A determination of the gamma-ray flux and photon spectral index distributions of blazars from the \u3ci\u3eFermi\u3c/i\u3e-LAT 3LAC

We present a determination of the distributions of gamma-ray photon flux – the so-called LogN–LogS relation – and photon spectral index for blazars, based on the third extragalactic source catalogue of the Fermi Gamma-ray Space Telescope\u27s Large Area Telescope, and considering the photon energy range from 100 MeV to 100 GeV. The data set consists of the 774 blazars in the so-called Clean sample detected with a greater than approximately 7σ detection threshold and located above ±20° Galactic latitude. We use non-parametric methods verified in previous works to reconstruct the intrinsic distributions from the observed ones which account for the data truncations introduced by observational bias and includes the effects of the possible correlation between the flux and photon index. The intrinsic flux distribution can be represented by a broken power law with a high-flux power-law index of −2.43 ± 0.08 and a low-flux power-law index of −1.87 ± 0.10. The intrinsic photon index distribution can be represented by a Gaussian with mean of 2.62 ± 0.05 and width of 0.17 ± 0.02. We also report the intrinsic distributions for the subpopulations of BL Lac and FSRQ (Flat Spectrum Radio Quasar)-type blazars separately and these differ substantially. We then estimate the contribution of FSRQs and BL Lacs to the diffuse extragalactic gamma-ray background radiation. Under the simplistic assumption that the flux distributions probed in this analysis continue to arbitrary low flux, we calculate that the best-fitting contribution of FSRQs is 35 per cent and BL Lacs 17 per cent of the total gamma-ray output of the Universe in this energy range