Measuring black hole mass of type I active galactic nuclei by spectropolarimetry

Black hole (BH) mass of Type I active galactic nuclei (AGN) can be measured or estimated through either reverberation mapping (RM) or empirical $R-L$ relation, however, both of them suffer from uncertainties of the virial factor ($f_{\rm BLR}$), thus limiting the measurement accuracy. In this letter, we make an effort to investigate $f_{\rm BLR}$ through polarised spectra of the broad-line regions (BLR) arisen from electrons in the equatorial plane. Given the BLR composed of discrete clouds with Keplerian velocity around the central BH, we simulate a large number of spectra of total and polarised flux with wide ranges of parameters of the BLR model and equatorial scatters. We find that the $f_{\rm BLR}$-distribution of polarised spectra is much narrower than that of total ones. This provides a way of n accurately estimating BH mass from single spectropolarimetric observations of type I AGN whose equatorial scatters are identified.