Astronomy & astrophysics supplement series vol:104 issue:3 pages:401-427
A theory is developed for the passage through resonance of a dynamic tide with a free oscillation mode of a rapidly evolving star. The orbital motion of the companion is assumed to be Keplerian and to remain unchanged during the passage through resonance. Tides are treated as forced, linear, isentropic oscillations of a non-rotating star. A multiple-variable perturbation method is applied for the derivation of asymptotic expansions for the components of the tidal displacement before, during, and after the passage through resonance. As the small expansion parameter epsilon, the ratio of the orbital period to the time scale of the star's evolution is used. The amplitude of the tide is of the order epsilon-1/2 during the passage through resonance and remains of that order afterwards. At time of resonance, the tidal displacement displays a phase delay of 3pi/4 or pi/4 with respect to the tide-generating potential according as the frequency of the free oscillation mode increases or decreases due to the star's evolution. As an example, the passage through resonance of a dynamic tide with a free oscillation mode of a homologously contracting star is considered.