H2 self-shielding with non-LTE rovibrational populations: Implications for cooling in protogalaxies

The abundance of molecular hydrogen (H2), the primary coolant in primordial gas, is critical for the thermodynamic evolution and star-formation histories in early protogalaxies. Determining the photodissociation rate of H2 by an incident Lyman-Werner (LW) flux is thus crucial, but prohibitively expensive to calculate on the fly in simulations. The rate is sensitive to the H2 rovibrational distribution, which in turn depends on the gas density, temperature, and incident LW radiation field. We use the publicly available cloudy package to model primordial gas clouds and compare exact photodissociation rate calculations to commonly-used fitting formulae. We find the fit from Wolcott-Green et al. (2011) is most accurate for moderate densities n~10^3 cm^{-3} and temperatures, T~10^3K, and we provide a new fit, which captures the increase in the rate at higher densities and temperatures, owing to the increased excited rovibrational populations in this regime. Our new fit has typical errors of a few percent percent up to n =<10^7 cm^{-3}, T =< 8000K, and H2 column density NH2 =<10^{17} cm^{-2}, and can be easily utilized in simulations. We also show that pumping of the excited rovibrational states of H2 by a strong LW flux further modifies the level populations when the gas density is low, and noticeably decreases self-shielding for J_21 > 10^3 and n < 10^2 cm^{-3}. This may lower the "critical flux" at which primordial gas remains H2-poor in some protogalaxies, enabling massive black hole seed formation.