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.