Massive black hole formation in Population III star clusters

The James Webb Space Telescope (JWST) has revealed a population of active galactic nuclei (AGNs) that challenge existing black hole (BH) formation models. These newly observed BHs seem overmassive compared to the host galaxies and have an unexpectedly high abundance. Their exact origin remains elusive. The primary goal of this work is to investigate the formation of massive BH seeds in dense Population III (Pop III) star clusters. Using a cosmological simulation of Pop III cluster formation, we present models for the assembly and subsequent evolution of these clusters. The models account for background gas potential, stellar collisions and associated mass loss, gas accretion, stellar growth, their initial mass function (IMF), and subsequent star formation. We conduct $N$-body simulations of these models over a span of 2 million years. Our results show that BHs of $> 400$ M$_\odot$ are formed in all cases, reaching up to $\sim 5000$ M$_\odot$ under optimistic yet reasonable conditions and potentially exceeding 10$^4$ M$_\odot$ provided that high accretion rates of 10$^{-3}$ M$_\odot$ yr$^{-1}$ onto the stars can be sustained. We conclude that massive BHs can be formed in Pop III stellar clusters and are likely to remain within their host clusters. These BHs may experience further growth as they sink into the galaxy's potential well. This formation channel should be given further consideration in models of galaxy formation and BH demographics.