The $M_{\mathrm{BH}}$$-$$R_{\mathrm{b}}$ relation and the high-mass end of the $M_{\mathrm{BH}}$$-$$\sigma$ relation

Abstract

Using a sample of 151 galaxies with dynamically measured black hole (BH) masses ($M_{\mathrm{BH}}$), we investigate the scaling relations between $M_{\mathrm{BH}}$ and the stellar velocity dispersion, $\sigma$, and, for a subsample of 30 core-Sérsic galaxies, between $M_{\mathrm{BH}}$ and the size of the partially depleted core, $R_{\mathrm{b}}$. Core-Sérsic galaxies, identified using high-resolution $HubbleSpaceTelescope$ imaging and spanning both the normal-core $(R_{\mathrm{b}}<0.5$ kpc) and large-core ($R_{\mathrm{b}}>0.5$ kpc) regimes, define an updated $M_{\mathrm{BH}}$$-$$R_{\mathrm{b}}$ relation of the form $M_{\mathrm{BH}}\propto R_{\mathrm{b}}^{1.16\pm 0.10}$, with an rms scatter of ${\Delta }_{\mathrm{rms}}\simeq 0.28$ dex in $\log M_{\mathrm{BH}}$. We find that Sérsic and normal-core galaxies together follow a common log-linear $M_{\mathrm{BH}}$-$\sigma$ relation with a slope of $4.95\pm 0.29$ and a scatter ${\Delta }_{\mathrm{rms}}\simeq 0.46$ dex. Deviations from this relation arise at the highest BH masses, where large-core galaxies, including six with direct $M_{\mathrm{BH}}$ measurements, drive a significant upturn. We find that these galaxies typically host ultramassive black holes whose masses scale more strongly with $R_{\mathrm{b}}$ than $\sigma$, and lie $\sim (1-4$) $\times$ the intrinsic scatter (0.39 dex) above the relation defined by Sérsic and normal-core galaxies. The $M_{\mathrm{BH}}$$-$$R_{\mathrm{b}}$ relation shows $\sim 30$-$47\%$ less scatter in $\log M_{\mathrm{BH}}$ than the corresponding $M_{\mathrm{BH}}$$-$$\sigma$ relation for the same sample. We interpret the high-mass upturn in the $M_{\mathrm{BH}}$$-$$\sigma$ diagram as a consequence of successive major, dry mergers, a scenario that naturally explains the observed flattening of the $\sigma -L_V$ relation at $M_V<-23.5$ mag.

15 pages, 3 figures, 5 tables, accepted for publication in ApJ