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.

21 pages, 5 figures. To appear in Journal of Physics A

References in corpus (4)

• Measurement of Relativistic Orbital Decay in the PSR B1534+12 Binary System
• Dynamical Friction and Resonance Trapping in Planetary Systems
• Millisecond and Binary Pulsars as Nature's Frequency Standards. II. Effects of Low-Frequency Timing Noise on Residuals and Measured Parameters
• Chaos in the Kepler System

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• Partial Averaging and Resonance Trapping in a Restricted Three-Body System
• Resonance Behavior and Partial Averaging in a Three-Body System with Gravitational Radiation Damping
• Resonant Locking Between Binary Systems Induced by Gravitational Waves