Origin of the Black Hole Mass - Bulge Velocity Dispersion Relation: A   Critical Surface Density For Disk Accretion
  It is shown that, if gas accretion via a disk onto the central supermassive black hole is efficient only for surface density Sigma >= 10 g/cm^2, the black hole mass - galactic bulge velocity dispersion relation (Tremaine et al 2002) is naturally borne out, so is the modest dispersion in that relation, in the context of hierarchical structure formation theory. This relation is not expected to evolve with redshift in this model. 
Renyue Cen