On the intrinsic shape of the gamma-ray spectrum for Fermi blazars

The curvature of the γ-ray spectrumin blazarsmay reflect the intrinsic distribution of emitting electrons, which will further give some information on the possible acceleration and cooling processes in the emitting region. The γ-ray spectra of Fermi blazars are normally fitted either by a single power-law (PL) or a log-normal (call Logarithmic Parabola, LP) form. The possible reason for this difference is not clear. We statistically explore this issue based on the different observational properties of 1419 Fermi blazars in the 3LAC Clean Sample.We find that the γ-ray flux (100MeV-100GeV) and variability index follow bimodal distributions for PL and LP blazars, where the γ-ray flux and variability index show a positive correlation. However, the distributions of γ-ray luminosity and redshift follow a unimodal distribution. Our results suggest that the bimodal distribution of γ-ray fluxes for LP and PL blazars may not be intrinsic and all blazars may have an intrinsically curved γ-ray spectrum, and the PL spectrum is just caused by the fitting effect due to less photons.