Ruling Out Chaos in Compact Binary Systems

Details Ruling Out Chaos in Compact Binary Systems Ruling Out Chaos in Compact Binary Systems

2001-07-25

arxiv.org/abs/gr-qc/0107082v1

Phys.Rev.Lett. 87 (2001) 121101

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages, 4 figures, submitted to Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.87.121101

We investigate the orbits of compact binary systems during the final inspiral period before coalescence by integrating numerically the second-order post-Newtonian equations of motion. We include spin-orbit and spin-spin coupling terms, which, according to a recent study by Levin [J. Levin, Phys. Rev. Lett. 84, 3515 (2000)], may cause the orbits to become chaotic. To examine this claim, we study the divergence of initially nearby phase-space trajectories and attempt to measure the Lyapunov exponent gamma. Even for systems with maximally spinning objects and large spin-orbit misalignment angles, we find no chaotic behavior. For all the systems we consider, we can place a strict lower limit on the divergence time t_L=1/gamma that is many times greater than the typical inspiral time, suggesting that chaos should not adversely affect the detection of inspiral events by upcoming gravitational-wave detectors.

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