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Depleted Galaxy Cores and Dynamical Black Hole Masses

Shallow cores in bright, massive galaxies are commonly thought to be the result of scouring of stars by mergers of binary supermassive black holes. Past investigations have suggested correlations between the central black hole mass and the stellar light or mass deficit in the core, using proxy measurements of $M_{\rm BH}$ or stellar mass-to-light ratios ($Υ$). Drawing on a wealth of dynamical models which provide both $M_{\rm BH}$ and $Υ$, we identify cores in 23 galaxies, of which 20 have direct, reliable measurements of $M_{\rm BH}$ and dynamical stellar mass-to-light ratios ($Υ_{\star,{\rm dyn}}$). These cores are identified and measured using Core-Sérsic model fits to surface brightness profiles which extend out to large radii (typically more than the effective radius of the galaxy); for approximately one fourth of the galaxies, the best fit includes an outer (\sersic) envelope component. We find that the core radius is most strongly correlated with the black hole mass and that it correlates better with total galaxy luminosity than it does with velocity dispersion. The strong core-size-- $M_{\rm BH}$ correlation enables estimation of black hole masses (in core galaxies) with an accuracy comparable to the $M_{\rm BH}$--$σ$ relation (rms scatter of 0.30 dex in $\log M_{\rm BH}$), without the need for spectroscopy. The light and mass deficits correlate more strongly with galaxy velocity dispersion than they do with black hole mass. Stellar mass deficits span a range of 0.2--39 \mbh, with almost all (87%) being $< 10 \, M_{\rm BH}$; the median value is 2.2 $M_{\rm BH}$.