The MASSIVE survey – XIX. Molecular gas measurements of the supermassive black hole masses in the elliptical galaxies NGC 1684 and NGC 0997

Supermassive black hole (SMBH) masses can be measured by observing their dynamical effects on tracers, such as molecular gas. We present high angular resolution Atacama Large Millimeter/submillimeter Array observations of the 12CO(2–1) line emission of the early-type galaxies (ETGs) NGC 1684 and NGC 0997, obtained as part of the MASSIVE survey, a volume-limited integral-field spectroscopic study of the most massive local ETGs. NGC 1684 has a regularly rotating central molecular gas disc, with a spatial extent of ≈6 arcsec (≈1.8 kpc) in radius and a central hole slightly larger than the expected SMBH sphere of influence. We forward model the data cube in a Bayesian framework with the KINEMATIC MOLECULAR SIMULATION (KINMS) code and infer a SMBH mass of 1.40+0.44-0.39 x 109 M⊙ (3σ confidence interval) and an F110W-filter stellar mass-to-light ratio of (2.50 ± 0.05) M⊙/L⊙, F110W. NGC 0997 has a regularly rotating central molecular gas disc, with a spatial extent of ≈5 arcsec (≈2.2 kpc) in radius and a partially filled central hole much larger than the expected SMBH sphere of influence, thus preventing a robust SMBH mass determination. With the same modelling method, we nevertheless constrain the SMBH mass to be in the range 4.0 × 107–1.8 × 109 M⊙ and the F160W-filter stellar mass-to-light ratio to be (1.52 ± 0.11) M⊙/L⊙, F160W. Both SMBH masses are consistent with the SMBH mass–stellar velocity dispersion (MBH–σe) relation, suggesting that the overmassive SMBHs present in other very massive ETGs are fairly uncommon

The MASSIVE survey – XIX. Molecular gas measurements of the supermassive black hole masses in the elliptical galaxies NGC 1684 and NGC 0997

Supermassive black hole (SMBH) masses can be measured by observing their dynamical effects on tracers, such as molecular gas. We present high angular resolution Atacama Large Millimeter/submillimeter Array (ALMA) observations of the 12CO(2-1) line emission of the early-type galaxies (ETGs) NGC 1684 and NGC 0997, obtained as part of the MASSIVE survey, a volume-limited integral-field spectroscopic study of the most massive local ETGs. NGC 1684 has a regularly-rotating central molecular gas disc, with a spatial extent of ≈6″ (≈1.8 kpc) in radius and a central hole slightly larger than the expected SMBH sphere of influence. We forward model the data cube in a Bayesian framework with the Kinematic Molecular Simulation (KinMS) code and infer a SMBH mass of M⊙ (3σ confidence interval) and a F110W-filter stellar mass-to-light ratio of (2.50 ± 0.05) M⊙/L⊙, F110W. NGC 0997 has a regularly-rotating central molecular gas disc, with a spatial extent of ≈5″ (≈2.2 kpc) in radius and a partially-filled central hole much larger than the expected SMBH sphere of influence, thus preventing a robust SMBH mass determination. With the same modelling method, we nevertheless constrain the SMBH mass to be in the range 4.0 × 107 to 1.8 × 109 M⊙ and the F160W-filter stellar mass-to-light ratio to be (1.52 ± 0.11) M⊙/L⊙, F160W. Both SMBH masses are consistent with the SMBH mass – stellar velocity dispersion (MBH – σe) relation, suggesting that the over-massive SMBHs present in other very massive ETGs are fairly uncommon

WISDOM Project – XIX. Figures of merit for supermassive black hole mass measurements using molecular gas and/or megamaser kinematics

The mass (MBH) 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 Rmin normalised by respectively the SMBH’s Schwarzschild radius (RSchw ≡ 2GMBH/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 σe is the stellar velocity dispersion within the galaxy’s effective radius) and equality radius (the radius Req at which the SMBH mass equals the enclosed stellar mass, MBH = M*(Req), where M*(R) is the stellar mass enclosed within the radius R). All metrics lead to analogous simple relations between Rmin and the highest circular velocity probed Vc. 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 RSchw but is slightly farther in terms of RSOI and Req. However, molecular gas observations of nearby galaxies using the most extended configurations of the Atacama Large Millimeter/sub-millimeter Array can resolve the SOI comparably well and thus enable SMBH mass measurements as precise as the best megamaser measurements

WISDOM Project – XXIII. Figures of merit for supermassive black hole mass measurements using molecular gas and/or megamaser kinematics

The mass (MBH) 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 Rmin normalised by respectively the SMBH’s Schwarzschild radius (RSchw ≡ 2GMBH/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 σe is the stellar velocity dispersion within the galaxy’s effective radius) and equality radius (the radius Req at which the SMBH mass equals the enclosed stellar mass, MBH = M*(Req), where M*(R) is the stellar mass enclosed within the radius R). All metrics lead to analogous simple relations between Rmin and the highest circular velocity probed Vc. 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 RSchw but is slightly farther in terms of RSOI and Req. However, molecular gas observations of nearby galaxies using the most extended configurations of the Atacama Large Millimeter/sub-millimeter Array can resolve the SOI comparably well and thus enable SMBH mass measurements as precise as the best megamaser measurements