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 1 GeV and at latitudes below and above 30 degrees. The derived source-count distribution is consistent with the distribution found by the Fermi collaboration based on the first Fermi point source catalogue. In particular, we find that the contribution of resolved and unresolved active galactic nuclei (AGN) 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 extra-galactic 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 extra-galactic weak sources, such as star-forming galaxies. Possible systematic uncertainties are discussed.