Ruling Out Chaos in Compact Binary Systems

TL;DR

This study numerically investigates the orbital dynamics of compact binary systems during inspiral, finding no evidence of chaos even with high spins and misalignments, thus supporting reliable gravitational-wave detection.

Contribution

The paper provides the first comprehensive numerical analysis showing that chaos does not occur in realistic compact binary inspirals with spin effects.

Findings

No chaotic behavior observed in simulated systems.

Chaos divergence times exceed inspiral timescales.

Results support stable waveforms for gravitational-wave detection.

Abstract

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.