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

## TL;DR

This study investigates how Lyman-alpha trapping influences the initial collapse of massive black hole seeds, showing that it delays collapse by increasing the Jeans mass and affecting the thermal evolution of the collapsing gas.

## Contribution

It provides the first detailed Monte Carlo radiation transport analysis of Lyman-alpha trapping effects during direct collapse black hole formation.

## Key findings

- Lyman-alpha trapping marginally occurs in the central cloud.
- Temperature increases to 50,000 K at certain densities.
- Jeans mass increases by a factor of five due to trapping.

## Abstract

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.