How important is the dark matter halo for black hole growth?

Abstract: 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.