The estimation of γ-ray Doppler factor for Fermi/LAT-detected blazars

Blazars are a subclass of active galactic nuclei with extreme observation properties, which is caused by the beaming effect, expressed by a Doppler factor ( $\delta$ ), in a relativistic jet. Doppler factor is an important parameter in the blazars paradigm to indicate all of the observation properties, and many methods were proposed to estimate its value. In this paper, we present a method following Mattox et al. to calculate the lower limit on $\gamma$ -ray Doppler factor ( $\delta_{\gamma}$ ) for 809 selected Fermi/LAT-detected $\gamma$ -ray blazars by adopting the available $\gamma$ -ray and X-ray data. Our sample included 342 flat-spectrum radio quasars (FSRQs) and 467 BL Lac objects (BL Lacs), out of which 507 sources are compiled with available radio core-dominance parameter (R) from our previous study. Our calculation shows that the average values of the lower limit on $\delta_{\gamma}$ for FSRQs and BL Lacs are $\left\langle\delta_{\gamma}|_{\textrm{FSRQ}}\right\rangle = 6.87 \pm 4.07$ and $\left\langle\delta_{\gamma}|_{\textrm{BL\ Lac}}\right\rangle=4.31 \pm 2.97$ , respectively. We compare and discuss our results with those from the literature. We found that the derived lower limit on $\delta_{\gamma}$ for some sources is higher than that from the radio estimation, which could be possibly explained by the jet bending within those blazars. Our results also suggest that the $\gamma$ -ray and radio regions perhaps share the same relativistic effects. The $\gamma$ -ray Doppler factor has been found to be correlated with both the $\gamma$ -ray luminosity and core-dominance parameter, implying that the jet is possibly continuous in the $\gamma$ -ray bands, and R is perhaps an indicator for a beaming effect.