ASYMPTOTIC REPRESENTATION OF LOW-FREQUENCY DYNAMIC TIDES IN CLOSE BINARIES

An asymptotic representation of low-frequency dynamic tides in close b inaries is developed. The dynamic tides are treated as low-frequency, linear, isentropic, forced oscillations of a non-rotating spherically symmetric star. The asymptotic representation is developed to the seco nd order in the forcing frequency. For the sake of simplification, the star is assumed to be everywhere in radiative equilibrium. As asympto tic approximation of order zero, the divergence-free static tide of wh ich the radial component is solution of Clairaut's equation, is adopte d. In the asymptotic approximation of order two, the oscillatory prope rties of the star play a role. The asymptotic solutions are constructe d by means of a two-variable expansion procedure. The regions near the star's centre and surface are treated as boundary layers. The Euleria n perturbation of the gravitational potential caused by the star's tid al distortion is incorporated in the asymptotic treatment. An expressi on for that perturbation at the star's surface is derived to the secon d-order approximation. The expression is determined by the non-oscilla tory parts of the asymptotic solutions valid near the star's surface.