Sustained resonance: a binary system perturbed by gravitational radiation

Abstract

The general phenomena associated with sustained resonance are studied in this 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 gravitational wave. In this case, the second-order partially averaged equations are 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 nearly balance each other.