Seeds to success: growing heavy black holes in dense star clusters

TL;DR

This work investigates how intermediate-mass black holes (IMBHs) form and grow in dense star clusters by using the B-pop semi-analytic population synthesis code. It examines two primary IMBH formation channels—runaway stellar collisions creating very massive stars (VMSs) that seed IMBHs, and hierarchical mergers of binary black holes (BBHs)—under three cluster-family contexts (young clusters, globular clusters, and nuclear star clusters) and varying formation histories. The study finds that stellar collisions reliably dominate IMBH production across cluster types, with hierarchical growth mainly contributing in NSCs; the resulting IMBH populations show distinct retention, ejection, and merger signatures, and a simple Bayes framework is developed to compare observed IMBH candidates to GC or NSC hosts. Model comparisons reveal that a mild-density, low-metallicity seeding scenario (Model B) better matches local IMBH candidates, including potential NSC-origin cases like G1 and $\omega$ Cen, and predict wandering IMBHs in galaxy halos. Overall, the results highlight the critical role of environment and formation history in shaping IMBH demographics and provide observationally testable predictions for future GW, microlensing, and astrometric surveys.

Abstract

The observational dearth of black holes (BHs) with masses between $\sim$100 and 100,000 $M_\odot$ raises questions about the nature of intermediate-mass black holes (IMBHs). Proposed formation channels for IMBHs include runaway stellar collisions and repeated binary BH (BBH) mergers driven by dynamical interactions in stellar clusters, but the formation efficiency of these processes and the associated IMBH occupation fraction are largely unconstrained. In this work, we study IMBH formation via both mechanisms in young, globular, and nuclear star clusters. We carry out a comprehensive investigation of IMBH formation efficiency by exploring the impact of different seeding models and star cluster formation histories. We employ a new version of the B-POP population synthesis code, able to model several seeding mechanisms as well as hierarchical BBH mergers. We quantify the efficiency of IMBH production across different cluster families, and estimate the fraction of BBH mergers involving an IMBH primary. Comparison with low-redshift IMBH candidates suggests that, depending on the seeding mechanism, stellar collisions can play a pivotal role in explaining potential IMBHs in local globular clusters. Our simulations highlight stellar collisions as the primary IMBH formation channel across a wide range of cluster types. They further suggest that wandering IMBHs may populate Milky Way-like galaxies and that correlations between cluster and IMBH masses can help distinguish the origins of Galactic globular clusters.

Figures (5)

• Figure 1: Initial distribution of clusters' formation redshift. Different colors refer to different assumptions on the initial formation histories of GCs (solid lines) and NSCs (dashed lines). The initial redshift distribution of YCs is fixed in all models (grey solid line). Distributions are conveniently scaled such that the area subtended by the curve is 1.
• Figure 2: Left panel: Initial cluster mass and half-mass radius for YCs (bottom left area), GCs (central area), and NSCs (upper right area). The clusters distribution are cut at the 99$\%$ contour. Clusters with $t_{\rm cc} < 5\,\rm Myr$ lie below the dot-dashed black line, those with central density $\rho_{\rm cl, 0} > 10^5\,{\rm M}_\odot \rm \, pc^{-3}$ above the shaded dotted gray line. We also identify regions of the parameter space in which (i) a BBH binary is ejected before merging due to strong Newtonian recoils ("Newtonian recoils" region, in pink), (ii) the merger remnant is tipically kicked out of the cluster due to its relativistic kick ("GW kicks" region, in purple), (iii) the BBH merger time exceeds a Hubble time ("No merger" region, in yellow). Right panel: Schematic overview of a BH dynamical growth in a star cluster. The colored boxes refer to the regions highlighted in the left plot.
• Figure 3: Clusters hosting an IMBH at $z = 0$ in Model A (left panel) and Model B (right panel) compared to different classes of IMBH host candidates observations. Note that the masses reported for low-mass AGN refer to the host galaxy mass (up to $\sim$ 100 times larger than the mass of the galactic nuclei). The gray dashed line shows the theoretical prediction for the initial mass of an IMBH seeded via stellar collisions (Eq. \ref{['eq::mvms_simplified']} in the left panel and Eq. \ref{['eq::mvms_bifrost']} in the right panel).
• Figure 4: Comparison of simulated IMBH candidates in Model B with observational data. (a) Corner plot showing the GCs (purple) and NSCs (orange) clusters in our simulations hosting an IMBH at $z=0$, compared to observations of potential IMBHs in Milky Way globular clusters and G1 (b) One-dimensional IMBH mass distribution with comparison to estimated masses for G1 and 47 Tuc.
• Figure 5: GCs hosting an IMBH at $z = 0$, compared to observed host candidates in local GCs lutz2013_gcs and a potential TDE tde_lin_2018, for two sets of initial mass--half-mass radius conditions. The orange-edged star marks the $\omega$ Cen cluster haberle_omegacen_2024. As in Figure \ref{['fig::allIMBHs']}, the dashed lines correspond to mass ratios $M_{\rm IMBH}/ M_{\rm cl} = 10^{-1}, 10^{-2}, 10^{-3}$. The top panel shows results from a B-pop simulation of $10^8$ GCs, while the bottom panel shows results from a simulation in which the same GCs have initial masses larger by 0.5 dex and half-mass radii smaller by 1 dex.