Tidal perturbations of linear, isentropic oscillations in components of circular-orbit close binaries - II. Validity of the perturbation method applied to equilibrium tides

The paper is devoted to a verification of the validity of a first-order perturbation method that was developed in an earlier paper and allows one to determine the effects of an equilibrium tide on linear, isentropic oscillations of a component in a close binary. The verification is done by a comparison between results obtained by the perturbation method and results obtained in other ways, in the cases of two simple models: the compressible equilibrium sphere with uniform mass density and the polytropic model with index n = 3. In the first case, a comparison is made with second-harmonic oscillations in compressible Jeans spheroids with a small eccentricity, and in the second case, with results determined by Saio (1981) for a rotationally and tidally distorted polytrope. For the comparison, the second-harmonic oscillations of the incompressible and the compressible Jeans spheroids are redetermined by means of a method of direct integration of the governing equations which has the advantage of yielding exact analytical solutions of the eigenfrequency equations.