Black Hole Mass Estimation: How Good is the Virial Estimate?

Black hole mass is a key factor in determining how a black hole interacts with its environment. However, the determination of black hole masses at high redshifts depends on secondary mass estimators, which are based on empirical relationships and broad approximations. A dynamical disk wind broad line region model (BLR) of active galactic nuclei is built in order to test the impact of different BLR geometries and inclination angles on the black hole mass estimation. Monte Carlo simulations of two disk wind models are constructed to recover the virial scale factor, f, at various inclination angles. The resulting f values strongly correlate with inclination angle, with large f values associated with small inclination angles (close to face-on) and small f values with large inclination angles (close to edge-on). The recovered f factors are consistent with previously determined f values, found from empirical relationships. Setting f as a constant may introduce a bias into virial black hole mass estimates for a large sample of active galactic nuclei. However, the extent of the bias depends on the line width characterisation (e.g. full width at half maximum or line dispersion). Masses estimated using $f_{\text{FWHM}}$ tend to be biased towards larger masses, but this can generally be corrected by calibrating for the width or shape of the emission line.