Authors: Benjamin Davis, Alister W. Graham, Francoise Combes
Using the latest sample of 48 spiral galaxies having a directly-measured supermassive black hole mass, MBH, we determine how the maximum disk rotational velocity, vmax (and the implied dark matter halo mass, MDM), correlates with MBH, central velocity dispersion (σ0), and spiral arm pitch angle (φ). We find that MBH ∝ vmax10.58±1.35 ∝ MDM4.34±0.65, significantly steeper than previously reported, and with a total root mean square scatter (0.63 dex) equal to that about the MBH-σ0 relation for spiral galaxies - in stark antithesis with claims that MBH does not correlate with disks. Moreover, this MBH-vmax relation is consistent with the unification of the Tully-Fisher relation (involving the total stellar mass, M*,tot) and the steep MBH ∝ M*,tot3.05±0.53 relation observed in spiral galaxies. We also find that σ0 ∝ vmax1.54±0.25 ∝ MDM0.63±0.11, consistent with past studies connecting stellar bulges (with σ0≳ 100 km s-1), dark matter halos, and a non-constant vmax/σ0 ratio. Finally, we report that tan|φ| ∝ (-1.17±0.19)log(vmax) ∝ (-0.48±0.09)log(MDM), providing a novel formulation between the geometry (i.e., the logarithmic spiral arm pitch angle) and kinematics of spiral galaxy disks. While the vmax-φ relation may facilitate distance estimations to face-on spiral galaxies, via the Tully-Fisher relation and using φ as a proxy for vmax, the MDM-φ relation provides a path for determining dark matter halo masses from imaging data alone. Furthermore, based on a spiral galaxy sample size which is double that used previously, the self-consistent relations presented here provide dramatically revised constraints for theory and simulations.