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

## TL;DR

This study analyzes the gamma-ray spectra of Fermi blazars, revealing that the apparent spectral differences are likely due to observational effects rather than intrinsic properties, suggesting all blazars have curved spectra.

## Contribution

It provides a statistical comparison of spectral fitting models and proposes that all blazars intrinsically have curved gamma-ray spectra, challenging previous assumptions.

## Key findings

- Gamma-ray flux and variability index show bimodal distributions for different spectral fits.
- Gamma-ray luminosity and redshift follow unimodal distributions.
- The apparent spectral differences are likely due to observational effects, not intrinsic properties.

## Abstract

The curvature of the $\gamma$-ray spectrum in blazars may reflect the intrinsic distribution of the emitting electron distribution, which will further give some information on the possible acceleration and cooling processes in the emitting region. The $\gamma$-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 differnece is not unclear. We statistically explore this issue based on the different observational properties of 1419 Fermi blazars in the 3LAC Clean sample. We find that the $\gamma$-ray flux (100 MeV-100 GeV) and variability index follow bimodal distributions for PL and LP blazars, where $\gamma$-ray flux and variability index show {a positive correlation}. However, the distributions of the $\gamma$-ray luminosity and redshift follow a unimodal distribution. Our results suggest that the bimodal distribution of $\gamma$-ray flux for LP and PL blazars may be not intrinsic and all blazars may have an intrinsic curved $\gamma$-ray spectrum and the PL spectrum is just caused by the fitting effect due to the less photons.