WISDOM project -- XIV. SMBH mass in the early-type galaxies NGC0612, NGC1574, and NGC4261 from CO dynamical modelling

We present a CO dynamical estimate of the mass of the super-massive black hole (SMBH) in three nearby early-type galaxies: NGC0612, NGC1574 and NGC4261. Our analysis is based on Atacama Large Millimeter/submillimeter Array (ALMA) Cycle 3-6 observations of the \(^{12}\)CO(2-1) emission line with spatial resolutions of \(14-58\) pc (\(0.01"-0.26"\)). We detect disc-like CO distributions on scales from \(\lesssim200\) pc (NGC1574 and NGC4261) to \(\approx10\) kpc (NGC0612). In NGC0612 and NGC1574 the bulk of the gas is regularly rotating. The data also provide evidence for the presence of a massive dark object at the centre of NGC1574, allowing us to obtain the first measure of its mass, \(M_{\rm BH}=(1.0\pm0.2)\times10^{8}\) M\(_{\odot}\) (1\(\sigma\) uncertainty). In NGC4261, the CO kinematics is clearly dominated by the SMBH gravitational influence, allowing us to determine an accurate black hole mass of \((1.62{\pm 0.04})\times10^{9}\) M\(_{\odot}\) (\(1\sigma\) uncertainty). This is fully consistent with a previous CO dynamical estimate obtained using a different modelling technique. Signs of non-circular gas motions (likely outflow) are also identified in the inner regions of NGC4261. In NGC0612, we are only able to obtain a (conservative) upper limit of \(M_{\rm BH}\lesssim3.2\times10^{9}\) M\(_{\odot}\). This has likely to be ascribed to the presence of a central CO hole (with a radius much larger than that of the SMBH sphere of influence), combined with the inability of obtaining a robust prediction for the CO velocity curve. The three SMBH mass estimates are overall in agreement with predictions from the \(M_{\rm BH}-\sigma_{\star}\) relation.