Linear and nonlinear pulsation models with the variable Eddington factor approximation of radiative hydrodynamics

Context. Linear and also nonlinear pulsation models with the variable Eddington factor approximation of the radiative transfer are constructed. Aims. The aim of the study is to apply hydrodynamic models of radial pulsation to the observed variability in some post-AGB stars. It has been shown that the pulsation behavior could be strongly effected by the radiative field of the envelope of these stars because of high luminosity in these low mass supergiant stars. Thus, it is important to treat the radiative field with a higher approximation than the diffusion approximation which has been used successfully in classical Cepheids. Methods. The moment equations of radiative transfer are integrated into the hydrodynamic equations with a variable Eddington factor. The factor is calculated independently by solving the transfer equation of spherical geometry. The linear eigen value problem of the radial perturbation from hydrostatic equilibrium is solved, and nonlinear simulations of radial pulsation are performed with the same approximation of the radiative transfer. The method is applied to pulsation of low mass supergiant stars and, for comparison, classical Cepheids. Results. The properties of the strange modes that appear often in low mass supergiant star models e.g. post-AGB stars are seriously affected by different treatments of the radiative field in the linear analyses and nonlinear simulations