The empirical bremsstrahlung shape of the low-energy GRB spectrum prompted early models to attribute its origin to thermal bremsstrahlung by a hot diffuse intergalactic gas at a temperature of ~ 4 x 108 K (Marshall et al. 1980; Daly 1988; Brown & Stecker 1979; Olive & Silk 1985). These models were essentially ruled out after the recent observations by COBE (Mather et al. 1990). The lack of significant deviations from a blackbody spectrum in the microwave background implies a much smaller Sunyaev-Zel'dovich y-parameter than predicted, thereby excluding the possibility that the Universe was filled with hot intergalactic gas in the past (Terasawa 1991; Rogers & Field 1991).
Other models attempted to explain the low-energy GRB spectrum by the integrated flux of extragalactic sources. These were confronted by the well-known spectral paradox: AGNs such as Seyferts and quasars which are the most likely, contributors produce continuum spectra that are markedly different from that of the GRB. The average AGN spectrum is characterized by a power law of energy index ~ 0.7, whereas the GRB spectrum has an index of ~ 0.4 below ~ 60 keV. To calculate properly the contribution of cosmological sources to the GRB, one needs to take in account the evolutionary effects of the AGN luminosity function. Avni (1978) found that the contribution from AGN depends on the form and amount of density evolution, on the deceleration parameter, and on the AGN formation epoch. The observed integrated flux is given by
where IN(E) is the flux in keV per sec-cm2-keV, BN(E, Z) is the emissivity in erg per sec-Mpc3-keV, and ZF is the epoch of first formation. V(z) is the comoving volume to redshift z, dL(z) is the luminosity-distance to redshift z (Weinberg 1972), and q0 is the deceleration parameter. For a pure density evolution where the source density (z) can be parametrized by (1 + z)k, the emissivity is given by BN(E(1 + z), z) = (1 + z)k+aBN(E, z = 0), and is the energy spectral index.
Rothschild et al. (1983) and Bassani et al. (1985) integrated the X-ray luminosity function of the HEAO-1 AGNs as derived by Piccinotti et al. (1982) to compute the relative contributions of different classes of AGNs. The results are shown in Fig. 3. They found that Seyferts are the most important contributors to the GRB. Their contribution increases from energies beyond ~ 40 keV until at ~ 160 keV, they can account for all of the observed background. The observed spectral shape and intensity of GRB are used to set limits on the luminosity cutoff and spectrum break energy of AGNs (Rothschild et al. 1983; Zycki et al. 1993) to prevent an overproduction of diffuse background above 100 keV. Indeed recent AGN observations by Compton and GRANAT are indicating that Seyferts do typically have low-energy spectral breaks (see Section 6).
Figure 3. Contributions of the different classes of AGNs to the GRB (Bassani et al. 1985).
After subtracting the Seyfert contribution, a significant residual GRB remains below 100 keV that needs to be explained. Various authors have postulated the existence of different AGN populations in earlier epochs to explain the residual spectrum: for example, Eddington-limited thermal-type sources (Boldt 1987), AGN precursors with high compactness (Leiter & Boldt 1991), and AGNs with harder power-law spectra (Gruber 1992). The recent ROSAT deep survey detected an unexpectedly high number of faint QSOs at 1 < z < 2 (Shanks et al. 1991; Griffiths et al. 1993). When the new QSO X-ray luminosity function with its derived evolution is integrated to a maximum redshift of zmax ~ 4 (Boyle et al. 1993), it is found that QSOs can account for 30 to 90% of the diffuse background at ~ 2 keV.