Studies on stellar rotation: I. The theoretical apsidal motion for evolved rotating stars

The quasi-spherical approximation, with some modifications, was implemented in our stellar evolution code to take into account the effect of rotation on the internal structure of the stars and, in particular, on the apsidal motion constant. Three models with masses 2, 7 and 15 M⊙ were used since they are representative of the mass range where apsidal motion is detected in binary stars. We adopted two limiting cases of angular momentum redistribution: local conservation and rigid body rotation. It was found that the influence of rotation on internal structure depends strongly on the distortion of the configuration characterized by the parameter λ = 2v2/(3gR) at the surface of the model. Such results make the work of introducing the correction for rotation in the apsidal motion analysis an easier task since it is sufficient to decrease the theoretical log k2 by 0.87 λs.