Constraints on black hole massess with timescales of variations in blazars

In this paper, we investigated the issue of black hole masses and minimum timescales of jet emission for blazars. We proposed a sophisticated model that sets an upper limit to the central black hole masses $M_{\bullet}$ with the minimum timescales $\Delta t^{\rm{ob}}_{\rm{min}}$ of variations observed in blazars. The value of $\Delta t^{\rm{ob}}_{\rm{min}}$ presents an upper limit to the size of blob in jet. The blob is assumed to be generated in the jet-production region in the vicinity of black hole, and then the expanding blob travels outward along the jet. We applied the model to 32 blazars, 29 of which were detected in gamma rays by satellites, and these $\Delta t^{\rm{ob}}_{\rm{min}}$ are on the order of hours with large variability amplitudes. In general, these $M_{\bullet}$ estimated with this method are not inconsistent with those masses reported in the literatures. This model is natural to connect $M_{\bullet}$ with $\Delta t^{\rm{ob}}_{\rm{min}}$ for blazars, and seems to be applicable to constrain $M_{\bullet}$ in the central engines of blazars.