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

Context . Recent observations with the James Webb Space Telescope (JWST) have revealed the presence of young massive clusters (YMCs) as building blocks of the first galaxies during the first billion years of the Universe. They are not only important constituents of the galaxies, but also potential birthplaces of very massive stars (VMSs) and black hole (BH) seeds. Aims . In this paper, we investigate whether runaway stellar collisions in extremely dense clusters inevitably lead to the formation of VMSs and BH seeds. We focus on clusters with initial half-mass densities of ρ h ≳ 10 8 M ⊙ pc −3 at very low metallicity ( Z = 10 −4 ), using idealized initial conditions that assume a fully formed, gas-free, monolithic stellar system. Our goal is to follow their early internal evolution and quantify the efficiency of collisional growth. Methods . We use NBODY 6++ GPU and MOCCA, including the latest updates of the single stellar evolution (SSE) and binary stellar evolution (BSE), along with specific routines to handle the formation, growth through collisions, and dynamical evolution of VMSs. Results . Our direct N -body and Monte Carlo simulations show that VMSs form rapidly and unavoidably through repeated collisions, reaching final masses of ~5 × 10 3 to 4 × 10 4 M ⊙ , before collapsing into BH seeds of similar mass in less than 4 Myr. These results confirm the existence of a critical mass scale at which collisional growth becomes highly efficient, enabling the formation of VMSs and potentially intermediate-mass BHs. Conclusions . We identify a critical mass–density threshold beyond which clusters undergo runaway collisions, leading to efficient BH-seed formation. For YMCs detected with JWST, we expect efficiencies up to ~10%, corresponding to BH masses as large as 10 5 M ⊙ . We predict a BH mass–cluster mass scaling relation of log( M BH / M ⊙ ) = −0.76 + 0.76 log(M / M ⊙ ). Frequent VMS formation in this regime may also provide a natural explanation for the strong nitrogen enrichment observed in some high-redshift galaxies.