Water in star-forming regions with Herschel (WISH) II. Evolution of 557 GHz 110-101 emission in low-mass protostars

Context. Water is a key tracer of dynamics and chemistry in low-mass star-forming regions, but spectrally resolved observations have so far been limited in sensitivity and angular resolution, and only data from the brightest low-mass protostars have been published. Aims. The first systematic survey of spectrally resolved water emission in 29 low-mass (L < 40 L-circle dot) protostellar objects is presented. The sources cover a range of luminosities and evolutionary states. The aim is to characterise the line profiles to distinguish physical components in the beam and examine how water emission changes with protostellar evolution. Methods. H2O was observed in the ground-state 1(10)-1(01) transition at 557 GHz (E-up/k(B) similar to 60 K) as single-point observations with the Heterodyne Instrument for the Far-Infrared (HIFI) on Herschel in 29 deeply embedded Class 0 and I low-mass protostars. Complementary far-IR and sub-mm continuum data (including PACS data from our programme) are used to constrain the spectral energy distribution (SED) of each source. H2O intensities are compared to inferred envelope properties, e.g., mass and density, outflow properties and CO 3-2 emission. Results. H2O emission is detected in all objects except one (TMC1A). The line profiles are complex and consist of several kinematic components tracing different physical regions in each system. In particular, the profiles are typically dominated by a broad Gaussian emission feature, indicating that the bulk of the water emission arises in outflows, not in the quiescent envelope. Several sources show multiple shock components appearing in either emission or absorption, thus constraining the internal geometry of the system. Furthermore, the components include inverse P-Cygni profiles in seven sources (six Class 0, one Class I) indicative of infalling envelopes, and regular P-Cygni profiles in four sources (three Class I, one Class 0) indicative of expanding envelopes. Molecular bullets moving at greater than or similar to 50 km s(-1) with respect to the source are detected in four Class 0 sources; three of these sources were not known to harbour bullets previously. In the outflow, the H2O/CO abundance ratio as a function of velocity is nearly the same for all line wings, increasing from 10(-3) at low velocities (< 5 km s(-1)) to greater than or similar to 10(-1) at high velocities (> 10 km s(-1)). The water abundance in the outer cold envelope is low, greater than or similar to 10(-10). The different H2O profile components show a clear evolutionary trend: in the younger Class 0 sources the emission is dominated by outflow components originating inside an infalling envelope. When large-scale infall diminishes during the Class I phase, the outflow weakens and H2O emission all but disappears.