Estimates of AGN Black Hole Mass and Minimum Variability Timescale

Black hole mass is one of the fundamental physical parameters of active galactic nuclei (AGNs), for which many methods of estimation have been proposed. One set of methods assumes that the broad-line region (BLR) is gravitationally bound by the central black hole potential, so the black hole mass can be estimated from the orbital radius and the Doppler velocity. Another set of methods assumes the observed variability timescale is determined by the orbital timescale near the innermost stable orbit around the Schwarzschild black hole or the Kerr black hole, or by the characteristic timescale of the accretion disk. We collect a sample of 21 AGNs, for which the minimum variability timescales have been obtained and their black hole masses (Mσ) have been well estimated from the stellar velocity dispersion or the BLR size-luminosity relation. Using the minimum variability timescales we estimated the black hole masses for 21 objects by the three different methods, the results are denoted by Ms, Mk and Md, respectively. We compared each of them with Mσindividually and found that: (1) using the minimum variability timescale with the Kerr black hole theory leads to small differences between Mσand Mk, none exceeding one order of magnitude, and the mean difference between them is about 0.53 dex; (2) using the minimum variability timescale with the Schwarzschild black hole theory leads to somewhat larger difference between Mσand Ms: larger than one order of magnitude for 6 of the 21 sources, and the mean difference is 0.74 dex; (3) using the minimum variability timescale with the accretion disk theory leads to much larger differences between Mσand Md, for 13 of the 21 sources the differences are larger than two orders of magnitude; and the mean difference is as high as about 2.01 dex.

Estimates of AGN Black Hole Mass and Minimum Variability Timescale