A Consistent Set of Empirical Scaling Relations for Spiral Galaxies: The (v_max, M_oM)–(σ₀, M_BH, ϕ) Relations

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 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.4 If we calculate the Tully-Fisher relation from our dataset, we find that M * ,tot ∝ v 3.94±1.01 rot , which is consistent with Equation (1) at the level of 0.05 σ. 5 The dynamics of newly assembled massive objects (DY-NAMO) project (Green et al. 2010(Green et al. , 2014Bassett et al. 2014) demonstrated that their more local (z ∼ 0.1) sample of galaxies, selected to have high star-formation rates, are analogs of turbulent z 2 disk galaxies, with similar vrot/σ 0 ratios. 46 The quantity vmax should not be confused with the circular rotation velocity of the disk of our Galaxy at the location of the Sun and equal to (238 ± 15) km s −1 (Bland-Hawthorn & Gerhard 2016) or (229.0 ± 0.2) km s −1 (Eilers et al. 2019).

WISDOM project – VI. Exploring the relation between supermassive black hole mass and galaxy rotation with molecular gas

“…The most significant systematic deviations from this fit are when we restrict the sample to LTGs. When we consider only the spatially resolved LTGs, the slope steepens to 10.0 ± 3.5, in agreement with the results of Davis et al (2019b) from H I and invoking the dischalo conspiracy. The sample of unresolved LTGs do not adequately constrain the relation's slope, and exhibit a much higher total (and intrinsic) scatter.…”

“…The same argument cannot be made for ETGs, as we discuss in Section 1.4. In a sample of 48 spiral galaxies with dynamically measured SMBH masses and H I line widths, Davis et al (2019b) obtained a relation of M BH ∝ V 10.62±1.37 H I , consistent with the prediction. Notably, both the predicted and the observed relation are substantially steeper than found in earlier works (e.g.…”

“…Nevertheless, Davis, Graham & Combes (2019b) combined the CO TFR of Tiley et al (2019) with the M BH -M * ,tot correlation of Davis et al (2018b) to yield a prediction of M BH ∝ V 12.2±2.1 CO .For spiral galaxies, the disc-halo conspiracy enables the replacement of the CO line widths in the Tiley et al (2019) TFR with those of H I. The same argument cannot be made for ETGs, as we discuss in Section 1.4.…”

“…The most recent works investigating V H I −σ * have also found morphologically varying results. In ETGs, Serra et al (2016) found a linear relation with total scatter of 12 per cent, whereas in latetype spirals Davis et al (2019b) excluded a linear relation, obtaining σ * ∝ V 1.55±0.25 H I . This accords with the early work of Ho (2007a), that indicated that V/σ * varies systematically with Hubble-type, albeit with less compelling data.…”

The hidden heart of the luminous infrared galaxy IC 860

“…However, the σ value may still suffer from extinction and should be viewed with some caution. As an alternative, a relation between the larger-scale disk rotation velocity and M SMBH can be used (Davis et al 2019). Using a value from Hyperleda on the rotation velocity of IC 860 of ν rot = 226 km s −1 implies a M SMBH of 4 × 10 7 M .…”