Mg. Haehnelt et G. Kauffmann, The correlation between black hole mass and bulge velocity dispersion in hierarchical galaxy formation models, M NOT R AST, 318(3), 2000, pp. L35-L38
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 g
alaxy. We show that the model of Kauffmann & Haehnelt, in which bulges and
supermassive black holes both form during major mergers, produces a correla
tion between M-bh and sigma with a slope and scatter comparable to the obse
rved relation. In the model the M-bh-sigma relation is significantly tighte
r than the correlation between black hole mass and bulge luminosity, or the
correlation between bulge luminosity and velocity dispersion. There are tw
o reasons for this: (i) the gas masses of bulge progenitors depend on the v
elocity dispersion but not on the formation epoch of the bulge, whereas the
stellar masses of the progenitors depend on both; (ii) mergers between gal
axies move black holes along the observed M-bh-sigma relation, even at late
times when the galaxies are gas-poor and black holes grow mainly the by me
rging of pre-existing black holes. We conclude that the small scatter in th
e observed M-bh-sigma relation is consistent with a picture in which bulges
and black holes form over a wide range in redshift.