Molecule survival in magnetized protostellar disk winds II. Predicted H2O line profiles versus Herschel/HIFI observations

Context. The origin of molecular protostellar jets and their role in extracting angular momentum from the accreting system are important open questions in star formation research. In the first paper of this series we showed that a dusty magneto-hydrodynamic (MHD) disk wind appeared promising to explain the pattern of H-2 temperature and collimation in the youngest jets. Aims. We wish to see whether the high-quality H2O emission profiles of low-mass protostars, observed for the first time by the HIFI spectrograph on board the Herschel satellite, remain consistent with the MHD disk wind hypothesis, and which constraints they would set on the underlying disk properties. Methods. We present synthetic H2O line profiles predictions for a typical MHD disk wind solution with various values of disk accretion rate, stellar mass, extension of the launching area, and view angle. We compare them in terms of line shapes and intensities with the HIFI profiles observed by the WISH key program towards a sample of 29 low-mass Class 0 and Class 1 protostars. Results. A dusty MHD disk wind launched from 0.2-0.6 AU AU to 3-25 AU can reproduce to a remarkable degree the observed shapes and intensities of the broad H2O component observed in low-mass protostars, both in the fundamental 557 GHz line and in more excited lines. Such a model also readily reproduces the observed correlation of 557 GHz line luminosity with envelope density, if the infall rate at 1000 AU is 1-3 times the disk accretion rate in the wind ejection region. It is also compatible with the typical disk size and bolometric luminosity in the observed targets. However, the narrower line profiles in Class 1 sources suggest that MHD disk winds in these sources, if present, would have to be slower and/or less water rich than in Class 0 sources. Conclusions. MHD disk winds appear as a valid (though not unique) option to consider for the origin of the broad H2O component in low-mass protostars. ALMA appears ideally suited to further test this model by searching for resolved signatures of the warm and slow wide-angle molecular wind that would be predicted.