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 $\gamma$. For all systems considered, we find no chaotic behavior, placing a lower limit on the divergence time $t_{\mathrm{L}}\equiv 1/\gamma$ that is many times greater than the typical inspiral time, suggesting that chaos should not adversely affect the detection of inspiral events.