2024MNRAS.530.3240Z

The mass (M_BH) of a supermassive black hole (SMBH) can be measured using spatially resolved kinematics of the region where the SMBH dominates gravitationally. The most reliable measurements are those that resolve the smallest physical scales around the SMBHs. We consider here three metrics to compare the physical scales probed by kinematic tracers dominated by rotation: the radius of the innermost detected kinematic tracer R_min normalized by the SMBH's Schwarzschild radius (R_Schw ≡ 2GM_BH/c², where G is the gravitational constant and c the speed of light), sphere-of-influence (SOI) radius ($R_\mathrm{SOI}\equiv GM_\mathrm{BH}/\sigma _\mathrm{e}^2$, where σ_e is the stellar velocity dispersion within the galaxy's effective radius), and equality radius [the radius R_eq at which the SMBH mass equals the enclosed stellar mass, M_BH = M_*(R_eq), where M_*(R) is the stellar mass enclosed within the radius R]. All metrics lead to analogous simple relations between R_min and the highest circular velocity probed V_c. Adopting these metrics to compare the SMBH mass measurements using molecular gas kinematics to those using megamaser kinematics, we demonstrate that the best molecular gas measurements resolve material that is physically closer to the SMBHs in terms of R_Schw but is slightly farther in terms of R_SOI and R_eq. However, molecular gas observations of nearby galaxies using the most extended configurations of the Atacama Large Millimeter/submillimeter Array can resolve the SOI comparably well and thus enable SMBH mass measurements as precise as the best megamaser measurements.