Formation of intermediate-mass black holes in young massive clusters detected with JWST: Analytic mass estimates

The Space Telescope (JWST) has revealed a population of dense stellar systems at high redshifts, including the "Cosmic Gems" arc (z ∼ 10.2) and the "Firefly Sparkle" (z ∼ 8.3). With masses in the range 10^5 M_⊙-10^7 M_⊙ and half-mass radii in the range sim0.4-15 pc, these systems are ideally suited to form intermediate-mass black holes (IMBHs) via collision-based models. Since direct N-body simulations are unfeasible for such a large population, and given the high masses in many of the clusters, we estimated 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 applied this model to a sample of massive high-redshift clusters observed with JWST. Our estimates yield typical IMBH masses in the range sim10^2 M_⊙ to sim4 _⊙. The low metallicity (Z łesssim 0.02 , James Webb 10^3 M_⊙, implying typical formation efficiencies on the few percent level. The extreme compactness of the Cosmic Gems clusters (R_h ∼ 1 pc) facilitates the formation of black hole seeds with high masses of 1600-2700 , ̊m M ̊m Z _⊙) is a critical factor for retaining the seed mass despite 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 that are capable of growing into the supermassive black holes observed in the early Universe.