Formation of intermediate-mass black holes in young massive clusters detected with JWST: analytic mass estimates
The James Webb Space Telescope (JWST) has revealed a population of dense stellar systems at high redshift, including the "Cosmic Gems" arc ($z \sim 10.2$) and the "Firefly Sparkle" ($z \sim 8.3$). With masses in the range of $10^5$ M$_\odot$-$10^7$M$_\odot$ and half-mass radii in the range from $\sim0.4$-$15$ pc, these systems are ideally suited to form intermediate-mass black holes (IMBHs) via collision-based models. While direct N-body simulations are unfeasible for such a large population and given the high masses in many of the clusters, we estimate the IMBH masses formed via runaway stellar collisions in these specific environments utilizing a Fokker-Planck model together with an analytical framework for runaway collisions and mass loss through winds, which has been validated against direct N-body simulations of compact star clusters. We apply this model to a sample of massive high-redshift clusters observed with JWST. Our estimates yield typical IMBH masses in the range of $\sim10^2$ M$_\odot$ up to $\sim4\times 10^3$ M$_\odot$, implying typical formation efficiencies on the few percent level. The extreme compactness of the Cosmic Gems clusters ($R_h \sim 1$ pc) facilitates the formation of black hole seeds with high masses of $1600-2700 {\rm M}_\odot$. Low metallicity ($Z \lesssim 0.02 \, {\rm Z}_\odot$) is a critical factor for retaining the seed mass against stellar winds. We further demonstrate that the efficiencies obtained here are consistent with expectations based on direct N-body simulations. Our results suggest that these dense, metal-poor clusters are viable factories for heavy seeds, capable of growing into the supermassive black holes observed in the early Universe.