  We investigate the delivery of regular and deuterated forms of water from
prestellar cores to circumstellar disks. We adopt a semi-analytical
axisymmetric two-dimensional collapsing core model with post-processing gas-ice
astrochemical simulations, in which a layered ice structure is considered. The
physical and chemical evolutions are followed until the end of the main
accretion phase. When mass averaged over the whole disk, a forming disk has a
similar H2O abundance and HDO/H2O abundance ratio as their precollapse values
(within a factor of 2), regardless of time in our models. Consistent with
previous studies, our models suggest that interstellar water ice is delivered
to forming disks without significant alteration. On the other hand, the local
vertically averaged H2O ice abundance and HDO/H2O ice ratio can differ more, by
up to a factor of several, depending on time and distance from a central star.
Key parameters for the local variations are the fluence of stellar UV photons
en route into the disk and the ice layered structure, the latter of which is
mostly established in the prestellar stages. We also find that even if
interstellar water ice is destroyed by stellar UV and (partly) reformed prior
to disk entry, the HDO/H2O ratio in reformed water ice is similar to the
original value. This finding indicates that some caution is needed in
discussions on the prestellar inheritance of H2O based on comparisons between
the observationally derived HDO/H2O ratio in clouds/cores and that in
disks/comets. Alternatively, we propose that the ratio of D2O/HDO to HDO/H2O
better probes the prestellar inheritance of H2O. It is also found that icy
organics are more enriched in deuterium than water ice in forming disks. The
differential deuterium fractionation in water and organics is inherited from
the prestellar stages.
