  Recent interferometer observations have found that the D2O/HDO abundance
ratio is higher than that of HDO/H2O by about one order of magnitude in the
vicinity of low-mass protostar NGC 1333-IRAS 2A, where water ice has
sublimated. Previous laboratory and theoretical studies show that the D2O/HDO
ice ratio should be lower than the HDO/H2O ice ratio, if HDO and D2O ices are
formed simultaneously with H2O ice. In this work, we propose that the observed
feature, D2O/HDO > HDO/H2O, is a natural consequence of chemical evolution in
the early cold stages of low-mass star formation: 1) majority of oxygen is
locked up in water ice and other molecules in molecular clouds, where water
deuteration is not efficient, and 2) water ice formation continues with much
reduced efficiency in cold prestellar/protostellar cores, where deuteration
processes are highly enhanced due to the drop of the ortho-para ratio of H2,
the weaker UV radiation field, etc. Using a simple analytical model and gas-ice
astrochemical simulations tracing the evolution from the formation of molecular
clouds to protostellar cores, we show that the proposed scenario can
quantitatively explain the observed HDO/H2O and D2O/HDO ratios. We also find
that the majority of HDO and D2O ices are likely formed in cold
prestellar/protostellar cores rather than in molecular clouds, where the
majority of H2O ice is formed. This work demonstrates the power of the
combination of the HDO/H2O and D2O/HDO ratios as a tool to reveal the past
history of water ice formation in the early cold stages of star formation and
when the enrichment of deuterium in the bulk of water occurred. Further
observations are needed to explore if the relation, D2O/HDO > HDO/H2O, is
common in low-mass protostellar sources.
