  In this paper, we examine if the properties of central black holes in
galactic nuclei correlate with their host dark matter halo. We analyze the
entire sample of galaxies where black hole mass, velocity dispersion, sigma,
and asymptotic circular velocity, Vc, have all been measured. We fit M-sigma
and M-Vc to a power law, and find that in both relationships the scatter and
slope are similar. This model-independent analysis suggests that although the
black hole masses are not uniquely determined by dark matter halo mass, when
considered for the current sample as a whole, the M-Vc correlation may be as
strong (or as weak) as M-sigma. Although the data are sparse, there appears to
be more scatter in the correlation for both sigma and Vc at the low--mass end.
This is not unexpected given our current understanding of galaxy and black hole
assembly. In fact, there are several compelling reasons that account for this:
(i) SMBH formation is likely less efficient in low-mass galaxies with large
angular momentum content; (ii) SMBH growth is less efficient in low-mass disk
galaxies that have not experienced major mergers; (iii) dynamical effects, such
as gravitational recoil, increase scatter preferentially at the low-mass end.
Therefore, the recent observational claim of the absence of central SMBHs in
bulgeless, low mass galaxies, or deviations from the correlations defined by
high-mass black holes in large galaxies today is, in fact, predicated by
current models of black hole growth. We show how this arises as a direct
consequence of the coupling between dark matter halos and central black holes
at the earliest epochs.
