Constraining the high redshift formation of black hole seeds in nuclear
  star clusters with gas inflows
  In this paper we explore a possible route of black hole seed formation that
appeal to a model by Davies, Miller & Bellovary who considered the case of the
dynamical collapse of a dense cluster of stellar black holes subjected to an
inflow of gas. Here, we explore this case in a broad cosmological context. The
working hypotheses are that (i) nuclear star clusters form at high redshifts in
pre-galactic discs hosted in dark matter halos, providing a suitable
environment for the formation of stellar black holes in their cores, (ii) major
central inflows of gas occur onto these clusters due to instabilities seeded in
the growing discs and/or to mergers with other gas-rich halos, and that (iii)
following the inflow, stellar black holes in the core avoid ejection due to the
steepening to the potential well, leading to core collapse and the formation of
a massive seed of $<~ 1000\, \rm M_\odot$. We simulate a cosmological box
tracing the build up of the dark matter halos and there embedded baryons, and
explore cluster evolution with a semi-analytical model. We show that this route
is feasible, peaks at redshifts $z <~ 10$ and occurs in concomitance with the
formation of seeds from other channels. The channel is competitive relative to
others, and is independent of the metal content of the parent cluster. This
mechanism of gas driven core collapse requires inflows with masses at least ten
times larger than the mass of the parent star cluster, occurring on timescales
shorter than the evaporation/ejection time of the stellar black holes from the
core. In this respect, the results provide upper limit to the frequency of this
process.
