Propagation of gamma-rays at cosmological redshifts

Nuclear Physics B (Proc. Suppl.) 10B (1989) 81-88 North-Holland, Amsterdam

81

PROPAGATION OF GAMMA-RAYS AT COSMOLOGICAL REDSHIFTS

Andrzej A. ZDZIARSKI Space Telescope Science Institute, 3700 San Martin Dr., Baltimore, MD 21218, USA ttoland SVENSSON NORDITA, Blegdamsvej 17, 2100 Copenhagen O, Denmark

We discuss absorption and reprocessing of 7-rays at cosmological redshifts. We co,sider Compton scattering and pair production by "l-cays .~-n the cosmic baryonic matter, and photon-photon scatte lng and phot,~:~-photon pair production by 7-rays and Compton scattering of relativistic pairs on the cosmic blackbody background. Vv'epoint out the cosmological importance of photon-photon scattering (a process not previously considered in astrophysics). We determine the region where the universe is transparent to -/-rays and the regions of dominance of the elementary processes on the photon-energy-redshift plane. We discuss the current status of this field of research and its future directions. The problem of cosmological -/-ray reprocessing is relevant, e.g., for observational "),-ray astronomy, for which the signatures of the cosmological origin need to be determined, and for studies of the effects that pair cascades, caused by the decay of unstable particles from a hot Big Bang, have on the primordial nudeosynthesis.

Reprocessing of 7-rays may also be important at red-

I. I N T R O D U C T I O N

shifts at which the reprocessed radiation is not directly obThis paper discusses the current status of the research on

servable. Long-lived unstable particles (e.g., gravitinos) have

physical processes occurring during propagation of 7-rays ~t

been predicted in some theories to be produced in the initial

cosmological redshifts. These physical processes are inter-

stages of the hot Big Bang. The particles decay at some red-

actions with the cosmic thermal background and baryonic

shift giving rise to x large number of 7-rays s-9, e.g., from

matter, which change the spectra and directio,lsof thc orig-

decay of neutral pions, or from Compton scattering by rel-

inally emitted 7-rays.

ativistic electrons from charged muon decay. The 7-rays

The universe is transparent up to a redshift of z ~-.103 in

interact mainly with the cosmic blackbody background pro-

the photon e~ergy range from ,,,100 keV to ,,,100 MeV, and

ducing e+e - pairs, giving rise to electromagnetic cascades

becomes opaque at z <<: 1 only above ,,, 100 TeV I. Thus,

with alternating generations of 7-rays and e+e - pairs. If

it is possible that some 7-r~.vs originating at very high red-

this process occurs at z ,~ 106-10¢, the reprocessed pho-

shifts reach the earth. Studying the physical processes that

tons have energies in the MeV range and photo-dissociate

reprocess "),-raysat cosmological redshifts may lead to find-

light elements. Thus, this process affects the primordial

ing a way of distinguishing cosmological 7-rays from local

abundances s-~. Also, the energy release associated with

ones. This reprocessing m a y lead to the formation of uni-

the decay affects the rate of universal expansion.

versal spectra and time profiles of the observable 7-rays.

When studying the reprocessing of 7-rays, only photons

Studies of such effects appear particularly important in the

and baryonic matter are of interest. The photon tempera-

advent of the G a m m a

ture is proportional to (1 + z),

Ray Observatory, scheduled for launch

in 1990. The sources of cosmological "/-rays proposed so far include superconducting cosmic strings2-4, antimatter annihilation I, strange matter, and others.

0920-5632/89/$03.50 © Elseviel Sc,evce Publishers B.V. (North-tlolland Physics Publishing Division)

O = Oo(1 + z) ~ 4.55 x 10-1°T2.7(1 + z), where O --

kT/(mec2) is a

(1)

dimensionless temperature, me

A.A. Zdziarski, R. Svenssor/Gamma-rays at cosmological redshifts

$2

is the electron mass, and T2.7 = T0/2.7K. Hereafter, the

where f~ is the ratio of the total density to the density re-

subscript 0 refers to the quantities at z = 0. The photon

quired to close the universe, c / [ H 0 ( l + z)] is the local tlubble

distribution is given by the Planck law, with the photon

length, #

density o~ (1 + z) a. The t£mperature of matter equals that

C

of equation (1) at z ~ 10a, i.e., before the recombination

//0(1 + z)

- 1.85 × 102Sh~'0s(1 + z) -1 cm,

(5)

epoch. Up to z ~, 10s, the matter is nonrelativistic, and its

hs0 - H o / ( 5 0 k m s - l M p c - 1 ) , and H0 is the Hubble con-

temperature does not affect the reprocessing of 7-rays. The

stamt.

average electron density is

If the major contribution to integral (4) comes from the

ne = ne,o(1 + z) 3 = 2.46 × 10-Tf~o.lh~o cm-3(1 + z) 3 , (2) where f~o.1 = (~b/0.1), and fib is the fraction of the clc~qure

high-redshift limit, Zdziarski and Svensson 11 (hereinafter abbreviated as ZS) shewed that

~(~,flz ~ 1) _~ ~ - ~ / ' r ( ~ = 1),

(6)

density of the universe in bary¢ ~s. The densities of hydrogen and helium are given by n H = (6/7)he, and nile = (1/14)ne,

implying that in the high-redshift llm;~ it suffices to calculate

assuming the mass fraction of He of 25%.

~" in the fl - 1 case only.

The photon energy evolves with the redshift due to the universal expansion.

listed above and the way they reprocess -/-rays. (3)

c = co(1%z), where • =

In the following section, we will discuss the processes

2. THE PHYSICAL PROCESSES 2.1 Compton scattering

E/(mec 2) is the dimensionless photon energy.

High energy photons in the presence of blackbody pho-

The total cross section for tLis process is given b~ the

tons and cold matter interact predominantly in the following

Klein-Nisldna formula t2. In the nonrelativistic limit, • <<~1,

ways.

this process is called Thomson scattering. The Compton cross section is consta,~t in the Thomson limit (UT -- 6.65

by Compton scattering on electrons, 7e --* 7e,

×

10 -2s cm 2) and decreases with ener&v as ,,, 1/• at • ~ 1. The by producing pairs on free electrons, 7e --* ee+e - , by produdng pairs on free nuclei, 7Z ~

optical depth of the universe to Thomson scattering is then

Ze+e -,

constant as well and was given by Gunn and Peterson 13.

by producing pairs on atoms, 7A --* Ae+e -,

The Thomson depth of unity is reached for •0 <~ 10 -2 at

by producing single pairs on blackbody photons, 77 --* e + e - ,

1 + z ~_ 63fll13(flo.lhso)-2/3.

(7)

by producing double pairs on blackbody photons, 77 -'+ e+e-e+e-,

The exact Compton scattering optical depth in the case fl = 1, and the optical depth at any f~ in the high-energy

by scattering blackbody photons, 77 --+ 77. The optical depth of the Universe to an interaction process from a matter-dominated redshift z to z = 0 is given by an integral '_o over the interaction probability per unit

(Klein-Nishina) limit, • >~ l, have been calculated by ZS 11. The former result can be used for any fl at flz >~ I by using equation (6). As ~- = 1 is reached only at z ~ 1 (~ z of eq. [7]), this range of z is most important. Figure 3 in §3 shows

length, d~'/dl,

the contour of the unit optical depth in the energy-redshift

c / r(E0, z) = ~00

dr/dl (1 + z')2(1 +

0

plane, and Figure 4 shows the region in which Compton

f~z')l/2 dz',

(4)

scattering is the dominant process.

A.A. Zdziar~.J, R. Svensson ~Gamma-rays at cosmological redshifts

83

For radiation from a discrete source, a single Compton

relativistic, and they can upscatter photons of the cosmic

scattering will deflect the photon from the line of sight. The

blackbody background giving rise to new X-rays and 7-rays.

optical depth for scattering then provides a measure of ob-

This effect is needed to be included in future studies of cos-

servability of cosmological 7-rays from discrete sources. On

mological reprocessing of 7-rays.

the other hand, isotropic background X-rays may originate

2.3. Pair-photon cascades from photon-photon pair pro-

at redshifts larger than those given by z 0" = 1) in the Thom-

duction and Compton upscattering

son regime, as pointed out by Arons and McCray 14 and Rees 15. This is because a photon loses only a small frac-

Gamma-rays can interact with photons of the cosmic

tion of its energy per scattering at c ~ 1. The cosmological

blackbody background producing positron-electron pairs. In

photon transfer of isotropic radiatic~n was studied in detail

the center-of-momentum reference frame, the threshold for

by Arons 16,17 ZS 11 calculated the optical depth of the uni-

pair production corresponds to ~CM = 1. The cros~ sec-

verse for the relative energy loss in Compton scattering.

tion reaches its maximum of ~ 0.3CrT at cCM ~ 1.4~ and decreases like ~ 1_/~far above the threshold. Because of the

2.2. Photon-matter pair production

very large density of the cosmic blackbody photons, absorp-

Pair production takes place on free electrons and ions

tion of 7-rays occurs even at such low energies that pails

before the recombination epoch and on atoms after it. The

are produced only in interactions with the photons deep in

cross sections for those processes differ and the exact cal-

exponential tail of the blackbody distribution. Therefore,

culations of the optical depth in the two cases need to ~e

the condition for the optical depth of unity corresponds

carried out separately. Such calculations are performed in

to ~ x (101-I02)0 = I, with only a weak dependence on

ZS 11. The pair production cross section is ~ a faT, where

the redshift and cosmologiCZ'r, parameters. An approximate

a ! is the fine structure constant. Pair production on neu-

expression for the optical depth was deriv~od by Fazio and

tral matter with cosmological abundances dominates over

Stecker 19. More exact expressions were derived by ZS 11

Compton scattering at E ~ 60 MeV.

The optical depth of unity corresponds approximately to ii,19

As the cross section for photon-matter pair production

1 + z ~ 8.8

x 103E 0"485 ,

(9)

varies slowly in the high-energy limi'~, ~ ~>~>1, one can approximate it as constant 1,18. In fact, the cross section for

at 1.1 _ z _< 300 and hs0 = fl = 1. The proximity of the

pair production on atoms approaches a constant in the high-

exponent to 1/2 reflects the effect of pair absorption by the

energy limit. One then obtains an expression for z 0" = 1)

exponential blackbody tail, discussed above. At z << 1 the universe becomes opaque at above ~ 100

analogous to equation (7) 11,

TeV. At E -~ 1 PeV, which corresponds to the peak of the

1 + z ~- 670f~l/3(f~o.lhso)-2/3,

~oZ ~) 825.

(8)

cross section, the mean free path is as short as ~ 8T2-3 kpc.

The regions where the universe is transparent to this process

Thus, this process is important both localiy and cosmologi-

and where pair production on m~tter dominates are shown

caliy.

in Figures 3 and 4 in §3.

The cross section for pair production decreases with en-

The process of "y-ray absorption by photon-matter pair

ergy as 1/~. Thus, one could expect that at a certain very

production was included along with Compton scattering by

high ?-ray energy the universe would again become trans-

Arons 16,17 in his treatment of cosmological radiative trans-

parent to photon-photon pair production.

fer of isotropic 7-rays.

lower energy She process of double pair production becomes

We note that pairs produced by high-energy 7-rays are

H~wever, at a

dominant, causing the universe to be opaque at all above-

A.A. Zdz ~rski, R. Svensson / Gamma-rzys at cosmological redshifts

84

the-threshold energies~.0. The cross section for double pair

ccmes much more tractable. The reprocessed spectra can

production, ,,, a ) w r , is independent of energy. Absorption

be obtained by iteratively solving the kinetic equation de-

of v-rays by double pair production dominates over single

scribing the cascade. As the mean free path for either pair

pair production at c ~ 6.7 × 10s/O (see Fig. 4), and the

production or Compton scattering is many o~,.lers of mag-

optic~ depth of unity at those energies corresponds to 11,2o,

nitude shorter than the local Hubble length, the cascade process can be considei'ed without including the effects of

z~" 0 021hsoT2-~

(10)

Photon-photon pair production on soft (blackbody) pho-

the cosmological expansion on the energies and occupation numbers.

tons produces electrons and positrons with energies com-

Figure 1 shows examples of reprocessing of isotropic mo-

parable to the v-ray energy. The electrons and positrons

noenergetic v-rays by pair cascades on blackbody photons 2a.

immediately scatter blackbody photons, as the cross sec-

The primary v-rays are injected at energies 10 and 100 times

tions for pair production and Compton scattering are simi-

larger than the threshold energy, eta, which was assumed to

lar. The physical circumstances of Compton scattering here

correspond to 300. One sees that the resulting spectra do

differ from those of Compton scattering discussed in §2.1.

not depend on the injection energy. The obtained photon

There a hard v-ray scattered on the cold electrons of the

power laws are approximately h(E) cc c-1"8 and h(c) cc E- l ' s ,

baryonic matter, whereas now a relativistic electron scat-

above and below ,,, 0.03 of the threshold energy, cth, respec-

ters on the soft photons of the blackbody background•

tively. The latter dependence is characteristic of injection of

Close to the threshold for pair production, there is an approximate eno:s-y equipartition among the members of the

monoenergetic relativistic electrons in the Thomson limit. It appears here because the pair cascade converts a large

pair, and at eP.ergies far above the threshold one member of the pair r e c ~ s

most of the energy. Scattering of the elec-

~'""1

' '"'"'1

' '"'"'1

' '"'"N

' '"'"I

........

I

' '""

100

tron (positron) that received most of the v-ray energy is now in the Klein-Nishina limit, in which the upscattered photon

iiii ............

receives most of the electron energy. Thus, consecutive pair production and Compton scattering produce a v-ray with energy only slightly less than the energy of the original 7-

•~ %

1 !

ray. This means ~hat a v-ray with energy far above the threshold will initiate an electromagnetic cascade consisting of many generations of e+e - pairs and v-rays. The cascade .01

continues un~i| all v-rays have energies below the threshold for pair production. When this happens, the electrons still continue losing energy through Compton scatterings,

.00|

...... I

.~01

........

I

,001

, , ...... I

.01

, ,,,,,,,I

~ ,~,,,i,l

o ,,,,t,,l

.I

1

lO

, ,,nnl

iO0

producing photons with energies decreasing with decreasing electron energy. The process of pair cascades has been simulated by means of Monte Carlo methods 9,21-22. Recently, Zdziarski 23 has reconsidered the prol-!em and derived analytical e>'pressions for the redistribution functions for pair production and Compton scattering on blackbody photons. The problem then be-

FIGURE 1 Photon spectra from pair cascades on blackbody photons (solid curves). The lower and upper curves correspond to monoenergetic v-ray injection at energies 10 and 100 times above the threshold for pair production, eth, respectively. The dot-dashed curves show the photon production rates in the optically thick region.

A.A. Zdziarski, R. Svensson / Gamma-rays at cosmological redshifts

85

fraction of the original 7-ray (or high-energy electron) into tO ~1

a number of electrons with energies just at the boundary of

. . . . . . . .

I

. . . . . . . .

the Thomson limit 23.24.

I

. . . . . . . .

I..

A

2.4. Photon-photon scattering

,

\

The cosmological importance of this process was first oooo

pointed out by ZS 11. They calculated the scattering probability per unit length, and the optical depth of the universe

%

:o the process. Both quantities are proportional to the cube of the photon energy up to the energy corresponding to the

.1

threshold for photon-photon pair production. The maximum cross section is of the order 0.01~}~T. As photonphoton pair production has a cross section ,,~ c~ s times larger, it dominates the scattering completely above the

.01 ,001

threshold. The redshift corresponding to unit optical depth is given by,

.01

.I

1

E/~th

nant process are shown in Figures 3 and 4, respectively, in

FIGURE 2 Effects of reprocessing Ly photon-photon scattering on black body photons. The universal pair-photon cascade spectrum from Fig. 1 (dashed curve here) is reprocessed into a peaked spectrum (solid curve). The absorbed energy appears as a peak at the photon energies, where the optical depth to photon-photon scattering is of order unity. An exact treatment would give a smooth peak.

§3. For blackbody photons, photon-photon scattering domi-

a cutoff in an observed 7-ray spectrum would then be a

nates over photon-photon pair production at 11 e < 1/(22e).

signature of cosmological photon-photon scattering. As a

Below this energy photon-photon scattering can dominate

specific example, Figure 2 shows the effect of reprocessing

over photon-matter pair production for a decade or less, de-

by photon-photon scattering of the (universal) pair-photon

pending on the cosmological parameters (see Fig. 4 and §3).

cascade spectrum in Figure 1. The artificial spike is due to

The effect of 7-ray reprocessing by this process was stud-

the optically thin ar.d thick approximations made above and

ied in detaii by Svensson and Zdziarski 25. They found

below the boundary of the optically thick energy range. The

--

l+z~4.80x.,,

1N3

q~--4151~2115nl/15~--215 ,s.7 'oso ,~ -o •

(11)

The regions where the universe is transparent to this process and where photon-photon scattering is the domi-

the exact redistribution function for scattering on isotro-

spike would be replaced by a smooth peak in a more exact

pic blackbody photons and solved analytically the kinetic

treatment.

equation describing photon transfer due to repeated photon-

3. REGIONS OF DOMINANCE OF THE ELEMENTARY

photon scattering. A single scattering on blackbody photons

PROCESSES

converts a 7-ray into two 7-rays, with an approximate energy equipartition between the two new photons. Repeated scatterings of a power law 7-ray photon spectrum lead to the attenuation of the photons with energies in the optically thick region. The absorbed energy reappears as up-scattered blackbody photons forming a peak in the spectrum at the boundary of the optically thick region. A peak followed by

The various dotted and dashed lines in Figure 3 show contours of unit optical depths to the processes discussed above as functions of the observed photon energy, E0. The lower solid curve gives z corresponding to the total optical depth for absorption and scattering equal to unity. The upper solid curve corresponds to the total absorption and

86

A.A. Z&iarski, R. Svensson/Gamma-rays at cosmological redshifts

'""

.... "

'""

'""

.... "

.... "

scattering dominates the opacity from ,,, ,50 MeV to ~, 1 GeV. Above ,,, 1 GeV, the main source of opacity is photonphoton pair production. Above ,,~ 100 TeV, this process causes the universe to be opaque locally. Figure 4 shows the regions in the e-z plane in which the various radiative processes discussed in §2 dominate. Here e is the energy measured at z. The cosmological parameters are the same as in Figure 3. The bottom solid and dashed

%.:

,

"

curves give the contours of unit optical depth to combined scattering and absorption, and energy loss and absorption, respectively. F ~ , ~ t ~ r~g'.'cn~ ~ I c w t!,o~e c.~rves (labeled I) the radiation emitted by discrete and diffuse sources, re-

.0001 .001

,01

.!

1

10

i00 10001000010 ~ !0 e 10

I0 °

~o

spectively, can be received at the earth. Compton downscattering dominates in region II. The area between the dashed and the bottom solid curve belongs to either region

FIGURE 3 The contours of unit optical depth at matter dominated redshifts for photon-photon pair production (short dashes), photon-photon scattering (dots and long dashes), photonmatter pair production (dots and short dashes), Compton scattering (long dashes), and Compton energy loss (short and long dashes). The bottom and top soIid curves correspond to the combined scattering and absorption and energy loss and absorption optical depths of unity, respectively. Those two curves are important for discrete and diffuse sources, respectively. The assumed values of the cosmological parameters are: f~ = 1, hs0 = 1, fib "- 0.1.

°r\" ,0"

~,,.,~

...... ~ ...... ~ ....... 1 ....... I ...... ~ ...... ~ xC'~

10 ~ [

.....

~

-s_

lOS

II t 0 o 0 o r-

lll

energy loss optical depth equal to unity. Below the lower solid curve, unreprocessed radiation from discrete sources

I000 r

can be observed. Below the upper solid curve, radiation from source~ contributing to the isotropic background can 10 r

reach the earth. The assumed cosmological parameters are f~ = f20.1 = ha0 = 1.

.I

1

10

I00

tO00 10000 106

lOS

10"

lOS

At energies ~ 0.5 keV, the unit optical depth to scattering and absorption is due to Thomson scattering and is reached at z = 62 for our choice of cosmological parameters. Above this energy, the curve of r = 1 turns upward, reflecting the Klein-Nishina reduction of the Compton cross section. Around ,,, 100 keV, pair production on atoms becomes the dominant source of opacity. From ,,, 100 keV to ,,, 300 MeV, there is a window of reduced opacity, as pointed ,~. 9ut by Axons and McCray :'- and Stecker i. Photon-photon

FIGURE 4 The plane e-z divided into regions of dominance ~.f the various absorption and scattering processes responsible for reprocessing "prays in the universe. Tile bottom solid and dashed curves correspond to r - 1 for combined scattering and absorption and energy loss and absorption, respectively. The regions labeled from I to VI correspond to: I - r < 1; II - dominant Compton scattering; III - matter pair production; IV - pair production on matter; V - single photonphoton pair production; VI - double pair production. The cosmological parameters are the s a ~ e as in Fig. 3.

A.A. Zdziarski, R. Svensson/Gamma-rays at cosmological redshifts I or II depending on whether diffuse or discrete sources are considered. Radiation emitted in region III will be absorbed in pair-producing interactions with baryonic matter. The discontinuities at z - 1500 in the boundaries of that region correspond to the recombination epoch, when the rate of matter pair production changes slightly. Photon-photon scattering dominates in region IV'. For fib -" 0.1 this region extends as a diagonal strip for 300 z ~ 10s, with the widths of the strip in c and z being as large as a factor of ~tbout 4. For fib = 0.01, the maximum widths of the diagonal region would increase to a factor of 10 in both E anal z. Note that this process can be important down to relatively low energies of e ~ 1. Finally, single and double photon-photon pair production dominate in the regions V and VI, respectively. 4. FUTURE WORK So far, all of the work on cosmological reprocessing of ?-rays has been done without considering the effects of the c~anges of the directions of photons emitted in the elemen-

t~':y processes. This is appropriate for isotropic ?-rays, when the contribution of a process to the cosmic radiation backSr ound is calculated. However, the effect of changing photon di:ections may turn out to be dominant in determining the spectra] and temporal characteristics of incoming radiation from discrete sources. No work on the effect of secondary pairs from absorption of ?-rays in photon-matter pair production has l~een done yet. Further work on Compton reprocessing is needed as

wall.

87

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259 (1985) 175. 6. Juszkiewicz,R., Silk,J.,and Stebbins,A., Phys. Letters, 158B (1985) 463. 7. Audouze, J., Lindley, D., and Silk, J., Ap. J. (Letters), 293 (1985) L53. 8. Lindley, D., Ap. J., 294 (1985) 1. 9. Domfnguez-Tenreiro, R., Ap. J., 313 (1987) 523. 10. Weinberg, S., Gravitation and Cosmology (Wiley, New York, 1972). 11. Zdziarski, A. A., and Svensson, R., Ap. J., (1989) submitted. 12. Jauch, J. M., and Rohriich, F., The Theory of Photons and Electrons (Springer. Berlin, 1980). 13. Gunn, J. E., and Peterson, B. A., Ap. J., 142 (1965) 1633. 14. Arons, J., and McCray, R., Ap. J. (Letters), 158 (1969) L91. 15. Rees, M. J., Ap. Letters, 4 (1969) 113. 16. Arons, J., Ap. J., 164 (1971) 437. 17. Arons, J., Ap. J., 164 (1971) 457. 18. Stecker, F. W., Cosmic Gamma Rays (NASA, Scientific and Technical Publication Office, Washington, 1971). 19. Fazio, G. G., and Stecker, F. W., Nature, 226 (1970) 136. 20. Brown, R. W., Mikaelian, K. O., and Gould, R. J., Astr. Lett., 14 (1973) 203. 21. Aharonian, F. A., Kirillov-Ugryumov, V. G., and Vardanian, V. V., Astr. Sp. Sci., 115 (1985) 201. 22. Protheroe, R. J., M. N. R. A. S., 221 (1986) 769. 23. Zdziarski, A. A., Ap. J., 335 (1988) 786. 24. Svensson, R., M. N. R. A. S., 227 (1987) 403. 25. Svensson, R., and Zdziarski, A. A., (1989) in preparation.