Measuring black hole masses from tidal disruption events: Testing the $M_{\rm BH}-\sigma_*$ relation

Liu and colleagues recently proposed an elliptical accretion disk model for tidal disruption events (TDEs). They showed that the accretion disks of optical/UV TDEs are large and highly eccentric and suggested that the broad optical emission lines with complex and diverse profiles originate in the cool eccentric accretion disk of random inclination and orientation. In this paper, we calculate the radiation efficiency of the elliptical accretion disk and investigate the implications for the observations of TDEs. We compile the observational data of the peak bolometric luminosity and the total radiation energy after peak brightness of 18 TDE sources and compare the observations to the expectations from the elliptical accretion disk model. Our results show that the observations are well consistent with the expectations and that the majority of the orbital energy of the stellar debris is advected onto the black hole (BH) without being converted into radiation. By comparing the observations and the expectations, we derive the masses of the disrupted stars and BHs of the TDEs. The BH masses obtained in this paper are well consistent with those calculated with the M_BH-sigma_* relation. Our results provide an effective method to measure the masses of BHs from thousands or more of the TDEs to be discovered in the ongoing and next-generation sky surveys, no matter whether the BHs are located at the centers of the galactic nuclei or wandering in disks and halos.