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

TL;DR

Kremer and collaborators explore a universal link between black holes and galactic cores by connecting globular clusters and massive ellipticals through a shared $M_{\bullet}$–$r_c$ relation. Using ~150 Monte Carlo $N$-body globular cluster simulations with the CMC code and COSMIC stellar evolution, they fit observed surface brightness and velocity-dispersion profiles to estimate total BH masses in 25 Milky Way clusters, finding $\log_{10}(M_{\bullet}/M_\odot) = (2.92\pm0.12) + (1.43\pm0.23)\log_{10}(r_c/\text{pc})$ with $0.60$ dex scatter. They show that both GC BH populations and massive ellipticals exhibit a similar slope in the $M_{\bullet}$–$r_c$ plane, though offset due to differing core-scouring efficiencies, and provide a global fit $\log_{10}(M_{\bullet}/M_\odot) = (3.22\pm0.14) + (2.62\pm0.09)\log_{10}(r_c/\text{pc})$ with $0.80$ dex scatter. The results imply core radii can constrain BH-merger rates across gravitational-wave bands, from kilohertz sources in clusters to millihertz/nanohertz sources in galaxies, highlighting a potentially unified framework for BH growth and core evolution across more than 10 orders of magnitude in BH mass.

Abstract

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, respectively rich and depleted 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 ($M_\bullet$) and core radius ($r_c$), and that these individual relations share a common power-law exponent to within $1σ$ statistical precision: $M_\bullet \sim r_c^{1.3}$. 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 $M_{\bullet}-r_c$ connection across over 10 orders of magnitude in $M_\bullet$. 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.

Figures (10)

• Figure 1: Left panel: Surface brightness profiles (V-band) for Galactic globular clusters from NoyolaGebhardt2006, illustrating the diversity of cluster core sizes. We highlight five particular clusters that are discussed in further detail in the text. Right panel: Surface brightness profiles (also V-band) for a sample of core and coreless elliptical galaxies out to a distance of $100\,$Mpc from Lauer2005. We highlight the brightest galaxies in the Leo Cluster (NGC 3842), Coma Cluster (NGC 4889), and Virgo Cluster (NGC 4472 as well as NGC 4486). We also highlight NGC 1600 from Thomas2016, which has one of the faintest stellar cores of any galaxy with a black hole mass measurement.
• Figure 2: Time evolution of the core radius---using the density-weighted definition of CasertanoHut1985---for all globular cluster simulations computed by Kremer2020. Curve color denotes the total mass in black holes at the end of each simulation ($t=13\,$Gyr). As shown, clusters with larger core radius generally host more-massive black hole populations. Blue ticks on the right hand side denote present-day core radii of Milky Way globular clusters from BaumgardtHilker2018.
• Figure 3: Total mass of the stellar black hole populations predicted for various Milky Way globular clusters versus core radius. Blue scatter points show the black hole predictions using the methods of this paper (see Table \ref{['table:nbh_mbh']}), with stars highlighting a few specific clusters discussed further in the text. For the core-collapsed clusters NGC 6293 and NGC 6681, we plot the mass of the final black hole ejected from the best-fit simulations ($12\,M_{\odot}$), with the arrows indicating these clusters may host zero black holes at present. All core radius measurements are taken from BaumgardtHilker2018. The dashed black curve shows our best-fit linear correlation $\log_{10} (M_{\bullet}/M_{\odot}) = (2.92 \pm 0.12) + (1.43 \pm 0.23 )\log_{10}(r_c/\rm{pc})$.
• Figure 4: Black hole mass versus core radius across stellar populations. In red we show massive elliptical galaxies from Rusli2013 with resolved cores and dynamical black hole mass measurements. The red curve shows the best-fit linear correlation to these data from Thomas2016. In blue we show predicted masses of stellar-mass black hole populations for a number of Galactic globular clusters, with the best-fit linear correlation from Figure \ref{['fig:Mbh_rc_GC']} shown again here in blue. The slopes of these two populations are consistent to within $1\sigma$, despite spanning orders of magnitude across both axes. The dashed black curve shows our best-fit global correlation for globular clusters and massive ellipticals combined.
• Figure 5: Effective radius versus core radius (left panel) and total stellar mass versus core radius (right panel) for Galactic globular clusters (blue) and massive elliptical galaxies (red). Filled blue circles show the full population of Galactic globular clusters; open blue circles show those in Figure \ref{['fig:Mbh_rc']} with black hole mass estimates. Filled red circles show the massive early-type galaxies cataloged by Lauer2007; open circles show those with black hole mass and core measurements by Rusli2013---also shown in Figure \ref{['fig:Mbh_rc']}. Blue and red bands show the best-fit local linear correlations for globular clusters and massive ellipticals, respectively.