Updating the (supermassive black hole mass)–(spiral arm pitch angle) relation: a strong correlation for galaxies with pseudobulges

Abstract

We have conducted an image analysis of the (current) full sample of 44 spiral galaxies with directly measured supermassive black hole (SMBH) masses, $M_{\rm BH}$, to determine each galaxy's logarithmic spiral arm pitch angle, $\phi$. For predicting black hole masses, we have derived the relation: $\log({M_{\rm BH}/{\rm M_{\odot}}}) = (7.01\pm0.07) - (0.171\pm0.017)[|\phi|-15\deg]$. The total root mean square scatter associated with this relation is 0.43 dex in the $\log{M_{\rm BH}}$ direction, with an intrinsic scatter of $0.33\pm0.08$ dex. The $M_{\rm BH}$-$\phi$ relation is therefore at least as accurate at predicting SMBH masses in spiral galaxies as the other known relations. By definition, the existence of an $M_{\rm BH}$-$\phi$ relation demands that the SMBH mass must correlate with the galaxy discs in some manner. Moreover, with the majority of our sample (37 of 44) classified in the literature as having a pseudobulge morphology, we additionally reveal that the SMBH mass correlates with the large-scale spiral pattern and thus the discs of galaxies hosting pseudobulges. Furthermore, given that the $M_{\rm BH}$-$\phi$ relation is capable of estimating black hole masses in bulge-less spiral galaxies, it therefore has great promise for predicting which galaxies may harbour intermediate-mass black holes (IMBHs, $M_{\rm BH}<10^5$ ${\rm M_{\odot}}$). Extrapolating from the current relation, we predict that galaxies with $|\phi| \geq 26.7\deg$ should possess IMBHs.