Statistics of gamma-ray point sources below the Fermi detection limit

An analytic relation between the statistics of photons in pixels and the number counts of multi-photon point sources is used to constrain the distribution of gamma-ray point sources below the Fermi detection limit at energies above 1GeV and at latitudes below and above 30°. The derived source-count distribution is consistent with the distribution found by the Fermi Collaboration based on the first Fermi point-source catalog. In particular, we find that the contribution of resolved and unresolved active galactic nuclei (AGNs) to the total gamma-ray flux is below 20%-25%. In the best-fit model, the AGN-like point-source fraction is 17% 2%. Using the fact that the Galactic emission varies across the sky while the extragalactic diffuse emission is isotropic, we put a lower limit of 51% on Galactic diffuse emission and an upper limit of 32% on the contribution from extragalactic weak sources, such as star-forming galaxies. Possible systematic uncertainties are discussed.