Eight New Ultramassive Black Hole Masses confirm Best Correlation with Galaxy Core Sizes

We analyse black-hole scaling relations at the high-mass end, focusing in particular on the regime of ultra-massive black holes, $\mathrm{M}_\mathrm{BH} > 10^{10}\,\mathrm{M}_\odot$ (UMBHs). In a sample of 16 Brightest Cluster Galaxies (BCGs) without previous black-hole mass measurements we discover 8 UMBHs based on direct dynamical detections with triaxial Schwarzschild models. This first sample of triaxial black-hole mass determinations increases the number of known UMBHs by a factor of two and dramatically increases the constraints for BH mass scaling relations at the high-mass end. We find that BCGs are outliers in the canonical BH - $\sigma$ relation, while the size of their depleted cores - the central light-deficient region - is a much better unbiased predictor of the black hole mass and should be used as a proxy at the high-mass end. BCGs smoothly join the trend already established for massive core galaxies in previous studies. This also holds for tight correlations between core size and sphere-of-influence radius and core size and core density. All these relations strongly support the black-hole binary model for the formation of the centers of the most massive galaxies.