Black hole wind speeds and the M - σ relation

We derive an M-BH-Sigma relation between supermassive black hole mass and stellar velocity dispersion in galaxy bulges that results from self-regulated, energy-conserving feedback. The relation is of the form M(BH)v(w) proportional to Sigma(5), where v(w) is the velocity of the wind driven by the black hole. We take a sample of quiescent early-type galaxies and bulges with measured black hole masses and velocity dispersions and use our model to infer the wind speeds they would have had during an active phase. This approach, in effect, translates the scatter in the observed M-BH-Sigma relation into a distribution of v(w). There are some remarkable similarities between the distributions of black hole wind speeds that we obtain and the distributions of outflow speeds observed in local active galactic nuclei, including a comparable median of v(w) = 0.035c.