Spectropolarimetric measurements of hidden broad lines in nearby megamaser galaxies: a lack of clear evidence for a correlation between black hole masses and virial products

High-accuracy black hole (BH) masses require excellent spatial resolution that is only achievable for galaxies within ~100 Mpc using present-day technology. At larger distances, BH masses are often estimated with single-epoch scaling relations for active galactic nuclei. This method requires only luminosity and the velocity dispersion of the broad line region (BLR) to calculate a virial product, and an additional virial factor, $f$, to determine BH mass. The accuracy of these single-epoch masses, however, is unknown, and there are few empirical constraints on the variance of $f$ between objects. We attempt to calibrate single-epoch BH masses using spectropolarimetric measurements of nine megamaser galaxies from which we measure the velocity distribution of the BLR. We do not find strong evidence for a correlation between the virial products used for single-epoch masses and dynamical mass, neither for the megamaser sample alone or when combined with dynamical masses from reverberation mapping modeling. Furthermore, we find evidence that the virial parameter $f$ varies between objects, but we do not find strong evidence for a correlation with other observable parameters such as luminosity or broad line width. Although we cannot definitively rule out the existence of any correlation between dynamical mass and virial product, we find tension between allowed $f$ values for masers and those widely used in the literature. We conclude that the single-epoch method requires further investigation if it is to be used successfully to infer BH masses.