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

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 deprojected integrated CO emission-line width as an alternative tracer of this rotation velocity, which 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 spatially resolved and unresolved CO observations, respectively. The tightest correlation is found using the resolved sample of 25 galaxies as log(M-BH/M-circle dot) = (7.5 +/- 0.1) + (8.5 +/- 0.9)[log(W-50/ sin i km s(-1)) - 2.7], where MBH is the central SMBH mass, W50 is the full width at half-maximum of a double-horned emission-line profile, and i is 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 deprojected 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.