Spherically Symmetric Model Atmospheres for Late  Giant Stars
Abstract
The ATHENA computer code has been developed to model the extended atmospheres of latetype giant and supergiant stars. The atmospheres are assumed to be static, spherically symmetric and in radiative and hydrostatic equilibrium. Molecular line blanketing (for now) is handled using the simplifying assumption of mean opacity. The complete linearization method of Auer and Mihalas (7), adapted to spherical geometry, is used to solve the model system. The radiative transfer is solved by using variable Eddington factors to close the system of moment transfer equations, and the entire system of transfer equations plus constraints is solved efficiently by arrangement into the Rybicki (83) block matrix form. The variable Eddington factors are calculated from the full angledependent formal solution of the radiative transfer problem using the impact parameter method of Hummer, Kunasz (47). We were guided by the work of Mihalas and Hummer (72) in their development of extended models of O stars, but our method differs in the choice of the independent variable. The radius depth scale used by Mihals and Hummer was found to fail because of the strongly temperaturedependent opacities of latetype atmospheres. Instead, we were able to achieve an exact linearization of the radius. This permitted the use of the numerically wellbehaved column mass or optical depth scales. The resulting formulation is analogous to the planeparallel complete linearization method and reduces to this method in the compact atmosphere limit. Models of M giants were calculated for T _{eff} = 3000K and 3500K with opacities of the CN, TiO and H_2O molecules included, and the results were in general agreement with other published spherical models. These models were calculated assuming radiative equilibrium. The importance of convective energy transport was estimated by calculating the convective flux that would result from the temperature structure of the models. The standard local mixing length theory was used for this purpose. Convection was found to be important only at depths with tau_{RM}>15 for the low gravity models with log g=0 , but significant out to tau_ {RM}~ 1 at the most transparent frequencies for the higher gravity models with log g=2 . Thus, the temperature structure of the surface layers and the emergent flux for the log g=0 models should be accurately modelled but the emergent flux for the log g=2 models may be in error by up to 5% at the most transparent frequencies.
 Publication:

Ph.D. Thesis
 Pub Date:
 1991
 Bibcode:
 1991PhDT........14B
 Keywords:

 STELLAR ATMOSPHERES;
 Physics: Astronomy and Astrophysics;
 Atmospheric Models;
 Convective Heat Transfer;
 Late Stars;
 Radiative Heat Transfer;
 Stellar Atmospheres;
 Stellar Models;
 Supergiant Stars;
 Atmospheric Temperature;
 Mixing Length Flow Theory;
 Temperature Dependence;
 Astrophysics