WISDOM Project – XXIV. Cross-checking supermassive black hole mass estimates from ALMA CO gas kinematics and SINFONI stellar kinematics in the galaxy NGC 4751

Supermassive black hole (SMBH) masses can be measured by observing the impacts of the SMBHs on dynamical tracers around them. We present high angular resolution (0.19 arcsec or ≈24 pc) Atacama Large Millimeter/submillimeter Array observations of the ^12CO(3-2) line emission of the early-type galaxy NGC 4751, which reveal a highly-inclined regularly-rotating molecular gas disc with clear central Keplerian motions. Using a Hubble Space Telescope image to constrain the stellar mass distribution, we forward model the molecular gas kinematics and data cube in a Bayesian framework using the Kinematic Molecular Simulation code. Assuming a constant mass-to-light ratio (M/L), we infer a SMBH mass M_BH=3.43^+0.45_-0.44×10^9 M_⊙ and a F160W filter stellar M/L M/L_F160W=(2.68±0.11) M_⊙/L_⊙,F160W (all quoted uncertainties are at 3σ confidence). Assuming a linearly spatially-varying M/L, we infer M_BH=2.79_-0.57^+0.75×10^9 M_⊙ and (M/L_F160W)/(M_⊙/L_⊙,F160W)=3.07^+0.27_-0.35-0.09^+0.08_-0.06 (R/arcsec), where R is the galactocentric radius. We also present alternative SMBH mass estimates using the Jeans Anisotropic Modelling (JAM) method and SINFONI stellar kinematics. Assuming a cylindrically-aligned velocity ellipsoid (JAM_cyl) we infer M_BH=(2.52± 0.36)×10^9 M_⊙, while assuming a spherically-aligned velocity ellipsoid (JAM_sph) we infer M_BH=(3.24±0.87)×10^9 M_⊙. Our derived masses are all consistent with one another, but they are larger than (and inconsistent with) one previous stellar dynamical measurement using Schwarzschil's method and the same SINFONI kinematics.