POSSIBIX SOlJgCE MECHANISM- FOR LOW-ENERGY GALACTIC… · POSSIBIX SOlJgCE MECHANISM- - FOR LOW-ENERGY GALACTIC ... POSSIBLE SOuizcE NECIUNISM FOR LOW-ENERGY GALACTIC ELECTRONS ...

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' POSSIBIX SOlJgCE MECHANISM- - FOR LOW-ENERGY GALACTIC' ELECTRONS

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' KARL A. BRUNSTE4N

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60DDARD SPACE FLI6MT CENTER GREEWYLT, MARYLASID I

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https://ntrs.nasa.gov/search.jsp?R=19650010112 2018-07-12T23:25:18+00:00Z

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POSSIBLE SOuizcE NECIUNISM FOR LOW-ENERGY GALACTIC ELECTRONS

Karl A. Brunstein

ABSTRACT

19713 A calculat ion is made of the expected secondary electron flux

resul t ing f r o m the knock-on co l l i s ions of the primary nuclear beam w i t h

the in ters te l lar gas. The model includes ionization los ses and a statisti-

c a l F e r m i mechanism energy gain. Comparison is made w i t h recent satellite

1 experimental data.

b POSSIBLE SOURCE NECHANISM FOR LOW-ENERGY GALACTIC ELECTRONS

i

by

Karl A. Brunstein*

Goddard Space F l i g h t Center Greenbelt, Maryland

*NASA-National Academy of Sciences-National Research Council Regular Post- & Doctoral Resident Research Associate.

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f INTRODUCTION

Kecent i n t e r e s t i n cosmic-ray e l ec t rons has been confined l a rge ly t o

higher energies. S p e c i f i c a l l y , experimental r e s u l t s ’ ~ ” 3 ~ i n the energy:

region of the order of 100 MeV t o seve ra l BeV have been of i n t e r e s t because

of t he i r bearing on the problem of g a l a c t i c r a d i o emission. The s tudy of

lower energy e l ec t rons , although probably not of d i r e c t importance t o the

r ad io emission quest ion, i s of importance because of its r e l a t i o n s h i p t o

the higher-energy e l ec t ron spectrum, and because of i t s bearing upon the

*

questions of s o l a r modulation and ene rge t i c e l e c t r o n production.

Several workers i n the f i e l d have a r r ived at t h e conclusion t h a t the

primary cosmic ray beam must traverse several g/c$ of i n t e r s t e l l a r material

p r i o r to being sampled a t o r near t he ear th . *s6a6 This necessa r i ly implies

a f l u x of low-energy e l ec t rons i n equi l ibr ium with the primary beam due t o

the knock-on process i n t h e i n t e r s t e l l a r gas. This problem has been exten-

s i v e l y s tudied f o r knock-on e l ec t rons due t o p-mesons i n var ious sub-

stances.’ The equi l ibr ium problem i n the i n t e r s t e l l a r gas is somewhat

d i f f e r e n t from the labora tory experiments descr ibed i n re ferences 7 and 8

due t o t h e absence of t h e cascading process i n the i n t e r s t e l l a r gas and the

enhanced ion iza t ion loss ra te i n the p a r t i a l l y ionized hydrogen.” I n

addi t ion, there is the p o s s i b i l i t y of f u r t h e r acce le ra t ion of t he secondary

e lec t rons i n the i n t e r s t e l l a r material.”

It is not clear t h a t t hese g a l a c t i c e l ec t rons of low r i g i d i t y could

pene t ra te i n t o t h e s o l a r cav i ty ; however, recent work by Palmeira and

Balasubrahmanyanl” suggests , t h a t a t least during s o l a r minimum, they can.

This question is not considered here. The ques t ion of s o l a r modulation is

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i

a sep6ra te one.

absence of s o l a r in f luence and comparing with experimental d a t a obtained

ou t s ide the magnetosphere, new information concerning s o l a r in f luence may :

be in fe r r ed .

By considering t h e knock-on f l u x as expected i n the

PROCJiDURE

A model is adopted i n which t h e knock-on e l ec t rons , once produced,

l o se energy due t o the ion iza t ion e f f e c t and ga in energy due t o a statisti-

c a l Fermi mechanism. It is f u r t h e r assumed t h a t the e l ec t rons tend t o

remain i n t h e somewhat loca l ized regions i n which they are produced and

t h a t t he l o s s e s due t o d i f f u s i o n ou t of t he galaxy are neg l ig ib l e at these

l o w r i g i d i t i e s .

energ ies i n ques t ion here.

and t h e predominance of the ion iza t ion l o s s and statist ical ga in mechanism^,

a c a l c u l a t i o n of the l o w energy e lec t ron spectrum is made.

I n addi t ion , synchrotron losses are neglected at t h e

Then, assuming a source of knock-on e l ec t rons

Assuming a primary proton beam not varying appreciably wi th t i m e , One

can w r i t e the equat ion for the dens i ty of knock-on e l e c t r o n s as

+ cyN(E , t ) - (k-& aN(E,tl = Q(E) a t all

with N(E,O) P 0, where

N ( E , t ) = e lec t ron dens i ty a$ energy E and t i m e t i n electrons/$-MeV,

Fermi = (r(E+Meca) def ines cy, (9 k =(Eipc*Meca, dE being the ion iza t ion l o s s rate, and

Q(E) = production rate i n electrons/u?-MeV-sec. d s

It is poss ib l e t o so lve the d i f f e r e n t i a l equat ion for a r b i t r a r y production

rate Q(E). The s o l u t i o n is found to be

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Adopting t h e Bhabhag c ross sec t ion f o r knock-on production and t h e r i g i d i t y

spectrum of McDonald and Webbe$' f o r t he g a l a c t i c proton beam, w e may

w r i t e for the production rate

. '

Q(E) = y q - m, where E E

C = .150 cma/g, and F'

= 5420. (* -sr-sec)'l -l O Z 6

The dependence of CQ and Y upon E nukes t h i s r igorous approach impract ical .

Instead, by use of t he mean value theorem, one f i n d s t h a t Q(E) may be

approximated by

6 Q(E) 2 AE

where A and 6 a r e r ead i ly evaluated. Subs t i t u t ion of Q(E) = AE3 i n t o

the d i f f e r e n t i a l equation f o r N(E,t) , enables one t o use the method of

c h a r a c t e r i s t i c s t o so lve the equation t o y i e ld

Taking p = 2 x lO-'"g/cd l 4 and l e t t i n g t-, w e g e t , s e t t i n g dJ I N(E) dE 4n

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k -1.616 dJ 2.48 x ;(e) - = dE 1.62% -

(Y

I n add i t ion to t h i s f l u x calculated f o r t h e primary proton on hydrogen

i n t e r a c t i o n , t he re w i l l be a s ign i f i can t cont r ibu t ion from t h e heavier

nuc le i i n the cosmic-ray beam. The knock-on production rate a t a given

primary v e l o c i t y is very near ly a funct ion of Z'. '' W e then write t h e

r e l a t i o n f o r the cont r ibu t ion of nuclei of charge Z as i

Using re la t ive f luxes as given i n t h e review by Ginzburg and Syrova t sk94

w e a r r i v e a t the conclusion t h a t t he knock-on cont r ibu t ion from primaries

of charge Z22 w i l l be approximately .75 times the proton contr ibut ion.

t o t a l expected knock-on f l u x is then approximately 1.75 times the proton

cont r ibu t ion .

The

The ion iza t ion loss rate f o r e lec t rons of 3 t o 15 MeV is near ly

independent of energy f o r materials of low Z. I n t h e i n t e r s t e l l a r hydrogen

gas, however, i t is f a i r l y s t rongly a funct ion of the degree of ion iza t ion .

A degree of i on iza t ion of 10% wi th a corresponding dE/ds va lue of 5 MeV/g/crr?

has been taken.lo

The ca lcu la ted e l ec t ron f luxes for d i f f e r e n t values of (Y are p lo t t ed

i n f i g u r e s 1 and 2.

func t ion of a, the parameter i n the s t a t i s t i c a l acce le ra t ion mechanism.

Typical e l ec t ron f luxes as measured with IMP-A are a l s o shown i n the f igures .

It is seen t h a t t h e range of a values selected, 1 - 3 x le4 sec t o

It i s seen t h a t t h e r e s u l t a n t i n t e n s i t y is a s t rong

o!

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1 - = 3 x 1016sec, allows a f a i r l y good matching of the t h e o r e t i c a l and Q I

experimental f luxes. The value ct - 10’16sec-1 does not appear unrea-

s0nab1e . l~ sl’

It is not c l e a r a t t h i s t i m e whether the measured flux increase o r

the e n t i r e measured f l u x can be a t t r i b u t e d t o t he knockron process.

Both p o s s i b i l i t i e s a r e suggested by the reasonableness of t h e CY values

required.

CONCLUSION

The e lec t ron-pos i t ron f lux r e s u l t i n g from the proton-proton i n t e r -

act ions i n the i n t e r s t e l l a r mater ia l has been discussed by seve ra l au-

thors.” DeShong, Hildebrand , and Meyer3 conclude, based on e lec t ron-

posi t ron r a t i o s , t h a t a s u b s t a n t i a l po r t ion of t he e l ec t ron flux above

50 MeV must have an o r i g i n other than proton-proton c o l l i s i o n s . It is

speculated t h a t a s u b s t a n t i a l por t ion of the lower energy e l ec t ron f l u x

seen i n space may be a t t r i b u t e d t o knock-on e l ec t rons acted upon pr imari ly

by ion iza t ion losses i n the i n t e r s t e l l a r gas and a Fermi type acce le ra t ion

process.

should be composed l a rge ly of negat ive e lec t rons . I n addi t ion , any long

term solar modulation should be of an inverse s o l a r a c t i v i t y dependence,

s imi la r t o t h e p r imary nuclear beam. Both of these expectat ions w i l l be

subjected t o experimental test by proposed experiments during the next s o l a r

This , of course, requi res t h a t the low energy e l ec t ron f l u x

ha l f -cycle. 3

The knock-on process should produce secondary e l ec t rons i n the BeV

energy range also, The t h e o r e t i c a l c ros s sec t ion i n this case contains

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The knock-on process should produce secondary e l ec t rons i n the BeV

The t h e o r e t i c a l cross sec t ion i n t h i s case contains energy range also.

s p i n dependent terms, and one doesn ' t f e e l as t r u s t i n g of i t as i n t h e

low energy case where t h e i n t e r a c t i o n is one of Coulomb force only. I n

add i t ion , these higher energy e lec t rons may d i f f u s e out of the g a l a c t i c

d i s k more r e a d i l y and w i l l a l s o be subject t o synchrotron losses . It is

neverzheless iazerestizg :O ?lot the l o w ezergj e lec t ron i ? ~ a?,ori:g vir';:

the hisher energy f l u x as has been done i n f i g u r e 3. It is suggested by

iigurc? 3 tha t t he knock-on process at higher energies may a l s o be of

s ign i f i cance . Adopting f o r t he moment the conclusion t h a t t h e low-energy e l ec t rons

as seen by IMP-A are due t o the knock-on process, l eads t o the conclusion

t h a t t he Fermi mechanism must be moderately e f f e c t i v e f o r these low energy

e l ec t rons and t h a t t he parameter cr has the value cy - 10'16sec'1.

ACKNOWLEDGMENT

I would l i k e t o express my appreciat ion f o r help given by D r . P h i l l i p

Abraham i n overcoming mathematical complexities. D r . Thomas L. Cl ine

kindly made h i s d a t a ava i l ab le p r i o r t o publ icat ion.

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REFERENCES

l J . A . Earl, Phys. Rev. Letters 6 , 125 (1961)

2P. Meyer and R. Vogt, Phys. Rev. L e t t e r s 6 , 193 (1961) e

3 J . A . DeShong, R.H. Hildebrand, and P. Meyer, Phys. Rev. Letters 12, 3 ( 1964)

4F.W. O ' D e l l , M.M. Shapiro, and B. S t i l l e r , I n t e r n a t i o n a l Conference* on Cosmic Rays and the Ea r th Storm, Kyoto, 1961

5 S . Hayakawa, K. I t o , and Y. Terashima, Prog. Theoret. Phys., Osaka, Suppl. 6 , (1958)

6 H . A i m , Y. Fujimoto, S. Hasegawa, M. Koshiba, I. I t o , J. Nishimura, and K. Yokoi, Suppl. Prog. Theor. Phys. l.6, 54 (1960)

7W.W. Brown, A.S. McKay, and E.D. Pa lmat ie r , Phys. Rev. 76, 506 (1949)

'W.E. Hazen, Phys. Rev. 64, 7 (1943)

'H .J . Bhabha, Proc. Roy. SOC. A164, 257 (1938)

l 0 S . Hayakawa and K. Kitao, Prog. Theoret. Phys. l6, 139 (1956)

"E. F e r m i , Phys. Rev. 75, 1169 (1949)

'"R. P a h e i r a and V.K. Balasubrahmanyan, J. Geophys. R e s . , t o be pub 1 ished

1 3 F . B . McDonald and W.R. Webber, Goddard Space F l i g h t Center Contributions t o 1961 Kyoto Conference on Cosmic Rays and t h e Ea r th Storm, Greenbelt , Maryland, 1961 (unpublished)

14V.L . Ginzburg and S . I . Syrovatsky, Prog. Theoret. Phys. Suppl. 2, 1 (1961)

15N.F. Mott, Proc. Roy,. .Soc. (London) A124, 425 (1929)

A6T.L. Cl ine , F . B . McDonald, G.H. Ludwig, Phys. Rev. Letters, t o be pub 1 i s hed

17V.L. Ginzburg, Progress & Elementary P a r t i c l e s Cosmic Ray Physics (North Holland, Amsterdam, 1958) Vol I V , Chap. V , p 335

"P. Morrison, S. Olber t , and B. Ross i , Phys. Rev. 94, 440 (1954)

. *

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19s. Ifayakawa and H. Okuda, Prog. Theoret. Phys. 28, 517 (1962)

aoF.C. Jones, Journal Geophys. Res. 68, 4399 (1963) '<

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F I G U U CMTIOXS

Figure 1.

CalculaEed spectra for *

o s of cy indicated. Circles: average electron f lux frorir reference 16.

Figure 2 .

1 Calculated spectruin for - = 3 x 101'sec. Circles: a typical f lux CC increase, taken from reference 16.

Figure 3.

The average electron f lux from reference 16 shown along with the excess electron flux arrived at i n reference 3.

. I

- - - - x 1 0 ' ~ s e c - 7

I

- -

Measured average electron f lux,

reference 16 - - rn

rn - - - -

I I > I 1 I l l I I I 1 1 1 1

100

50

10

5

2 I 2 5 10 20 50 I00

Fiqure I Kinetic energy, MeV

i

io3

IO2

IO 1

IO0

IO”

lo-*

I MP-A spectrum,

reference 16 \

I 1 I I I I I IO 100 1,000 10,000

Rigidity, MV

Figure 3