Combined effects of tidal and rotational distortions on the equilibrium configuration of low-mass, pre-main sequence stars

Context. In close binary systems, the axial rotation and the mutual tidal forces of the component stars deform each other and destroy their spherical symmetry by means of the respective disturbing potentials. Aims. We present new models for low-mass, pre-main sequence stars that include the combined distortion effects of tidal and rotational forces on the equilibrium configuration of stars. Using our theoretical results, we aim at investigating the effects of interaction between tides and rotation on the stellar structure and evolution. Methods. The Kippenhahn & Thomas (1970, in Stellar Rotation, ed. A. Slettebak) approximation, along with the Clairaut-Legendre expansion for the gravitational potential of a self-gravitating body, is used to take the effects of tidal and rotational distortions on the stellar configuration into account. Results. We obtained values of internal structure constants for low-mass, pre-main sequence stars from stellar evolutionary models that consider the combined effects of rotation and tidal forces due to a companion star. We also derived a new expression for the rotational inertia of a tidally and rotationally distorted star. Our values corresponding to standard models (with no distortions) are compatible with those available in literature. Our distorted models were successfully used to analyze the eclipsing binary system EK Cep, reproducing the stellar radii, effective temperature ratio, lithium depletion, rotational velocities, and the apsidal motion rate in the age interval of 15.5-16.7 Myr. Conclusions. In the low-mass range, the assumption that harmonics greater than j = 2 can be neglected seems not to be fully justified, although it is widely used when analyzing the apsidal motion of binary systems. The non-standard evolutionary tracks are cooler than the standard ones, mainly for low-mass stars. Distorted models predict more mass-concentrated stars at the zero-age main-sequence than standard models.