Cosmic antimatter annihilation and gamma ray background spectru

Bredekamp, J.

Morgan, D. L.

Stecker, F. W.

English

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17
COSMIC ANTI MATTER ANNIHILATION
AND THE
Y-RAY BACKGROUND SPECTRUM
F. W. STECKER
D. L. MORGAN
J. BREDEKAMP
APRIL 1971
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Cosmic Antimatter Annihilation
and the Y-Ray Background Spectrum
F.W. Stecker
D. 1. Morgain*
J. Bredekamp
Theore al Studies Branch
NASA
	
Idard Space Flight Center
Greenbelt, Marylanc 20771
ABSTRACT:
We present here some initial results of a detailed
calculation of the cosmological ^-ray spectrum from matter-
antimatter annihilation in the universe. The similarity of
the calculated spectrum with the present, observations of
the Y/-ray background spectrum above 1 MeV suggests that
such observations may be evidence of the existence of
antimatter on a large scale in the universe. Quantitativ*
comparison of Lhe calculations with the existing observa-
tions indicates that the product of interacting matter and
antimatter densities at present is np'0 T1'--
 
0 ^ 4 X 10-26 cm 6
*NAS-NRC Postdoctoral Resident Research Associate
The question of the existence a" antimatter on a cosmological
scale is one of the most basic problems of physics and cosmology.
Recently it has t".en on added interest because of :he- suggested
possible role of antimatter in galaxy formation and the evolution
of the universe ( Alv®n, 1965 ; Harrison, A9 4..7 ; Omnes, 1969 ) .
It has long been recognized that the most promising way to search
for evidence of antimatter on a cosmological. scale is to attempt
to observe -rays of cosmic origin which would be prcduced by the
decay of neutral pions arising from matter-antimatter annihilation.
In order to determine the annihilation-origin of such ?-rays, one
	 }
must first calculate the ^-ray spectrum which would be produced by
such annihilations so that the calculated spectrum may be compare.
with observational data on the --ray background ^pectrum for possible
identification.
Because of their possible significance, we present here the re-
sults of such a detailed calculation, the details of which will be
presented in full in a future article.
The cross sections for H-A, p-p, p-h', and H-17 annihlation as a
function of temperature for '"low temperatures" ( T < 10 11K ) have
been included in the calculation. They are based on the recent cal-
culations of Morgan and Hughes (1910) and are shown in Figure 1. Our
calculations also include the effects of /-ray absorptioh by pair
production interactions with the intergalactic medium and photon
transport by Compton interactions of the /-rays with the intergalactic
medium at high redshifts.
1
As can be seen in figure 1, the annihilation cross sections as
a function of relative velocity can be expressed in various energy
regions as a power law of the form
T M	 v	 (l)
C
where i - 1,2,3 and where
^'1 s 4.8 X 10 25 cm2  ^ 1	 , for	 101 ' K T 'Z^ 1013K
o-2 - 2.2 X 10 0'27 cm2 , ^2 a 2	 , f or 104 K T ti1011K
and 
cr3 2.6 X 10
-18 cm2 a3 : 0.64 , for 10 K <- T 1 10 4 K
If Q (E^) is definedas the source spectrum of 1-rays from theA
Y	 decay of neutral pions produced by annihilation, the annihilation
-ray so_  spectrum taking redshift effects into account and con-
sider'.ng isotropic cosmological models(with the cosmological constant,
1L, set equal to zero) is given by
HO
^l
^-1T 	 h^P	 14  
	
) yi
where HO is the Hubble constant, n n— it the product of the
P.9 0 P,0
effective mean densities of interacting matter and antimatter
protons at a redshift z = 0 0 T is the temperature of the inter-
_	 acting gas, k is Boltzmann's constant # 11is the ratio of the average
matter density in the universe at present to the critical density no-
s
3H2 /9oG and rw is the gamma function. In a. riving equation (2)
it is assumed that np(s)n ( s)•^ ( 1 +u) g . Tie matter temperature
	
2.7 C (4+)	 Z zoo
(3)
(Zeldovich, at a1. , 1969 ).
It oan be shown thit equations (2) and (3) together with the
bounded form of the function GFA(E j) yield source spectra of the form
E- r as shown in table 1.
At high redshifte, when pair production and Compton scattering
become important, it becomes necessary to solve a oesmological-photon-
transport (CPT) equation in order to determine the 4-ray spectrum
(Axons, lg?la,b). For a differential photon energy spectrum we find
this equation to be of the form
GAS=
	
- %Z I
	
_	
/^ -.
a 	 ( 4)
k, _ ^^	 („ 1
where I • I(E,y) is the annihilation i-ray flux*
y;1+Z
E = S ./ /mec2
V S (1-A) /a
Sa2.5 X 10-2.ai
3
IThe source function a A (E') is taken from Stacker (1967) .
Me annihilation-rate function
_ p LT(,,,
CTS
	
V[V^	 (5)
where
-1O-u = Vne c) Ho	 ,	 (6)
The function A(r) is proportional to the total closs section
for absorption and scattering of /-rays by pair production and Compton
interactions. The scattering function B((_^r') is proportional to the
probability that a 7-ray of energy c:' wijYL Compton scatter to energy,
The upper limit
^tF} =	 (7)
°'a 	s E i
The function IA(Epyzl)/np,,0 F,0 ,obtained by numerical solution
of the CPT equation, is shown by the solid line in figure 2. If we
chose a value for n n	 Of 4 X 10-26 cm-6 for the product of the
p , 0 $,0
mean densities of interacting matter and antimatter at present (z=0) ,
we obtain a theoretical annihilation spectrum compatible in both
form and intensity to tha observed spectrum of cosmic background
^-radiation -between 1 and 6 MeV (Tette, at al. 1970) . We thus eon-
elude that these observations may be evidence of the existence of
antimatter on a cosmological scale. This conclusion, however, is sub-
ject to the following conditions:
I
x
4
(1) There must be an additijnal power-law background component
of X-rays below 1 MeV of another origin. Our calculations of the an-
nihilation /-ray spectrum below 1 WeV (not presented in their entirety
here) fall well below the observed power-law spectrum in that energy
range.
(2) The peak in the calculated annihilation spectrum near 1 MeV
is caused by absorption and scattering of the /-rays  by interactions
with an intergalactic medium having an average density near the critic-
value nc .
(3) There is strong evidence that at a redshift of z--2.5 (or
perhaps somewhat greater) the intergalactic medium is strongly ion-
ized and equation (3)  do es not hold ( Gunn and Peterson 1965, Rees
1969). At the redshift there reionization occurs there will be a
rapid drop in the cross section for annihilation ( see figure 1) re-
sulting in a sharp steepening of the fray spectrum at an energy E,/ c
X50 MeV. Above F.y c the spectrum will drop off much more rapidly than
s
the power-law dependence NE`2.86 shown in figure 2. It is thus not
expected to conflict with the upper limit on 'the isotropic background
of ^-1 3  X 10 -5 cm-2sec-l sr-1 for the integral flux above 100 MeV as
reported by Clark, et al.(1970).
(4) The obs --rvati oval data on the /-ray spectrum above 1 MeV do
not provide enough information at present to yield a unique identif-
ication of their origin. There have been several alternative attempts
to explain the background flux as being due to the decay of neutral
5
pions produced by oosmic-ray interactions at high redshifts ( the
protar hypothesis ( Stacker 1969a9b,1971)) , galactic electron
bremsstrahlung (Rees and Silk 1970), extragalactic electron brems-
strahlung ( Silk 1970) extragalactic proton bremestrahlung ( Brown
1970) and nuclear emission lines (Clayton and Silk 1969). More
recent work shows that none of these alternatives except the protar
hypothesis seem capable of explaining both the form and intensity
of the observed flux ( Vette, et al. 1970 9 3tecker,et &1.1971; Stecker
and Morgan 1971, Jones 1971). An observational test between the pro-
a.
tar hypothesis and the annihilation hypothesis can be made at energies
f' gies above 50 MeV. The annihilation hypothesis predicts a steepening
N
in the background spectrum above 50 MeV whereas the protar hypothesis
predicts a steepening the the spectrum at about 7 GeV( Fazio and
Stecker 1970). Should fixture investigations indicate that the back-
ground ^-radi at ion above 1 MeV is not due primarily to matter anti-
matter annihilation, this will place an upper limit on the product
np Ong 0 0f the order of 1026 am 6.
REFERENCES
Alven, H. 1965. Rev. Mod. Phys. 37, 652.
Arons, J. 1971a. Ap.J. 164 9 437.
1971b. Ap.J. 164, 457.
Brown, R.L. 1970. Lettere al Nuovo Cimento 4, 941.
Clark, G.W. , Garmire, G.P. and Kraushaar, Y.L. 1970. Private commun-
ication.
Clayton,D.D., and Silk,J. 1969. ApJ.(Letters) 158, L43.
Fazio, G.G. and Stecker, F.W. 1970. Nature 226, 135.
Gunn,J.E. and Peterson.B.A. 1965. ApJ. 142, 1.633,
Harrison, E.R. 1967. Phys.Rev.Letters 18; 1011.
Jones, F.C. 1571. To be published.
Morgan,D. L. and Hughes, V. 1970. Phys. Rev. D2, 1389.
Omnes,€.. 1969. Phys. Rev. Letters 23, 48.
Rees, M.1.1969. Ap 'Letters 4, 113.
Rees, M.J. and Silk,J. 1969. Astron. and Ap. 3, 452.
Si1k,J. 1970. Space Sci. Rev. 11, 671.
Stecker, F.W. 1967 *
 Smithsonian Astrophys. Obs. Special Rpt. NO.261.
1969&. Ap.J. 157, 507.
1969b. Nature 224, 870.
1971. Nature 229, 105.
Stecker, F.W. and Morgan, D.L. 1971. To be published.
Stecker, F.W., Vette, J.I. , and Trombka, J.I.1971. Bill. JUt. Phys.
Soc. Ser. II, 16 9 630.
Vette, J.I., Gruber,D., IMMatteson,J.L. and Peterson,L.E. 1970.
Ap.J.(Letters) 160, L161.
Zel+dovich,Y.B. , Kurt,V.G. and Syunyaev,R.A. 1969. Sov.Phys.JETP 28,146.
O
7
Table 1
Exponents of the Cosmological Annihilation Y( ray source Spectra
z E V S r,
2.86	 (S1
0-150 560keV-70MeV 0.64 3.36	 t s►. ^< ^- )
150-103 70keV-500keV 0.64 s 2 .68	 (s--,= i )Z 3.18	 (rte<<3'1
103-108 70k eV 2 2.00	 ^rL1 2.50
FIGURE CAPTIONS
Figure 1. Cross section times velocity for hydrogen-antihydrogen
annihilation of nLaleons as a sum for the interactions
listed below integrated over a Maxwell-Boltzmann dis-
tribution at temperature T and taking ionization into
account ( Morgan and Hughes 1970) . ( a) 0'.. N ( extrapolated) ,
(b)a^ . (nalculated),(c)a - C- ,- C,.. multiplied bj the
44 7
appropriate factors to take account of fractional ion-
ization, W o-r.P taking coulomb attractimn into account,
(e) a 25from high energy accelerator data. v r 2.5 X 10-25
cm2.
Figure 2. The cosmological 7-ray annihilation spectrum calculated
by numerical solution of the CPT equation (equation (4))
for f!' 1. The solid line represents the completA solution.
The other curves show the effect of neglectin g, the ab-
sorption and scattering terms in the CPT equation.
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Cosmic antimatter annihilation and the gamma-ray background spectrum

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