RESONANT DYNAMIC TIDES AND APSIDAL MOTION IN CLOSE BINARIES

The resonance of a dynamic tide with a free oscillation mode in a comp onent of a close binary system of stars is treated by means of a two-t ime variable expansion procedure. The treatment is developed with resp ect to a frame of reference corotating with the star. Both the free os cillation mode and the dynamic tide are considered as linear, isentrop ic perturbations of a spherically symmetric star. At the lowest order of approximation in the small expansion parameter, the resonant dynami c tide corresponds to the tidally excited oscillation mode. Furthermor e, the effect of the resonance on the secular apsidal motion is determ ined. A resonant dynamic tide can contribute to a much larger secular apsidal motion than the static tide and the non-resonant dynamic tides of the same degree can do. The contribution can be oriented in the se nse opposite to the orbital motion as well as in the same sense. From numerical applications to polytropic models, it appears that especiall y resonances of dynamic tides with an f-mode or a lower-order g(+)-mod e bring about larger apsidal motions. In this context, the determinati on of the contributions to the secular apsidal motion stemming from th e static tides and the non-resonant dynamic tides is reviewed. Sterne' s theory (1939) for the effect of the tidal distortion on the apsidal motion in close binary stars, which is used as standard theory, is als o reconsidered. The theory is shown to rest on the consideration of no n-resonant, low-frequency dynamic tides taken in their lowest-order as ymptotic representation.