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

The possibility that the masses of supermassive black holes (SBHs) correlatewith the total gravitational mass of their host galaxy, or the mass of the darkmatter halo in which they presumably formed, is investigated using a sample of16 spiral and 20 elliptical galaxies. The bulge velocity dispersion, typicallydefined within an aperture of size less than 0.5 kpc, is found to correlatetightly with the galaxy's circular velocity, the latter measured at distancesfrom the galactic center at which the rotation curve is flat, 20 to 80kpc. Byusing the well known M-sigma relation for SBHs, and a prescription to relatethe circular velocity to the mass of the dark matter halo in a standard CDMcosmology, the correlation between velocity dispersion and circular velocity isequivalent to one between SBH and halo masses. Such a correlation is found tobe nonlinear, with the ratio between the two masses decreasing from 2X10^-4 forhalos 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 areincreasingly less efficient -- perhaps unable -- at forming SBHs.Comment: The Astrophysical Journal, accepted (October 10 2002 issue