Draft version May 28, 2019 Typeset using L A T E X twocolumn style in AASTeX62 A Consistent Set of Empirical Scaling Relations for Spiral Galaxies: The (v max ,M DM )–(σ 0 ,M BH ,φ) Relations Benjamin L. Davis, 1 Alister W. Graham, 1 and Franc ¸oise Combes 2, 3 1 Centre for Astrophysics and Supercomputing, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia 2 Observatoire de Paris, LERMA, CNRS, PSL Universit´ e, Sorbonne Universit´ e, F-75014 Paris, France 3 Coll` ege de France, 11 Place Marcelin Berthelot, F-75005 Paris, France (Received 2019 Janurary 19; Revised 2019 April 4; Accepted 2019 April 16; Published 2019 May 24, ApJ, 877, 64) ABSTRACT 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 M BH ∝ v 10.62±1.37 max ∝ M 4.35±0.66 DM , 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 M BH ∝ M 3.05±0.53 ∗,tot relation observed in spiral galaxies. We also find that σ 0 ∝ v 1.55±0.25 max ∝ M 0.63±0.11 DM , 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 tan |φ|∝ (−1.18 ± 0.19) log v max ∝ (−0.48 ± 0.09) log M 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 –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. Keywords: black hole physics – dark matter – galaxies: evolution – galaxies: fundamental parameters – galaxies: spiral – galaxies: structure 1. INTRODUCTION Building on the possibility of unseen mass in the so- lar neighborhood (Jeans 1922; Kapteyn 1922; Lindblad 1926; Oort 1932), dark matter has been considered by many astronomers to be prevalent in galaxy clusters since the 1930s (Zwicky 1933; Smith 1936; Zwicky 1937; Schwarzschild 1954; Rood 1965). In addition, the study of galaxy rotation curves provided strong evidence for the existence of dark matter (Babcock 1939; Oort 1940; Freeman 1970; Rubin & Ford 1970; Rogstad & Shostak 1972; Roberts & Rots 1973; Rubin et al. 1977, 1978; Krumm & Salpeter 1979; Rubin et al. 1980; Bosma 1981; Persic & Salucci 1988; Broeils 1992). The no- Corresponding author: Benjamin L. Davis benjamindavis@swin.edu.au tion of nonbaryonic dark matter subsequently grew as a mechanism to explain this anomalous gravitational phe- nomenon (Gershtein & Zel’dovich 1966; Marx & Sza- lay 1972; Cowsik & McClelland 1972; Szalay & Marx 1976). Intriguingly, dark matter is believed to account for 84% ± 1% of the total mass in the universe (Planck Collaboration et al. 2018), but it remains elusive de- spite considerable efforts to achieve direct instrumen- tal detection of its theorized particles (e.g., Tan et al. 2016; Akerib et al. 2017; Aprile et al. 2018). 1 The con- cept of supermassive black holes (SMBHs) lurking in the center of galaxies has also had an interesting history of study (see Kormendy & Richstone 1995; Longair 1996, 1 See Seigar (2015), Arcadi et al. (2018), Hooper (2018), and Salucci (2019) for reviews on searches for dark matter. arXiv:1901.06509v2 [astro-ph.GA] 25 May 2019