Time series analysis of gamma-ray blazars and implications for the central black-hole mass

Radiation from the blazar class of of active galactic nuclei (AGN) exhibits fast time variability which is usually ascribed to instabilities in the emission region near the central supermassive black hole. The variability time scale is generally faster in higher energy region, and data recently provided by the {\it Fermi} Gamma-ray Space Telescope in the GeV energy band enable a detailed study of the temporal behavior of AGN. Due to its wide field-of-view in the scanning mode, most sky regions are observed for several hours per day and daily light curves of many AGN have been accumulated for more than 4 years. In this paper we investigate the time variability of 15 well-detected AGNs by studying the normalized power spectrum density (NPSD) of their light curves in the GeV energy band. One source, 3C 454.3, shows a specific time scale of $6.8\times10^5$ s, and this value suggests, assuming the internal shock model, a mass for the central black hole of $(10^8$--$10^{10})M_\odot$ which is consistent with other estimates. It also indicates the typical time interval of ejected blobs is $(7$--$70)$ times the light crossing time of the Schwarzschild radius.