Thermal Bifurcations in the Circumstellar Envelopes of C-Stars

The energy balance of the gas in the extended atmospheres of carbon stars is investigated by detailed analysis of heating and cooling rates. We focus on the inner part of the circumstellar envelope (r / R_*~1...5), where the temperature structure is of crucial importance concerning the onset of dust formation and the generation of the wind. The investigations are performed on top of the results of a model calculation of Winters et al. providing the density-, dust- and radiation field conditions in a C-star envelope. At each radial point we vary the gas temperature between 200 K and 10000 K and calculate the radiative heating and cooling rates. We obtain the radiative equilibrium (RE) temperature, where the radiative gains and losses balance each other, and the relaxation time scale towards RE (cooling time scale) as function of radial distance and temperature. The calculations are based on a steady-state non-LTE description of the gas. For the neutral and singly ionized atoms we take into account several thousand fine-structure, forbidden and permitted line transitions and (in case of neutrals) bound-free transitions. The model atoms contain between 5 levels (HI) and 200 levels (FeI). The rotational and vibrational heating/cooling rates of 12 diatomic molecules are calculated including the first and second overtone transitions for CO and SiO. Further heating and cooling processes considered are H_2 quadrupole, H^- free-free and bound-free, H_2^- free-free, He^- free-free, C^- free-free and thermal accommodation on dust grain surfaces. The relevance of the different radiative processes under the various conditions is discussed. The gas is generally found to be substantially cooler than a black body in RE which possibly allows for dust formation to occur closer to the star than usually assumed. The radiative relaxation of the gas in response to traveling shock waves is discussed. Furthermore, we explore the possibility of thermal bifurcations to occur in these envelopes, where cold molecule-rich gas phases may coexist besides warm molecule-poor phases, both in stable RE and in pressure balance with each other. Such a multi-stable behavior of the condition of RE might be related to dust cloud formation.