Assessing indirect methods to determine black hole masses using NGC 4151

Accurately determining the black hole mass (M_BH) in active galactic nuclei (AGNs) is crucial to constraining their properties and to studying their evolution. While direct methods yield reliable measurements of M_BH in unobscured type 1 AGNs, where the dynamics of stellar or gas components can be directly observed, only indirect methods can be applied to the vast majority of heavily absorbed type 2 AGNs, which represent most of the AGN population. Since it is difficult to evaluate the accuracy and precision of these indirect methods, we utilize the nearby X-ray bright Seyfert galaxy NGC 4151, whose M_BH has been tightly constrained with several independent direct methods, as a laboratory to assess the reliability of three indirect methods that have been applied to obscured AGNs. All three, the X-ray scaling method, the Fundamental Plane of BH activity, and the M-σ correlation, yield M_BH values consistent with those inferred from direct methods and can therefore be considered accurate. However, only the X-ray scaling method and the M-σ correlation are precise because the substantial scatter in the Fundamental Plane of BH activity allows only for crude estimates. Of the four M-σ correlations we used, only the one from Kormendy and Ho yields a value consistent with the dynamical estimates. This study suggests that the best approach to estimating the BH mass in systems where direct dynamical methods cannot be applied is to utilize a combination of indirect methods, taking into account their different ranges of applicability.