Doppler Factor Estimation for Fermi Blazars

In this work, we exploit the luminosity of the broad-line region (BLR) for 50 Fermi blazars through matching the coordinates between the Sloan Digital Sky Survey catalog, Fermi Large Area Telescope Third Source Catalog, and the Fermi Large Area Telescope Fourth Source Catalog and fitting their emission lines. In total, we collected a sample of 350 blazars with broad-line emissions including 50 new objects and 300 blazars from published works to revisit the correlation between the γ-ray luminosity and the broad-line luminosity, and proposed a new method to estimate the Doppler factors based on the correlation between the radiative power of the jet and luminosity of the BLR. We come to following conclusions. (1) For the 50 Fermi blazars, their broad-line luminosity (log L _BLR) ranges from 41.82–45.2 erg s⁻¹ with a mean value of 44.39 erg s⁻¹. (2) The Doppler factor (δ) ranges from δ = 0.35 to δ = 85.66 with a mean value of 12.54, which is consistent with the results in the literature. (3) There are positive correlations between γ-ray luminosity and broad-line luminosity, and between γ-ray luminosity and the Doppler factor.