Using binaries containing giants to constrain theories of stellar and tidal evolution

Aims. Investigations of stellar and tidal evolution of binary stars with giant components are rare. In this paper, we will investigate such features in three binary systems for which at least one component is a giant star. As some of these giants seem to be in the blue loop, it is an excellent opportunity to investigate the sensitivity of core overshooting on their location in the HR Diagram. We expect that these characteristics shall serve as an incentive to observers to investigate such kinds of binaries, increasing the accuracy of measurements and the number of systems to test the evolutionary models. Methods. Prior to performing the study of the circularization and synchronization levels, an analysis of the capability of our stellar evolutionary models to reproduce the observed masses, radii and effective temperatures is carried out. Next, the differential equations of tidal evolution are integrated and the corresponding critical times are compared with the inferred age of the system and with the observed eccentricity and rotational velocities (when available). Results. We have found good agreement between our stellar models and the astrophysical properties of η And, V2291 Oph and SZ Cen by adopting a moderate core overshooting amount ($\alpha_{\rm ov}$ = 0.20). Three mechanisms were used to try to explain the observed levels of circularization and synchronization: the hydrodynamical mechanism, turbulent dissipation and radiative damping. In the cases of η And and SZ Cen, for which the rotational velocities are available, by assuming solid body rotation for both stars of each system we have found that the theoretical ratio between the rotational velocities $V_{\rm rot A}/V_{\rm rot B}$ at the inferred ages are in good agreement with the observational ratios