WISDOM project -- VI. Exploring the relation between supermassive black hole mass and galaxy rotation with molecular gas

Abstract: Empirical correlations between the masses of supermassive black holes (SMBHs) and properties of their host galaxies are well-established. Among these is the correlation with the flat rotation velocity of each galaxy measured either at a large radius in its rotation curve or via a spatially-integrated emission line width. We propose here the use of the de-projected integrated CO emission line width as an alternative tracer of this rotation velocity, that has already been shown useful for the Tully-Fisher (luminosity-rotation velocity) relation. We investigate the correlation between CO line widths and SMBH masses for two samples of galaxies with dynamical SMBH mass measurements, with respectively spatially-resolved and unresolved CO observations. The tightest correlation is found using the resolved sample of 24 galaxies as $\log (M_\mathrm{BH}/\mathrm{M_\odot})=(7.5\pm0.1)+(8.5\pm0.9)[\log(W_\mathrm{50}/\sin i \,\mathrm{km\,s}^{-1})-2.7]$, where $M_\mathrm{BH}$ is the central SMBH mass, $W_{50}$ the full-width at half-maximum of a double-horned emission line profile, and $i$ the inclination of the CO disc. This relation has a total scatter of $0.6\,$dex, comparable to those of other SMBH mass correlations, and dominated by the intrinsic scatter of $0.5\,$dex. A tight correlation is also found between the de-projected CO line widths and the stellar velocity dispersions averaged within one effective radius. We apply our correlation to the COLD GASS sample to estimate the local SMBH mass function.