On the gas temperature in the shocked circumstellar envelopes of pulsating stars

In this paper, we examine the mass loss mechanism of C-rich AGB stars by means of spherically symmetric model calculations, which combine hydrodynamics, grey radiative transfer (with constant gas and variable dust opacity) and time-dependent dust formation (based on equilibrium chemistry and modified classical nucleation theory) with a time-independent non-LTE description of the state functions of the gas, in particular concerning the radiative heating and cooling function. According to our models, the dissipative heating by shock waves created by the stellar pulsation does not lead to a long-lasting increase of the gas temperatures close to the star, because the radiative cooling is too effective. The gas results to be mostly in radiative equilibrium (RE), except for some narrow but hot post-shock cooling zones. Consequently, the dust formation and wind acceleration proceeds in a similar way as described by Fleischer et al. ([CITE]) and we find a dust-driven wind triggered by the stellar pulsation, but no evidence for a purely pulsation-driven mass loss. Several new effects occur in the models which are causally connected with the non-LTE state functions. In particular, the dissociation/re-formation of H2 consumes/liberates so much energy that the radiative relaxation towards RE can be significantly delayed in regions where the phase transition $\rm H \rightleftharpoons H_2$ takes place. These regions may stay in non-RE for a considerable fraction of the stellar pulsation period. The radiative cooling behind the strongest, dissociative shock waves ($\ga$ $20~ \rm km\,s^{-1}$) usually proceeds in a two-step process where the initially rapid cooling by permitted atomic lines down to ≈ $6000\,$K is followed by a second phase of intense radiative cooling below ≈3000 K, as soon as the first molecules (e.g. CO) have formed. In the meantime, the gas cools slowly by forbidden metal emission lines, or by adiabatic expansion. This re-increase of the radiative cooling function with decreasing gas temperature causes a radiative instability which may temporarily lead to a coexistence of cool molecule-rich and warm molecule-poor regions in the radiative relaxation zone