Beyond the Bulge: A Fundamental Relation between Supermassive Black Holes and Dark Matter Halos

Abstract

The possibility that the masses of supermassive black holes (SBHs) correlate with the total gravitational mass of their host galaxy, or the mass of the dark matter halo in which they presumably formed, is investigated using a sample of 16 spiral and 20 elliptical galaxies. The bulge velocity dispersion, typically defined within an aperture of size less than 0.5 kpc, is found to correlate tightly with the galaxy's circular velocity, the latter measured at distances from the galactic center at which the rotation curve is flat, 20 to 80kpc. By using the well known M-sigma relation for SBHs, and a prescription to relate the circular velocity to the mass of the dark matter halo in a standard CDM cosmology, the correlation between velocity dispersion and circular velocity is equivalent to one between SBH and halo masses. Such a correlation is found to be nonlinear, with the ratio between the two masses decreasing from 2X10^-4 for halos of 10^14 solar masses, to 10^-5 for halos of 10^12 solar masses. Preliminary evidence suggests that halos smaller than ~5X10^11 solar masses are increasingly less efficient -- perhaps unable -- at forming SBHs.