Three-body recombination of hydrogen during primordial star formation

ABSTRACT

We consider the formation and destruction of H₂ and HD during the gravitational contraction of condensations of the primordial gas, which led to the formation of the first generation of stars (Population III stars). The determination of the populations of the bound rovibrational levels of molecular hydrogen is considered in detail. Initially, the rates per unit volume at which these levels are populated and depopulated are not in equilibrium. As the density increases, equilibrium between the rates of population and depopulation is established first, and then the levels gradually thermalize (i.e. their populations tend towards a Boltzmann distribution at the kinetic temperature of the gas), with the lowest energy levels thermalizing first. Ultimately, both the bound and the continuum states thermalize (i.e. attain a Saha distribution), but this process is not complete until densities  n_H≈ 10¹³ cm⁻³  are reached. Using the principle of microscopic reversibility, we derive an expression for the rate coefficient for three-body recombination of hydrogen which is found to differ significantly from the much used expression of Jacobs et al.