Recent X-ray observations of intense high-speed outflows in quasars suggest
that supercritical accretion on to the central black hole may have an important
effect on a host galaxy. I revisit some ideas of Silk and Rees, and assume such
flows occur in the final stages of building up the black hole mass. It is now
possible to model explicitly the interaction between the outflow and the host
galaxy. This is found to resemble a momentum-driven stellar wind bubble,
implying a relation M_BH = (f_g kappa/2 pi G^2) sigma^4 = 1.5 10^8 sigma_200^4
Msun between black hole mass and bulge velocity dispersion (f_g = gas fraction
of total matter density, kappa = electron scattering opacity), without free
parameters. This is remarkably close to the observed relation in both slope and
normalization.
This result suggests that the central black holes in galaxies gain most of
their mass in phases of super-Eddington accretion, which are presumably
obscured or at high redshift. Observed super-Eddington quasars are apparently
late in growing their black hole masses.Comment: 8 pages, no figures Accepted for publication in ApJ Letters; typos
and references correcte