Nonadiabatic resonant dynamic tides and orbital evolution in close binaries

This investigation is devoted to the effects of nonadiabatic resonant dynamic tides generated in a uniformly rotating stellar component of a close binary. The companion is considered to move in a fixed Keplerian orbit, and the effects of the centrifugal force and the Coriolis force are neglected. Semi-analytical solutions for the linear, nonadiabatic resonant dynamic tides are derived by means of a two-time variable expansion procedure. The solution at the lowest order of approximation consists of the resonantly excited oscillation mode and displays a phase shift with respect to the tide-generating potential. Expressions are established for the secular variations of the semi-major axis, the orbital eccentricity, and the star's angular velocity of rotation caused by the phase shift. The orders of magnitude of these secular variations are considerably larger than those derived earlier by Zahn (1977) for the limiting case of dynamic tides with small frequencies. For a 5 solar mass ZAMS star, an orbital eccentricity e = 0.5, and orbital periods in the range from 2 to 5 days, numerous resonances of dynamic tides with second-degree lower-order gravity modes are seen to induce secular variations of the semi-major axis, the orbital eccentricity, and the star's angular velocity of rotation with time scales shorter than the star's nuclear life time.