Massive star clusters detected by JWST as natural birthplaces of intermediate-mass black holes

The James Webb Space Telescope (JWST) has detected, through gravitational lensing, several young massive star clusters (YMCs), which are considered as relevant building blocks of high-redshift galaxies. In this work, we show how a significant fraction of these YMCs could act as relevant birthplaces for intermediate-mass black holes (IMBHs). We first consider the formation of massive clusters and show that the population of YMCs is consistent with a steep mass-radius relation, which includes a relevant spread of roughly an order of magnitude. We pursue a comparison of this population with young star clusters in the local Universe and Milky Way globular clusters, including an analysis of the characteristic timescales. The YMCs show a wide spread over these properties, but include systems with both short relaxation times as well as relatively short collision timescales, implying they could go through efficient core collapse, which would lead to runaway collisions. We provide quantitative estimates of the sizes of the clusters that could efficiently form IMBHs through a runaway collision-based channel, suggesting that these roughly correspond to the systems beyond the 1 sigma scatter in the mass-radius relation. This implies a fraction of similar to 16% of YMCs as candidates to form IMBHs. We show that above a mass limit of similar to 6 & times; 10(6) M-circle dot, compact star clusters are likely to retain gas even in the presence of strong supernova feedback, altering the dynamics in the central core and providing the possibility to rapidly grow the central object both via gas dynamical friction and Bondi accretion. Finally, we consider the possibility of a gas-dominated regime, in which strong gravitational torques may inhibit star cluster formation and instead directly form a high-mass black holes, as is suggested to have occurred in the infinity galaxy.