AGN black hole mass estimates using polarization in broad emission lines

Context. The innermost regions in active galactic nuclei (AGNs) have not yet been spatially resolved, but spectropolarimetry can provide insight into their hidden physics and geometry. From spectropolarimetric observations in broad emission lines and assuming equatorial scattering as a dominant polarization mechanism, it is possible to estimate the mass of supermassive black holes (SMBHs) residing at the center of AGNs. Aims. We explore the possibilities and limits, and put constraints on the method for determining SMBH masses using polarization in broad emission lines by providing more in-depth theoretical modeling. Methods. We used the Monte Carlo radiative transfer code STOKES to explore polarization properties of Type-1 AGNs. We modeled equatorial scattering using flared-disk geometry for a set of different SMBH masses assuming Thomson scattering. In addition to the Keplerian motion, which is assumed to be dominant in the broad-line region (BLR), we also considered cases of additional radial inflows and vertical outflows. Results. We modeled the profiles of polarization plane position angle φ, degree of polarization, and total unpolarized lines for different BLR geometries and different SMBH masses. Our model confirms that the method can be widely used for Type-1 AGNs when viewing inclinations are between 25° and 45°. We show that the distance between the BLR and scattering region (SR) has a significant impact on the mass estimates and the best mass estimates are when the SR is situated at a distance 1.5–2.5 times larger than the outer BLR radius. Conclusions. Our models show that if Keplerian motion can be traced through the polarized line profile, then the direct estimation of the mass of the SMBH can be performed. When radial inflows or vertical outflows are present in the BLR, this method can still be applied if velocities of the inflow/outflow are less than 500 km s−1. We also find that models for NGC 4051, NGC 4151, 3C 273, and PG0844+349 are in good agreement with observations.