  We investigate whether the broad wings of H2O emission identified with
Herschel towards low-mass Class 0 and Class 1 protostars may be consistent with
an origin in a dusty MHD disk wind, and the constraints it would set on the
underlying disk properties. 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. We find that 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, 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. In
conclusion, 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.
