Combined stellar structure and atmosphere models for massive stars: Wolf-Rayet models with spherically outflowing envelopes
We present a simple analytical method to describe the structure of a spherically expanding envelope with strong mass outflow. The structure is consistently connected to the hydrostatic stellar interior and provides an adequate description of the outer boundary conditions for stellar models with large mass loss rates. We apply our treatment to evolutionary models of Wolf-Rayet (WR) stars in order to study the possible influence of the stellar winds on the interior, and to determine more reliable radii of WR stars. The interior structure and evolution of WR stars is found to be unaffected by the outer layers. For hydrogen rich WR stars (WNL) we find the existence of a temperature domain in the HR-diagram, where a transient concentration of stars on their blueward track is predicted in case of a strong backwarming from the wind. For WNE and WC/WO stars we also derive subphotospheric radii corresponding to Rosseland optical depths of ~ 10-20. With respect to wind-free stellar models the subphotospheric radii are increased by up to a factor of ~ 4 for the most luminous WNE or WC stars. These radii and the corresponding effective temperatures should roughly be comparable with the stellar parameters of non-LTE atmosphere models of WR stars. Comparisons using the newly derived radii yield a better agreement with observations. The stellar parameters obtained with the new treatment allow a better assignment of theoretical spectra to evolutionary tracks of evolved WR stars. This also provides the base for future studies of the spectral evolution of post-MS massive stars and their descendants. We also point out the possible importance of the iron opacity peak for the acceleration of WR winds in the optically thick part, which may be essential for the understanding of the dynamics of WR winds.