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