The central black hole masses and Doppler factors of the $γ$-ray loud blazars

Abstract

In this paper, The central black hole masses and the Doppler factors are derived for PKS 0528+134, PKS 0537-441, 3C279, PKS 1406-074, PKS 1622-297, Q1633+382, Mkn 501, and BL Lacertae. The masses obtained are in the range of (1 -7)$\times 10^{7}M_{\odot}$ and compared with that obtained with the Klein-Nishina cross section considered (Dermer & Gehrels 1995). If we considered only the Thomson cross section, the masses are in the range of 2.6$\times 10^{6}M_{\odot}$ - 2$\times 10^{11}M_{\odot}$. The masses obtained from our method are less sensitive to the flux than those obtained from Dermer & Gehrels (1995) method. The masses obtained from two flares (1991 and 1996 flares) of 3C279 are almost the same. For 3C279 and BL Lacertae, viewing angle, $θ$, and Lorentz factor, $Γ$, are estimated from the derived Doppler factor and the measured superluminal velocity. For 3C279, $θ= 10^{\circ}.9-15^{\circ}.6$, $Γ$ = 2.4-14.4 for $δ$ = 3.37; $θ= 8^{\circ}.45-9^{\circ}.7$, $Γ$ = 2.95-11.20 for $δ$ = 4.89; For BL Lacertae, $θ= 25^{\circ}-29^{\circ}.4$, $Γ$ = 2.0-4.0.