Deuterium fractionation on interstellar grains studied with modified rate equations and a Monte Carlo approach

The formation of singly and doubly deuterated isotopomers of formaldehyde and of singly, doubly, and multiply deuterated isotopomers of methanol on interstellar grain surfaces has been studied with a semi-empirical modified rate approach and a Monte Carlo method in the temperature range 10-20 K. Agreement between the results of the two methods is satisfactory for all major and many minor species throughout this range. If gas-phase fractionation can produce a high abundance of atomic deuterium, which then accretes onto grain surfaces, diffusive surface chemistry can produce large abundances of deuterated species, especially at low temperatures and high gas densities. Warming temperatures will then permit these surface species to evaporate into the gas, where they will remain abundant for a considerable period. We calculate that the doubly deuterated molecules CHD2OH and CH2DOD are particularly abundant and should be searched for in the gas phase of protostellar sources. For example, at 10 K and high density, these species can achieve up to 10-20% of the abundance of methanol.