Molecular hydrogen formation on dust grains in the high redshift universe

We study the formation of molecular hydrogen on dust grain surfaces and apply our results to the high redshift universe. We find that a range of physical parameters, in particular dust temperature and gas temperature, but not so much dust surface composition, influence the formation rate of H$_2$. The H$_2$ formation rate is found to be suppressed above gas kinetic temperatures of a few hundred K and for dust temperatures above 200-300 K and below 10 K. We highlight the differences between our treatment of the H$_2$ formation process and other descriptions in the literature. We also study the relative importance of H$_2$ formation on dust grains with respect to molecular hydrogen formation in the gas phase, through the H$^-$ route. The ratio of formation rates of these two routes depends to a large part on the dust abundance, on the electron abundance, and also on the relative strength of the FUV (extra-)galactic radiation field. We find that for a cosmological evolution of the star formation rate and dust density consistent with the Madau plot, a positive feedback effect on the abundance of H$_2$ due to the presence of dust grains can occur at redshifts $z\ge 3$. This effect occurs for a dust-to-gas mass ratio as small as 10$^{-3}$ of the galactic value.