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1.3. Models of the Extragalactic gamma-ray Background

A large number of possible origins for the extragalactic diffuse gamma-ray emission have been proposed over the years. Theories of diffuse origin include scenarios of baryonic symmetric universes (Stecker et al. 1971), primordial black hole evaporation (Page and Hawking 1976), massive black holes that collapsed at redshifts of z ~ 100 (Gnedin and Ostriker 1992), and annihilation of exotic particles (Silk and Srednicki 1984, Rudaz and Stecker 1991). All of the theories predict continuum and line contributions that are not observed to date.

Models based on discrete source contributions have considered a variety of source classes. The gamma-ray intensity expected from normal galaxies has been estimated to be 5-10% of what is observed (e.g. Lichti et al. 1978). Cosmic ray interactions with intergalactic gas in groups and clusters of galaxies may add to this (Dar and Shaviv 1995). However, the energy spectra of the Galactic and intergalactic diffuse gamma-rays are significantly different from those measured by EGRET for the extragalactic diffuse radiation, hence these proposed sources are unlikely to provide much more than 10% of the observed extragalactic intensity.

It has been postulated for over 2 decades that unresolved active galactic nuclei (AGN) might be the source of the extragalactic diffuse emission (Bignami et al. 1979). Now the EGRET data prove that a sub-class of AGN, namely blazars, are strong gamma-ray emitters (Mukherjee et al. 1997). A comparison of the spectra of gamma-ray blazars with the diffuse spectrum gives ambiguous results. Averaging the best-fit indices of power law fits to the individual gamma-ray spectra blazars yields (2.15 ± 0.04), in good agreement with the index of the diffuse spectrum (Mukherjee et al. 1997). Co-adding the individual intensity spectra of blazars on the other hand results in an ``average'' spectrum which is distinctively softer than the extragalactic background and not well represented by a power law (Pohl et al. 1997a).

For any estimate of the intensity of diffuse emission from unresolved blazars, knowledge of the luminosity distribution and the evolution function is needed. Chiang and Mukherjee (1998) have used the EGRET gamma-ray blazar data alone to calculate the evolution and luminosity function of gamma-ray loud AGN. These authors report evidence for a low-luminosity cutoff in the gamma-ray AGN luminosity function. With this part of the luminosity function better constrained, they estimate that gamma-ray loud AGN contribute an intensity of IAGN = (3 ± 1) · 10-6 cm-2 sec-1 sr-1 to the diffuse background, which is about 25% of the background observed by EGRET.

Several authors have estimated the contribution from blazars by assuming an intimate relationship between gamma-ray and radio emission from blazars. Beyond applying the radio evolution function to the gamma-ray emitting blazars, the gamma-ray fluxes have been compared with catalogued radio fluxes to derive a luminosity correlation which can be integrated to obtain the blazar contribution to the diffuse background (Padovani et al. 1993; Stecker et al. 1993; Setti and Woltjer 1994; Erlykin and Wolfendale 1995). In most cases, the calculations are within 50% of the observed intensity. A word of caution about these estimates seems appropriate: there is certainly some sort of loose relation between radio and gamma-ray emission of blazars visible, for example, in that EGRET preferentially sees radio bright objects (Mattox et al. 1997), but careful analysis shows that there is no direct correlation with dispersion of less than a factor 2 (Mücke et al. 1997).

Recently, Mücke and Pohl (1997, 1998) have presented a calculation in which they assumed that radio loud and gamma-ray loud blazars are the same sources in principle. They would share properties like evolution, geometry, and energy input into the jet, but the actual radiation processes responsible for radio and gamma-ray emission would be different. Using a specific inverse-Compton scattering model for the gamma-ray production, these authors deduce that AGN could provide only about 40% of the observed diffuse background. However, they also state possible systematic problems in their study in properly accounting for the contribution of BL Lacs.

All these studies either assume evolution similar to that observed in radio source studies, or attempt to deduce the evolution directly from the few high-z sources observed with EGRET. All of them need to introduce a redshift cutoff at which to stop integration of the blazar luminosity function. The choice of redshift cutoff has considerable influence on the estimate of the diffuse radiation from blazars.

Gamma-rays of energy geq 10 GeV emitted at redshifts of z geq 4 should be reprocessed in a pair creation/annihilation cascade before reaching the earth. One may therefore argue that the power law shape up to 100 GeV exhibited by the observed diffuse background is incompatible with a significant fraction of it originating from z geq 4 objects. Nevertheless, the systematic uncertainty imposed by the redshift cutoffs is considerable. It is disturbing though, that two independent studies indicate that AGN underproduce the diffuse background. If nothing else, it tells us that to date we do not understand the origin of the diffuse extragalactic gamma-ray radiation.

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