We have modeled the emission of H2O rotational lines from the extreme C-rich star IRC+10216. Our treatment of the excitation of H2O emissions takes into account the excitation of H2O both through collisions, and through the pumping of the nu2 and nu3 vibrational states by dust emission and subsequent decay to the ground state. Regardless of the spatial distribution of the water molecules, the H2O 1_{10}-1_{01} line at 557 GHz observed by the Submillimeter Wave Astronomy Satellite (SWAS) is found to be pumped primarily through the absorption of dust-emitted photons at 6 $mu$m in the nu2 band. As noted by previous authors, the inclusion of radiative pumping lowers the ortho-H2O abundance required to account for the 557 GHz emission, which is found to be (0.5-1)x10^{-7} if the presence of H2O is a consequence of vaporization of orbiting comets or Fischer-Tropsch catalysis. Predictions for other submillimeter H2O lines that can be observed by the Herschel Space Observatory (HSO) are reported. Multitransition HSO observations promise to reveal the spatial distribution of the circumstellar water vapor, discriminating among the several hypotheses that have been proposed for the origin of the H2O vapor in the envelope of IRC+10216. We also show that, for observations with HSO, the H2O 1_{10}-1_{01} 557 GHz line affords the greatest sensitivity in searching for H2O in other C-rich AGB stars.
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