Estimating supermassive black hole masses in AGNs using polarization of broad MgII, H${\alpha}$ and H${\beta}$ lines

For type-1 active galactic nuclei (AGNs) for which the equatorial scattering is the dominant broad-line polarization mechanism, it is possible to measure the supermassive black hole (SMBH) mass by tracing the Keplerian motion across the polarization plane position angle phi. So far, this method has been used for 30 objects but only for H alpha emission line. We explore the possibilities of this method for determining SMBH masses using polarization in broad emission lines by applying it for the first time to MgII.2798A spectral line. We use three-dimensional (3-D) Monte Carlo radiative transfer code STOKES for simultaneous modelling of equatorial scattering of H alpha, H beta, and MgII lines. We included vertical inflows and outflows in the Mg II broad-line region (BLR). We find that polarization states of H alpha and H beta lines are almost identical and SMBH-mass estimates differ by 7 per cent. For MgII line, we find that. exhibits an additional 'plateau' with a constant phi, which deviates than the profiles expected for pure Keplerian motion. SMBH-mass estimates using Mg II line are higher by up to 35 per cent than those obtained from H alpha and H beta lines. Our model shows that for vertical inflows and outflows in the BLR that are higher or comparable to the Keplerian velocity, this method can be applied as a first approximation for obtaining SMBH mass.