Star Formation–Regulated Growth of Black Holes in Protogalactic Spheroids

The observed relation between central black hole mass and spheroid velocitydispersion is interpreted in terms of a self-regulation model that incorporatesa viscous Keplerian accretion disk to feed the black hole, embedded in amassive, self-gravitating star forming disk that eventually populates thespheroid. The model leads to a constant ratio between black hole mass andspheroid mass which is equal to the inverse of the critical Reynolds number forthe onset of turbulence in the accretion disk surrounding the central blackhole. Applying the fundamental plane correlation for spheroids, we find thatthe black hole mass has a power-law dependence on the spheroid velocitydispersion with a slope in the range of 4-5. We explain the larger scatter inthe Magorrian relation with respect to the black hole mass-spheroid velocitydispersion relationship as a result of secular evolution of the spheroid thatprimarily affects its luminosity and to a much lesser extent its velocitydispersion.Comment: 12 pages, no figures, submitted to ApJ Letter