Unveiling the gamma-ray source count distribution below the Fermi detection limit with photon statistics

The source-count distribution as a function of their flux, dN/dS, is one of the main quantities characterizing gamma-ray source populations. We employ statistical properties of the Fermi Large Area Telescope (LAT) photon counts map to measure the composition of the extragalactic gamma-ray sky at high latitudes (|b|⩾30°) between 1 and 10 GeV. We present a new method, generalizing the use of standard pixel-count statistics, to decompose the total observed gamma-ray emission into (a) point-source contributions, (b) the Galactic foreground contribution, and (c) a truly diffuse isotropic background contribution. Using the 6 yr Fermi-LAT data set (P7REP), we show that the dN/dS distribution in the regime of so far undetected point sources can be consistently described with a power law with an index between 1.9 and 2.0. We measure dN/dS down to an integral flux of ∼2×10{sup −11} cm{sup −2} s{sup −1}, improving beyond the 3FGL catalog detection limit by about one order of magnitude. The overall dN/dS distribution is consistent with a broken power law, with a break at 2.1{sub −1.3}{sup +1.0}×10{sup −8} cm{sup −2} s{sup −1}. The power-law index n{sub 1}=3.1{sub −0.5}{sup +0.7} for bright sources above the break hardens to n{sub 2}=1.97±0.03 for fainter sources below the break. A possible second break of the dN/dS distribution is constrained to be at fluxes below 6.4×10{sup −11} cm{sup −2} s{sup −1} at 95% confidence level. The high-latitude gamma-ray sky between 1 and 10 GeV is shown to be composed of ∼25% point sources, ∼69.3% diffuse Galactic foreground emission, and ∼6% isotropic diffuse background.