H2O Maser Emission in Circumstellar Envelopes around AGB Stars: Physical
  Conditions in Gas-Dust Clouds
  The pumping of 22.2-GHz H$_2$O masers in the circumstellar envelopes of
asymptotic giant branch stars has been simulated numerically. The physical
parameters adopted in the calculations correspond to those of the circumstellar
envelope around IK Tau. The one-dimensional plane-parallel structure of the
gas-dust cloud is considered. The statistical equilibrium equations for the
H$_2$O level populations and the thermal balance equations for the gas-dust
cloud are solved self-consistently. The calculations take into account 410
rotational levels belonging to the five lowest vibrational levels of H$_2$O.
The stellar radiation field is shown to play an important role in the thermal
balance of the gas-dust cloud due to the absorption of emission in
rotational-vibrational H$_2$O lines. The dependence of the gain in the 22.2-GHz
maser line on the gas density and H$_2$O number density in the gas-dust cloud
is investigated. Gas densities close to the mean density of the stellar wind,
10$^7-10^8$ cm$^{-3}$, and a high relative H$_2$O abundance, more than
10$^{-4}$, have been found to be the most likely physical conditions in maser
sources.
