2019ApJ...877...64D

Using the latest sample of 48 spiral galaxies having a directly measured supermassive black hole mass, M_BH, we determine how the maximum disk rotational velocity, v_max (and the implied dark matter halo mass, M_DM), correlates with the (i) black hole mass, (ii) central velocity dispersion, σ₀, and (iii) spiral-arm pitch angle, ph. We find that M_BH∝v_{max}^10.62±1.37^∝M_DM^4.35±0.66^, significantly steeper than previously reported, and with a total root mean square scatter (0.58 dex) similar to that about the M_BH-σ₀ relation for spiral galaxies-in stark disagreement with claims that M_BH does not correlate with disks. Moreover, this M_BH-v_max relation is consistent with the unification of the Tully-Fisher relation (involving the total stellar mass, M_*,tot) and the steep M_BH∝M_* ,tot_^3.05±0.53^ relation observed in spiral galaxies. We also find that σ₀∝v_{max}^1.55±0.25^∝M_DM^0.63±0.11^, consistent with past studies connecting stellar bulges (with σ₀ >= 100 km s^–1), dark matter halos, and a nonconstant v_max/σ₀ ratio. Finally, we report that tan| φ| ∝(-1.18±0.19)logv_{max}∝(-0.48±0.09)logM_DM, providing a novel formulation between the geometry (i.e., the logarithmic spiral-arm pitch angle) and kinematics of spiral galaxy disks. While the v_max-ph relation may facilitate distance estimations to face-on spiral galaxies through the Tully-Fisher relation and using ph as a proxy for v_max, the M_DM-ph relation provides a path for determining dark matter halo masses from imaging data alone. Furthermore, based on a spiral galaxy sample size that is double the size used previously, the self-consistent relations presented here provide dramatically revised constraints for theory and simulations.