Beyond the bulge: A fundamental relation between supermassive black holes and dark matter halos

The possibility that the masses M-BH of supermassive black holes (SBHs) correlate with the total gravitational mass of their host galaxy, or the mass M-DM 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 sigma(c), typically defined within an aperture of size Rless than or similar to0.5 kpc, is found to correlate tightly with the galaxy's circular velocity v(c), the latter measured at distances from the Galactic center at which the rotation curve is at, R similar to 20-80 kpc. By using the well-known M-BH-sigma(c) relation for SBHs and a prescription to relate v(c) to the mass of the dark matter halo M-DM in a standard LambdaCDM cosmology, the correlation between sigma(c) and v(c) is equivalent to one between M-BH and M-DM. Such a correlation is found to be nonlinear, with the ratio M-BH/M-DM decreasing from 2 x 10(-4) for M-DM similar to 10(14) M. to 10(-5) for M-DM similar to 10(12) M.. Preliminary evidence suggests that halos of mass smaller than similar to5 x 10(11) M. are increasingly less efficient at forming SBHs-perhaps even unable to form them.