Supernova (SN) exploding in dense cloudlets produce large fluxes of gamma-rays. They would shine on gamma-ray sources, but their life time is small. Flux distribution of these sources in the Galaxy are calculated and compared with the COS-B catalogue of sources

Stephens, S. A.

English

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20S _ 2.s-s
suP_.r_ovA_.xPnosio_ I_ D_S_. Cr_OUDSIN T_ C,2U_Y
AND THE COS-B GAMMA RAY SOURCES
S.A. Stephens
Tara Institute of Fundamental Research
Homi Bhabha Road, Bombay 400005, India
ABSTRACT
Supernova (SN)exploding in dense cloudlets produce large flux
of y-rays. They would shine on Y-ray sources, but their life
time is small_ ,We calculate the flux distribution of these
sources inthe Galaxy and compare with the Cos-B catalogue of
sources.
1. Introduction. It has been pointed out recently that large flux of
secondary antiprotons (p) is produced in envelopes of SN which explode in
dense cloudlets in the Galaxy [i]. Taking into account all energy loss
processes, including adiabatic cooling, _T is shown that the resultant
spectral shape of these p match the observations[2]. These SN should
also be an intense source of y-rays [3], but their life time in the
cloud is small. The absolute brightness and time evolution of these
sources depend upon the density of the cloudlets [4]. Because of these
reasons, the number of such sources in the Galaxy at a _iven time, is
small and its brightness depends upon its age and the distance from the
Sun. We have calculated the flux 5100 MeV) distribution of these 7-ray
sources, by folding in the surface density of molecular hydrogen in the
Galaxy and the density distribution of cloudlets. These estimates are
compared with the observed distribution of Cos-B sources [5].
2. y-ra[ Production inSources. During the evolution of SN in dense
clouds, cosmic ray nucleons interact with matter to produce T ° decay y-
rays. As the matter traversal increases, the spectral shape of nucleons,
which is initially assumed to be a simple power law in rigidity, flattens
due to ionization loss, and the yrray spectrum near 70 MeV peak is also
altered [4]. Electrons interact with matter to produce bremsstrahlung
y-rays. Electron spectrum evolves rapidly withthe age of SN. The
initially accelerated electronsare depleted by synchrotron energyloss
process at high energies, and the spectrumis dominated by secondary
electrons during the late stages of evolution. At low energies, the
spectrum is flattened due %o ionization loss. As a result of these, the
relative contribution of bremsstrahlung Y-rays decreases with time. We
have calculated the y-ray spectrum from these sources as described else-
where [4].
From the study of p produced from these sources, it is shown that
about" 30% of the observed nucleons inlcosmicray_come from such sources
[1,2]. The remaining cosmic ray_ucleons come from sNexploding in ordi-
nary clouds with n_ = 10 atom.cm- in the Galaxy.i If the rate of SN
explosion in the cIouds is about once in 30 years in the Galaxy, the
• 
aOI 
SUPERNOVA EXPLOSION IN DENSE CLOUDS IN THE GALAxy 
ND E OS-B GA MA R Y S URCES 
. . tephens 
ata I stitute f Fundamental esearch 
omi habha oad, ombay 0 05, I dia 
ABSTRACT 
OG 2.5-3 
upernova ( ) exploding i  ense cloudlets roduce l rge fl x 
f -rays. hey ould shine n y-ray sources, ut eir life 
ti e i  ma l~ " e alculate t e fl x aistribution f t ese 
sources i  the alaxy d pare ith t e os-B atalogue f 
sources. 
. I troduction. It has en ointed ut r cently t at l r e l x f 
condary ntiprotons   roduced  velopes f  ~hich explode  
dense loudlets i  t e alaxy [1]. aking t  count l nergy ss 
roces es, cluding diabatic oling, i't  n at t e sultant 
spectral ape f t ese  atch t e bservations [2]. hese  ould 
also be an i t nse s urce f -rays [ ], ut eir li e t e i  t e 
l ud is s all. he bsolute rightness and ti e volution f t ese 
s urces depend pon t e ensity f t e loudlets ]. ecause of t ese 
reasons, the nu ber of such sources in the alaxy at a given ti e, is 
s all nd t  rightness epends pon its ge nd t e istance fr  t e 
un. e have alculated t e fl x (>100 eV) istribution f t ese r-ray 
sources, y f lding i  t e surface ensity f olecular ydrogen i  t e 
alaxy and t e ensity istribution f cloudlets. hese sti ates re 
pared ith t e bserved istribution f os-B urces ). 
. -ray roduction i  sources. uring t e volution f   ense 
l uds, cosmic r y ucleons i teract ith atter t  produce nO ecay -
r ys. s t e atter versal i creases, t e ectral ape f ucleons, 
hich is i itially ss ed t  e  i ple ower l  i  i idity, l ttens 
ue t  i nization l s, and t e :-ray ctrum ear 0 eV eak is lso 
ltered [ ). lectrons nt~ract ith atter t , roduce remsstrahlung 
-rays. lectron s ectrum volves rapidly \\,i the ge f . he 
i itially ccelerated lectrons are epleted by synchrotron ergy loss 
process at igh nergies, nd t e s ectrum is ominated y secondary 
lectrons uring t e l te s,tages f volution. t  nergies, t e 
spectrum  l tt ned ue t  i nization l s. s  sult f t ese, t e 
lative ontribution f remsstrahlung y-rays ecreases ith t e. we 
have alculated t e y-ray spectrum  t ese sources s escribed lse-
here [ ]. 
Fro  the t dy f,  roduced f  t ese sources, t  n t at 
about' 3  f t e bserved ucleons'i  cosmic'rays:come fr  ch urces 
[1,2]. The remaining cosmic ray_~ucleons come from SN exploding in ordi-
ary clouds ith u  0 tom.cmi  t e alaxy. f t e r te of  
explosion i  t e t uds i  bout nce '  ears i 'th , alaxy, e 
https://ntrs.nasa.gov/search.jsp?R=19850025647 2020-03-20T17:53:27+00:00Z
206 OG 2.5-3
energy release _ the form of cosmic rays soon after acceleration, about
200 yrs, is ~I0-- eV [4] ; it is assumed that adiabatic cooling takes
place only upto the end of the adiabatic phase when remnant fragements.
We consider that the total energy release in the form of cosmic rays is
the same for all sources. With this information, the brightness evolu-
tion of SN with time is calculated. Observations show that cloudlets have
H2 densities varying from about a few times 103 molecules/cm 3 to about
105/cm 3 [6]. In Fig. I, we have shown the brightness above i00 MeV as a
function of time for SN exploding in cloudlets for different nH values.
The adiabatic loss is higher for SN exploding in rarer medium, and it is
seen that the brightness decreases rapidly with time for sources in rarer
medium.
3. Luminosity Distribution of y'ray Sources. We consider in this analy-
sis that cosmic rays are accelerated in dense source by the beginning of
the adiabatic phase; th_ remnant leaves the cloudlet when cosmic rays
_traverse about 50 g.cm of matter. One can estimate from the observed
p the relative number of SN, which explodes in dense clouds to that in
ordinary clouds. Our calculation show that the ratio is 1.34:1.0,
0.82:1.0, 0.6:1.0 and 0.44:1.0 respectively for nH = 104 , 4x104, 105 and
2.5xi05 atom.cm -3. We make use of this to calculate SN rate in the
Galaxy. The flux distribution is evaluated by the integral
N_L) =fIIN(R,n H) R dR. d_ . _(nH,t)/4_d 2} dt (I)• o g
In this equation L = B/4_d 2, where d2 = R2 + R2-2 R R Cos$ ; here
Ro = i0 kpc the abundance of galactic centre and, R°the radius and ¢ the
azimuthal angle between radius R and the Sun-Centre line. The restri-
ction in this integral is that the integrant becomes zero when
{B(nH,t)/4_d2 }<L. In this equation N(R,n H) is the number of SN per unit
area, weighted according to the molecular hydrogen density [7] and is
normalized to the number of SN produced per unit time in the entire ga-
laxy for a given cloud of density nH.
1043 , .... ] _ i ''''"I l , ,,,,,,] , , ,,L,, t
> I00 MeV PHOTONS
Z I042
i0_, cl._ 3 "
mI __ Fig. 1 Brightness of y-ray
sources_ 100 MeV is
z I_' loSc_ shown as a function "
of time for differentbJ
Z _ _ 4X 104cm 3
- nH values
-r
,o_
m ,o__
l,,,,,i , i , ,iii,I i I , ,,,III I I l I ILl
i01 102 iO s i04
TIME IN YEARS
8 OG 2.S-3 
energy release ~~ the form of cosmic rays soon after acceleration, about 
200 yrs, is -10 eV [4]; it is assu ed that adiabatic cooling takes 
place only upto the end of the adiabatic phase when re nant frage ents. 
e consider that the t tal energy release in the for  of cos ic rays is 
t  sa e f r ll s rces. it  t i  inf r ation, t  ri htness e l -
ti    it  tim  i  l ulated. bservations h  t t l dlets h  
2 nsities r ing fro  ut a fe  tim s 1 3 olecu1es/cm3 t  ut 
S/ 3 [ ]. I  i . 1, e e sh  th  ri htness e 1  e    
function of time for SN exploding in cloudlets for different n  values.  iabatic l  i  i her  S  loding i  r edi , a    
 t t t  i htness creases i ly ith ti e  rces i  r r 
ediu . 
3. Luminosity istribution of y-ray sources. We consider in this analy-
sis that cos ic rays are acCelerated in dense source by the beginning of 
the adiabatic phase; t~~ remnant leaves the cloudlet when cosmic rays 
trav rs  a ut SO .c  f atter. ne ca  sti ate fro  t  served  t  r l tive ber f , hich plodes i  se l ds t  t t i  
ordinary clouds. ur calculation sho  t at the rati  is 1.34:1.0, 
0.82:1.0, 0.6:1.0 and 0.44:1.0 respectively for n  = 10
4
, 4x104, lOS and 
.S 10S .cm 3 • e ake   is  lculate  t    
alaxy. e fl x istribution i  aluated  t  i t gral 
N (> L) =:JJJ N (R,n ) R dR. di4> .' fu (nH,t) /47fd2} t (1) 
 is uation   / 7fd , here 2    2_2   s~ ; ere, 
Ro  10 kpc the abundance of galactic cen~re and, ROthe radius and ~ the 
i uthal gle t en ius  d t  un-Centre e. e stri-
tion  t is i t gral i  t at t  i t rant es r  hen 
{B(n ,t)/47fd2 }<L. In this equation N(R,n ) is the number of SN per unit 
area, eighted according t  the olecular hydrogen density [7] and is 
rmalized t  t e nu ber f S  r duced er nit ti e i  t e tire a-
laxy for a given cloud of density n • 
!Q ~ OO v Z 42 0 10 ' ~-3 ~ ~2x1  em 
Z 
- 41 
en 10 
en 
W 
Z 
I-
:I: 
!:2 ~ 
a: 10 
III 
TIME I  YEARS 
TONS 
Fig. 1 Brightness of y-ray 
urces'> 00 eV  
n s  f nction 
f t e f r ifferent 
n  values 
• 
IOT OG2.+-3
i , + ,,l+t
........ I ........ I
nH
B)4XIO .
-_ _ C) '10+
Fig. 2 Integral source distribu-
_ lJ _ tion is plotted as a
c_._ function of observable
" flux; for comparison
Cos-B data is shown.
z
i_7 166 iO"_ 16+.
FLUX (> I00 P4_) / tam2, £)
We haveplotted in Fig. 2, the number of expected y-ray sources in
the Galaxy with flux>L as a function of L. We have considered a range
of L values from 10-7 to 10-4 photon/(cm2.s). Curves B, C and D corres-
pond to nH values 4x10 4, 105 and 2.5x10 5 atom. cm-3 respectively. The
observed Cos-B source distribution is shown by the step function. It is
clear fromthisfigure that anti-protons are produced in dense cloudlets
do not contradict the ¥-ray observations. The good agreement Curve A has,
withtheobserved data_suggests that indeed Cos-B sources could have this
origin.
The observation of dense cloudlets show that the densitypeaks
around nH = 105 atom cm-3. We have evaluatedN(nH,R) distribution using
_he available information on the density distribution of clouds [6].
Making use of the weighted distribution of N(nH,R) we have integrated
Eqn. 1 over nH and the result is shown as dashed curve in Fig. 2. The
agreement with data is not as good as that for nH = 104 atom cm-2.
4. Discussion. Wehave shown that if antiprotons are produced in enve-
lopes of SN, which explodes in dense cloudletsin the Galaxy, the y-ray
produced in these sources do not contradict the observed Cos-Bdata.
It is also seen from Fig. 2 that the source distribution calculated
fOrnH = 104 atom.cm-3isin good agreement with the observed data. How-
ever, the calculated distribution after folding the distribution of
observed mean densities in cloudlets predicts too small a number of y-ray
sources at low flux values. This may perhaps be due to the following
reason. We have assumed a uniformdensity of matter in the cloud during
the entire evolution ofSN. Observations show [8] that the radial gra-
diant in density varies between r-_-5 and r-2, with densities _10 4 atom.
cm-3 beyond 0.1 pc. Therefore, when SN explodes in these clouds, the
remnant would spend most of its time in regions of low densities _ 104
atom. cm-3
• 
" 
.. 
c 
I'lH 
R) 104 
8) 1< 10'" 
C) '106" 
]))2·5 Xll 
___ COMBI N EX> 
10' 
i . 2 
G .5  
I tegral s urce istribu-
tion is plotted as a 
function of observable 
fl x; f r comparison 
Cos-B data is shown. 
We have plotted in Fig. 2, the number of expected y-ray sources in 
the Galaxy with flux> L as a function of L. We have considered a range 
f  alues fr  -7 t  -4 oton/(cm2.s). Urves ,  d  rres-
pond to nH values 4xl04 , 105 and 2.Sx105 atom. cm-3 re$Pectively. The 
bserved os-B s rce istribution i  s n  t  st  f nction. It i  
lear fro · this figure ~t ti-protons r  r duced i  ense l udlets 
do not contradict the r-ray observations. The good agreement Curve  has, 
with the observed data,suggests that indeed Cos-a sources could have this 
origin. 
e servation f ense l udlets s  t t t  nsity' peaks 
around n  = 105 atom cm-3 • We have evaluated N(nH,R) distribution using 
the available infor ation on the density distribution of clouds [6]. 
aking use of the weighted distribution o~ N(nH,R) we have integrated 
Eqn. lover n  and tpe result is shown as dashed curve in Fig. 2. The 
agreement with data is not as good as that for nH = 104 atom cm-2• 
. iscussion. e have s n t t i  ti rotons r  r duced i  ve-
lopes of SN, which explodes in dense cloudlets in the Galaxy, the Y-ray 
produced in these sources do not contradict the observed Cos-B data. 
It is also seen fro  Fig. 2 that the source distribution calculated 
for nJi = 104 atom.cm-3 is. in good agreement with the observed data. How-
e er, t e calculated istri ution fter f l i g t e istri ution f 
served ean nsities i  l dlets redicts t  s all  ber f -r  
sources t low', flux values. his ay perhaps be due t  the follo ing 
reason. We have assu ed a unifor  density f atter i  t e cloud during 
t  tire olution f SN. bservations sho  [ ] t t t  r ial r -
di~nt in density varies between r-"·~ and r-2, with densities ~104 atom. 
c -3 beyond 0.1 pc. Therefore, hen SN explodes in these clouds, the 
re nant would spend ost of its time in regions of low densities ~ 104 
-3 ' t . e  • 
_0_ OG 2.5-3
On the basis of Curve A in Fig. 2, one expects about i00 y-ray
sources in the Galaxy with flux densities > 10-7photon/(cm2.s) at ener-
gies > I00 MeV. This can be checked by GRO. We can predict the hardness
of spectrum in such sources, which can also be measured accuratelyby
GRO. Our calculations show that the variation of F _300 MeV)/F _I00) is
from 0.26 to 0.34 over the life of SN and this is consistent with the
observations [5]. The high energy V-ray spectrum is dominated by T °-
decay and the spectral shape will be indicative of the accelerated spec-
trum of nucleons in these sources.
We have shown elsewhere [9] that the observed positron data can be
well explained by secondary production of e+ in these sources. It is
important at this stage to calculate the radio spectrum emitted by elec-
trons in these sources.
References.
[i] B.G. Mauger and S.A. Stephens, Proc. 18th ICRC (Bangalore), 9,
171 (1983).
[2] S.A. Stephens & B.G. Mauger, Proc. 19th Rencentre de Moriond
Astrophysics Meeting, p.217 (1984); Ap. Sp. Sci. (1985)in press.
[3] V.L. Ginzburg & V.S. Ptuskin, J. Ap. Astron. _, 99, (1984)
[4] S.A. Stephens, This Conference OG 2.5-2
[5] W. Hermson, Ph.D. Thesis, University of Leiden (1980)
[6] R.A. Linke and P.F. Goldsmith, Ap.J., 235, 437 (1980)
[7] W.B. Burton and M.A. Gorden, Ap.J., 207, L189 (1976)
[8] R.B. Loren et al., Ap.J., 270, 620 (1983)
[9] S.A. Stephens, This Conference, OG 6.2-9
208 OG 2.5-3 
On the ba is of Curve A in Fig. 2, one expects about 1 0 y-ray 
sources in the G laxy with flux densities >10-7 photon/(cm2.s) at ener-
gies > 1 0 MeV. This can be checked by GRO. We can predict the hardness 
of spectrum in such sources, which can also be measured accurately'by 
GRO. Our calculations show that the variation of F (> 300 MeV) /F (> 100) is 
from 0.26 to 0.34 over the life of SN and this is consistent with the 
observations [5). The high energy y-ray spectrum is dominated by no-
decay and the spectral shape will be indicative of the a.ccelerated spec-
trum of nucleons in these sources. 
We have shown elsewhere [9) that the observed positron data can be 
well explained by secondary production of e+ in these sources. It is 
important at this stage to calculate the radio spectrum emitted by elec-
trons in these sources. 
References. 
[1] B.G. Mauger and S.A. Stephens, Proc. 18th ICRC (Bangalore), ~, 
171 (1983). 
[2) S.A. Stephens & B.G. Mauger, Proc. 19th Rencentre de Moriond 
Astrophy ics Meeting, p.217 (1984); Ap. Sp. Sci. (1985) in press. 
[3] V.L. Ginzburg & V.S. ptuskin, J. Ap. Astron. 5, 9, (1984) 
[4) S.A. stephens, This Conf rence OG 2.5-2 -
[5] W. Hermson, Ph.D. Thesis, University of Leiden (1980) 
[6] R.A. Linke and P.F. Goldsmith, Ap.J., 235, 437 (1980) 
[71 W.B. Burton and M.A. Gorden, Ap.J., 20~ 89 (1976) 
[8] R.B. Loren et al., Ap.J., 270, 620 (1983) 
[9] S.A. Stephens, This Conf rence, OG 6.2-9 
• 


Supernova explosion in dense clouds in the galaxy and the COS-B gamma-ray sources

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