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One viable seeding mechanism for supermassive black holes is the directgaseous collapse route in pre-galactic dark matter halos, producing objects onthe order of $10^4 - 10^6$ solar masses. These events occur when the gas isprevented from cooling below $10^4$ K that requires a metal-free and relativelyH$_2$-free medium. The initial collapse cools through atomic hydrogentransitions, but the gas becomes optically thick to the cooling radiation athigh densities. We explore the effects ofLyman-$\alpha$ trapping in such acollapsing system with a suite of Monte Carlo radiation transport calculationsin uniform density and isotropic cases that are based from a cosmologicalsimulation. Our method includes both non-coherent scattering and two-photonline cooling. We find that Lyman-$\alpha$ radiation is marginally trapped inthe parsec-scale gravitationally unstable central cloud, allowing thetemperature 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 effectiveequation of state changes from isothermal at low densities to have an adiabaticindex of 4/3 around the temperature maximum and then slowly retreats back toisothermal at higher densities. Our results suggest that Lyman-$\alpha$trapping delays the initial collapse by raising the Jeans mass. Afterward thehigh density core cools back to $10^4$ K that is surrounded by a warm envelopewhose inward pressure may alter the fragmentation scales at high densities.

On the effect of Lyman alpha trapping during the initial collapse of massive black hole seeds