2008A&A...487..975V

Within low-mass star formation, water vapor plays a key role in the chemistry and energy balance of the circumstellar material. The Herschel Space Observatory will open up the possibility to observe water lines originating from a wide range of excitation energies. Our aim is to simulate the emission of rotational water lines from envelopes characteristic of embedded low-mass protostars. A large number of parameters that influence the water line emission are explored: luminosity, density, density slope, and water abundances. Both dust and water emission are modeled using full radiative transfer in spherical symmetry. The temperature profile is calculated for a given density profile. The H₂O level populations and emission profiles are in turn computed with a non-LTE line code. The results are analyzed to determine the diagnostic value of different lines, and are compared with existing observations. Lines can be categorized in: (i) optically thick lines, including ground-state lines, mostly sensitive to the cold outer part; (ii) highly excited (E_u>200-250 K) optically thin lines sensitive to the abundance in the hot inner part; and (iii) lines which vary from optically thick to thin depending on the abundances. Dust influences the emission of water significantly by becoming optically thick at the higher frequencies, and by pumping optically thin lines. A good physical model of a source, including the correct treatment of dust, is a prerequisite for inferring the water abundance structure and possible jumps at the evaporation temperature from observations. The inner warm (T>100 K) envelope can be probed by highly excited lines, while a combination of excited and spectrally resolved ground state lines probes the outer envelope. Observations of H₂¹⁸O lines, although weak, provide even stronger constraints on abundances.