Optimal neighbourhood to nurture giants: a fundamental link between star forming galaxies and direct collapse black holes

TL;DR

This paper establishes a fundamental relation between galaxy star formation rate and the maximum distance for direct collapse black hole formation, simplifying the identification of potential black hole seeds in the early universe.

Contribution

It introduces a new relation linking galaxy SFR to the maximum radius for DCBH formation, reducing reliance on detailed LW flux calculations.

Findings

A fundamental relation between galaxy SFR and DCBH formation distance.

Significant scatter in LW flux at maximum distance, indicating variability in critical flux.

The relation enables easier identification of DCBH formation sites near galaxies.

Abstract

Massive $10^{4-5}\rm\ M_{\odot}$ black hole seeds resulting from the \textit{direct} collapse of pristine gas require a metal-free atomic cooling halo with extremely low H$_2$ fraction, allowing the gas to cool isothermally in the presence of atomic hydrogen. In order to achieve this chemo-thermodynamical state, the gas needs to be irradiated by both: Lyman-Werner (LW) photons in the energy range $11.2-13.6$ eV capable of photodissociating H$_2$, and $0.76$ eV photons capable of photodetaching H$^-$. Employing cosmological simulations capable of creating the first galaxies in high resolution, we explore if there exists a subset that favours DCBH formation in their vicinity. We find a fundamental relation between the maximum distance at which a galaxy can cause DCBH formation and its star formation rate (SFR), which automatically folds in the chemo-thermodynamical effects of both H$_2$ photo-dissociation and H$^-$ photo-detachment. This is in contrast to the scatter in the LW flux parameter seen at the maximum distance. It shows up to a 3 order of magnitude scatter, which can be interpreted as a scatter in `J$_{crit}$'. Thus, computing the rates and/or the LW flux from a galaxy is no longer necessary to identify neighbouring sites of DCBH formation, as our relation allows one to distinguish regions where DCBH formation could be triggered in the vicinity of a galaxy of a given SFR.