Is H-3(+) cooling ever important in primordial gas?

Studies of the formation of metal-free Population III stars usually focus primarily on the role played by H-2 cooling, on account of its large chemical abundance relative to other possible molecular or ionic coolants. However, while H-2 is generally the most important coolant at low gas densities, it is not an effective coolant at high gas densities, owing to the low critical density at which it reaches local thermodynamic equilibrium (LTE) and to the large opacities that develop in its emission lines. It is therefore possible that emission from other chemical species may play an important role in cooling high-density primordial gas. A particularly interesting candidate is the H-3(+) molecular ion. This ion has an LTE cooling rate that is roughly a billion times larger than that of H-2, and unlike other primordial molecular ions such as H-2(+) or HeH+, it is not easily removed from the gas by collisions with H or H-2. It is already known to be an important coolant in at least one astrophysical context-the upper atmospheres of gas giants-but its role in the cooling of primordial gas has received little previous study. In this paper, we investigate the potential importance of H-3(+) cooling in primordial gas using a newly developed H-3(+) cooling function and the most detailed model of primordial chemistry published to date. We show that although H-3(+) is, in most circumstances, the third most important coolant in dense primordial gas (after H-2 and HD), it is nevertheless unimportant, as it contributes no more than a few per cent of the total cooling. We also show that in gas irradiated by a sufficiently strong flux of cosmic rays or X-rays, H-3(+) can become the dominant coolant in the gas, although the size of the flux required renders this scenario unlikely to occur.