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As part of the mm-Wave Interferometric Survey of Dark Object Masses (WISDOM),we present a measurement of the mass of the supermassive black hole (SMBH) inthe nearby early-type galaxy NGC 0383 (radio source 3C 031). This measurementis based on Atacama Large Millimeter/sub-milimeter Array (ALMA) cycle 4 and 5observations of the 12CO(2-1) emission line with a spatial resolution of58x32pc2 (0."18x0."1). This resolution, combined with a channel width of 10km/s, allows us to well resolve the radius of the black hole sphere ofinfluence (measured as R_SOI = 316pc = 0."98), where we detect a clearKeplerian increase of the rotation velocities. NGC 0383 has akinematically-relaxed, smooth nuclear molecular gas disc with weak ring/spiralfeatures. We forward-model the ALMA data cube with the Kinematic MolecularSimulation (KinMS) tool and a Bayesian Markov Chain Monte Carlo method tomeasure a SMBH mass of (4.2+/-0.7)x10^9 Msun, a F160W-band stellarmass-to-light ratio that varies from 2.8+/-0.6 Msun/Lsun in the centre to2.4+/-0.3 Msun/Lsun at the outer edge of the disc and a molecular gas velocitydispersion of 8.3+/-2.1 km/s (all 3-sigma uncertainties). We also detectunresolved continuum emission across the full bandwidth, consistent withsynchrotron emission from an active galactic nucleus. This work demonstratesthat low-J CO emission can resolve gas very close to the SMBH (~140,000Schwarzschild radii) and hence that the molecular gas method is highlycomplimentary to megamaser observations as it can probe the same emittingmaterial.

WISDOM project -- V. Resolving molecular gas in Keplerian rotation around the supermassive black hole in NGC 0383