A relationship between nuclear black hole mass and galaxy velocity dispersion

We describe a correlation between the mass Mbh of a galaxy's central black hole and the luminosity-weighted line-of-sight velocity dispersion σe within the half-light radius. The result is based on a sample of 26 galaxies, including 13 galaxies with new determinations of black hole masses from Hubble Space Telescope measurements of stellar kinematics. The best-fit correlation is Mbh = 1.2(±0.2) × 108 M⊙(σe/200 km s-1)3.75 (±0.3)over almost 3 orders of magnitude in Mbh; the scatter in Mbh at fixed σe is only 0.30 dex, and most of this is due to observational errors. The Mbh-σe relation is of interest not only for its strong predictive power but also because it implies that central black hole mass is constrained by and closely related to properties of the host galaxy's bulge