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.
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