Comparing indirect methods for black hole masses in AGN: the good, the bad, and the ugly

The black hole mass M_BH is crucial in constraining the growth of supermassive black holes within their host galaxies. Since direct measurements of M_BH with dynamical methods are restricted to a limited number of nearly quiescent nearby galaxies and a small minority of active galactic nuclei (AGN), we must rely on indirect methods. In this work, we utilize an unbiased, volume-limited, hard X-ray selected sample of AGN to compare the reliability of some commonly used indirect methods, emphasizing those that can be applied to obscured AGN. Based on a subsample of AGN with M_BH determined via dynamical methods, our study suggests that X-ray-based techniques, such as the scaling method and the one based on the variability measured through the excess variance, are in good agreement with the dynamical methods. On the other hand, the M-σ_⋆ correlation based on inactive galaxies tends to systematically overestimate M_BH, regardless of the level of obscuration. We provide a correcting factor that produces an acceptable agreement with dynamical values and can be used to quickly correct the M_BH computed with this method. We also derive an alternative M-σ_⋆ correlation based on this unbiased sample of AGN with a slope considerably shallower than the ones obtained using inactive galaxies, suggesting that the latter may not be appropriate to compute the M_BH in AGN. Finally, we find that no quick fix can be applied to correct the M_BH obtained from the fundamental plane of black hole activity, casting doubts on the reliability of this method.