Role of the $\mathrm{H}_2^+$ channel in the primordial star formation under strong radiation field and the critical intensity for the supermassive star formation

Abstract

We investigate the role of the H + 2 channel on H 2 molecule formation during the collapse of primordial gas clouds immersed in strong radiation fields which are assumed to have the shape of a diluted blackbody spectra with temperature T rad . Since the photodissociation rate of H + 2 depends on its level population, we take full account of the vibrationally resolved H + 2 kinetics. We find that in clouds under soft but intense radiation fields with spectral temperature T rad 7000 K, the H + 2 channel is the dominant H 2 formation process. On the other hand, for harder spectra with T rad 7000 K, the H -channel takes over H + 2 in the production of molecular hydrogen. We calculate the critical radiation intensity needed for supermassive star formation by direct collapse and examine its dependence on the H + 2 level population. Under the assumption of local thermodynamic equilibrium (LTE) level population, the critical intensity is underestimated by a factor of a few for soft spectra with T rad 7000 K. For harder spectra, the value of the critical intensity is not affected by the level population of H + 2 . This result justifies previous estimates of the critical intensity assuming LTE populations since radiation sources like young and/or metal-poor galaxies are predicted to have rather hard spectra.