Tidal resonances in binary star systems

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Abstract
The gravitational potential energy of tidal interactions in a binary system is formulated as a perturbation Hamiltonian which couples the normal mode oscillations of the stars with their orbital motion in a self-consistent way. The stellar oscillations are treated in the linear approximation for a non-rotating star. In order to examine resonances between normal mode oscillations and orbital motion, the Hamiltonian is transformed to action-angle variables of the zero-order problem. Approximate expressions are derived for the case of small orbital eccentricities and a pair of dominant stellar eigenmodes, characterized by a single value of the azimuthal index m. The positions of exact resonance and motion in the vicinity of resonance is derived. Numerical integration is performed on the tidal capture of two stars, using the self-consistent treatment. Angular momentum transferred to the stars as a result of tidal interactions is sufficiently large to invalidate the assumption (Press & Teukolsky) that the stars’ rotation can be ignored.

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