  We have modeled the far-infrared water line emission 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 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 80 rotational states of water and thereby
obtained predictions for the luminosity of a large number of far-infrared
rotational transitions of water. In common with previous models, our model
predicts that water will be copiously produced in the warm circumstellar gas,
and that water rotational emission will dominate the radiative cooling.
However, our use of a realistic radiative cooling function for water leads to a
lower gas temperature than that predicted in previous models. Our predictions
for the far-infrared water line luminosities are consequently significantly
smaller than those obtained in previous studies. Observations to be carried out
by the Infrared Space Observatory will provide a crucial test of the models
presented here.
