Connecting Cores and Black Hole Dynamics across Scales: From Globular Clusters to Massive Ellipticals

The centers of massive elliptical galaxies exhibit a wide range in density profiles, from central cusps to resolved cores with order kiloparsec sizes. The cored ellipticals have been linked to the presence of supermassive black hole binaries that excavate their hosts' central stellar populations through three-body encounters. This connection between cores and black holes similarly operates in globular clusters, which also exhibit a bimodality in cored and core-collapsed architectures, rich and depleted, respectively, in stellar black holes. We report new estimates of the total black hole mass in 25 Galactic globular clusters based on a suite of roughly 150 Monte Carlo N -body simulations that fit observed surface brightness and velocity dispersion profiles. We show that both globular clusters and massive elliptical galaxies individually exhibit strong correlations between total black hole mass ( M • ) and core radius ( r c ) and that these individual relations share a common power-law exponent to within 1 σ statistical precision: M• ∼ r_c^(1.3). The individual relations appear to be offset, suggesting swarms of stellar black holes scour globular cluster cores more efficiently than lone supermassive black holes scour the cores of massive ellipticals. Yet the shared basis of core scouring via black hole binaries hints at a unified M• – r_c connection across over 10 orders of magnitude in M•. Our findings imply core radius measurements may offer a powerful observational constraint on black hole merger rates, from kilohertz sources detectable by LIGO/Virgo/KAGRA formed in globular clusters to millihertz and nanohertz sources formed in massive elliptical galaxies.

We thank the anonymous referee for the constructive comments on the interpretation of our results, which significantly improved the manuscript. N.Z.R. acknowledges support from the National Science Foundation Graduate Research Fellowship under grant No. DGE-1745301, from the United States–Israel Binational Science Foundation through grant BSF-2022175 and through the NASA Hubble Fellowship grant HST-HF2-51589.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. C.S.Y. acknowledges support from the Natural Sciences and Engineering Research Council of Canada (NSERC) DIS-2022-568580.

This work was conceived by K.K. and fleshed out in discussions with N.C.W. and P.F.H. K.K. led the write-up with key contributions from N.C.W. and feedback from all other authors. Data analysis and presentation were split evenly between K.K. and N.C.W. and based heavily on data from N.Z.R. (N. Z. Rui et al. 2021a), some previously unpublished. C.S.Y. also contributed the data on black holes in her models for NGC 104 and NGC 1851.