Constraining the high-redshift formation of black hole seeds in nuclear star clusters with gas inflows

Abstract

In this paper we explore a possible route of black hole seed formation that\nappeal to a model by Davies, Miller & Bellovary who considered the case of the\ndynamical collapse of a dense cluster of stellar black holes subjected to an\ninflow of gas. Here, we explore this case in a broad cosmological context. The\nworking hypotheses are that (i) nuclear star clusters form at high redshifts in\npre-galactic discs hosted in dark matter halos, providing a suitable\nenvironment for the formation of stellar black holes in their cores, (ii) major\ncentral inflows of gas occur onto these clusters due to instabilities seeded in\nthe growing discs and/or to mergers with other gas-rich halos, and that (iii)\nfollowing the inflow, stellar black holes in the core avoid ejection due to the\nsteepening to the potential well, leading to core collapse and the formation of\na massive seed of $<~ 1000\\, \\rm M_\\odot$. We simulate a cosmological box\ntracing the build up of the dark matter halos and there embedded baryons, and\nexplore cluster evolution with a semi-analytical model. We show that this route\nis feasible, peaks at redshifts $z <~ 10$ and occurs in concomitance with the\nformation of seeds from other channels. The channel is competitive relative to\nothers, and is independent of the metal content of the parent cluster. This\nmechanism of gas driven core collapse requires inflows with masses at least ten\ntimes larger than the mass of the parent star cluster, occurring on timescales\nshorter than the evaporation/ejection time of the stellar black holes from the\ncore. In this respect, the results provide upper limit to the frequency of this\nprocess.\n