  The hydrogen and water molecules respond very differently to the
collisional-radiative processes taking place in planetary atmospheres.
Naturally, the question arises whether H2O-rich atmospheres are more (or less)
resilient to long-term mass loss than H2-dominated ones if they radiate away
the incident stellar energy more (or less) efficiently. If confirmed, the
finding would have implications on our understanding of the evolution of
sub-Neptune exoplanets. As a key step towards answering this question, we
present a non-local thermodynamic equilibrium (NLTE) model of H2O for the
atmospheric region where the gas accelerates to escape the planet and
conditions relevant to close-in sub-Neptunes. Our exploratory calculations for
isothermal gas composed of H2, H2O and e- reveal that: 1) In the pressure
region ~1e-2 - 1e-4 dyn cm-2 where the stellar extreme-ultraviolet (XUV)
photons are typically deposited in the atmosphere, H2O is in rotational LTE but
vibrational NLTE. Vibrational LTE is facilitated by high H2O abundances and
fractional ionizations, and we report critical densities for the LTE-NLTE
transition; 2) Vibrational cooling may locally dominate over rotational
cooling, partly because of the comparatively small opacities of ro-vibrational
lines; 3) Even low H2O abundances notably enhance the cooling, foreseeably
offsetting some of the stellar heating; 4) Heating due to the deposition of
stellar infrared (IR) photons is significant at pressures >=0.1 dyn cm-2. We
estimate the contribution of H2O excitation to the internal energy of the gas
and speculate on the photodissociation from the excited vibrational states.
Ultimately, our findings motivate the consideration of NLTE in the mass loss
rate calculations of H2O-rich atmospheres.
