We present a new model of the blazar gamma-ray luminosity function (GLF) and the spectrum of the extragalactic gamma-ray background (EGRB), which is consistent with the observed distributions of EGRET (Energetic Gamma-Ray Experiment Telescope) blazars. The unified sequence of blazar spectral energy distribution is taken into account to make a nontrivial prediction for the EGRB spectrum and more realistic comparison with the data than previous studies. We then try to explain the EGRB data by the two AGN populations: one is blazars, and the other is nonblazar AGNs that are responsible for the EGRB in the MeV band. We find that ~80% of the EGRB photon flux at 100 MeV can be explained by the sum of the two populations, while ~45% can be accounted for only by blazars. The predicted EGRB spectrum is in agreement with a wide range of the observed data from X-ray to GeV, within the systematic uncertainties in the EGRB determination by EGRET. These results indicate that AGNs including blazars are the primary source of EGRB. Blazars are dominant in EGRB at higher energy bands of 100 MeV, while nonblazar AGNs dominate at 100 MeV. Almost all of the EGRB flux from blazars will be resolved into discrete sources by the Fermi Gamma-ray Space Telescope, while that from nonblazar AGNs will largely remain unresolved. Therefore, the comparison between the integrated source counts and diffuse EGRB flux as a function of photon energy will give a simple and clear test of our model. Various quantitative predictions for Fermi observations are also made. Especially, our model predicts 600-1200 blazars in all sky down to 2 × 10–9 photons cm–2 s–1 (100 MeV), which is considerably smaller than most of previous studies. We find that the fraction of EGRB energy flux absorbed in intergalactic medium (IGM) is not large, and the cascade component reprocessed in IGM does not significantly alter the EGRB spectrum.
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