Minimal variability time scale - Central black hole mass relation of the γ -ray loud blazars

Abstract

Context. The variability time scales of the blazar γ-ray emission contain the imprints of the sizes of their emission zones and are generally expected to be larger than the light-crossing times of these zones. In several cases the time scales were found to be as short ~10 min, suggesting that the emission zone sizes are comparable with the sizes of the central supermassive black holes. Previously, these measurements also led to the suggestion of a possible connection between the observed minimal variability time scales and the masses of the corresponding black holes. This connection can be used to determine the location of the γ-ray emission site, which currently remains uncertain. Aims. The study aims to investigate the suggested minimum time scale - black hole mass" relation using the blazars, detected in the TeV band. Methods. To obtain the tightest constraints on the variability time scales this work uses a compilation of observations by the Cherenkov telescopes HESS, MAGIC, and VERITAS. These measurements are compared to the blazar central black hole masses found in the literature. Results. The majority of the studied blazars show the variability time scales which are at least comparable to the period of rotation along the last stable orbit of the central black hole - and in some cases as short as its light-crossing time. For several sources the observed variability time scales are found to be smaller than the black hole light-crossing time. This suggests that the detected γ-ray variability originates, most probably, from the turbulence in the jet, sufficiently far from the central black hole.