The M(BH)-Sigma Relation for Supermassive Black Holes

Abstract

We investigate the differences in the M(BH)-sigma relation derived recently by Ferrarese & Merritt (2000) and Gebhardt et al. (2000). The shallower slope found by the latter authors (3.75 vs. 4.8) is due partly to the use of a regression algorithm that ignores measurement errors, and partly to the value of the velocity dispersion adopted for a single galaxy, the Milky Way. A steeper relation is shown to provide a better fit to black hole masses derived from reverberation mapping studies. Combining the stellar dynamical, gas dynamical, and reverberation mapping mass estimates, we derive a best-fit relation M(BH) = 1.30 (+/- 0.36) X 10^8 (sigma_c/200)^{4.72(+/- 0.36)}, where M(BH) is in solar masses, and sigma in km/s.