Role of the H+2 channel in the primordial star formation under strong radiation field and the critical intensity for the supermassive star formation

We investigate the role of the H+2 channel on H2 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 Trad. 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 Trad ≲ 7000 K, the H+2 channel is the dominant H2 formation process. On the other hand, for harder spectra with Trad ≳ 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 Trad ≲ 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.