FROST-CLUSTERS – I. Hierarchical star cluster assembly boosts intermediate-mass black hole formation

Abstract

Observations and high-resolution hydrodynamical simulations indicate that massive star clusters assemble hierarchically from subclusters with a universal power-law cluster mass function. We study the consequences of such assembly for the formation of intermediate-mass black holes (IMBHs) at low metallicities (Z = 0.01 Z⊙) with our updated N-body code bifrost based on the hierarchical fourth-order forward integrator. bifrost integrates few-body systems using secular and regularized techniques including post-Newtonian equations of motion up to order PN3.5 and gravitational-wave recoil kicks for BHs. Single stellar evolution is treated using the fast population synthesis code sevn. We evolve three cluster assembly regions with Ntot = 1.70–2.35 × 106 stars following a realistic IMF in ∼1000 subclusters for t = 50 Myr. IMBHs with masses up to m• ∼ 2200 M⊙ form rapidly mainly via the collapse of very massive stars (VMSs) assembled through repeated collisions of massive stars followed by growth through tidal disruption events and BH mergers. No IMBHs originate from the stars in the initially most massive clusters. We explain this by suppression of hard massive star binary formation at high velocity dispersions and the competition between core collapse and massive star lifetimes. Later the IMBHs form subsystems resulting in gravitational-wave BH–BH, IMBH–BH, and IMBH–IMBH mergers with a m• ∼ 1000 M⊙ gravitational-wave detection being the observable prediction. Our simulations indicate that the hierarchical formation of massive star clusters in metal poor environments naturally results in formation of potential seeds for supermassive black holes.

From Seeds to Supermassive Black Holes: Capture, Growth, Migration, and Pairing in Dense Protobulge Environments

“…It is worth mentioning that hierarchical star cluster assembly is a process with ample dynamics that may produce massive seed BHs. For example, Rantala et al (2024) found that the Figure 2. BH capture, migration, and growth as subclusters merge.…”

“… , where t Sal = κ es c/(4πG) ≈ 45 Myr is the Salpeter time and ò ref is an assumed radiative efficiency (typically 0.1; Inayoshi et al 2020). Thus, to grow to SMBH masses from "seed" masses =10 6 M e (Greene et al 2020) at high redshifts generally requires either accretion well above this naive Eddington limit (Inayoshi et al 2016;Shi et al 2023) or exotic intermediatemass black hole (IMBH) seed formation scenarios like the direct collapse of unfragmented giant molecular clouds (GMCs) to single hypermassive stars (with SMBH masses themselves; Bromm & Loeb 2003), exotic dark matter/new physics processes (Xiao et al 2021), or runaway mergers of stars (Portegies Zwart et al 2004;Shi et al 2021;Rantala et al 2024).…”