Basic properties of Gamma-ray loud blazars

In this paper, a method is proposed to determine the basic properties of $\gamma$-ray loud blazars, among them the central black hole mass, M, the Doppler factor, $\delta$, the propagation angle of the $\gamma$-rays with respect to the symmetric axis of a two-temperature accretion disk, $\Phi$, and the distance (i.e. the height above the accretion disk), d at which the $\gamma$-rays are created, for seven $\gamma$-ray loud blazars with available GeV variability timescales and in which the absorption effect of a $\gamma$-ray and the beaming effect have been taken into account. Our results indicate that, if we take the intrinsic $\gamma$-ray luminosity to be $\lambda$ times the Eddington luminosity, $L_{\gamma}^{in} = \lambda L_{Edd.}$, the masses of the blazars are in the range of $(4 \sim 131)\times 10^{7}M_{\odot}$, the Doppler factors ($\delta$) lie in the range of 0.57 to 5.33 the angle ($\Phi$) is in the range of $13^{\circ}$ to 43$^{\circ}$ and the distance (d) is in the range of 26R_{g} to 411R_{g}. Our model results are independent of $\gamma$-ray emission mechanisms but they do depend on the X-ray emission mechanism of the accretion disk.