Observations of Water Vapor Outflow from NML Cygnus

We report new observations of the far infrared and submillimeter water vapor emission of NML Cygnus based on data gathered with the Infrared Space Observatory and the Submillimeter Wave Astronomy Satellite. We compare the emission from NML Cyg to that previously published for VY CMa and W Hya in an attempt to establish the validity of recently proposed models for the outflow from evolved stars. The data obtained support the contention by Ivezi\'{c} & Elitzur (1995, 1997) that the atmospheres of evolved stars obey a set of scaling laws in which the optical depth of the outflow is the single most significant scaling parameter, affecting both the radiative transfer and the dynamics of the outflow. Specifically, we provide observations comparing the water vapor emission from NML Cyg, VY CMa and W Hya, and find, to the extent permitted by the quality of our data, that the results are in reasonable agreement with a model developed by Zubko & Elitzur (2000). Using this model we derive a mass loss based on the dust opacities, spectral line fluxes, and outflow velocities of water vapor observed in the atmospheres of these oxygen-rich giants. For VY CMa and NML Cyg we also obtain an estimate of the stellar mass.