its level populations reach their local thermodynamical equilibrium (LTE) values), and at higher densities, the gas begins to reheat. Gas falling into the dark matter halo therefore tends to fragment once it reaches this temperature and density, and the resulting fragments have masses of the order of the local Jeans mass, $M_{\rm J} \sim 1000 \: {\rm M_{\odot}}$.[^1] Following this period of fragmentation, the gas in the fragments undergoes a further period of gravitational collapse, eventually reaching a density of $n \sim 10^{8}$–$10^{10} \: {\rm cm^{-3}}$, at which point three-body H$_{2}$ formation becomes effective. This rapidly converts almost all of the available atomic hydrogen into H$_{2}$, but the significant energy release that accompanies this process heats the gas, which typically attains a temperature of 1000–2000 K during this phase of the collapse.

Continued collapse next leads to the gas becoming optically thick in the main H$_{2}$ cooling lines (at $n \sim 10^{10} \: {\rm cm^{-3}}$; @ra04, @yoha06), the onset of collision-induced emission cooling (at $n
\sim 10^{14} \: {\rm cm^{-3}}$; @ra04), and finally to the gas becoming optically thick in the continuum as well as in the H$_{2}$ lines ($n \sim 10^{16}
\: {\rm cm^{-3}}$; @yoh08). H$_{2}$ dissociation cooling allows 