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We have modeled the far-infrared water line emission that is expected from circumstellar outflows from oxygen-rich late-type stars, as a function of the mass-loss rate and the terminal outflow velocity. For each mass-loss rate and terminal outflow velocity that we considered, we computed self-consistently the gas density, temperature, outflow velocity, and water abundance as a function of distance from the star. We then used an escape probability method to solve for the equilibrium level populations of 200 rotational states of water and thereby obtained predictions for the luminosity of a large number of far-infrared rotational transitions of water. Our model is based upon the most reliable estimates currently available of the rate coefficients for chemical reactions that lead to the formation and destruction of water, the rate coefficients for collisional excitation of water, and the total radiative cooling rate.
In common with previous models, our model predicts that water will be copiously produced in the warm circumstellar gas. Water is expected to account for almost all of the gas-phase oxygen that is not locked up in CO, and water rotational emission is expected to dominate the radiative cooling. However, our use of a realistic radiative cooling function for water leads to a gas temperature profile which lies substantially below that predicted in previous models. Our predictions for the far-infrared line luminosities are consequently significantly smaller than those obtained previously. The lower gas temperatures predicted in our study are supported by the fact that previous models for circumstellar outflows have tended to overpredict the luminosity of water maser emissions from late-type stars. Observations to be carried out with the Infrared Space Observatory will provide a crucial test of the models presented here.
We gratefully acknowledge the support of NASA grant NAGW-3147 from the Long Term Space Astrophysics Research and Analysis Program.
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