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 various species) and the master equation (which tracks the expectation values of various species). 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 = 10 and 12 K) and two different masses (1 and 10 M-circle dot)) of the cloud when olivine grains were used. Because at higher temperatures, the recombination is very small for these grains, we also studied similar hydrodynamic processes at higher temperatures (T = 20 and 25 K) when amorphous carbon grains were used. We find that generally, for olivine grains, more than 90 per cent H is converted to H-2 within similar to 10(5-7) yr whereas for amorphous grains it takes _ 10(6-7) yr. H-2 formed in this manner can be adequate to produce the observed complex molecules.