On the effect of Lyman alpha trapping during the initial collapse of
  massive black hole seeds
  One viable seeding mechanism for supermassive black holes is the direct
gaseous collapse route in pre-galactic dark matter halos, producing objects on
the order of $10^4 - 10^6$ solar masses. These events occur when the gas is
prevented from cooling below $10^4$ K that requires a metal-free and relatively
H$_2$-free medium. The initial collapse cools through atomic hydrogen
transitions, but the gas becomes optically thick to the cooling radiation at
high densities. We explore the effects ofLyman-$\alpha$ trapping in such a
collapsing system with a suite of Monte Carlo radiation transport calculations
in uniform density and isotropic cases that are based from a cosmological
simulation. Our method includes both non-coherent scattering and two-photon
line cooling. We find that Lyman-$\alpha$ radiation is marginally trapped in
the parsec-scale gravitationally unstable central cloud, allowing the
temperature to increase to 50,000 K at a number density of $3 \times 10^4$
cm$^{-3}$ and increasing the Jeans mass by a factor of five. The effective
equation of state changes from isothermal at low densities to have an adiabatic
index of 4/3 around the temperature maximum and then slowly retreats back to
isothermal at higher densities. Our results suggest that Lyman-$\alpha$
trapping delays the initial collapse by raising the Jeans mass. Afterward the
high density core cools back to $10^4$ K that is surrounded by a warm envelope
whose inward pressure may alter the fragmentation scales at high densities.
