The performance of the uorescence detector of the Pierre Auger … · 2008. 11. 10. · the Pierre Auger Observatory for the ultra high energy cosmic rays Federico A. S anchez January

The performance of the fluorescence detector of

the Pierre Auger Observatory for the

ultra high energy cosmic rays

Federico A. Sánchez

January 16, 2006

ii

“In metaphorical terms the fluorescence technique resembles a beautiful primadonna who needs constant pampering. Then she will sing with such beauty thatshivers run up and down yous spine. By contrast, the surface array techniquereminds one of a chanteuse in a smoky bar who sings with the same passsion,no matter how she feels or how she is treated.”

J. Cronin

Contents

Introduction vii0.1 What is a cosmic ray? . . . . . . . . . . . . . . . . . . . . . . . . vii0.2 Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii0.3 Propagation and GZK cutoff . . . . . . . . . . . . . . . . . . . . ix0.4 Sources and arrival direction distribution . . . . . . . . . . . . . xiii0.5 Air shower and detection methods . . . . . . . . . . . . . . . . . xv

1 The extensive air showers and experimental techniques 11.1 EAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Particle content and the electromagnetic development . . 11.1.2 The hadronic development . . . . . . . . . . . . . . . . . . 3

1.2 Detection methods . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.1 Ground arrays . . . . . . . . . . . . . . . . . . . . . . . . 61.2.2 Fluorescence telescopes . . . . . . . . . . . . . . . . . . . 71.2.3 The hybrid detectors . . . . . . . . . . . . . . . . . . . . . 10

2 The Pierre Auger Observatory detector 132.1 Scientific Objectives . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 The fluorescence detector . . . . . . . . . . . . . . . . . . . . . . 14

2.2.1 Optical system . . . . . . . . . . . . . . . . . . . . . . . . 142.2.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.3 Trigger and Electronics . . . . . . . . . . . . . . . . . . . 172.2.4 Atmospheric monitoring . . . . . . . . . . . . . . . . . . . 19

2.3 Surface detector . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.1 Sd electronics and trigger . . . . . . . . . . . . . . . . . . 23

3 The Pierre Auger Observatory performance 253.1 Real Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1.1 FD Monocular and Hybrid statistics . . . . . . . . . . . . 253.1.2 Fd Monocular vs Hybrid reconstruction: SDP and Axis

geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.1.3 FD Monocular vs Hybrid reconstruction: profile and en-

ergy determination . . . . . . . . . . . . . . . . . . . . . . 403.2 Simulated Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.2.1 Monocular performance and accuracy: geometry recon-struction . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.2.2 Monocular performance and accuracy: profile and energyreconstruction . . . . . . . . . . . . . . . . . . . . . . . . 54

iii

iv CONTENTS

3.2.3 Monocular reconstruction efficiency . . . . . . . . . . . . . 63

4 Physics Results 714.1 Validation of MC simulation . . . . . . . . . . . . . . . . . . . . . 714.2 Elongation rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.3 Proton-Air inelastic cross section . . . . . . . . . . . . . . . . . . 81

5 The shower size parameter as energy estimator 895.1 The standard energy estimation . . . . . . . . . . . . . . . . . . . 895.2 Nmax fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . 905.3 Shower and Telescope Simulation . . . . . . . . . . . . . . . . . . 925.4 Primary Energy Reconstruction . . . . . . . . . . . . . . . . . . . 945.5 Relation between primary energy and Nmax . . . . . . . . . . . . 975.6 HiRes Telescope . . . . . . . . . . . . . . . . . . . . . . . . . . . 985.7 EUSO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1005.8 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6 Conclusion 107

A Ideal sky map estimation 109A.0.1 Sky exposure: the uniform case . . . . . . . . . . . . . . . 109A.0.2 Sky exposure: the non-uniform case . . . . . . . . . . . . 113

B Fd reconstruction web page 123

CONTENTS v

Acknowledgements

First of all, I would like to thank Prof. Daniel Camin for his support andfor the opportunity of working the past three years in an exciting experimentas the Pierre Auger Observatory is. During my stay in Italy, I appreciate verymuch the fruitful discussions and advices of Giuseppe Battistoni and the collab-oration with the Torino group, where I learn the basis of the FD reconstructionmethods (and a lot of C++ programming skills!).

A special mention is reserved to Prof. Gustavo Medina-Tanco of the Uni-versity if São Paulo and his group . Without him, his guide and friendship,this work would have been impossible. The time I spent in Brasil was a periodof great learning. It is difficult to express in a few words all my gratitude toGustavo and his group. Particular thanks deserve also V. de Souza (the manbeneath chapter 5) and J. Ortiz for their help and advices.

Finally, I’m grateful to all whose support me the past years with their friend-ship.

vi CONTENTS

Abstract

This thesis is the product of a close collaboration between the Milano andSão Paulo Auger groups. The original contributions of this work are essentiallyin the chapters 3, 4 and 5, as well as in appendixes A and B. Introduction andchapter 1 are a summary of the major cosmic ray topics while chapter 2 is ageneral description of the Pierre Auger Observatory.

In chapter 3 we analyze the performance of the fluorescence detector of thePierre Auger experiment, after its first year and a half of regular operation. Wecompare data reconstructed with both pure fluorescence and hybrid techniquein order to estimate the accuracy of the pure FD method. We also find a setof quality cuts that assure high accuracy level when showers are reconstructedwith FD data only. The fiducial cuts, based on real data analysis, and anypossible bias due to the detector response are analyzed in detail also with MonteCarlo simulations. The main objective of this analysis is an estimation of thereconstruction efficiency of the pure fluorescence method.

In chapter 4 we used the recontructed events to calculate the elongation rateand the proton-air inelastic cross section. We compare our results with those ofthe previuos experiments as well as with the expectations of different hadronicinteraction models. We show the capability of the FD measurements to givecrucial information on this two fundamental parameters.

Finally, in chapter 5 we study the power of the shower size parameter,NMax ,as an energy estimator. In particular, we analyze Hires and EUSO experiments,a traditional ground-based fluorescence detector and a innovative space-basedtelescope. The content of this chapter was presented in [64] and has been sub-mitted to press [65].

In appendix A we show that, in an ideal case, a semi-analytical formulafor the FD sky exposure can be found. Predicted values are compared withobservations. We show that the FD exposure evolutes towards uniform exposureafter a sufficient exposition time.

A by-product of this work is a web page (http://beethoven.iag.usp.br/) in-tended to be a service for the Auger Collaboration. The site is devoted to purefluorescence reconstruction and the data therein can be accessed either in ASCIIformat or directly visualized event by event for each eye and run. The analysisavailable in the page starts on January 2004 and we pretend to keep it updatedby the end of each new shift. In appendix B are shown some screen shots of thesite as well as a short despcription of its content.

Remarks and conclusions are in chapter 6.

Introduction

0.1 What is a cosmic ray?

Since its discovery in 1912 by the austrian physicist Victor Hess, the cosmic raysfield has been a long story of technology and experimental developments, mixedwith many theoreticals success and some unavoidable wrong speculations. Infact, it was R. A. Millikan in 1926 who coined the name of cosmic rays reflectingthe early belief that this extraterrestrial radiation was made of gamma rays (themost penetrating form of radiation known at that time). Nowadays, we knowthat most of that cosmic rays first detected by Hess at altitudes close to 5300 mwere atomic nuclei, ranging from hydrogen to uranium, whith only a smallfraction of gamma. Nevertheless, we still preserve the tradition of calling raysevery kind of unknown radiation arriving at the Earth from the outer space.This is the case of the most energetic cosmic radiation we are able to measureaccurately with the modern detectors and which is in the range of 1018−1020 eV .This energy scale, much higher than the one achievable today with any kind ofaccelerator, is at present the very end of the cosmic ray energy spectrum andis the main subject of this work. The fact that a single particle, most probablyan atomic nucleus, can be accelerated to this huge amount of energy (nearly∼ 16 J the same energy of a mass of 1.5 kg -a little brick for example- fallingfrom a height of 1 m) is one of the reasons why this field has regained somuch interest in the physics community in the recent years. As the history ofcosmic rays teach us, in the early days around the beginning of the 20th century,astroparticle physics and fundamental particle physics shared common roots:observing cosmic rays in a cloud chamber, in 1932, Carl Anderson discoveredantimatter (the positron) and only five years later, togheter with Neddermeyer,he discovered the moun. Actually, during the 1930s the dominant motivationfor investigating cosmic rays was by the particle’s physic field. It was not until1938, when the energy scale known to science was extended beyond 1015 eVthanks to the discovery by Pierre Auger of what was denominated as extensiveair showers , that the astrophysical interested revived. Today there is a clearlygreat hope that the present and operating experiments, as the Pierre AugerObservatory and Hires, as well as the next generation experiments, as OWLand EUSO, will solve some of the still open questions in astrophysics (and evencosmology) and at the same time contribute to our knwoledge of fundamentalparticle interactions at the highest energies (i.e. the still unexplored energyscale by modern accelerators).

Some of the crucial questions which play a major role in the cosmic rayspuzzle are: What is the nature of the particles which we observe as cosmic

vii

viii INTRODUCTION

rays? What is its chemical composition and its energy spectrum? How can theyacquire such macroscopic energy? What and where are their sources? Does thedistribution of cosmic rays in the sky follow the distribution of matter withinour galaxy or the distribution of nearby extragalactic matter? Or, is there norelation with any distribution of known matter? Are there point sources or verytigh clusters? How do they propagate through interstellar and intergalacticspace to reach the Earth?

In the following paragraphs I will shortly present some general features andinformation about the cosmic rays needed to have a first survey to this fasci-nating field. Some specific topics will be treated more deeply in the followingchapters.

0.2 Spectrum

The existence of cosmic particles with energy ∼ 5 × 1019 eV is beyond anydoubt. Indeed it is problable that the cosmic ray spectrum extends to at least∼ 3 × 1020 eV and there is no clear evidence that this should be its end. Oneof the most striking facts is that the spectrum spans over roughly 11 decadesof energy with a flux that falls down from 104 particles per m2 per second at1GeV to 10−2 particles per km2 per year at the highest energies as shown infigure 1. As a whole, its shape is remarkably featureless. A little deviationfrom a constant power law, dN/dE ∝ E−α, from α ∼ 2.7 to ∼ 3.0 occursnear 3 × 1015 eV . And a further steepening, α ∼ 3.3 around ×1017.7 eV .Beyond 1018 eV the spectrum seems to flatten again to α ∼ 2.7. Beside thislittle, although significant, structure in the energy ranges mentioned before, theunique power law spectrum, as well as its smooth continuity over such widerange of energies, could be suggesting that a unique acceleration process shouldbe working in the sources.

Figure 1: Cosmic ray spectrum showing the agreement between many air showerexperiments, above 1015 eV , as a continuous extension of the (mainly) balloon-borne experiments at, 1011 − 1015 eV . (from [1])

The cosmic rays energy density integrated over all energies turns out to

0.3. PROPAGATION AND GZK CUTOFF ix

be approximately 1 eV/cm3, while starlight and galactic magnetic field haverespectively an energy density of 0.6 eV/cm3 and 0.2 eV/cm3 (with a typicalgalactic field strengh of ≈ 3 µG). It is clear that cosmic rays form a majorcostituent of interstellar medium. At the highest energies, i.e. near 1020 eV ,the resultant energy density causes great problems in terms of source energy.This is because the place where they are produced might be astrophysical sitescontaining unusually amounts of energy. This statement can be qualitativelyseen by a very general arguments. If the energy density of cosmic rays of 1020 eVis what is believed, i.e. 10−8 eV/cm3, and if we consider that these cosmicrays fill the local supercluster of galaxies (which has a length scale of roughly50 Mpc ≈ 150 × 1022 m) and have a lifetime of about 108 years, then theirsources must pump

10−8 eV/cm3

108 y× (4π/3 · (50 Mpc)3) ∼ 5× 1041eV/s (1)

in order to keep the flux constant. Another qualitative estimation to demon-strate that the energy of the sources must be extremely large, due originally toGreisen [2], is also possible. Assuming that the accelerator region must be of asize R in order to match the Larmor radius of the particle being accelarated andassuming also that the magnetic field B whitin it is sufficiently weak to limitsynchrotron loss below the energy gain, then it can be shown that the totalmagnetic field energy in the source, B2/4π × (4/3πR3), grows as γ5, where γis the Lorentz factor of the particle. For 1020 eV the magnetic energy shouldbe � 1057 ergs/s with B < 0.1 G. Such sources are likely to be strong radioemitters unless hadrons are being accelerated and electrons are not.

0.3 Propagation and GZK cutoff

Assuming that the accelerated particles can get out of the source region, howdo they get to us? If the particle is produced within our galaxy it must traversethe interstellar medium to arrive at the Earth. If it is of extragalactic originand its source is one among all the astrophysical objetcs at present known, itmust traverse the medium of the region where it was created, then traverse theintergalactic space between the source and our galaxy, and finally, traverse theinterstellar medium to reach us.

Let us first consider the propagation within our galaxy. It is widely ac-cepted nowadays that cosmic rays with energies per particle up to 1018 eV areprotons and nuclei of galactic origin. In their journey to the Earth this parti-cles must traverse the interstellar medium of the Milky Way which is mainlycomposed of clouds of neutral and ionized gases, predominantly hydrogen, andthat has embedded magnetics fields with a regular and a chaotic component.Cosmic rays of energy below 1018 eV are bent and scattered by the magneticfields. The ubiquitous 2.7◦ K blackbody radiation is also present and aroundgalactic sources there are optical photons from starlight and soft UV photons.All these parameters must be taken into account when propagation studies aremade and therefore realistic and precise predictions are very difficult. Importantconsequences in what we actually observe will depend upon all the mentionedvariables. As an example let us consider the subtle change in the spectrumwe already mentioned that occurs in the range 1015 − 1017.7 eV and is called

x INTRODUCTION

the “knee” of the spectrum. The attemps made so far to explain the physicalorigin of this feature in the spectrum can be roughly classified in three kindof models. One of them exploits the possibility that the acceleration mecha-nism could be less effective above the knee [58, 60, 61], while the second oneassumes that leakage from the galaxy plays the dominant role in suppressingcosmic rays above the knee [62]. On the other hand, the third scenario considernuclear photodisintegration processes and proton energy losses by photomesonproduction in the presence of a background of optical and soft UV photons, asthe main responsable for the mentioned change in the spectrum. Even if anyof these three proposals are acceptable, they have opposite conclusion on whichwould be the dominant composition beyond the knee. The first two scenarios,because are based on a rigidity (E/Z) dependent effects, predict the suppres-sion of the proton and lighter nuclei and consenquentely claim for a heaviermass composition beyond the knee. While the third scenario predicts a lightercomponent above the knee due to the disintegration of the propagating nuclei.Only accurate measurements of the chemical composition in this energy rangecould reject false scenarios. So far, the third kind of explanation seems to befavoured [3, 17].

But composition would not be the only observable affected by propagationprocesses. The distribution of arrival directions would also have propagationsignatures. Because the deflection angle φ of a particle of charge Ze and energyE through a distance d is typically φ ∼ d × rL, where rL = E/ZeB is theLarmor radius and B the magnetic field strengh, a proton of 1018 eV travellingin a 3 µG field would have a rL ∼ 300 pc which is roughly the thickness ofthe galactic disc. Thus the rate of loss of particles from the galaxy increaseswith energy and, if many primaries in this energy range are protons, a highanisotropy may be expected above 1018 eV . Many authors have studied indetail propagation effects with differents kind of galactic and/or extragalacticmagnetic field structures [11, 12, 13, 14, 15, 16].

Usually what we see when we observe the universe is the electromagneticradiation that arrives from differents regions of the space to our detectors. Invisible wavelength, since remote times, in others wavelengths more recently.The cosmic rays of the highest energy could provide us with a new tool to looktowards the sky where an entirely new class of objects would be only visible inthe light of cosmic rays with energies above ∼ 5 × 1019 eV . At this energiesthe cosmic rays are supposed to have an extragalactic origin. This is stronglysupported by the lack of a clear excess of events arriving from the region ofthe sky cover by the galactic disc (although very extended halo with regularmagnetic field can confine and isotropize this particles if they are heavy nuclei)and by the fact that there are no astrophysical candidates inside our galaxy toaccelerate the particles to such energies (disregarding the galactic center). But,in the frame of the standard model, there is a finite volume where we can lookfor sources. This is because at ∼ 5 × 1019 eV the universe is opaque to cosmicrays (of any specie, with the exception of neutrinos) due to their interaction withthe cosmic microwave background radiation (CMB). Soon after its discovery byPenzias and Wilson in 1965, Greisen and Zatsepin-Kuz’min predicted that therewould be a cutoff, nowadays widely known as GZK-cutoff , in the spectrum ofprotons around ∼ 5 × 1019 eV due to photopion production with microwavephotons. The principal reactions of protons p with the CMB are,

0.3. PROPAGATION AND GZK CUTOFF xi

p+ γ2.7◦K → ∆+ → n+ π+→ p+ πo→ p+ e+ + e−.

(2)

The peak energy of the CMB is of 6 × 10−4 eV and has a density of about400 ph/cm3. Though the threshold energy for pair production is about 1018 eVand the mean free path is ∼ 1 Mpc, compared to the 1019.6 eV and ∼ 6 Mpc ofthe corresponding values for the pion production, the energy loss per interactionfor the pair production is only 0.1% compared with the 20% for pion production.Thus, this latter process is the dominant one in the proton reaction. As indicatedin (2), in the photopion production, a neutron and a charged pion or a protonand a neutral pion are created with significant loss of energy for the nucleon.The neutron mean decay length is 1 Mpc at 1020 eV so on the Mpc scale itquickly becomes a proton again. The mean energy of a proton as a functionof the propagation distance through the CMB is shown in figure 2(a) whilethe fluctuation of the energy about the mean is shown in figure 2(b). Largevalues of the fluctuation means that a significant amount of energy can be lostin a single collision. Almost independently of the initial energy, after travellingdistances of the order of DGZK ∼ 100 Mpc, the mean proton energy falls toEGZK ∼ 5 × 1019 eV .

While figure 2(a) and figure 2(b) represent the physics underlying the prop-agation of protons in the CMB, the observer has to answer the inverse question:if a cosmic ray is observed with an energy E greater than EGZK , what is theprobability that it have come from a certain distance D > DGZK? To answer,we have to assume some injection spectrum in the source. If we assume thatat their origin cosmic rays follow an energy law given by E−2.5, then the prob-ability we are looking for is plotted in figure 3. As can by noted, the GZKinteraction begins to be significant at an energy of ∼ 8 × 1019 eV where thereis only a 10% probability that the cosmic ray traveled a distance greater than100 Mpc. It is worth and instructive to note that the highest energy event sofar detected, the Fly’s Eye event with 3 × 1020 eV , if it is not a fluctuationit would have a 0.1% chance probability of arriving from a distance lager than50 Mpc.

In the case of heavy nuclei, photodisintegration and pair production pro-cesses are important. If we consider a nuclei if mass A, then we have

A+ γ2.7◦K → (A− 1) +N→ (A− 2) + 2N→ A+ e+ + e−,

(3)

where N is a nucleon, either a proton or a neutron. The single nucleonchannels are about one order of magnitude greater than that of double nucleonemission. Though the nucleus does not disintegrate through pair creation, itloses energy in such process. The consequence is that there is a net energy lossmost notably in the region between 5 × 1019 eV and 2 × 1020 eV .

In the case of gamma rays, pair creation through interaction with the CMBis the most important process in a wide energy range from the lower thresholdof 4 × 1014 eV to energies up to 2 × 1019 eV through the collision

γ + γ2.7◦K → e+ + e−. (4)

xii INTRODUCTION

For energies above 2×1019 eV the dominant process becomes the attenuationdue to pair creation on diffuse background radio photons.

To finish I would like to mention two more signatures which should be presentin the extragalactic component of the energy spectrum due to the interaction ofcosmic rays with the CMB: a dip and a bump which precede the cutoff. Both areshown in figure 4 for sources at several distances. The bump is a consequence

(a)

(b)

Figure 2: Mean value (a) and fluctuations (b) of proton energy as a function ofpropagation distance through the CMB. (from [4])

0.4. SOURCES AND ARRIVAL DIRECTION DISTRIBUTION xiii

of the conservation of the number of protons in the spectrum: protons looseenergy in the propagation and are accumulated at an energy just before the oneafter which they are unable to reach us, i.e. the cutoff. The dip is formed dueto pair creation energy losses, the last to be turned off for protons because itslower energy threshold as above mentioned.

0.4 Sources and arrival direction distribution

The possibles energetic sites in the galaxy where the particles are likely to beaccelerated are the supernovae shocks, the galactic wind terminal shock and theyoung pulsars. A shock propagating in the interstellar medium can acceleratecosmic rays to a maximum energy of about ∼ 1016 eV . If it propagate througha region of pre-supernovae stellar wind with a strong magnetic field, it canprovide energies up to ∼ 1018 eV . The same limit can be reached if the particlefinds more than one accerelator site in its journey. A bit higher energies couldbe achieved in the galactic wind if it terminates by a standing shock. Otherpotential sources (where shocks are not involved) are young pulsars in which∼ 1019 eV is the maximum energy attainable. In any case, in the energy rangearound 1018 eV and for galactic sources, magnetic fields are not sufficient toisotropize cosmic rays. Therefore they would have some memory of the sourcesthey are coming from and a strong galactic disc anisotropy should be produced.

Shocks could also provide the acceleration mechanism in sources outside ourgalaxy. Astrophysical objects considered as accelerator candidates are activegalactic nuclei (AGN), shocks in the AGN jets, shocks in the cluster of galaxies

Figure 3: Probability that an observed event at a given energy has its source ata distance greater than the indicated by the plot. The source spectrum assumedin the calculation is E−2.5 (from [4])

xiv INTRODUCTION

Figure 4: The Hires-I and Hires-II monocular spectra with the result of the bestfit spectrum (from [34]). The black line is the sum of hte galactic (green) andextragalactic (red) components.

or ultra-relativistic shocks (gamma-ray bursters). On the other hand, large elec-tric potentials due to unipolar induction could be the accelerators in accretiondisc around massive black holes. Since the attenuation length of protons andnuclei just below the GZK cutoff energy exceeds 1000 Mpc, the expected arrivaldirection distribution of these cosmic rays, if they are of extragalactic origin, isisotropic. On the other hand, if their energies is above the GZK cutoff energy,the distance to the source is limited to several tens of Mpc and hence a cor-relation with nearby sources distribution is expected, i.e. the arrival directionshould be correlated with the distribution of galaxy clusters. Not great dealis known about magnetic fields outside of galaxies. Upper limits are imposedby Faraday rotation measurements of radio signals from distant powerful radiogalaxies. Many authors have discussed the possibility of studying cosmologi-cal magnetic fields with UHECRs [6, 7, 8, 9, 10]. Indeed, the time delay withrespect to linear propagation could be a potential tool to distinguish betweenburst acceleration model and continuous source model [5] because in the burstmodel a strong correlation between arrival time and energy might be observed.

0.5. AIR SHOWER AND DETECTION METHODS xv

0.5 Air shower and detection methods

It is instructive to estimate the numbers of cosmic ray particles a detector ofrealistic dimension could directly observe at a given energy. We can take asexample the dimensions of the University of Chicago “Egg” detector shownschematically in figure 5 and one of the largest ever flown. It was designedto fly on a space shuttle and it was actually carried on board the Challengerspacecraft during 4 days in 1985. Since weight limitations on the space aresevere, dimensions are alse stricly limited. If we consider that the instrumentshould trigger when the upper and lower detector (taken as circular plates) havecoincidence signals, it is easy to show that the effective area is,

Aeff =∫

cos(θ)dΩ = π2 · r2(1 − cos(θmax)) ≈ 5 m2 sr

θmax = tan−1(r/d) ≈ 45◦.

(5)

Around the knee, at ∼ 1015 eV energies, the integrated flux which can becalculated from figure 1 is ∼ 10−7 m−2s−1sr−1. Therefore, in a hypoteticalone year of operation, a device like “Egg” would have detected no more than 5events. Direct detection, although highly desiderable, is impossible in practiceat the energies we are interested in.

ScinitllatorPhotomultipliers

Cosmic particle

d

r

θ

Figure 5: Schematic view of a cosmic ray detector as the University of Chicago“Egg” experiment which was designed to fly on the space shuttle.

Fortunatly, above the knee of the spectrum, the energy carried by the cos-mic ray particle is high enough to interact with molecules in the top of theatmosphere and generate a shower of secondaries particles which in turn can bemeasured by ground based detectors. A primary particle of 1019 eV will haveabout 1010 particles in the resulting cascade when it reaches the observationlevel if it is situated after the shower maximum. The Coulomb scattering ofthe secondary particles (mainly electrons) and the transverse momentum asso-

xvi INTRODUCTION

ciated with the strong force interaction of protons, nuclei and mesons early inthe cascade development, are the responsables for the spread of secondaries overa wide area. Basically the air shower is a “pancake” of charged particles long afew tens of meters and wide hundreds of meters (at 1019 eV will cover an areaof 10 km2 at ground) which moves through the atmosphere nearly at the speedof light. The main direction of the shower reflects the direction of the incomingprimary and is usually referred as the shower axis. In a first order approxima-tion we can consider the development of the shower to be symmetric aroundthe axis (nevertheless deviations from such symmetry are observables for veryinclined showers). Other general characteristics of the extensive air showers willbe discussed in chapter 1. Three major observables have become useful in mod-ern detection techniques hitherto: the density profile of particles as a functionof distance from the shower axis (the lateral dirstribution function) at someobservational level, the direct cherenkov emmission produced in atmosphere ina narrow cone of few degrees with respect to the shower axis and, finally, theflourescence light produced by the de-excitation of the nitrogen molecules in theair. These three techniques where already used successfully, but individually, indifferent experiments. The Pierre Auger Observatory is the first detector whichwill operate in what is called the hybrid mode, i.e. measuring simultaneouslythe density of particles at ground and the fluorescence light produced along theshower development in the atmosphere. The details of Auger experiment willbe discussed in chapter 2.

Chapter 1

The extensive air showers

and experimental

techniques

An extensive air shower (EAS) is a cascade, or swarm, of particles generatedby the interaction of a single high energy primary cosmic ray nucleus or photonnear the top of the atmosphere. At first, the number of particles multiplies, thenreach a maximum and eventually attenuates as more and more particles fallbelow the threshold for further particle production. Schematically the showerconsist of a thin disk of relativistic particles (mainly electrons, positrons andphotons distributed within a radius that, increasing with energy, may be ofseveral kilometers) propagating through the atmosphere with the velocity oflight. In the first section of the present chapter I will shortly review somegeneral aspects of EAS that are the basis of the experimental techniques in thisfield. In the second section I will discuss the experimental techniques used todetect cosmic rays of the highest energies.

1.1 EAS

1.1.1 Particle content and the electromagnetic develop-

ment

A cosmic ray induced air shower has threee components: electromagnetic, muonicand hadronic. The shower consist of a core of high energy hadrons that continu-ously feeds the electromagnetic part of the shower primarly by photons from thedecay of neutral pions and etas. Each high energy photon, generates an electro-magnetic sub-shower of alternate pair production and bremsstrahlung startingat its point of injection. Nucleons and other high energy hadrons contributefurther to the hadronic cascade. Lower energy charged pions and kaons decayto feed the muonic component. The competition between the meson decay andinteraction depends on energy and depth in the atmosphere.

At each hadronic interaction, slighty more than a third of the energy goesinto the electromagnetic component. Since most hadrons re-interact, most of

1

2CHAPTER 1. THE EXTENSIVE AIR SHOWERS AND EXPERIMENTAL TECHNIQUES

the primary energy eventually finds its way into the electromagnetic part of theshower. In addition, because of the rapid multiplication of the electromagneticcascades, electron and positrons are the most numerous particles in cosmic rayair showers. Thus, most of the shower energy is eventually dissipated by ioniza-tion losses of the electron and positrons. It is correct to think of the atmosphereas an absorption calorimeter to be sampled by an air shower detector. Apartfrom the small fraction, F (E0), of energy lost to neutrinos, the primary energy,E0, is given by the integral

(1 − F ) ×E0 ∼ α×∫ ∞

0

N(X) dX, (1.1)

where N(X) is the number of charged particles in the shower at atmosphericdepth X (measured along the shower axis) and α is the energy loss per unit pathlength in the atmosphere.

The number of low energy (1 to 10 GeV) muons increase as the showerdevelops, then reaches a plateau because muons rarely interact, but only loseenergy relatively slowly by ionization of the medium. Because they have a smallcross section for interactions (their mean life time τ is ∼ 2 · 10−6 s), they arevery penetrating and were called the penetrating component of the cosmic rays.In constrast, the number of positrons and electrons declines rapidly after themaximum because radiation and pair production subdivide the energy down tothe critical energy, Ec ∼ 80 MeV after which electrons lose the remaining energyto ionization quickly.

A very simple but unrealistic model illustrates some generals features of airshowers. The following discussion regards the pure electromagnetic cascadesbut its basic structure applies also to air showers initiated by hadrons.

Let us assume an incident photon of energy E0 that after traversing a dis-tance λ creates and electron-positron pair. The leptons of the pair have, onaverage, half of the initial energy. After travelling another λ each particleof the pair will emit a photon by bremsstrahlung which in turn will produceanother e−e+ pair, and so on. After n = X/λ repetitions of this multiplica-tive process, where X is the slant depth along the shower axis, the number ofparticles created is N(X) = 2X/λ. Therefore, on average, the energy per par-ticle is E(X) = E0/N(X). The splitting continues until a critical energy, Ec(the energy below which the dominant energy loss is by ionization rather thanbremsstrahlung), is reached. When the energy is such that E(X) = Ec particlesare no more created and the shower has its maximum, being the number of par-ticles NMax = N(XMax) = E0/Ec = 2

XMax/λ. This basic features which holdsfor electromagnetic cascades and also, approximately, for hadronic showers canbe summarized as:

NMax ∝ E0 XMax ∝ log(E0). (1.2)

The former relation regarding the shower size will be analyzed in detail in thecontext of the Hires and EUSO experiments in chapter 5. The latter expressionwhich relates the depth of the maximum and the energy will be used in thecalculation of the elongation rate from Auger fluorescence data in chapter 4.

1.1. EAS 3

1.1.2 The hadronic development

Hadronic showers can be considered to be a superposition of individual electro-magnetic showers produced by π0 decays and fed, at different depths, by thehadronic core. At atmospheric depth beyond the shower maximum there is alittle influence from the hadronic core and the shower behaves like an electro-magnetic cascade. The shower size decreases exponentially with an approximateattenuation length of 200 g/cm2. In contrast the shower rise and positons of theshower maximum is dependent on the details of the hadronic interaction andthe nature of the primary particle. The depth of the first interaction depends onthe interaction length which, at 1015 eV energies, is about 70 g/cm2 for protonsand 15 g/cm2 for iron nuclei. For protons, roughly half of the initial energy islost in the first interaction. The subsequent depth of the shower maximum isstrongly influenced by fluctuations in the position of the first interaction andthe energy loss that occurs there. In fact, the depth of the shower maximumdepends on the product of the inelastic proton-air cross section, σp−air , and theinelasticity defined as (E0 −E′)/(E0 +MN) where E0 is the incident energy, E ′is the energy of the nucleon after collision and MN is the target mass. Both,the cross section and the inelasticity have a slow energy dependence. Note thatif the cross section increases while the inelasticity decreases, we would have thesame longitudinal development as would be if the two parameters were constant.These illustrate the difficulty in working backward from the measured proper-ties of the EAS to the fundamental physics parameters of the incoming particle.Since protons have much longer interaction length than heavy nuclei, they willhave larger fluctuations in the depth of the first interaction and develop deeperin the atmosphere. Furthermore, if we assume that the heavy nucleus fragmentsin the first interaction, the individual hadronic subshower produced by heavynuclei will be lower in energy by a factor E0/A where A is the atomic number.In reality what happens when a heavy nucleus enter the atmosphere is that itinteracts very quickly. However, in the first collision, only a few nucleons inthe nucleus interact inelastically with an air nucleus to create secondary pions.Several other nucleons and light nuclear fragments may also be released andthere is generally one heavy fragment. By studying fragmentation histories ofnuclei in photographic emulsion and the multiplicities of the secondary parti-cles produced in the various fragmentation events, it is possible to build up amore realistic picture on how heavy nuclei break up and when their costituentnucleons first interact. In figure 1.1 are the distribution of points of first inter-action for the superposition model as compared to that inferred from the data.The distributions become steeper at higher energy because of the increase withenergy of the nucleon cross section.

In any case, the net result is that heavy nuclei will have shallower depthand smaller fluctuations than the proton induced showers with details of showerdevelopment depending on the hadronic model assumed.

There is an approximate analytic expression for the longitudinal developmentof a shower based on Monte Carlo calculations given by [19]. This profile isin good agreement with real data observation, and state that the number ofparticles at depth X is


Figure 1.1: Distribution of points of first interaction in atmosphere of nucleonsincident iron nuclei.(from [18])

N(X) = NMax ·(

X −X0XMax −X0

)

XMax−X0

λ

· exp(

XMax −Xλ

)

, (1.3)

where X0 is a free parameter and λ is the interaction length.The lateral distribution of particles in a shower at a given depth, observed

in a plane perpendicular to the shower axis, is determined primarly by elec-tron multiple Coulomb scattering since the electromagnetic component is byfar the dominant in a standard EAS. Therefore the characteristic size of thelateral spread is determined by the Moliere unit, rM , which is the natural unitof lateral spread due to Coulomb scattering. For low energy particles in ashower rM ≈ 78 m at sea level while for higher energetic particles the spread issmaller. Hadronic interaction angles are negligible since the average transversemomentum in a hadronic interaction is approximately constant with 〈p⊥〉 = 400MeV/c. In fact, if one excludes muons, experimental evidence finds that thelateral distribution is, on average, very similar to what one would expect froma purely electromagnetic cascade,

ρ(r) =Ner2M

f(s, r/rM ), (1.4)

1.2. DETECTION METHODS 5

where Ne is the total number of electrons in the EAS and s(X) = 3/(1 + 2 ·ln(E0/Ec)/X) is named the shower age. The function f(s, r/rM ) originally de-duced from electromagnetic cascade theory can be adapted to represent hadroniclateral distribution functions (LDF) and is known as NKG (Nishimura-Kamata-Greisen) function.

The lateral distribution and the number of muons found in hadronicallyinitiated showers depends on the distribution of its charged π parents and onthe likelihood they have to decay rather than interact. Hence the muon LDFdepends eventually on the pion energy and the local air density. Low energypions are most likely to decay at smaller heights than higher energy pions whichhave chance to decay at higher heights where the air density is smaller. It followsthat the highest energy muons detected at sea level reflect processes occuringearly in the shower development. The muon component is also directly coupledto the hadronic component of the EAS and reflects more directly than theelectromegnetic component the properties of the initial hadron. The resultantmuon LDF is quite a bit flatter than that of electrons.

Finally it should be mentioned that the extensive air showers also producecopious amounts of Cherenkov radiation which can be detected at the surfaceof the earth.

1.2 Detection methods

If the incoming cosmic ray particle has an energy of about 1015 eV or more,there are enough secondary particles left at sea level to trigger an array of de-tectors deployed on the ground. The study of the extensive air shower usingground arrays of scintillation counters is the oldest technique in the field and isknown as the surface detection method. Later on, other types of indirect detec-tion methods were implemented. When the primary particle reaches energiesof about 1017 eV, the isotropically emitted light by the nitrogen molecules pre-viuosly excited by the ionization trail of the shower, can be detected. Altoughthis technique, named fluorescence detection, was suggested around the 1960’s,it was succesfully implemented for the first time in the 1980’s in the Fly’s Eyeexperiment [66]. At lower energies, around ∼ 1012 eV, showers can be observedby means of the Cherenkov light produced by the secondary particles high inthe atmosphere, near the shower maximum. The Cherenkov light is generallycollected by an array of telescopes reflectors. This method is widely used ingamma ray astronomy.

The Pierre Auger Observatory is the first experiment that was designed tooperate simultaneously with a surface detector (SD) and a fluorescence detector(FD) in the highest cosmic ray energy range. The two methods are complemen-tary because the ground array measures the lateral distribution development ofthe cascades while the fluoresecence telescopes observes the longitudinal devel-opment. Both detectors combined constitute an hybrid (HYB) detector whichhighly improves the stand alone operation of either the surface or the fluores-cence. Let resume the basics of the surface and fluorescence detection tech-niques.


1.2.1 Ground arrays

The ground array experiments sample the charged secondary shower particlesas they reach the ground. They determine the primary energy from the parti-cle density, the arrival direction from the detector trigger times, and may inferthe primary chemical composition from the ratio of the muon to electron com-ponent. The typical detection system is an array which consist of distributedsurface detectors to measure the density of particles. The detectors could beplastic scintillatiors or water Chrenkov detectors. In the former case, what ismeasured is essentially the energy deposited by the charged particles penetrat-ing the detector. The energy deposit, in turn, can be converted to a numberof particles by normalizing it with the energy deposit of a muon. In the waterCherenkov detectors, the particle density (electron, mouns and photons con-verted into electron-positron pairs) is estimated by the Cherenkov light theparticles generate in the water when they cross the detector. Both type ofdetectors, measure the particle density as a function of the distance from theshower core. The required area over which the particle counters are distributedis related to the rate of events initiated by the cosmic rays and the separation ofthe detectors is optimized to match the size of the footprint left by the EAS onthe ground. Once the air shower is detected, it is reconstructed in the followingsteps:

1. A first guess for the core location of the EAS can be determined from thepattern of counter hits and their pulse shape.

2. The zenith angle of the shower is determined from an analysis of timingdifference between counters assuming, at first, that the shower front isplanar (corrections to this assumption can be performed later).

3. The pulse height amplitudes in different detectors, converted into equiva-lent particle numbers, can be used to find the lateral distribution functionρ(r).

Actually, what the ground array measures, is a discrete sample of the particledensity, ρobsi = ρ(ri), where ri are the positions of the particle counters withrespect to the core. The expected density ρexpi = ρ

expi (θ, ri) can be parametrized

and, by an iterative minimization of

χ2 =

N∑

i=1

(

ρobsi − ρexpiσ

)2

, (1.5)

the best value for the core location, the zenith and azimuth angle, (θ, φ),and the crucial value of the density at a given distance from the core, ρg , arefound. The role of ρg, named the ground parameter (and usually referred asS(rg) with rg ∼ 600 m or 1000 m), is to relate the density of the showerto its primary energy. It has been found that the primary energy is directlyproportional to the number of particles at the shower maximum of an EASand therefore NMax is a good indicator of the primary energy. Nevertheless,in practice, ground arrays does not detect the showers at their maximum. Theatmospheric slant depht, i.e. the total thickness of air traversed by the shower,actually depends on the zenith angle of the incident cosmic ray and often the


showers reach the detection level well after their maximum. Moreover, theshower maximum fluctuates considerably from event to event because of thestochastic nature of the hadronic cascades along the shower axis. It should benoted also, that an estimation of the energy by means of NMax from a groundarray, would have technical difficulties since the estimation of NMax must relyon the measurement of particles densities close to the core where, in most cases(because wide detector separation) there are no particle counters to record thedensity. Fortunately, fluctuations of the particles densities far from the core arereasonably small, as suggested by [20], and hence the density ρg at such distances(a few hundred meters to about one kilometer) can be used as a good energyestimator. This is due to the fact that the shower particles far from the coreare produced at an early stage of the shower cascading and are scattered out bythe well understood Coloumb interaction. Monte Carlo simulations have indeedshown that the density far from the core is quite stable, it is proportional tothe primary energy and it is only weakly dependent on the hadronic interactionprocess and on the primary composition of cosmic particles. The best distancefor the ground parameter to minimize the fluctuations depends on the detectorcharacteristic, but in any case can be expressed as

E = κ · ρg (1.6)

A last comment should be made about ρg. As mentioned above, it representthe density at a given distance from the core but, in practice, its relation with theprimary energy given in equation (1.6) is for vertical air showers. An additionalconversion should be made for showers entering the atmosphere with a givenzenith angle θ. Those showers will have smaller densities ρθg at detection levelbecause they have traversed more atmosphere. However, the attenuation effectof the density can be measured by “equi-intensity-cuts” and the relation betweenρg and ρ

θg can be determined.

1.2.2 Fluorescence telescopes

The air fluorescence technique consist in detecting the EAS by the mesurementof the ultraviolet fluorescence emitted by molecular nitrogen (typically 10 to 50nanoseconds after excitation) after they were excited by air shower particles.Unlike Cherenkov radiation, the fluorescence is isotropic and hence, given theshower geometry, the expected amount of light can be predicted. Furthermore,because most of the light is emitted between 3000 Å and 4000 Å wavelength theatmosphere is quite transparent. The fluorescence yields about four photonsper meter of ionizing particle trajectory along the EAS axis. Beacuse the hugeamount of secondary particles, the total light generated can be detected overthe background and can be also collected by reflection mirros and recordedby ultraviolet-sensitive camera like a mosaic of photomultiplier tubes. As anair shower develops, the emitted ultraviolet photons, passing through the fieldof view of the detector optical system generates time dependent signals. Thisdefines a moving track through the atmosphere, from which one can reconstructthe longitudinal profile. The integral of the reconstructed profile is directlyporportional to the primary energy of the cosmic ray initiating the EAS. Themethod is essential calorimetric. It consist in measuring the total energy depositin the atmosphere by the charged particles. In constrast to the surface detection


method, it does not need a complex Monte Carlo simulation to determine theenergy scale. The identification of the primary particles is made by examinigthe shape of the longitudinal profile of the shower. More specifically, is doneby means of the atmospheric depth of the shower maximum which has greatpotential to discriminate gamma rays and neutrinos from cosmic rays hadrons(separation of the different hadronics components is more difficult but can bedone).

Broadly speaking, the fluorescence method uses an optical detector whichconsist of a system of mirrors and light collecting opto-electronic devices. Itsgeneral features can be obtained by the following arguments: a signal in a singlephototube is significant for the reconstruction of an event only if it collects moreair fluorescence light emmitted from the shower track than the fluctuationsof the night sky background during a given integration time tg. Part of thefluorescence light is scattered out on its way to the detector due to collisionswith the air molecules (the Rayleigh scattering) or with dust, pollution, fog andclouds (the Mie scattering). To a good approximation the light can be assumedto be emmitted from a line source (corresponding to a segment of the showeraxis). The expected air fluorescence signal is thus given by,

Nph =Amir4πr2

·Ne · Ye ·Q · exp(

− rr0

)

· r · ∆θ (1.7)

where r is the distance from the detector to an emmission point along theshower axis , Amir is the area of the mirror in the detector, Ne is the number ofelectrons in the shower cascade viewed by a given phototube, r0 is the extinctionlength of light due to the atmospheric scattering, Ye is the fluorescence lightyield from an electron (expressed in photons/m), ∆θ is the phototube pixel size(therefore, r ·∆θ is the line source element) and Q is the quantum efficiency ofthe phototubes. On the other hand, the background light is given by

Nbg = nnb · tg · Amir ·Q · (∆θ)2 (1.8)where nnb is the night sky photon intensity (photons/m

2/µs/sr) and tg isthe gate time for collecting the signal. Typically, the night background is 40m−2µs−1sr−1. The noise is

√

Nbg and, therefore, the signal to noise ratio σ ≡Nph/

√

Nbg gives the threshold shower electron size for triggering a channel asa function of the distance r as follows:

Ne = σ ·√

4π

Q

(

r0Rmir

)

· Ye−1 ·√

nnb · tg ·(

r

r0

)

exp

(

r

r0

)

(1.9)

In desertic atmosphere, where usually detectors are located, the conditionr � r0 is the most frequent case, and therefore we can neglect the linear depen-dence on r and write equation (1.9) as

log(Ne) = 8.66 + log (σ · ξ) + 5.42× 10−2(

8 km

r0

)

( r

1 km

)

, (1.10)

where we have defined ξ as

ξ =( r0

8 km

)

(

Ye4 m−1

)−1 (Rmir1 m

)−1√

(

nnb106 m−2sr−1µs−1

) (

tg5µs

)

. (1.11)


In equation (1.11) Rmir is the radius of the mirrors and Q is assumed to be30%. The atmospheric slant width over which the shower cascade containsmore electrons than this threshold size N the can be numerically obtained as thefollowing expression [21]

X100%t ≡ Xt(Ne ≥ N the ) = 100(−η2 − 8η + 2) [g/cm2], (1.12)

where η = log(N the )− log(E/1GeV ). Using equation (1.10), η can be writtenas a function of r and thus X100%t is a function of E and r. To trigger showerswith a given geometry and energy, X100%t ≥ 0 must be required, which leads toa maximum shower distance at which the optical detector will trigger:

rmax = 18.45( r0

8 km

)

(

1.58 + log

(

E

1019eV

)

− log (σ · ξ))

(1.13)

At 1019 eV with a 2σ signal, we get that the maximum distance from the detectoris rmax ∼ 23 km.

From the above arguments, general consequences on this detection methodcan be obtained. First the typical distance scale to observable EAS from theoptical detector is ∼ 25 − 40 km as expressed in equation (1.13). It dependsonly weakly on the detector parameters such as the mirror area and the pixelsize of a phototube. This is because most of the light produced by the showeris scattered out by Rayleigh and Mie processes and is therefore significanltyreduced being the exponential term in equation (1.7) the one that dominatesthe overall contributions. This consideration leads to a second consequence:the atmospheric monitoring to measure the extinction length r0 is crucial. Theprimary energy of a cosmic ray particle is approximately porportional to thesignal from the initiated air shower and equation (1.7) shows that the uncertantyon the energy determination is related to the extinction length as,

∆E

E' rr0

· ∆r0r0

(1.14)

This means that we must determine r0 with an accuracy of 5% to estimatethe energy of events at 30 km from the detector with a systematic error of10%. This goal can be achieve because contribution of the well understood(and then predictable) Rayleigh scattering dominates over the more uncertainMie scattering process. One more consequence from these arguments is that theestimation of the primary energy relies on the geometrical reconstruction of theobserved events. This is because the signal intensity strongly depends on thedistance r. An ultra high energy shower can only produce very weak signals ifit very far from the detector, in constrast to the ground array technique wherethe higher energy event has a larger footprint on the array surface. Thereforethe accuracy of the geometrical reconstruction is important not only for studiesof the arrival direction distributions, but also for reliable energy determination.The other major source of uncertanty in the energy determination comes fromthe fluroescence yield Ye. The geometrical information is retrieved both by theevent track in the camera (the so called the shower-detector plane, SDP) and bythe timing of the signals. How the event geometry determines the signal profileis illustrated in figure 1.2.


Rn

ri

Fdχ0

t0

ti

Ground Plane

Shower Detector Plane

χ i

Figure 1.2: Geometrical relations between the event track and optical detectors.

The longitudinal direction χi along the shower axis of the light spot seenby the ith-phototube of one optical station is related to a given geometry andrelative time as

χi = π − ψ − 2 tan−1[

c

R⊥(ti − t0)

]

(1.15)

where R⊥ is the impact parameter (the perpendicular distance from theshower axis to the detector), n̂s is the direction of the shower axis, r̂i is thevector from the fluorescence station to the core position at the instant ti and t0is the time at R⊥. Consequently how the light spot crosses the field of view ofthe phototube, is a function of the geometrical parameters via equation (1.15).The shower geometry, in practice, is obtained by minimizing the χ2 built withthe square differences of the recorded signal profile at every sampling time withthe predicted time of equation (1.15). R⊥, ψ and t0 are the free parametersof the minimization. The geometry could be better reconstructed when morethan one optical station is part of the fluorescence detector apparatus. In sucha case and if the shower is recorded by both stations, i.e. stereoscopically,the χ2 minimization can be avoided (because there are no constraints on thetiming fit, systematic errors can be a problem) improving the accuracy of thereconstruction.

1.2.3 The hybrid detectors

The hybrid detectors constitute the most accurate way of recontructing the pa-rameters of an extremely high energy EAS. This is a novel technique that usecross information coming from a surface and a fluorescence detector. It hasalready been tested in the Hires-Mia prototype and is currently under construc-tion in the Auger Observatory. Much of the capability of an hybrid detectorstems from the accurate geometrical reconstruction it achieves. Informationfrom even one surface station can much improve the geometrical reconstructionof a shower over that achieved by a fluorescence detector alone. The surfacedata enters in the reconstruction in the χ2 time fit early mentioned. There are


two possible hybrid fitting scheme. In the first, the 3 free parameters of thestandard monocular fit are reduced to two parameters by specifying the angleχ0 = π − ψ in terms of the shower direction âSD derived independently by theground array, through

χ0 = cos−1(âSD · r̂) (1.16)

where r̂ is the unit vector from the optical station toward the shower coreposition. In the second hybrid fitting scheme the reduction of fit parametersis accomplished by specifying the time t0 which can be calculated from themeasured ground array trigger time tSD using

t0 = tSD +r̂SD · âc

, (1.17)

where r̂SD is the vector from the optical station to the surface array stationwhich triggered at tSD and â is the shower axis direction defined as pointingback along the cascade path as illustrated in figure 1.3. In the above expressionit is assumed that the shower arrival front is planar. In real situations this isnot the case and the curvature of the front must be taken in to account.

R

SDt

rSD

Fd

Sd

χ0

t0

ti

Ground Plane

Shower Detector Plane

a χ i

Figure 1.3: Geometrical relations used in hybrid reconstruction.

Chapter 2

The Pierre Auger

Observatory detector

The Pierre Auger Project is an international effort to make a high statisticsstudy of cosmic rays at the highest energies. To obtain full sky coverage, twonearly identical air shower detectors will be constructed, one to be placed in theNorthern Hemisphere and one in the Southern Hemisphere. Each installationwill have an array of about 1600 particle detectors spread over 3000 km2. At-mospheric fluorescence telescopes placed on the boundaries of the surface arraywill record showers that strike the array. The two air shower detector techniquesworking together form a powerful instrument for these studies.

2.1 Scientific Objectives

The scientific goal of the Pierre Auger Observatory is to discover and under-stand the source (or sources) of cosmic rays with energies exceeding 1019 eV.The experiment will measure the energy spectrum, the arrival directions, andthe nuclear composition of these particles. To achieve these goals it is necessaryto accumulate substantially more events than previous and current experiments.The experiment measures the properties of the highest energy cosmic particlesinderectly from the EAS. As already mentioned, the feature of the Auger Ob-servatory, which distinguish it from all previous experiments in the field, is thatit is an hybrid detector consisting of a surface detector and an atmosphericfluorescence detector. The duty cycle of the surface detector should be nearly100% whereas the fluorescence detector duty cycle may be only 10% because itoperates mainly in moonless nights. The hybrid data set obtained when bothdetectors are working together will be especially important for evaluating thesystematics of both detectors. It will also provide an energy spectrum withsmall energy uncertainties. The hybrid data set will also provide the best evalu-ation of the primary particle composition utilizing all of the known parametersthat are sensitive to the primary particle type. The hybrid data set will belimited in statistics, however. At the highest energies, the energy spectrumand arrival direction measurements will rely primarily on the surface detectoralone. The correlation of hybrid and surface-detector only analysis in the high-statistics regime will justify the reliance on surface-detector only data at the

13

14 CHAPTER 2. THE PIERRE AUGER OBSERVATORY DETECTOR

highest energies.

The surface array (SD) measures the lateral density distribution of particlesin the shower front. Muons and electromagnetic particles can be identified. Theshower energy is obtained by assessing the size of the shower, usually throughthe determination of the density at a particular distance from the shower axis(tipycally from 600 to 1000 m). This method is fairly independent of the typeof primary particle. The aperture of the surface array is 7350 km2 − sr forzenith angles less than 60 degrees. If events above 60 degrees can be effectivelyanalyzed, as appears likely, the above aperture will increase by about 50%.

The Auger fluorescence detector (FD) is expected to operate always in con-junction with the surface detector, in the so called hybrid mode. Its primarypurpose is to measure the longitudinal profile of showers recorded by the surfacedetector whenever it is dark and clear enough to make reliable measurementsof atmospheric fluorescence from air showers. The fluorescence detector re-quirements are driven by XMax resolution that is necessary for evaluating thecomposition of the cosmic ray primaries. The XMax resolution (i.e, the uncer-tainty in atmospheric depth where shower reaches its maximum size) should besmall compared to the (approximately 100 g/cm2) difference expected betweenXMax for a proton shower and for an iron shower of the same energy. Moreover,the experimental resolution should not significantly increase the spread of valuesfor any one component of the composition by itself. The width of the expectedXMax values for any nuclear type decreases with mass A and the distributionof iron XMax values has an rms spread of approximately 30 g/cm

2. It will betherefore required that the experimental XMax resolution be no greater than20 g/cm2. As explained in the previuos chapter, an accurate longitudinal profile(achieving 20 g/cm2 XMax resolution) requires precise geometric reconstructionof the shower axis. Nevertheless, at large zenith angles, a small error in zenithangle causes a significant error in atmospheric slant depth. This is mainly due tothe exponential behavior of the air density. Averaging over the range of hybridshower zenith angles (0-60 degrees) leads to a rule of thumb that an error ofone degree in zenith angle leads to an error of 20 g/cm2 in XMax . The angularresolution of the hybrid showers must therefore be significantly better than 1degree, since other uncertainties also contribute to the XMax uncertainty. Thelongitudinal profile of each shower must be well measured in order to determinethe depth of maximum with an accuracy smaller than 20 g/cm2. In particular,if the profile is well enough measured then, the profile integral (proportionalto the total shower electromagnetic energy) will have less than a 10% fittinguncertainty contributing to the shower energy uncertainty. Good energy reso-lution is therefore implicit in the XMax resolution requirement which, in turn,is strongly related to a good geometric reconstruction.

2.2 The fluorescence detector

2.2.1 Optical system

The Fluorescence Detector consists of 24 telescopes, grouped in sets of 6 unitsin each of the 4 Fluorescence Stations located at the periphery of the site. Eachtelescope comprises the Camera consisting of an array of 20 x 22 photomultipliertubes (PMTs) biased and readout by the Head Electronics (HE) units which

2.2. THE FLUORESCENCE DETECTOR 15

are soldered to the PMTs. Each PMT + HE assembly constitutes a pixel andrequires both high voltage (HV) and low voltage (LV) supplies. Each FD stationhas 2640 pixels. The total number required for the whole Southern site is closeto 12000 units. The scheme of the basic optical system is shown in figure 2.1.

One observatory eye, is one optical detector station with a field of view of180◦ in azimuth and 30◦ in elevation. As above mentioned, it is built from 6telescopes each covering 30◦ × 30◦. To achieve this large field of view with areasonable effort and good optical quality the layout of a Schmidt telescope isadapted. The elements of a telescope are the light collecting system (diaphragmand mirror) and the light detecting camera (a PMT array). The detailed de-sign of the optics contains a large spherical mirror with radius of curvatureRmir = 3.4 m, having a field of view of 30

◦ × 30◦ with a diaphragm at thecenter of curvature whose outer radius is 0.85 m. These parameters are theresult of signal/noise calculations for extensive air shower events at the exper-imental threshold, taking into account the amount of night sky background atthe southern site of the Auger project and the obscuration by the PMT cameraand its support structures. The diaphragm will eliminate coma aberration whileguaranteeing an almost uniform spot size over a large field of view. With theabove configuration the spot diameter (containing 90% of the mirror-reflectedlight) is kept under 0.5◦. The sensitivity of the telescope is improved by enlarg-ing the diaphragm to an outer radius of 1.1 m. This choice determines the lightcollection efficiency (which is nearly doubled) and the size of the mirror surface,about 3.8×3.8 m (square with rounded corners). The corresponding increase inspherical aberration can be fully compensated by a corrector lens annulus cov-ering the additional area between 0.85 m < r < 1.1 m. This lens is connected tothe wall of the building by an adjustable mechanical structure (aperture box)which keeps out the weather and stray light. This box also holds an opticalfilter transmitting in the nitrogen fluorescence wavelength range (300 to 400nm) and blocking most of the night sky background. In addition, it acts as aprotective window on the outside of the diaphragm. The (curved) focal surfaceis at approximately half the distance from the center of curvature, so the cam-era edge has a length of 1.70 × 30(/180) metres. The camera size and shape istherefore about 0.9 m×0.9 m square. Each pixel in the light detector has a fieldof view small enough to measure accurately the light trajectory on the detectorsurface but large compared to the spot size. A diameter of about 1.5◦ (26.2mrad) is a good compromise and it corresponds to a linear size on the detectorsurface of about 0.0262 × 170 cm = 4.5 cm, easily matched to commerciallyavailable PMTs. The image on the camera surface has finite dimensions dueto two effects: spherical aberration and blurring due to mirror imperfections oralignment inaccuracy. Blurring and additional light from the outer diaphragmarea with the corrector annulus should not substantially increase the spot sizeas determined primarily by spherical aberration

2.2.2 Calibration

The reconstruction of air shower longitudinal profiles and the ability to deter-mine the total energy of a reconstructed shower depend critically on being ableto convert an ADC count to a light flux for each pixel that receives a portionof the signal from a shower. To this end, it has been implemented a methodfor evaluating each pixel’s response to a given flux of incident photons from the


(a)

(b)

Figure 2.1: Schematic view of one Auger fluorescence building (a) and one ofits six opto-electronic devices (b).


solid angle covered by that pixel, including effects of mirror reflectivity, pixellight collection efficiency and area, cathode quantum efficiency, PMT gain, pre-amp and amplifier gains, and digital conversion. While this response could beassembled from independently measured quantities for each of these effects, theFD calibration is measured in a single end-to-end calibration. The techniqueis based on a portable light source that is mounted on the external wall of thefluorescence detector building, filling the diaphragm of a mirror with a uniformpulsed flux of photons and triggering all the PMTs in the camera array. Oneportable light source will be stationed at each FD building. Cameras will becalibrated one at a time. This source consists of a pulsed UV LED embeddedin a small teflon sphere, illuminating the interior of a 2.5 m diameter cylin-drical drum, 1.25 m deep. The sides and back surface of the drum are linedwith Tyvek, a material diffusively reflective in the UV. The front face of thedrum is made of thin sheet of teflon, which is diffusively transmitting. A sil-icon detector mounted near the LED monitors the relative intensity of eachflash. The geometry of the source and drum is arranged so that the intensityis independent of position on the diaphragm and uniform over the range of thecamera’s solid angle. Drum geometry gives non-uniformities of less than 5%.Ideally, this calibration would occur at many wavelengths in the N2 spectrum,between 300 and 400 nm, and at several intensities. The end-to-end calibrationusing the flat field drum illuminator (described above) is done on a periodicbut not on a nightly basis. To track the PMT response between end-to-endcalibrations, a relative optical calibration system provides light pulses to threecomputer-selectable places in each FD telescope: at the mirror center with thelight directed at the camera; at the middle of the 2 sides of the camera with thelight directed at the mirrors; at the entrance aperture with the light directed ata reflector (TYVEK screen or TYVEK targets on the telescope doors) to directlight back into the telescope entrance aperture. The light is distributed from aprogrammable light source (at each FD site) via optical fibers. Typically theoptical fibers end with a diffuser to equalize the light directed to the PMTs. Thegeometrical projection effects (for the fiber/diffuser at the mirror center) can becalculated, thus this source provides a relative calibration of the camera pixelswithin a single camera. The programmable light source provides light at dif-ferent intensities and/or wavelengths using neutral density and/or interferencefilters respectively. The light source is a xenon flash bulb with a characteristicpulse time of ∼ 1µs matched to typical fluorescence signals in the PMTs. Thehigh pulse to pulse stability of a xenon light source results in light calibrationsignals with RMS widths < 1%. Light source intensities are monitored andrecorded in the calibration data base. The nightly recorded data are analyzedto find changes in the calibration system.

2.2.3 Trigger and Electronics

The main tasks of the telescope electronics are to shape the PMT signals fromFD cameras, digitize and store them, generate a trigger based on the cameraimage and initiate the readout of the stored data. A computer network com-presses the data, refines the trigger decision, gathers data of the same event fromdifferent telescopes and transfers it to the central computing facility CDAS. Theorganization of the front-end (FE) electronics follows the structure of the tele-scopes in the FD buildings. Each of the 24 telescopes is readout by one FE


sub-rack through its associated Mirror PC. Each sub-rack covers 22 x 20 pixelsof the camera and contains 20 Analog Boards (AB), 20 First Level Trigger (FLT)boards and a single Second Level Trigger (SLT) board. The First Level Trigger(FLT) is the heart of the digital front-end electronics. Its main tasks are: digi-tize continuously the signals from the Analog Board with a sampling frequencyof 10 MHz, store 64 times 100 µs of digitized raw data in memory for laterreadout, discriminate efficiently for each channel the fluorescence light above acertain threshold from night sky fluctuations and generate a pixel trigger, mea-sure the pixel trigger rate for each channel, compensate changing backgroundlight intensities through automatic control of the pixel threshold to achieve con-stant pixel trigger rates and prevent increasing rates of random coincidences,transfer the pixel status and multiplicity on demand to the Second Level Trig-ger (SLT), support access to raw data memory and internal registers througha PBUS+ interface, calculate statistical data (

∑

x,∑

x2) of up to 65535 ADCvalues per channel, and provide a digital interface to the Analog Board in orderto generate test pulses and to set the gain of the analog amplifier stages.

Figure 2.2: Second level trigger patterns. Basic patterns (top) and rotations(bottom).

The pixel triggers generated for each channel of the 20 FLT boards in a sub-


rack are read via the backplane into a single Second Level Trigger (SLT) board.The functions of the SLT are shared between two FPGAs: the “Trigger FPGA(T-FPGA)” and the “Controller FPGA (C-FPGA)”. They are both connectedto a dual-port RAM, which works as a circular memory to store pixel trigger,multiplicity and other trigger information. Functions of the T-FPGA The taskof the T-FPGA is to generate an internal trigger if the pattern of triggeredpixel looks like a straight track that might be produced by fluorescence light.The algorithm of the T-FPGA regards as straight track the 5 fundamentaltopological types of pattern shown in figure 2.2 (top) and those created byrotation and mirror reflection (in figure 2.2 bottom). A lot of tracks will notpass through the center of the pixel and the PMT may not record enough lightto trigger. To allow for this situation and to be fault-tolerant against defectivePMTs the algorithm requires only 4 triggered pixels out of the 5-fold patternmentioned above. Taking into account that identical 4-fold pattern with a gapcan originate from different 5-fold hole combinations, we count 108 differentpattern - so called pattern classes. Instead of checking the full matrix for all108 classes at once (which would be 37 163 combinations) we have implementeda pipelined mechanism, which searches for track segments on a smaller 22x5 sub-matrix. Every 50 ns the T FPGA reads the pixel trigger of one FLT (22 pixels +parity) into a pipelined memory structure. While the full matrix is scanned inthis way within 1 s, a coincidence logic simultaneously analyses the contents ofthe pipelined memory structure to find track like patterns. Eventually, a thirdlevel trigger, T3, is software implemented at the eye level.

2.2.4 Atmospheric monitoring

The observed light intensity, I , from a shower is reduced from the light intensityof the fluorescence source, I0, by geometric and by transmission factors. Therelevant transmission factors are Tm and Ta corresponding to molecular andaerosol scattering of the light in the atmosphere between the air shower andthe fluorescence detector(s). There are also higher order corrections from multi-plescattered light and scattered air Cherenkov light (that increase the observedsignal somewhat). Uncertainties in the source light intensity will arise fromuncertainties in the (correction) factors. To minimize these atmospheric uncer-tainties, fluorescence experiments are located in dry desert areas with typicallyexcellent visibility (i.e. small corrections). The scattering of light in a pureor molecular atmosphere is from Rayleigh scattering. The scattering of lighton much larger scattering centers in the atmosphere called aerosols is referredto as Mie scattering. In practice the Rayleigh scattering related corrections,while large, can be made with precision using conventional atmospheric data:the temperature and pressure at the observation site, and the adiabatic modelfor the atmosphere. In contrast the corrections related to Mie scattering, whiletypically less than the Rayleigh corrections, are a priori unknown. Thus most ofthe atmospheric monitoring is focused on the aerosol (Mie scattering) compo-nent. In a 1-dimensional model of the atmosphere (not un-typical of the nighttime atmosphere in large, desert valleys at locations well away from the valleywalls -which is not the case of the Auger site-) the aerosol transmission correc-tion needs only the aerosol vertical optical depth (AVOD(z)) to height z abovethe fluorescence detectors. This can be measured using a number of differentinstruments. Multiple, and in some cases redundant, measurements provide a


monitor of non-1-dimensionality as well as cross checks and a monitor of sys-tematic uncertainties. In all cases the measured quantities include both aerosoland molecular contributions. The aerosol values are obtained by subtractingthe molecular (Rayleigh) contributions.

Automated weather stations are located at each of the FD sites (eyes). Theyprovide a record of the local ground temperature, pressure, wind speed, winddirection and humidity. The temperature and pressure are essential to definethe Rayleigh atmosphere. Wind speed (and direction) are important for safetyinterlocks for the FDs. Humidity provides information on the formation of fog.Periodical radio soundings are performed covering all seasons and daytimes withan emphasis on measurements during nights. Radio soundings are a commonmeteorological procedure for acquiring data on air temperature, air pressure,relative humidity of air, wind speed and wind direction in dependence of height.Radiosondes are small, full automatic sensors which are launched with heliumfilled balloons. The size of the helium filled balloon at ground is about 1m3 andbetween the balloon and the sonde is a small parachute for retarding the fallingvelocity after the balloon has burst.

The horizontal attenuation length is measured at 1 hour time intervals andalong 3 (independent) light paths across the Auger Southern array. They pro-vide information on site and instrument-related systematic uncertainties in thehorizontal extinction length. Each light path includes a Hg-vapor light sourceand a CCD based receiver. Measurements are done at 4 wavelength between365 and 546nm. These measurements, combined with the local temperature andpressure, determine the aerosol horizontal attenuation length at 365nm and thewavelength dependence of the attenuation length.

The observed fluorescence light signal must be corrected for the finite trans-mission of light from the extensive air shower to the fluorescence telescopes. Tomake this correction we need to know the cross section weighted, vertical profileof the atmosphere, and in particular of the aerosols. The Auger experimentuses scattered laser light as a light source to monitor the atmosphere. By usingsteerable laser beams, the light sources can be positioned to make a measure-ment of the vertical optical depth versus height, z, above the fluorescence eyes.In practice this is done using LIDARs which are installed at each of the fourfluorescence sites on the periphery of the Auger ground array. Each LIDARconsists of a pulsed, 355nm, laser beam and a receiver telescope. The four LI-DAR results monitors in detail the observation site. Furthermore, to have aprecise atmospheric monitor on a event per event basis a novel method, named“shoot the shower” is done by the LIDARs. The idea is to accurately scan theatmosphere in the direction of the more interesting events. At the moment,every time an hybrid event with more than 5 SD triggered tanks and more than5 FD triggered pixels is observed, the LIDAR scan the atmosphere whitin theshower-detector plane (SDP) along the axis direction. With the present criteria,the rate of “shoots” is of about 3 per night.

Another facility used to both calibration studies and atmospheric monitor,is the Central Laser Facility (CLF) located at the center of the SD array andwhich has a steerable calibrated laser. The CLF is close to one SD tank in orderto allow hybrid calibrationi ( the light of the laser can be injected to the closeSD tank through an optical fiber in order to emulate the cherenkov light).

The observed light from an extensive air shower includes both the air fluo-rescence signal plus some Cherenkov light (mostly in a few degree cone centered

2.3. SURFACE DETECTOR 21

on the air shower axis). Through scattering of the Cherenkov light in the air,some of the Cherenkov light appears as a background into the fluorescence data.To estimate the fraction of Cherenkov light scattered on aerosols we need theaerosol extinction length, at height z above the fluorescence detectors, and theaerosol phase function (normalized aerosol differential scattering cross section).The observed light from an extensive air shower also includes a contributionof multiple scattered light. This is true for the air fluorescence signal and forthe Cherenkov background light. In making a correction, it is most importantto know the Mie phase function at forward scattering angles where Mie dom-inates Rayleigh scattering. In the constant composition, 1-dimensional modelfor aerosols, it is sufficient to measure the aerosol phase function at the alti-tude of the fluorescence detectors. The measurement can then be made using anear-horizontal, pulsed light beam directed across the field of view of one of thefluorescence sites. As each fluorescence detector views ∼ 180◦ in azimuth, evena fixed direction light beam will allow the aerosol phase function to be measuredover most of the range of scattering angles. This is done using a dedicated lightsource located near two of the Auger fluorescence sites.

The presence of cloud is a key factor in the operation of the FD system. Itcan determine the effective aperture of the system, and the presence of brokencloud between the shower track and an eye can distort the apparent longitu-dinal development of individual showers. Cloud can be detected at night inthe absence of terrestrial light sources by its emission in the infra-red due to itshigher temperature than the night-sky background. Apart from the highest andcoldest cloud, such detection can be readily achieved for cloud at high elevationangles. Close to the horizon, particularly in humid conditions, detection againstthe warm atmosphere may be more difficult. Infra-red cameras (in the vicinityof 10µm) are installed at each of the FD eyes, and the sky is scanned with themusing a pan and tilt drive approximately every 10 minutes. They provide eachFD pixel with a cloud/cloudfree decision and, with a 0.2◦ angular resolution,are used collectively to triangulate sparse cloud over the array fiducial volume.

2.3 Surface detector

The role of the surface array is to measure the lateral density and time distri-bution of particles in the shower front at ground level. The instrumentation isspread over an area of 3000 km2 per site (northern and southern). The spac-ing of 1.5 km between detection stations is defined by the requirement of fulldetection efficiency above 1019 eV and of a good sampling of the lateral densitydistributions. The low density of particles (∼ 1/m2) to be measured with goodstatistical precision imposes a sampling area of ∼ 10 m2. The water Cherenkovdetection technique has been selected mainly from cost considerations but alsobecause of its own virtues: the water tank offers a natural way to optimizemuon pulse heights with respect to the electromagnetic component. Becauseof its large lateral cross-section it offers a good sensitivity to large zenith angleshowers. The surface array will be comprised of 1600 water Cherenkov de-tectors spaced by 1.5 km on a triangular matrix. Each detector consists of acylindrical, opaque tank having a diameter of 3.6 m and a water height of 1.2m. The water is contained in a sealed bag or liner that prevents contamination,provides a barrier against any remaining external light, and diffusely reflects


the Cherenkov light emitted in the water. Three large diameter (∼ 20 cm)hemispherical photomultipliers (PMTs) are mounted facing down and look atthe water through three sealed windows that are an integral part of the liner.The liner also provides filling ports and an additional sealed window hosting anLED calibration system. The PMTs are enclosed in housings to further protectthem from external light. On the outside, the tank has supports for solar panelsproviding the energy supply and for the communication system and GPS an-tenna. A battery is contained in a box attached to the tank. See figure 2.3 fora schematic overview of the Surface Detector (SD).

CommunicationAntenna

enclosureElectronic

boxBattery

waterdownward into the3 PMTs looking

Plastic tank

Solar panel

GPS system

Figure 2.3: Schematic view of a surface detector station

The height of the water Cherenkov detector tanks is defined to optimizethe muon pulse height. A vertical distance of 1.2 m of water is sufficient toabsorb 85% of the incident electromagnetic shower energy at core distances> 100 m, and gives a signal proportional to the energy of the electromagneticcomponent. Muons passing through the tank generate a signal proportional totheir geometric path length inside the detector. Muonic content, rise-time andtime profile, are extracted from the measured PMT signal waveforms.

Among the generals requirements fullfilled by the SD array, are:

1. The positions and altitudes of its tanks are determined with a precisionof less than 1 m.

2. It has good performance in typical semi-desert climates with extreme tem-peratures varying from -15◦ C to 50◦ C and resistence to the intense solarradiation.

2.3. SURFACE DETECTOR 23

3. It is waterproof (rains and flooding) and it is impermeable to dust andsnow. It support winds with a maximum velocity of 160 km/h.

4. It has resistance to 2.5-cm diameter hail and will resist wind-blown sandand other particles. It is resistant to the thermal/ultraviolet diurnal cycle.Each unit is resistant to strong corroding conditions caused by the saltand some chemical substances that are present in the terrain.

The tanks are made of a rotationally molded (also called rotomolded) high-density polyethylene and their color is selected to blend in with the naturalbackground of the site. They are filled with 12000 liters of ultra pure water ofresistivity above 15 Ω − cm.

2.3

The performance of the uorescence detector of the Pierre Auger … · 2008. 11. 10. · the Pierre Auger Observatory for the ultra high energy cosmic rays Federico A. S anchez January

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