A relationship between nuclear black hole mass and galaxy velocity dispersion

We describe a correlation between the mass M-bh of a galaxy's central black hole and the luminosity-weighted line-of-sight velocity dispersion sigma(e) 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 M-bh = 1.2(+/-0.2) x 10(8) M. (sigma(e)/200 km s(-1))(3.75(+/-0.3)) over almost 3 orders of magnitude in M-bh; the scatter in M-bh at fixed sigma(e) is only 0.30 dex, and most of this is due to observational errors. The M-bh-sigma(e) 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.