A Consistent Set of Empirical Scaling Relations for Spiral Galaxies: The (v _max, M _oM)-(σ ₀, M _BH, φ) Relations

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, σ ₀, and (iii) spiral-arm pitch angle, φ. We find that , significantly steeper than previously reported, and with a total root mean square scatter (0.58 dex) similar to that about the M _BH-σ ₀ 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 relation observed in spiral galaxies. We also find that , consistent with past studies connecting stellar bulges (with σ ₀ ≈ 100 km s^-1), dark matter halos, and a nonconstant v _max/σ ₀ ratio. Finally, we report that , 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-φ relation may facilitate distance estimations to face-on spiral galaxies through the Tully-Fisher relation and using φ as a proxy for v _max, the M _DM-φ 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.