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

TL;DR

This study estimates the formation of intermediate-mass black holes in high-redshift stellar clusters observed with JWST, using an analytical model validated against N-body simulations, highlighting the potential of these clusters as seeds for supermassive black holes.

Contribution

The paper introduces an analytical framework to estimate IMBH masses in high-redshift clusters, validated against N-body simulations, and applies it to JWST observations.

Findings

IMBH masses range from 100 to 4000 solar masses in these clusters.

Extreme compactness and low metallicity facilitate the formation of massive black hole seeds.

Estimated formation efficiencies are a few percent, supporting the clusters as seeds for supermassive black holes.

Abstract

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$_\odot$ {\bf 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.