POSSIBIX SOlJgCE MECHANISM- FOR LOW-ENERGY GALACTIC… · POSSIBIX SOlJgCE MECHANISM- - FOR...
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' POSSIBIX SOlJgCE MECHANISM- - FOR LOW-ENERGY GALACTIC' ELECTRONS
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' KARL A. BRUNSTE4N
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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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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.
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- - - - x 1 0 ' ~ s e c - 7
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- -
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
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