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

The possibility that the masses M• of supermassive black holes (SBHs) correlate with the total gravitational mass of their host galaxy, or the mass MDM 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 σc, typically defined within an aperture of size R < ∼ 0.5 kpc, is found to correlate tightly with the galaxy’s circular velocity vc, the latter measured at distances from the galactic center at which the rotation curve is flat, R ∼ 20 − 80 kpc. By using the well known M• −σc relation for SBHs, and a prescription to relate vc to the mass of the dark matter halo MDM in a standard ΛCDM cosmology, the correlation between σc and vc is equivalent to one between M• and MDM . Such a correlation is found to be nonlinear, with the ratio M•/MDM decreasing from 2×10−4 for MDM ∼ 1014 M⊙, to 10−5 for MDM ∼ 1012 M⊙. Preliminary evidence suggests that halos of mass smaller than ∼ 5× 1011 M⊙ are increasingly less efficient – perhaps unable – at forming SBHs.