quantum concepts, 13-20

Radiative association, 31, 32

Radiative dissociation, 31 Radiative recombination, 27, 28, 30 Radiative transfer theory

atmospheric problems with, 35 characteristic function, 58 equation of transfer, 38, 39f. fluorescence of 0,, 35, 318, 361, 377,

geocoronal Lyman alpha, 563 mesospheric emission, 537 photometry of airglow, 40, 46-49, 55-62,

photometry of aurora, 41-45 polarization, 39, 58f., 449-50 principles of invariance, 49f. resonance emission, 450-66 scattering and transmission functions,

sodium D lines, airglow, 34, 35, 417,

standard solutions, 58 Stokes parameters, 58 thermal radiation at 62p, 537, 552 X- and Y-functions, 42, 49f.

Radio absorption in the ionosphere; see

Radio-aurora, 147, 217

425, 482, 539

488-89, 492-93

50f.

444-66, 485, 494, 565

Ionospheric absorption

artificial, 330 aspect sensitivity, 221, 227-29, 233-35,

aurora, association with, 217-18, 229 backscatter echoes, 235 bistatic observations, 220, 222-23, 230,

critical reflection, 235-36, 242-43 daily variations, 222-23, 23 1 diffuse echo, 218-19 discrete echo, 218-19 Doppler broadening and shifts, direct

electron densities in, 295 fading, 224-25, 239, 242 geometry of reflection, 232-35 height, 220-21 hydrogen emission, association with, 230 intensity of reflection, 217, 229, 243 latitude dependence, 220-22 magnetic disturbances, association with,

motions, apparent, 223-26, 231-32

242-43

242-43

measurement of, 225-26

226, 231-32

SUBJECT INDEX 699

motions, relationship to ionospheric

off-perpendicular angle for reflection,

partial reflection, 236-38, 242-43 polarization, 227 range shifts, 224 ray structure, association with, 230 reflection coefficient, 237, 243 scattering by small-scale inhomogenei-

scintillations of radio stars, association

types of echo, 218-220 yearly and I 1 -year variations, 223

currents, 226, 231

228

ties, 238-43

with, 144, 230

Radio emission, auroral and related; also see Cerenkov radiation ; Gyro radiation ; Plasma oscillations ; Thermal radiation ; Whistlers

airglow, associated with, 145 aurora and magnetic activity, associated

with, 144-46 chorus, 145, 278 daily variations, 145 ionospheric absorption, association with,

latitude variations, 145 seasonal variations, 145 sunspot-cycle variations, 144

aurora, association with, 144 magnetic activity, association with, 144 radio-aurora, association with, 144, 230

Radio waves, propagation of absorption by ionized atmosphere, 83-84 magnetic field, in a, 275f. ordinary and extraordinary waves, 276f. uniform ionized atmosphere, 80-84, 275

Range, residual, 247 electron, 284-85 electrons, straight-line, 284 protons in air, 247, 250

gas-kinetic, 32

144

Radio stars, scintillations of, 143-44

Rate coefficient, 28-32

Rayleigh, photometric unit, 569-70 Ray structure, auroral, 117f.; also see

appearance simultaneously with motion

bremsstrahlung, association with, 141

Breakup

of homogeneous arc, 140

D-region radio reflections, association

hydrogen emission, 140, 203f. radio-aurora, association with, 230

Recombination coefficient, 27, 28, 85f. effective, 29, 86, 294f.

Recurrence tendencies, aurora; see under Occurrence of aurora

Red aurorae; also see Aurora of 11 February 1958; Type-A red aurorae; Type-B red aurorae

with, 142

diffuse, low-latitude arcs, 200-02

bidden transitions and lines Red lines; also see Oxygen (0 and O+) for-

airglow excitation, summary of, 523-24 aurora, latitude variation, 200f. auroral temperatures, 212f. dayglow intensity, 571 deactivation, 3 1 1, 3 16, 422-27, 474-76,

diffuse, low-latitude arcs, 200-02 excitation by dissociative-recombination,

excitation by electron collisions, 98,

excitation by photochemical reactions,

excitation by photodetachment, 475 excitation by resonance scattering, 33,

536, 543

313-14, 420, 476-79, 523-31

299-300, 310-12, 533-34, 535-36, 566

542-43

385, 418-20, 422-27, 473-75, 485, 523

ciation, 385, 473, 475, 523

ment, 536

excitation by Schumann-Runge disso-

excitation following associative detach-

excitation of airglow in F layer, 30, 87,

excitation of nightglow by photochemical reactions, 523

identification, 350 intensity ratio, 359, 506 nightglow correlation with other emis-

nightglow heights, 489-91, 496-98 nightglow irregular enhancements, 386 nightglow mean intensity, 386, 506, 571 nightglow patchiness, 518 nightglow temperatures, 503 nightglow variations, latitude, 509 nightglow variations: post-twilight and

98, 476-79, 515-16, 523-31, 533-35

sions, 516-17

700 SUBJECT INDEX

pre-dawn enhancements, 376, 385-86, 477-78, 506, 512, 531

nightglow variations, yearly, 514 polarization, 206, 485, 508 twilightglow discovery, 384-85 twilightglow height for resonance scat-

twilightglow intensity, 377, 385-86, 419,

twilightglow temperatures, 503

tering, 418-20

571

Reflection coefficient, radio-aurora, 237, 243

Resonant and fluorescent scattering; also see Bowen fluorescent mechanism

coherent, 447 hydrogen lines, night sky, 425-26,562-64 N lines, 480 N,+ bands, 438-44, 485 0, fluorescence, 35, 318, 361, 377, 425,

polarization, 428-37,449-50,485, 563-64 red lines, 33, 385-86, 418-20, 422-27,

single isotropic scattering, 422-27 sodium D lines, 429, 434-37,444-66,485 twilightglow intensities for, 425-26

Rest-mass energy, 269 Restoring force on oscillating dipole, 8 Retarded potential, 272 Retarded time, 273, 319 Rocket experiments

481, 539

473-75, 485, 523

airglow, 358, 390-91, 472-73, 545-47 atmospheric properties, 91, 93-94, 99 auroral particles, 140, 268-69, 283, 326 bremsstrahlung, auroral, 140, 269 ionospheric ion composition, 87, 88 radiative-transfer problems, 35 seeding, 472-73, 545-47 solar x-radiation, 88

Rotational constants and energy, 25-26 Rotational sum rule, 25 Rotational temperature; see Temperature,

rotational

S

Saha ionization equation, 28 Satellite experiments

airglow, 358, 547

atmospheric properties, 9 geomagnetically trapped particles, 326f.,

interplanetary gas, 321 Scale height, 89f.

tabulated, 576 variation with height, 91

330

Scattering; also see Resonant and fluorescent scattering

absorption, as distinct from, 34 auroral electrons, of, 288f. coefficients, Rayleigh scattering, 61 isotropic, 36, 39f., 47 optical, 34 phase function, 39, 62 radio-aurora, by, 238-43 Rayleigh, 39, 40f., 47, 48, 57f., 62,

Thomson, 239, 243 with an albedo, 34, 39

Screening, atmospheric, 393 height, 395, 404, 411-13, 421, 426, 482

Secondary electrons, auroral, 292 bremsstrahlung production of electrons,

density of, 294-97 electron production of bremsstrahlung,

energy distribution, 296-97, 310-1 1, 319 first-generation, 293 ionization by, 293, 309 maximum energy, proton impact, 293 production by primaries, 292-94, 535 radio emission, 306f. recombination of, 294-97 ultraviolet emission, produced by, 294

Sequence, spectral, 5 Simultaneity of aurorae borealis and

australis; see Characteristics of aurora Sodium, atmospheric

488

293

306

abundance, 459-66, 469 abundance variations, 459-66 ionization, 470-73 model for vertical distribution, 494 Na+ as contributor to D and E regions

origin, 379-80, 469, 472 photochemistry, 467-70 vertical distribution, 416-18, 494

and sporadic E, 88, 471

Sodium (Na) D lines

SUBJECT INDEX 70 I

airglow discovery and identification,

auroral occurrence, 179, 190-91, 197-98 broadening, 32, 381, 429, 445, 455-56,

dayglow intensity, 571 excitation in aurorae, 315 excitation in dayglow, 465-66 excitation in nightglow, 467-70, 473,

excitation in twilight by resonance scattering, 380, 425, 444-65, 485, 503

excitation in twilight by ultraviolet, 382 fine structure, 179, 429, 460 hyperfine structure, 32, 429, 445-46, 460 nightglow correlation with OH, 51 6- 17 nightglow DJD, ratio, 359, 461, 463-64,

nightglow height, 489-91,494,497, 565 nightglow mean intensities, 506, 571 nightglow patchiness, 51 8 nightglow polarization, 508 nightglow variation, daily, 512-13 relative heights, nightglow and twilight-

terrestrial absorption lines, 464-65 twilightglow DJD, ratio, 380-81, 444 twilightglow height, 379, 415-18 twilightglow intensities, 377-81, 383-84,

twilightglow latitude variation, 384 twilightglow morning/evening ratio, 384 twilightglow polarization, 382 twilight screening height, 381, 410,

wavelengths, 179 yearly variations, 381, 383-84, 459f.,

470f., 506, 514 Solar activity; also see Flares, solar;

M-regions ; Sunspot cycle delay time between central-meridian

passage of spots and magnetic storm, 112, 148

350, 379

460, 503

564-65

470, 494, 565

glow, 494, 565

410, 415, 427, 454-58, 460-63, 571

417-18

radio burst, solar, 148-49 sunspots, association with aurorae and

magnetic storms, 109-14, 148 Solar declination, table of, 403 Solar particles and streams

angular diameter of streams, 112, 324 direct observation of, 323-24

magnetic fields, 338, 340f. solar wind, 321, 324 travel time to Earth, 112, 148, 338 theoretical models for, 324-26

Solar wind; see Interplanetary gas; Solar particles and streams

Source function, 39f. Spectroscopic nomenclature, 4 Spectrum, aurora; also see under each atom

and molecule atlas of, 151-85 halftones, 152-58 height variations, 202f., 210-15 intensities, absolute, 196-200 intensity correlations, 205 latitude variations, 200f. microphotometer tracings, 159-72, 174-

polarization, 205-06 rapid fluctuations, 205 spectrometer tracings, 173-74 variations, 200-05 visual color effects, 124f. wavelength tables, 176-85

75

Spectrum, dayglow; see Dayglow Spectrum, nightglow; also see Continuum,

nightglow; and under each atom and molecule

atomic lines, 359 blue and near ultraviolet, 350-58 correlations, spectral, 5 15- 17 early work, 347-50 far infrared, 367, 376 far ultraviolet, 358 halftones, 353-57, 361, 363 microphotometer tracings, 353-54, 362,

red and near infrared, 359-75 spectrometer tracings, 366 variations, daily, 5 1 1 - 13 variations, latitude, 509-1 1 variations, yearly, 509- 1 1, 5 13- I5 wavelength tables, molecular features,

Spectrum, twilightglow; also see under each

identifications and wavelengths, 376-77,

Spherical-harmonic analysis, 64, 68, 287f. Spherical triangles

364-65

358, 368-75

atom and molecule

386

702 SUBJECT INDEX

geomagnetic and geographic coordinates,

nomogram for solving, 67, 402

aurora, association with, 141-42, 293f. blanketing of F region, 142 ion production, 88-89, 577 magnetic activity, association with,

persistence, 88 production by bremsstrahlung, 293 recombination, 88 reflection mechanism for radio waves, 88

Standard meridian, 401 Starlight, see Astronomical component of

State

66-67

Sporadic E

141-42

light of night sky

molecular, 5 Zeeman, 5, 15

Statistical equilibrium, 2, 14, 245-47 Statistical weight, 6, 16

rotational levels, 25 vibrational levels, 22

Steric factor, 31 Stokes parameters, 58, 428, 433 Stormer spirals, see Precipitation curve,

aurora; Stormer’s theory of aurora Stormer’s theory of aurora, 114f., 324-25,

333-34; also see Precipitation curve, aurora

Stratosphere, 95 Strength

band, 22-23, 25, 26 line, 16 LS coupling, 16 relation to f-value, 18 relation to matrix element, 15 relation to transition probability, 16, 25 rotational line, 25

Strhcture of aurorae, see Forms and structure of aurorae

Subauroral belt, 68-69, 101 Sunlit aurora, 125, 131, 202, 208-11, 214,

Sunset, time of, 403-04 Sunspot cycle; also see Solar activity

21 5

airglow, 516 aurora, 148, 324 auroral radio emission, 144 cosmic rays, 147, 323-24

Surface brightness, 36 constancy with distance of observer,

Synchrotron radiation, 279; also see Gyro

Synoptic view of aurora; see Characteristics

36-37

radiation

of aurora

T

Temperature, atmospheric; also see Atmos- pheric properties

latitude variations, 95, 99, 502 Temperature, color, 210 Temperature, Doppler, 4, 7

aurora, 212-13 interpretation, 4, 212-13, 503 nightglow, 349, 359, 503 twilightglow, 381

secondary electrons, auroral, 296f., 306f.

relation to rotational temperature, 26,

relation to vibrational temperature, 24,

Temperature, electron, 29

Temperature, kinetic, 4

208f., 499f.

213f. Temperature, rotational, 25-26

aurora, 207f., 299, 317 interpretation of, 26, 208f., 317, 499f. nightglow, 499-502 smearing function, instrumental broad-

ening, 499 Temperature, vibrational, 24

aurora, 213f., 299 interpretation of, 24, 213-15 ground state, 24

Term, atomic, 4 Terrella experiments, 325 Thermal collisions

aurora, 299-300, 313-17 excitation of optical, non-auroral emission, 98, 533-34, 537, 566 excitation of 62p line in F region, 96,

role in determining populations of

Thermal equilibrium, 1, 6, 14, 24, 28, 33,

536-37

excited levels, 6, 33

210, 308, 319

SUBJECT INDEX 703

Thermal radiation; also see Thermal collisions

bremsstrahlung, arising from, 306f. ozone, during aurora, 147 radio frequencies, 145, 304-08 terrestrial atmosphere, 367, 376

Thermosphere, 95f. heating mechanisms, 96-99

Three-body collisions, 29, 32 association by, 31

Tides, atmospheric airglow intensity variations, 522, 547-50 auroral height variations, 129

Transauroral transition ; see Forbidden

Transition array, 4; also see under each atom Transition probability, 13-19, 20, 23,

579-81; also see under each atom and molecule

lines

forbidden transitions, 17, 18, 579-81 permitted atomic transitions, 17 relation to strength, 16, 25 rotational, 22, 25 vibrational, 23-24

calculation of, 411-13, 421 Transmission function, 393, 426

Trapped-particle radiation ; see Auroral

Triangulation on aurora, 126f. Troposphere, 95 Turbulence

particles in geomagnetic field

Kolmogorov spectrum, 551 radio-aurora, 241-42 spectrum of, 550 tropospheric, 98 upper-atmospheric, 473, 522, 546-47, * 550-53, 566, 577

Twilight flash, see Twilightglow Twilightglow (Twilight airglow), 376;

also see Spectrum, twilightglow discovery, 378 distinguished from dayglow, 376 distinguished from nightglow, 376

Type-A red aurorae, 125, 129, 198, 202, 204; also see Aurora of 11 February 1958

radio emission from, 144 Type-B red aurorae, 125, 135, 137, 198-99,

202 excitation mechanisms, 314-15

U

Ultraviolet emission airglow, 35, 350, 358 aurora, 35, 36, 196f., 294, 318-19

Uncertainty principle, 17 Units, electromagnetic, 63

V

Van Allen radiation; also see Auroral particles in geomagnetic field; Par- ticle bombardment, airglow

artificial injection, 330-32 discovery, 326 energy spectrum, 328 intensity, 327-28

van Rhijn airglow layer, 486f., 508f.;

intensity equation, 47, 55, 57, 59, 395, also see Heights of nightglow

486, 520 van Rhijn function, 486-87 van Rhijn method, 486; also see Heights

of nightglow corrections, 492-94 fundamentals, 486-89 results, 490-91

Variations in aurora; see Occurrence of

Venus, night-sky emission, 347 Vertical extent, aurora; see Characteristics

of aurora; Intensity distribution with height in aurora

aurora

Vibrational constants and energy, 23-24 Vibrational excitation ; also see Tempera-

ture, vibrational airglow, O,, 539-40 airglow, OH, 553-58 aurora, Oz, 213, 316-17 aurora, N,, 215-16 aurora, N;, 214-15 Krassovskii’s mechanism, 560-61 photochemical reactions, role in pro-

sunlit aurora, N:, 214-15 ducing, 561

Vibrational temperature; see Temperature, vibrational

704 SUBJECT INDEX

w

Wave functions, quantum mechanical molecular, 20-23 relation to matrix element, 15

Whistlers, radio, 145, 329 Winds and circulation, upper-atmospheric,

413, 522, 531, 546-41, 566

X

X-radiation; also see Bremsstrahlung,

enhancement of solar x-radiation during auroral

flares, 88-89

ionosphere formation from solar x-radia-

nuclear explosions, 332 tion, 88-89

2

Zeeman component, 5 intensity rules, 434

Zeeman state, 5 Zenith, aurora1 and magnetic; see Magnetic

zenith Zenith-horizon comparisons; see Heights of

twilightglow Zodiacal light, 321 ; also see Astronomical

component of light of night sky spectral composition, 505

012167150 x Physics Auro

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