Sustained resonance: a binary system perturbed by gravitational radiation

The general phenomena associated with sustained resonance are studied in th is paper in connection with relativistic binary pulsars. We represent such a system by two point masses in a Keplerian binary system that evolves via gravitational radiation damping as well as an external tidal perturbation. For further simplification, we assume that the external tidal perturbation is caused by a normally incident circularly polarized monochromatic gravita tional wave. In this case, the second-order partially averaged equations ar e studied and a theorem of C Robinson is employed to prove that for certain values of the physical parameters resonance capture followed by sustained resonance is possible in the averaged system. We conjecture that sustained resonance can occur in the physical system when the perturbing influences n early balance each other.