The basic parameters of gamma-ray-loud blazars

We determined the basic parameters, such as the central black hole mass ($M$), the boosting factor (or Doppler factor) ($\delta$), the propagation angle ($\Phi$) and the distance along the axis to the site of $\gamma$-ray production ($d$) for 23 $\gamma$-ray-loud blazars using their available variability timescales. In this method, the absorption effect depends on the $\gamma$-ray energy, emission size and property of the accretion disk. Using the intrinsic $\gamma$-ray luminosity as a fraction $\lambda$ of the Eddington luminosity, $L^{in}_{\gamma}=\lambda L_{Ledd.}$ and the optical depth equal to unity, we can determine the upper limit of the central black hole masses. We found that the black hole masses range between $10^{7}M_{\odot}$ and $10^{9}M_{\odot}$ when $\lambda$ = 0.1 and 1.0 are adopted. Since this method is based on gamma-ray emissions and the short time-scale of the sources, it can also be used for central black hole mass determination of high redshift gamma-ray sources. In the case of the upper limit of black hole mass there is no clear difference between BLs and FSRQs, which suggests that the central black hole masses do not play an important role in the evolutionary sequence of blazars.