Deriving the Contribution of Blazars to the Fermi-LAT Extragalactic γ-ray Background at E > 10 GeV with Efficiency Corrections and Photon Statistics

The Fermi Large Area Telescope (LAT) Collaboration has recently released the Third Catalog of Hard Fermi-LAT Sources (3FHL), which contains 1556 sources detected above 10 GeV with seven years of Pass 8 data. Building upon the 3FHL results, we investigate the flux distribution of sources at high Galactic latitudes (vertical bar b vertical bar > 20 degrees), which are mostly blazars. We use two complementary techniques: (1) a source-detection efficiency correction method and (2) an analysis of pixel photon count statistics with the one-point probability distribution function (1pPDF). With the first method, using realistic Monte Carlo simulations of the gamma-ray sky, we calculate the efficiency of the LAT to detect point sources. This enables us to find the intrinsic source-count distribution at photon fluxes down to 7.5 x 10(-12) ph cm(-2) s(-1). With this method, we detect a flux break at (3.5 +/- 0.4) x 10(-11) ph cm(-2) s(-1) with a significance of at least 5.4 sigma. The power-law indexes of the source-count distribution above and below the break are 2.09 +/- 0.04 and 1.07 +/- 0.27, respectively. This result is confirmed with the 1pPDF method, which has a sensitivity reach of similar to 10(-11) ph cm(-2) s(-1). Integrating the derived source-count distribution above the sensitivity of our analysis, we find that (42 +/- 8)% of the extragalactic gamma-ray background originates from blazars.