Black hole formation in primordial galaxies: chemical and radiative
  conditions
  In massive primordial galaxies, the gas may directly collapse and form a
single central massive object if cooling is suppressed. Line cooling by
molecular hydrogen can be suppressed in the presence of a strong
soft-ultraviolet radiation field, but the role played by other cooling
mechanisms is less clear. In optically thin gas, Lyman-Alpha cooling can be
very effective, maintaining the gas temperature below 10^4 K over many orders
of magnitude in density. However, the large neutral hydrogen column densities
present in primordial galaxies render them highly optically thick to
Lyman-Alpha photons. In this letter, we examine in detail the effects of the
trapping of these Lyman-Alpha photons on the thermal and chemical evolution of
the gas. We show that despite the high optical depth in the Lyman series lines,
cooling is not strongly suppressed, and proceeds via other atomic hydrogen
transitions, in particular the 2s-1s and the 3-2 transitions. At densities
larger than 10^9 cm^{-3}, collisional dissociation of molecular hydrogen
becomes the dominant cooling process and decreases the gas temperature to about
5000 K. The gas temperature evolves with density as $T \propto
\rho^{\gamma_{\rm eff} - 1}$, with $\gamma_{\rm eff} = 0.97-0.98$. The
evolution is thus very close to isothermal, and so fragmentation is possible,
but unlikely to occur during the initial collapse. However, after the formation
of a massive central object, we expect that later-infalling, higher angular
momentum material will form an accretion disk that may be unstable to
fragmentation, which may give rise to star formation with a top-heavy IMF.
