A model of anisotropic winds from rotating stars for evolutionary calculations

Context: The surface properties of rotating stars can vary from pole to equator, resulting in anisotropic stellar winds which are not included in the currently available evolutionary models. Aims: We develop a formalism to describe the mass and angular momentum loss of rotating stars which takes into account both the varying surface properties and distortion due to rotation. Methods: Adopting the mass-loss recipe for non-rotating stars, we assigned to each point on the surface of a rotating star an equivalent non-rotating star, for which the surface mass flux is given by the recipe. The global mass-loss and angular momentum loss rates are then given by integrating over the deformed stellar surface as appropriate. Evolutionary models were computed and our prescription is compared to the currently used simple mass-loss enhancement recipes for rotating stars. Results: We find that mass-loss rates are largely insensitive to rotation for models not affected by the bi-stability jump. For those affected by the bi-stability jump, the increase in mass-loss rates with respect to time is smoothed. As our prescription considers the variation of physical conditions over the stellar surface, the region affected by the bi-stability jump is able to grow gradually instead of the whole star suddenly being affected. Conclusion: We have provided an easy to implement and flexible, yet physically meaningful prescription for calculating mass and angular momentum loss rates of rotating stars in a one-dimensional stellar evolution code which compares favourably to more physically comprehensive models. The implementation of our scheme in the stellar evolution code MESA is available online: https://zenodo.org/record/7437006