Recombination Efficiency of Molecular Hydrogen on Interstellar Grains-II A Numerical Study

A knowledge of the recombination time on the grain surfaces has been a major obstacle in deciding the production rate of molecular hydrogen and other molecules in the interstellar medium. We present a numerical study to compute this time for molecular hydrogen for various cloud and grain parameters. We also find the time dependence, particularly when a grain is freshly injected into the system. Apart from the fact that the recombination times seem to be functions of the grain parameters such as the activation barrier energy, temperature etc, our result also shows the dependence on the number of sites in the grain $S$ and the effective accretion rate per site $a_s$ of atomic hydrogen. Simply put, the average time that a pair of atomic hydrogens will take to produce one molecular hydrogen depends on how heavily the grain is already populated by atomic and molecular hydrogens and how fast the hopping and desorption times are. We show that if we write the average recombination time as $T_r \sim S^\alpha/A_H$, where, $A_H$ is the hopping rate, then $\alpha$ could be much greater than 1 for all astrophysically relevant accretion rates. Thus the average formation rate of $H_2$ is also dependent on the grain parameters, temperature and the accretion rate. We believe that our result will affect the overall rate of the formation of complex molecules such as methanol which require successive hydrogenation on the grain surfaces in the interstellar medium.