Molecular Hydrogen Formation During Dense Interstellar Cloud Collapse

We study the evolution of molecular hydrogen on the grain surfaces and in the gas phase using both the rate equation (which tracks the average number of molecules) and the master equation (which tracks the expectation values of molecules). We show that above a certain critical accretion rate of $H$ on the grains, the results from these two methods become identical. We used this result to follow the collapse of a dense interstellar cloud and studied the formation of molecular hydrogen for two different temperatures (T=10K and 12K) and two different masses ($1M_{\odot }$ and $10M_{\odot }$) of the cloud when olivine grains were used. Since at higher temperatures, the recombination is very small for these grains, we also studied a similar hydrodynamic processes at higher temperatures (T=20K and 25K) when amorphous carbon grains were used. We find that generally, for olivine grains, more than 90% $H$ is converted to $H_2$ within $\sim {10}^{5-7}$yr whereas for amorphous grains it takes $\sim 10^{6-7}$yr\mathrm{.}$H_2$ formed in this manner can be adequate to produce the observed complex molecules.