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 .
We investigate the source count distribution of 3FHL sources at Galactic latitudes |b| > 20 ^ { \circ } , where the sources 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 1-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 \times 10 ^ { -12 } ph cm ^ { -2 } s ^ { -1 } .
With this method we detect a flux break at ( 3.5 \pm 0.4 ) \times 10 ^ { -11 } \mathrm { ph } \mathrm { cm } ^ { -2 } \mathrm { 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 \pm 0.04 and 1.07 \pm 0.27 , respectively .
This result is confirmed with the 1pPDF method , which has a sensitivity reach of \sim 10 ^ { -11 } ph cm ^ { -2 } s ^ { -1 } .
Integrating the derived source count distribution above the sensitivity of our analysis , we find that ( 42 \pm 8 ) \% of the extragalactic \gamma -ray background originates from blazars .