A set of new, sensitive, and spectrally resolved, sub-millimeter line observations are used to probe the warm circumstellar gas around the S-type AGB star chi Cyg. The observed lines involve high rotational quantum numbers, which, combined with previously obtained lower-frequency data, make it possible to study in detail the chemical and physical properties of, essentially, the entire circumstellar envelope of chi Cyg. The data were obtained using the HIFI instrument aboard Herschel, whose high spectral resolution provides valuable information about the line profiles. Detailed, non-LTE, radiative transfer modelling, including dust radiative transfer coupled with a dynamical model, has been performed to derive the temperature, density, and velocity structure of the circumstellar envelope. We report the first detection of circumstellar H2O rotational emission lines in an S-star. Using the high-J CO lines to derive the parameters for the circumstellar envelope, we modelled both the ortho- and para-H2O lines. Our modelling results are consistent with the velocity structure expected for a dust-driven wind. The derived total H2O abundance (relative to H2) is (1.1 +/- 0.2)E-5, much lower than that in O-rich stars. The derived ortho-to-para ratio of 2.1 +/- 0.6 is close to the high-temperature equilibrium limit, consistent with H2O being formed in the photosphere.
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