  We are carrying out a physical and chemical study of the protostellar
envelopes in a representative sample of IM Class 0 protostars. In our first
paper (Crimier et al. 2010), we determined the physical structure
(density-temperature radial profiles) of the protostellar envelopes. Here, we
study the CO depletion and N2H+ deuteration. We observed the millimeter lines
of C18O, C17O, N2H+ and N2D+ toward the protostars using the IRAM 30m
telescope. Based on these observations, we derived the C18O, N2H+ and N2D+
radial abundance profiles across their envelopes using a radiative transfer
code. In addition, we modeled the chemistry of the protostellar envelopes. All
the C18O 1-0 maps are well fit assuming that the C18O abundance decreases
inwards within the protostellar envelope until the gas and dust reach the CO
evaporation temperature, 20-25K, where the CO is released back to the gas
phase. The N2H+ deuterium fractionation in Class 0 IMs is
[N2D+]/[N2H+]=0.005-0.014, two orders of magnitude higher than the elemental
[D/H] value in the interstellar medium, but a factor of 10 lower than in
pre-stellar clumps. Chemical models account for the C18O and N2H+ observations
if we assume the CO abundance is 2 times lower than the canonical value in the
inner envelope. This could be the consequence of the CO being converted into
CH3OH on the grain surfaces prior to the evaporation and/or the
photodissociation of CO by the stellar UV radiation. The deuterium
fractionation is not fitted by chemical models. This discrepancy is very likely
caused by the simplicity of our model that assumes spherical geometry and
neglects important phenomena like the effect of bipolar outflows and UV
radiation from the star. More important, the deuterium fractionation is
dependent on the ortho-to-para H2 ratio, which is not likely to reach the
steady-state value in the dynamical time scales of these protostars.
