Water in star-forming regions: physics and chemistry from clouds to disks as probed by <i>Herschel</i> spectroscopy

Context. Water is a key molecule in the physics and chemistry of star and planet formation, but it is difficult to observe from Earth. The Herschel Space Observatory provided unprecedented sensitivity as well as spatial and spectral resolution to study water. The Water In Star-forming regions with Herschel (WISH) key program was designed to observe water in a wide range of environments and provide a legacy data set to address its physics and chemistry. Aims. The aim of WISH is to determine which physical components are traced by the gas-phase water lines observed with Herschel and to quantify the excitation conditions and water abundances in each of these components. This then provides insight into how and where the bulk of the water is formed in space and how it is transported from clouds to disks, and ultimately comets and planets. Methods. Data and results from WISH are summarized together with those from related open time programs. WISH targeted ~80 sources along the two axes of luminosity and evolutionary stage: from low- to high-mass protostars (luminosities from &lt;1 to &gt; 10 5 L ⊙ ) and from pre-stellar cores to protoplanetary disks. Lines of H 2 O and its isotopologs, HDO, OH, CO, and [O I], were observed with the HIFI and PACS instruments, complemented by other chemically-related molecules that are probes of ultraviolet, X-ray, or grain chemistry. The analysis consists of coupling the physical structure of the sources with simple chemical networks and using non-LTE radiative transfer calculations to directly compare models and observations. Results. Most of the far-infrared water emission observed with Herschel in star-forming regions originates from warm outflowing and shocked gas at a high density and temperature (&gt; 10 5 cm −3 , 300–1000 K, v ~ 25 km s −1 ), heated by kinetic energy dissipation. This gas is not probed by single-dish low- J CO lines, but only by CO lines with J up &gt; 14. The emission is compact, with at least two different types of velocity components seen. Water is a significant, but not dominant, coolant of warm gas in the earliest protostellar stages. The warm gas water abundance is universally low: orders of magnitude below the H 2 O/H 2 abundance of 4 × 10 −4 expected if all volatile oxygen is locked in water. In cold pre-stellar cores and outer protostellar envelopes, the water abundance structure is uniquely probed on scales much smaller than the beam through velocity-resolved line profiles. The inferred gaseous water abundance decreases with depth into the cloud with an enhanced layer at the edge due to photodesorption of water ice. All of these conclusions hold irrespective of protostellar luminosity. For low-mass protostars, a constant gaseous HDO/H 2 O ratio of ~0.025 with position into the cold envelope is found. This value is representative of the outermost photodesorbed ice layers and cold gas-phase chemistry, and much higher than that of bulk ice. In contrast, the gas-phase NH 3 abundance stays constant as a function of position in low-mass pre- and protostellar cores. Water abundances in the inner hot cores are high, but with variations from 5 × 10 −6 to a few × 10 −4 for low- and high-mass sources. Water vapor emission from both young and mature disks is weak. Conclusions. The main chemical pathways of water at each of the star-formation stages have been identified and quantified. Low warm water abundances can be explained with shock models that include UV radiation to dissociate water and modify the shock structure. UV fields up to 10 2 −10 3 times the general interstellar radiation field are inferred in the outflow cavity walls on scales of the Herschel beam from various hydrides. Both high temperature chemistry and ice sputtering contribute to the gaseous water abundance at low velocities, with only gas-phase (re-)formation producing water at high velocities. Combined analyses of water gas and ice show that up to 50% of the oxygen budget may be missing. In cold clouds, an elegant solution is that this apparently missing oxygen is locked up in larger μ m-sized grains that do not contribute to infrared ice absorption. The fact that even warm outflows and hot cores do not show H 2 O at full oxygen abundance points to an unidentified refractory component, which is also found in diffuse clouds. The weak water vapor emission from disks indicates that water ice is locked up in larger pebbles early on in the embedded Class I stage and that these pebbles have settled and drifted inward by the Class II stage. Water is transported from clouds to disks mostly as ice, with no evidence for strong accretion shocks. Even at abundances that are somewhat lower than expected, many oceans of water are likely present in planet-forming regions. Based on the lessons for galactic protostars, the low- J H 2 O line emission ( E up &lt; 300 K) observed in extragalactic sources is inferred to be predominantly collisionally excited and to originate mostly from compact regions of current star formation activity. Recommendations for future mid- to far-infrared missions are made.