On the gas temperature in the shocked circumstellar envelopes of pulsating stars. I. Radiative heating and cooling rates.

Radiative heating and cooling in the circumstellar envelopes of cool stars is investigated, considering gas densities of 10^4...14^cm^-3^ and gas temperatures of 500...20000K. Various heating and cooling processes are included: rotational and ro-vibrational transitions of polar molecules and of H_2_, atomic line transitions, bound-free transitions, free-free transitions and photochemical reactions. Theoretical concepts and computational methods are worked out, which on the one hand can account for important non-LTE effects and radiative trapping and on the other hand allow for a fast and proper inclusion of these heating and cooling rates into time-dependent hydrodynamical model calculations. Radiative cooling timescales for a carbon-enriched gas typical for C-star atmospheres are calculated, and the thermal relaxation of the gas after the passage of shock waves is discussed. A gradual transition of the character of the propagating shock waves is expected to occur at densities around 10^6...8^cm^-3^, changing from predominantly isothermal to predominantly adiabatic with decreasing gas density.