  The deuterium fractionation of gas-phase molecules in hot cores is believed
to reflect the composition of interstellar ices. The deuteration of methanol is
a major puzzle, however, because the isotopologue ratio [CH2DOH]/[CH3OD], which
is predicted to be equal to 3 by standard grain chemistry models, is much
larger (~20) in low-mass hot corinos and significantly lower (~1) in high-mass
hot cores. This dichotomy in methanol deuteration between low-mass and massive
protostars is currently not understood. In this study, we report a simplified
rate equation model of the deuterium chemistry occurring in the icy mantles of
interstellar grains. We apply this model to the chemistry of hot corinos and
hot cores, with IRAS 16293-2422 and the Orion~KL Compact Ridge as prototypes,
respectively. The chemistry is based on a statistical initial deuteration at
low temperature followed by a warm-up phase during which thermal
hydrogen/deuterium (H/D) exchanges occur between water and methanol. The
exchange kinetics is incorporated using laboratory data. The [CH2DOH]/[CH3OD]
ratio is found to scale inversely with the D/H ratio of water, owing to the H/D
exchange equilibrium between the hydroxyl (-OH) functional groups of methanol
and water. Our model is able to reproduce the observed [CH2DOH]/[CH3OD] ratios
provided that the primitive fractionation of water ice [HDO]/[H2O] is ~ 2% in
IRAS 16293-2422 and ~0.6% in Orion~KL. We conclude that the molecular D/H
ratios measured in hot cores may not be representative of the original mantles
because molecules with exchangeable deuterium atoms can equilibrate with water
ice during the warm-up phase.
