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 nH≈ 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.

Rate of Formation of Hydrogen Molecules by Three-Body Recombination During Primordial Star Formation

“…The experiments were performed in a temperature range of 2900-4700 K. When the same comparisons for the equilibrium constant and TBR rate are made in this experimental temperature range, both discrepancies are reduced to a factor of four over the whole range. In order to see this, the exact H 2 partition function must be used to compute the equilibrium constant, not the fitted value (Flower & Harris 2007) which is valid only for T < 2000 K. The second reason is the choice of atomic partition function which was assumed to be 2 for hydrogen in its 1s 2 S ground state (Flower & Harris 2007). This choice accounts for the nuclear spin degeneracy but not the electron spin degeneracy.…”

“…The TBR rate adopted by Palla et al (1983) was identical to the expression given by Jacobs et al (1967) apart from a change in units. Flower & Harris (2007) used the CID expression given by Jacobs et al (1967) together with their own determination of the equilibrium constant to derive a very different TBR rate constant. The discrepancy between these two TBR rate constants, therefore, is due to the adopted equilibrium constants that were used.…”

“…Two of these rate constants (Palla et al 1983;Flower & Harris 2007) were based on the shock tube measurements of Jacobs et al (1967) who gave analytic expressions for TBR and the inverse process of collision-induced dissociation (CID). The TBR rate adopted by Palla et al (1983) was identical to the expression given by Jacobs et al (1967) apart from a change in units.…”

“…In this study, Turk et al (2011) used three different published rate constants (Palla et al 1983;Abel et al 2002;Flower & Harris 2007) for the TBR process H + H + H → H + H 2 .…”

“…The equilibrium constant used by Flower & Harris (2007) relies on the Saha equation and their determination of the H 2 partition function. When fitted to a simple temperature-dependent function, Flower & Harris (2007) found that their value is approximately 4.5 times greater than a similar fit obtained from the JANAF Thermochemical Tables at a temperature of 1000 K. Using this equilibrium constant together with the CID expression given in Jacobs et al (1967) yielded a TBR rate constant which was approximately six times larger at T = 1000 K than the TBR expression given in Jacobs et al (1967). It appears that there are two separate reasons for the factors of 4.5 and 6 discrepancies at 1000 K. The first reason is fitting error.…”