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 (vertical bar b vertical bar >= 30 degrees) 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 similar to 2 x 10(-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(-1.3)(+10) x cm(-2) s(-1). The power-law index n(1) = 3.1(-0.5)(+0.7) 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 6.4 x 10(-11) cm(-2) s(-1) at 95% confidence level. The high-latitude gamma-ray sky between 1 and 10 GeV is shown to be composed of similar to 25% point. sources, similar to 69.3% diffuse Galactic foreground emission, and similar to 6% isotropic diffuse background.