The Physics of Water Masers observable with ALMA and SOFIA: Model
  Predictions for Evolved Stars
  We present the results of models that were designed to study all possible
water maser transitions in the frequency range 0-1.91THz, with particular
emphasis on maser transitions that may be generated in evolved-star envelopes
and observed with the ALMA and SOFIA telescopes. We used tens of thousands of
radiative transfer models of both spin species of H2O, spanning a considerable
parameter space in number density, kinetic temperature and dust temperature.
Results, in the form of maser optical depths, have been summarized in a master
table, Table 6. Maser transitions identified in these models were grouped
according to loci of inverted regions in the density/kinetic temperature plane,
a property clearly related to the dominant mode of pumping. A more detailed
study of the effect of dust temperature on maser optical depth enabled us to
divide the maser transitions into three groups: those with both collisional and
radiative pumping schemes (22,96,209,321,325,395,941 and 1486\,GHz), a much
larger set that are predominantly radiatively pumped, and another large group
with a predominantly collisional pump. The effect of accelerative and
decelerative velocity shifts of up to 5km/s was found to be generally modest,
with the primary effect of reducing computed maser optical depths. More subtle
asymmetric effects, dependent on line overlap, include maximum gains offset
from zero shift by >1km/s, but these effects were predominantly found under
conditions of weak amplification. These models will allow astronomers to use
multi-transition water maser observations to constrain physical conditions down
to the size of individual masing clouds (size of a few astronomical units).
