We study the relation between the measured anisotropies in the extragalactic diffuse gamma-ray background (DGRB) and the DGRB spectral intensity, and their potential origin from the unresolved blazar population. Using a physical-evolution model for blazars with a luminosity dependent density evolution (LDDE) and an observationally-determined luminosity-dependent blazar spectral energy distribution (SED), we find that blazars can account for the observed anisotropy of the DGRB consistent with their observed source-count distribution, but are in turn constrained in contributing significantly to the observed DGRB intensity. For the best-fit LDDE model accounting for the DGRB anisotropy and source-count distribution, blazars only contribute 5.9+2.1−1.0% (68% CL) of the DGRB intensity above 1 GeV. Requiring a higher fraction of the DGRB intensity contribution by blazars overproduces the DGRB anisotropy, and therefore blazars in the LDDE+SED-sequence model cannot simultaneously account for the DGRB intensity as well as anisotropy.We discuss the limitations of LDDE models. However, these models do not require the many unjustified and observationally-inconsistent simplifying assumptions — including a single power law for all blazar spectra and a simple broken power-law model for their source-count distribution — that are present in much previous work.
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