THE ASTROPHYSICAL JOURNAL Preprint typeset using L ATEX style emulateapj 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 gr vitational mass of their host galaxy, or the mass of the dark matter halo i n wh ch they presumably formed, is investigated using a sample of 16 spiral and 20 elliptical galaxies. The bu lge velocity dispersionσc, typically defined within an aperture of sizeR < ∼ 0.5 kpc, is found to correlate tightly with the asymptotic valu e of the circular velocity vc, measured at radii R ∼ 20− 80 kpc. By using the well knownM• − σc relation for SBHs, and a prescription to relatevc to the mass of the dark matter halo MDM in a standard CDM cosmology, the correlation between σc and vc is equivalent to one between M• andMDM. Such a correlation is found to be nonlinear, with the ratio M•/MDM decreasing from 6 ×10−5 for MDM ∼ 1014 M⊙, to 5×10−6 for MDM ∼ 1012 M⊙. Preliminary evidence suggests that halos of smaller mass are increasingly less efficient – p erhaps unable – in forming SBHs.