Critical test of cosmological pion decay hypothesis for origin of isotropic gamma radiation above 1 Me

Fazio, G. G.

Stecker, F. W.

English

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PREPRINT
PREDICTED HIGH—ENERGY BREAK IN THE
ISOTROPIC GAMMA--RAY SPECTRUM:
A TEST OF COSMOLOGICAL ORIGIN
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G. G. FAZIO
F. W. STECKER
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PREPRINT
Predicted High-energy Break in the Isotropic Gamma-ray Spectrum;
A Test of Cosmological Origin
G. G. Fazio  and F. W. Ste cke r
b
January 1970
tPrc,lictcd Higli-t-nt • rgy Break in th( • Isotropic Gamma-ray Spectruill:
A Test of Cosmol(,,gical Origin
G. G FAZIO
Smithsonian Astrophysical Obs,, rvatory, and 1-1, , r%, ard C(-)11(, g( , Observatory,
Cambridge, Massachusetts
and
F. W. STECRER
NASA Goddard Space Flight Center, Grc(-nbelt, -Maryland
Recent -,vork by one of us (FWS) has emphasized the possiblo cosmological
significance of the study of the isotropic component of cosmic y radiation
5between I and 100 MeV energy 1-3
 Vette et al. 4, have present,,d evidence
for a new component of isotropic y radiation above I MeV energy being dis-
tinct in nature and origin from that at lower energies. At present, these
data are consistent only with the hypothesis previously discussed 6, 7 that these
,y-rays are th(--! redshifted remnant of pion-producing cosmic-ray interactions
at an earlier stage in the evolution of the universe corresponding to a redshift,
z ;:-- 10 0.
The purpose of this paper is io point out a critical test of the cosmological
pion-decay hypothesis for the origin of the isotropic y radiation above I T3 eV
and to predict, a high-energy break in this component. The test lies in t1he
detection of a break in the y-ray energy spectrum due to interactions of these
y-rays -,vith the universal blackbody radiation at large redshifts, these inter-
actions being of the form
y + y — e + + e -
	(1)
1
!.
Detailed calculatiuns of t1 w Y -ray absorption couffic-ient, K YY (1 Y ), for
this pro cc•ss liavc be-en made by Gould anti Schr dcr^. Phis absorption
coefficicu nt, which rc-presents thu probability per unit path length, Q, that a.
Y-ray will by dvst-royed by the pair -production process (1), can bc: c.-xprcrssc-d,
for Y-rays interacting with a blackbody radiation field of t(-niperat-urc, T, as
2	 3KYY(EY) = a2	 kT2 f(O	 (2)
nc
where
22
(( TE)	 (3)
Y
where a — 1/137 is the fine- structure constant (e2 /l= c),
A = ti /mc = 3. 86 X 10 1 1 cm, and k is the Boltzmann constant.
The function, f(^), has a maximum value = 1 at ^ — 1 and the asymptotic
forms
2
f
	
3 ^In	 0.11?	 ford<<1	 (4)
and
f()	 'vr^ t l /2 e -^	 for >> 1	 (5)
For cosmological applications, we must take into account the redshift
dependences of T and E  in an expanding universe
T = T 0(1 + z)
	 (6)
and
E  = EYO(1 + z)	 (7)
where the subscript zero refers to currently observed (z = 0) quantities, so
that T o = 2. 7 K.
2
Taking the z-dep:{ndc : nce,s into account, wt- find that octuation (5) is
applicable in the energy range 
E << 1. 12 X 106
 GeV	 (8)
Y	 (1 + z)2
The optical depth of the universe to y-rays is then given by
I 
max('jmax)
T(E
Y 0' zmax	 YY Y) ^ f	
di K CE 0 , 1(z)]
0
zmax
dz KyY ( EYO , z) l dz	 (^l)
0
where
d Q	
C14-
0 0)dz	 (1 + z) 2 (1 + 10 5 n0z)1 /2
Here HO is the Hubble constant so that cH 0 l = 1028 cm and n 0 is the present
mean atomic density of all the matter in the universe. We will consider here
two types of model universes: 1) a ''flat'' or Einstein-de Sitter n..zodel with
n0 = 10 -5 cm 3 ; and 2) an ''open'' model with n 0 << 10 - 5 /z.
For the flat model with ^ >> 1, equation (9) reduces tot
T(EYO , z) = 3. 9 X 10 8 EY11 /2
O
zf m ax
J
0
dz (1 + z) -1 /2 exp - 1. 12 v 1 0 
6
(1 + z)2 EYO-
(1 1)
with EYO in GeV.
3
WFor z	 ^-> 1, equation (11) can be furth(-r siniplifit-d to vl(.,Idinax
z	 10	 (1 + z	 C XI)
	
1. 12 '' 10
max	 0	 Max
_
 
(I	 N) 2
(12)
A nunierical solution found by setting equation ( 11.) for 
T(Ely 
0 1 z crit ) 
= 1,
which defines the critical redshift where the uni-,,(-rE7(-- be comes upaque to
V-rays of energy 
E Y 
0 ) can 
be 
well approxiniatod by the (2xt-) I- (? 8 s ion 2
+ z
crit C-- 2. 60 X 10 2 E -
0. 484
YO
For the open rnodel with t, >> 1, we find
(13)
T(E 
Y 
W z 
max ) = 3. 9 X 10 
8 
E 
-1/2
YO
z
fmax	
10
E0	
dz exp 
I - 
I 
	
) 2 , Vo l
(14)
For z max >> 1, equation (14) can be approximated by
2 
E 
1 /2	 3	 1. 12 - 10 6
T(E	 10
YO, z max
	
1. 7 X
	YO (I + z 
max
) e xp	
+ z	 ) 
2 
E
rn ax	 YO-
(15)
Thus
.
, there is no significant difference between the opacities of the
open and the flat universes. This being the case, we can invert equation
(13) to obtain an expression for the predicted cutoff energy, E c , above which
-y-rays originating at a redshift, z max , cannot reach us. This relation is
given by	 0
4
t2. 06
E ,^ 2. 6 0 X 102
c	 l + z
max
(16)
and is graphed in Fig. 1.
In the other extreme, ^ << I, we find that as the energy increases, the
universe will not become transparent .o y-rays again until we reach an
energy, E tr , where the optical depth, T(E tr' z max ) again falls to unity,
The expression for the optical depth when	 1 is given for a flat universe
by
z
max
T(Ey0' zmax) 4. 4 X 10 13 EYE	 dz(1 + z)-3/2 c, 8. 8 X 10" E-'
0
for zmax >> 1
	 (1.7)
and f or an ope n unive r s e by
z
max
T(Ey0' zmax) — 4. 4 X 1013 EY E	 dz(1 + z)-1
0
— 4.4 X 10 13 E -1 .fin (1 + z max) 	C1^)
In both cases, we find E tr > 10 13 GeV, so that we can safely
assume that the universe, owing to the blackbody radiation field, is essen-
tially opaque to y-rays of all energies greater than E c max(z	 ) as given by
equation (16).
5
tIt follows that if th• cosmological bypothvsis for tlit* origin t)f tbo isotropic
coniponent of cosi-nic y-rays above i NltN 1,4 valicl and if, indeed, most )f Owst-
y- rays originated at a redsbift -:- 100 as thc cosmological interpr( , tation of
the measurements of ViAte et al. would indicate, then we woulel expect, to
find a high-energy break in thc isotropic y-ray spectruni at E	 7. I G v T
9 1Gr,, , isvn oas suggested that pair-production interactions b(-tNvecn -y-rays
and optical photons occurring at redshifts =* 10 might also p-oduct- a high.
c•nergy break at — 10 GeV. However, the metagalactic optical photon density
even at present (z = 0) is only theoretically estimated and can only be hypoth-
esized at large r( , dshifts. It must thus be kept in mind that the alternative
prediction of a y-ray break proposed by Gr(,is(---n would occur only with th•
currently proposed starlight radiation density of 10 -2 OV / cn 1 3 existing out
to redshifts —10.
We should like to thank Dr. Frank C. Jones for some valuable discussion
of tAiis paper.
References
I Stecker, F. W. J Nature, 220, 675 (1968).
2 Stecker,, F. W. , Astrophys. J. , 157, 507 (1969).
3 StecRer, F. W. , and Silk, J. , Nature, 221, 1229 (1969).
4 Vette, J. I. , Gruber, D. , Matteson, J. L. , and Peterson, L. E.
Proc. I. A. U. Symp. No. 37, Rome (edit. by Gratton, L.) (in the press).
5 Vette ) J. I. . Gruber ., D. , Matteson, J. L. and Peterson, L. E. , to be
published.
6 Stecker, F. W. , Proc. I. A. U. Syn-ip. No. 37, Rome (edit. by Gratton, L.)
(in the press).
7 Stecker, F. W. , Nature, 224, 870 (1969).
8 Gould, R. J. and Schre'der, G. P. , Phys. Rev. , 155, 1404 (1967).
9 Greisen
.
, K. From a lecture given at the Brandeis Summer Institute in
Physics, 1968, Cornell Laboratory for Nuclear Science Report
(CL NS-77).
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Predicted high energy break in the isotropic gamma ray spectrum - A test of cosmological origin

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