Efficient black hole seed formation in low metallicity and dense stellar clusters with implications for JWST sources

Recent observations with the James Webb Space Telescope (JWST) reveal young massive clusters (YMCs) as key building blocks of early galaxies. They are not only important constituents of galaxies, but also potential birthplaces of very massive stars (VMSs) and black hole (BH) seeds. We explore stellar dynamics in extremely dense clusters with initial half-mass densities of $ρ_h \gtrsim 10^8M_\odot{\rm pc}^{-3}$ at very low metallicity, comparable to some of the densest clusters seen by JWST. Using direct N-body and Monte Carlo simulations with stellar evolution, we show that VMS formation through collisions is unavoidable, with final masses reaching $5\times10^3$ to $4\times10^4M_\odot$. These results support the existence of a critical mass scale above which collisions become highly efficient, enabling the formation of VMSs and intermediate-mass BHs (IMBHs). Our models, using nbody6++gpu and MOCCA with updated SSE/BSE routines, show that dense clusters rapidly form VMSs via stellar bombardment. The VMSs then collapse into BH seeds of a few $10^3$ to $10^4M_\odot$ in less than 4 Myr. We identify a critical mass-density threshold beyond which clusters undergo runaway collisions that yield massive BH seeds. For typical YMCs detected by JWST, efficiencies up to 10% are expected, implying BH masses up to $10^5M_\odot$ if formed via collisions. We predict a scaling relation for BH mass, $\log(M_{\rm BH}/M_\odot)=-0.76+0.76\log(M/M_\odot)$. Frequent VMS formation may also explain the high nitrogen abundance observed in galaxies at high redshift.

💡 Research Summary

This paper investigates whether the ultra‑dense, low‑metallicity young massive clusters (YMCs) recently identified by JWST can serve as efficient birthplaces of massive black‑hole (BH) seeds. The authors model isolated star clusters with initial half‑mass densities ρ_h ≳ 10⁸ M⊙ pc⁻³, metallicity Z = 10⁻⁴, and a range of particle numbers (5 × 10⁴ – 7.5 × 10⁵) and half‑mass radii (0.005 – 0.05 pc). All clusters follow a King (W₀ = 6) profile and a Kroupa IMF (0.08–150 M⊙).

Two state‑of‑the‑art simulation tools are employed: the direct N‑body code NBODY6++GPU (GPU‑accelerated Hermite integrator with KS and chain regularisation) and the Monte‑Carlo code MOCCA (Hénon‑type statistical relaxation combined with FEWBODY for strong encounters). Both incorporate the latest SSE/BSE stellar‑evolution updates (Hurley et al., Banerjee et al., Kamlah et al.) and custom routines to treat very massive star (VMS) formation, collision‑driven mass growth, and post‑collision mass loss.

The key dynamical finding is that when ρ_h exceeds ≈10⁸ M⊙ pc⁻³, the core‑collapse time becomes shorter than the main‑sequence lifetime of massive stars (≈3 Myr). Consequently, the core experiences a runaway collision cascade: repeated stellar impacts rapidly build up a single VMS whose mass can reach 5 × 10³–4 × 10⁴ M⊙. The growth is most efficient when the average time between collisions drops below ~10⁴ yr.

Because the metallicity is very low, stellar winds are weak, allowing the VMS to retain most of its mass. Within ≤4 Myr the VMS undergoes direct gravitational collapse, leaving a BH seed of 10³–10⁴ M⊙. The fraction of the initial cluster mass that ends up in the BH (the “efficiency”) depends on the initial mass‑density combination, ranging from ~1 % for marginally dense models up to ~10 % for the most massive (M ≈ 10⁶ M⊙) and densest (ρ_h ≈ 10⁸ M⊙ pc⁻³) clusters.

From the suite of simulations the authors derive an empirical scaling relation between the final BH mass and the initial cluster mass:
\