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, sigma(0), and (iii) spiral-arm pitch angle, phi. We find that M-BH proportional to v(max)(10.62 +/- 1.37) proportional to 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-sigma(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-*,M-tot) and the steep M-BH proportional to M-*,tot(3.05 +/- 0.53) relation observed in spiral galaxies. We also find that sigma(0) proportional to v(max)(1.55 +/- 0.25) proportional to M-DM(0.63 +/- 0.11), consistent with past studies connecting stellar bulges (with sigma(0) greater than or similar to 100 km s(-1)), dark matter halos, and a nonconstant v(max)/sigma(0) ratio. Finally, we report that tan vertical bar phi vertical bar proportional to (-1.18 +/- 0.19) log v(max) proportional to (-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)-phi relation may facilitate distance estimations to face-on spiral galaxies through the Tully-Fisher relation and using phi as a proxy for v(max), the M-DM-phi 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.