In the frame work of energy dependent confinement for cosmic rays, the energy spectrum inside the source is flatter than that observed. Antiproton observation suggests large amount of matter is being traversed by cosmic rays in some sources. As a result, secondary particles are produced in abundance. Their spectra was calculated and it is shown that the energy dependent confinement model is in conflict with some observations

Stephens, S. A.

English

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OBSERVED ANTIPROTONS AND ENERGY DEPENDENT CONFINEMENT 
OF COSMIC RAYS: A CONFLICT? 
S.A. Stephens 
Tata Institute of Fundamental Research 
Homi Bhabha Road, Bombay 400005, India 
ABSTRACT 
In the frame work of energy dependent confinement for cosmic 
rays, the energy spectrum inside the source is flatter than 
that observed. Antiproton (@) observation suggests large 
amount of matter is being traversed by cosmic rays in some 
sources. As a result, secondary particles are produced in 
abundance. We have calculated their spectra and it is shown 
that the energy dependent confinement model is in conflict 
with some observations. 
1. Introduction. The observed secondary to primary nuclei in cosmic 
rays decrease with energy suggesting that matter traversed by cosmic 
rays depends upon energy. Therefore, it was postulated (Eg. Juliusson 
et al. [I]) that the confinement of cosmic rays in the Galaxy is energy 
dependent. Recent observations show that the behaviour of this depen- 
dence is a R - ~  above - 2 GV/C with 6 = 0.6 to 0.7 [2,3] . This would 
mean that the accelerated spectrum of cosmic rays has a spectral index 
f-3 = 2.15 to 2.05. P observations show that cosmic rays traverse a 
large amount of matter inside some sources. Because of the flatness 
of source spectrum, secondary particles are copiously produced [41, and 
the effect of energy loss processes is less felt by the particles. 
Recently, it is shown that supernova (SN) explosion in dense cloudlets 
can explain p observations [5]. This work was based on the Nested 
Leaky Box Model 161, in which cosmic ray source spectrum has = 2.75. 
In this paper, we calculate the secondary particle production in SN, 
which explode in dense cloudlets, in the framework of energy dependent 
confinement model. We then compare the spectra of y-rays, electrons 
and positrons with observation. 
2 We have established a set of coupled 
differential equations to describe the propagation of protons, F, ef 
inside SN envelope, by taking into account all energy loss processes 
including adiabatic cooling during expansion [7]. The initially acce- 
lerated spectra is obtained by normalizinq the interstellar spectra at 
2 GV/c and thus we obtained 1.65~10~ R'~- 5/ (m2.sr. S.GV/C) for nucleons 
and 90 ~-~.l~/(m2. sr. s. GV/C) for electrons. We consider that the 
SN expansion continues in the cloudlet till about 50 g.cm-2 matter is 
being traversed by cosmic rays. Because of the flat spectrum of 
nucleons, it is found that only 10% of the observed nucleons in cosmic 
rays have to come from such sources in order to account for the observed 
p; the corresponding value for f-3 =2.75 is 30% [a] . The effect of syn- 
chrotron radiation on electron spectrum is also small and the spectrum 
350 
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I ' " " " ' I  ' " " " ' I  ' " I  
F i g .  1  I n t e g r a l  d i s t r i b u t i o n  o f  
y - r a y  s o u r c e s  i s  shown a s  
a  f u n c t i o n  o f  i n t e n s i t y  
a b o v e  1 0 0  MeV. T h e  d a s h e d  
c u r v e s  a r e  f o r  e n e r g y  
d e p e n d e n t  model  and the 
s o l i d  c u r v e s  a r e  f o r  
N e s t e d  Leaky  Box m o d e l .  
at high energies is not much depleted. 
We have calculated the spectrum of y-rays resulting from T o  decay 
and bremsstrahlung processes. If 90% of the observed cosmic rays come 
from SN exploding in normal interstellar medium, the 'scaling required to 
estimate the total brightness of the source from the normalized inter- 
stellar spectrum is In order to calculate this number, we con- 
sider a galactic volume of R = 15 kpc and h = 0.5 kpc, in which cosmic 
rays are stored for 3x10~ yrs. In this volume, the rate of SN explosion 
in interstellar medium is one in 30 yrs. We assume that acceleration is 
complete in -200 yrs and the adiabatic cooling effective during the adia- 
batic phase. The number of SN required in cloudlets to account for the 
observed jj is calculated and the relative number to that explode in in- 
terstellar space is found to be 0.129, 0.093, 0.075 and 0.061 for 
nH = 104 , 4x104, lo5 and 2.5~10~ at~m.cm-~ respectively. Making use of 
these parameters, we have calculated the luminosity distribution of y-ray 
sources in the Galaxy as described elsewhere 191. 
We have shown in Fig. 1, the luminosity distribution of y-ray 
sources for energies 100 MeV, assuming that the distribution of SN in 
the Galaxy is similar to the molecular hydrogen [lo]. The dashed 
Curve A is calculated for nH = lo4 cm-3 and Curve B after folding in the 
observed density distribution of clouds [Ill. These are compared with 
the Cos-B distribution [12], which is shown by the histogram. It is 
clear from this figure that there is no serious conflict with the data. 
For comparison, we have shop by solid curves the predictions with 
6 = 2.75 [9] . We have also estimated the spectral hardness of y -ray 
sources, which is defined as I ( >  300 MeV)/ I(> 100 MeV). It is found 
that over the life of the SN, this varies only by small amount from 
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i n  t h e  lower par t  and po- 
s i t r o n  spectrum i n  t h e  up- 
per  p a r t .  The s o l i d  cur-  
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Box model. 
ENERGY IN G ~ V  
0.475 to 0.46, due to the flat input spectrum. This value is indeed in 
conflict with the observed values [I21 , most of which are much smaller. 
3. Electron Spectrum. We have calculated the equilibrium spectrum of 
electrons and positrons in interstellar space by considering two kinds 
of source spectra Q 
e* 
One of them is from SN exploding in dense cloud- 
lets, which contribute r 10% of the observed nucleons, and the other 
from SN explosion in normal interstellar medium. The equilibrium spec- 
trum is obtained by solving the equation. 
in which T(E) is taken to be T ~ E - ~ ,  and To is varied to obtain a good 
fit to the data. We have plotted in the lower part of Fig. 2, the obser- 
ved flux values from recent experiments [13-151. The solid curve is 
the calculated spectrum using a value of To = 2x10~ yrs. This value of 
T, is inconsistent with 1.4~107 yrs obtained from 'Be data at low ener- 
gies [16]. We have also shown the calculated equilibrium spectrum for 
f3 = 2.75 [17] with T = 5x10~ yrs, which is consistent with the observed 
value within errors. 
Making use of the same value of To obtained from the study of elec- 
trons, we have calculated the equilibrium spectrum of positrons. This 
spectrum is shown in the upper part of Fig. 2 by solid curves. The two 
curves A and B correspond to magnetic fields in the dense cloudlets 
assuming that the field strength scales as (B, JnH) with Bo = 4 and 
8 pG respectively. It is clear that the observed spectrum [I81 is not 
, 
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in agreement with the calculations. If one reduces the value of Bo or 
To, the deviation from the data would increase further. We have also 
shown the calculated positron spectrum for (3 = 2.75 [I81 and one notices 
a good agreement with the observation. 
4. Discussion. Many difficulties associated with the energy dependent 
confinement model have been pointed out earlier 1191. They include power 
requirement, streaming velocity at high energies and the smooth spectral 
shape extending to very high energies. We have shown here that, though 
the expected luminosity distribution of sources is not in conflict with 
the Cos-B data, the observed spectral hardening of y-ray sources is not 
in agreement with the expectation. secondly, the observed electron spec- 
trum is clearly in conflict with the expectation 1131. Thirdly, the 
model predicts too large a flu of positrons. The above conclusions are 
further strengthened if the value of 6 is indeed 0.7 [21. 
The analysis made here is based on the hypothesis that antiprotons 
are produced in sources as secondary particles. However, if p comes 
from external galaxies [201, one may perhaps circumvent the present in- 
consistencies. However, it has been shown by Stephens [211 from a study 
of muon charge ratio at sea level that the extragalactic hypothesis and 
energy dependent confinement model cannot co-exist. 
References 
E. Juliusson et al., ~hys. Rev. Letters, 29, 445 (1972) 
J.F. Ormes and R.J. Protheroe, Ap.J., 272, 756 (1983) 
L. Koch-Miramond, Proc. 18th ICRC (Bangalore) , 9, 275 (1983) 
P.O. Lagage and C.J. Cesarsky, "High Energy Astrophysics" 
Ed. J. Audouze and J.T. Thanhvan, p.203 (1984) 
B.G. Mauger and S.A. Stephens, Proc. 18th ICRC (Bangalore) 9, 171 
(1983) 
R. Cowsik and L.W. Wilson, Proc. 13th ICRC (Denver), - 1, 500 (1973) 
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Audouze and J.T. Thanhvan, p.217 (1984); To appear in ~p.spSci(l985) 
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appear in Astron. Ap. (1985) . 
353 
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[1] . 1 so  t 1., P s. e . ett   1972) 
[2] . r e .J. r  p.J., ,  1983) 
[3] . oc i a  r . t CR  al r  ~, 1983) 
[4] . . .J. esar  i er st ysi
. udouz .  .  ) 
[5] . . auger . . s ep  r . t CR  1  ~,  
) 
[6] . o si . . il , r . t CR  e ver)  !,  ) 
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[10] .B. urt . . or  p.J.,   76) 
[11] . . i . . ol s it  p.J.,  80) 
[12] . er s  h. . hesi  niversit f ei  
[13] . u ler . , r . t CR  gal r  ~,  ) 
[14] . i ur t l., p. ., 2   ) 
[15] . . ol t l., p.J., 8~622 ) 
[16] . arci uno t l., p o~17t C  ri  ~,   
[17] . . t  hi onfer  .  
[18] . . ol t l., hi onfer
[19] . . engar j t 1., r c.' t CR  ver  !,  
[20] . . t t l., p. p. ci.,  ) 
[21] . . t  r . t C  angal r )  ~,  )   
r str . p. )  


Observed antiprotons and energy dependent confinement of cosmic rays: A conflict?

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