  Aims: The production of molecular hydrogen and its deuterated forms onto
carbonaceous dust grains is investigated in detail. The goal of this study is
to estimate the importance of the chemistry occuring on grain surfaces for the
deuteration of H2. Furthermore, we aim to find a robust and general surface
chemical model which can be used in different astrophysical environments.
Methods: Surface processes are described for the cases of graphitic and
amorphous--carbon grains, where laboratory work is available.
Langmuir--Hinshelwood as well as Eley--Rideal surface chemistries are included
in the model and their relative contributions are highlighted. Analytic
expressions are derived for H2, HD, and D2 formation efficiencies for both type
of grains. Rate equations are tested against stochastic methods. Results: As
expected, rate equations and stochastic methods diverge for grain sizes lower
than a critical value acrit. For grain sizes below this critical value, D2
formation decreases to favour HD formation. The formation efficiencies of H2
and D2 can be calculated by adding a correction factor to the rate equations
methods. We found that because of the presence of chemisorbed sites, which can
store atoms to form molecules up to high grain temperatures, the formation
efficiency of HD and D2 is very high compared to models where only
physisorption sites are taken into account. When considering a realistic
distribution of dust grains, we found that the formation rate of H2 and HD is
enhanced by an order of magnitude if small grains are taken into account. The
processes described in this paper, that allow a strong enhancement of the
deuterated forms of molecular hydrogen, could explain the high degree of
deuterium fractionation observed in protostellar environments.
