SIMBAD references

We compile a sample of 13 BL Lac objects for which rapid optical variabilities are reliably established and luminosities of the nuclei and the host galaxies have been well observed by the Hubble Space Telescope (HST). We present a new method for estimating the masses of the supermassive black holes (SMBHs) at the centers of these objects using the rapid optical variability, and find that the masses of the SMBHs range from 10^7.42 to 10^9.19 M_☉. This mass range is quite similar to that of dark compact objects in galaxies. To further investigate the reliability of our method, we also compile another sample with nine high-energy γ-ray emission sources of BL Lac objects and obtain the masses for the SMBHs in these objects using the Dermer & Gehrels method. We find that the masses derived from these two methods are quite similar. These results strongly imply that the estimation of masses of SMBHs by rapid optical variability is reliable. We examine the correlations of the masses with the luminosities of the nuclei and the host galaxies observed by HST, and find that the masses are significantly correlated with the luminosities of the nuclei, but not correlated with the luminosities of host galaxies at all. In addition, we examine the relation between the observed minimal timescale of variation and the bolometric luminosities of the objects. We find that they obey the Abromowicz & Nobili relation. These results possibly imply that the luminosities of the nuclei are produced by accretion of the central SMBHs.