The correlation between black hole mass and bulge velocity dispersion in hierarchical galaxy formation models.

Recent work has demonstrated that there is a tight correlation between the mass of a black hole and the velocity dispersion of the bulge of its host galaxy. We show that the model of Kauffmann & Haehnelt, in which bulges and supermassive black holes both form during major mergers, produces a correlation between M[sub bh] and σ with a slope and scatter comparable to the observed relation. In the model the M[sub bh]–σ relation is significantly tighter than the correlation between black hole mass and bulge luminosity, or the correlation between bulge luminosity and velocity dispersion. There are two reasons for this: (i) the gas masses of bulge progenitors depend on the velocity dispersion but not on the formation epoch of the bulge, whereas the stellar masses of the progenitors depend on both; (ii) mergers between galaxies move black holes along the observed M[sub bh]–σ relation, even at late times when the galaxies are gas-poor and black holes grow mainly the by merging of pre-existing black holes. We conclude that the small scatter in the observed M[sub bh]–σ relation is consistent with a picture in which bulges and black holes form over a wide range in redshift. [ABSTRACT FROM AUTHOR]