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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 deg) between 1 GeV 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-year 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 of index between 1.9 and 2.0. We measure dN/dS down to an integral flux of ~2x10^{-11} cm^{-2}s^{-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^{+1.0}_{-1.3}x10^{-8} cm^{-2}s^{-1}. The power-law index n_1=3.1^{+0.7}_{-0.5} for bright sources above the break hardens to n_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 6.4x10^{-11} cm^{-2}s^{-1} at 95% confidence level. The high-latitude gamma-ray sky between 1 GeV and 10 GeV is shown to be composed of ~25% point sources, ~69.3% diffuse Galactic foreground emission, and ~6% isotropic diffuse background.