The deuterium fractionation of water on solar-system scales in deeply-embedded low-mass protostars

Context. The chemical evolution of water through the star formation process directly affects the initial conditions of planet formation. The water deuterium fractionation (HDO/H2O abundance ratio) has traditionally been used to infer the amount of water brought to Earth by comets. Measuring this ratio in deeply-embedded low-mass protostars makes it possible to probe the critical stage when water is transported from clouds to disks in which icy bodies are formed. Aims. We aim to determine the HDO/H2O abundance ratio in the warm gas in the inner 150 AU for three deeply-embedded low-mass protostars NGC 1333-IRAS 2A, IRAS 4A-NW, and IRAS 4B through high-resolution interferometric observations of isotopologues of water. Methods. We present sub-arcsecond resolution observations of the 3(1,2)-2(2,1) transition of HDO at 225.89672 GHz in combination with previous observations of the 3(1,3)-2(2,0) transition of (H2O)-O-18 at 203.40752 GHz from the Plateau de Bure Interferometer toward three low-mass protostars. The observations have similar angular resolution (0 ''.7-1 ''.3), probing scales R less than or similar to 150 AU. In addition, observations of the 2(1,1)-2(1,2) transition of HDO at 241.561 GHz toward IRAS 2A are presented to constrain the excitation temperature. A direct and model independent HDO/H2O abundance ratio is determined for each source and compared with HDO/H2O ratios derived from spherically symmetric full radiative transfer models for two sources. Results. From the two HDO lines observed toward IRAS 2A, the excitation temperature is found to be T-ex = 124 +/- 60 K. Assuming a similar excitation temperature for (H2O)-O-18 and all sources, the HDO/H2O ratio is 7.4 +/- 2.1 x 10(4) for IRAS 2A, 19.1 +/- 5.4 x 10(-4) for IRAS 4A-NW, and 5.9 +/- 1.7 x 10(-4) for IRAS 4B. The abundance ratios show only a weak dependence on the adopted excitation temperature. The abundances derived from the radiative transfer models agree with the direct determination of the HDO/H2O abundance ratio for IRAS 16293-2422 within a factor of 2-3, and for IRAS 2A within a factor of 4; the difference is mainly due to optical depth effects in the HDO line. Conclusions. Our HDO/H2O ratios for the inner regions (where T > 100 K) of four young protostars are only a factor of 2 higher than those found for pristine, solar system comets. These small differences suggest that little processing of water occurs between the deeply embedded stage and the formation of planetesimals and comets.