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

TL;DR

This study addresses how black hole scaling relations behave at the ultra-massive end by analyzing 16–17 Brightest Cluster Galaxies with direct dynamical measurements via triaxial Schwarzschild orbit-based models. It finds that the canonical $M_{BH}-\sigma$ relation breaks down for BCGs, while core-based relations, especially $M_{BH}-r_c$ and $r_{SOI}-r_c$, remain tight and extend into the ultra-massive regime; the results also show UMBHs can exist in core-less galaxies, challenging core-centric demographics. The work strengthens the SMBH binary core-formation model by linking core size, sphere of influence, and core density, and demonstrates that core properties enable photometric prediction of $M_{BH}$, offering a practical path to identify UMBHs in large surveys. It also highlights implications for gravitational-wave backgrounds and plans to extend the analysis to higher redshift ($z\sim1$) with Euclid, broadening our understanding of BH–galaxy coevolution at the highest masses.

Abstract

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 - $σ$ 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.

Figures (6)

• Figure 1: The $\mathrm{M}_{\mathrm{BH}}$-$\sigma$ relation with data from the literature (blue points) with our new measurements (red points). The solid line is the best-fit relation from Rob16 omitting pseudobulges, while the dotted lines enclose the intrinsic scatter $\varepsilon = 0.380\,\pm 0.038$.
• Figure 2: The $\mathrm{M}_{\mathrm{BH}}$-core size relation with data from the literature (blue points) with our new measurements (red circles). The solid and dotted lines are the best-fit line and the intrinsic scatter, respectively.
• Figure 3: Same as Fig. \ref{['Fig.BH_sigma']} for the $\mathrm{M}_\mathrm{BH} - \mathrm{M}_\ast$ and $\mathrm{M}_\ast - \mathrm{r}_\mathrm{b}$ relations. In Figs. \ref{['Fig.mbh_mbul_G']} and \ref{['Fig.mgal_rb_G']} the stellar mass has been estimated using the total V-band magnitude, whereas in Figs. \ref{['Fig.mbh_mbul_U']} and \ref{['Fig.mgal_rb_U']} it comes from the integrated 1D best-fit Sersic profiles. In both cases the data are taken from Table 4 of Matthias20; the best-fit relations and intrinsic scatters (blue lines) come from Rob16 (top panels) and Rob24 (bottom panels), respectively.
• Figure 4: Same as Fig. \ref{['Fig.BH_core']} but the correlation between black hole sphere of influence $\mathrm{r}_\mathrm{SOI}$ and core size $\mathrm{r}_\mathrm{c}$ is shown.
• Figure 5: Same as Figs. \ref{['Fig.BH_core']} and \ref{['Fig.rcore_rSOI']} but the correlation between core density $\rho_\mathrm{core}$ and core size $\mathrm{r}_\mathrm{c}$ is shown.