Correlation between γ $\gamma$ -ray flux density and redshift for Fermi blazars

Abstract

Blazars are strong $\gamma$ -ray emitters, the $\gamma$ -ray emissions are likely strongly beamed, therefore, one should use the intrinsic (de-beamed) emissions to investigate its emission nature. In this work, we compiled a sample of Fermi blazars with available beaming Doppler factors, $\delta_{R}$ , to investigate the correlation between $\gamma$ -ray flux density, $\log f_{\gamma}$ , and redshift, $\log z$ . The analysis shows that there is no correlation between $\log f_{\gamma}$ and $\log z$ for the observed $\gamma$ -ray flux density, but there is a clear strong correlation between the intrinsic flux densities, $\log f_{\gamma}^{\mathrm{in}}$ and $\log z$ . We also discussed the relationship of $\gamma$ -ray luminosity and short time scale for the observed data and the intrinsic data. Our analysis suggests that the intrinsic $\gamma$ -ray flux density obeys the flux density and redshift relation, and the jet in $\gamma$ -rays maybe a continuous case. The intrinsic luminosity and the short time scales obey the Elliot and Shapiro relation and Abramowicz and Nobili relation as well.