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 $\rho_h \gtrsim 10^8M_\odot{\rm pc}^{-3}$ 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.