Ruling Out Chaos in Compact Binary Systems

We investigate the orbits of compact binary systems during the final inspiral stage before coalescence by integrating the post-Newtonian equations of motion. We include spin-orbit and spin-spin coupling, which, according to a recent study [J. Levin, Phys. Rev. Lett. 84, 3515 (2000)], may cause the orbits to appear chaotic. To examine this claim, we calculate the divergence of nearby trajectories and attempt to measure the Lyapunov exponent γ. For all systems considered, we find no chaotic behavior, placing a lower limit on the divergence time t_L≡1/γ that is many times greater than the typical inspiral time, suggesting that chaos should not adversely affect the detection of inspiral events.