WISDOM Project  XIX. Figures of merit for supermassive black hole mass measurements using molecular gas and/or megamaser kinematics
Abstract
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}/c^{2}, where G is the gravitational constant and c the speed of light), sphereofinfluence (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.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 May 2024
 DOI:
 10.1093/mnras/stae1106
 arXiv:
 arXiv:2404.16345
 Bibcode:
 2024MNRAS.530.3240Z
 Keywords:

 masers;
 galaxies: ISM;
 galaxies: kinematics and dynamics;
 galaxies: nuclei;
 Astrophysics  Astrophysics of Galaxies
 EPrint:
 13 pages, 9 figures. Accepted by MNRAS