Resurvey of order and chaos in spinning compact binaries

TL;DR

This study uses the Lyapunov indicator to clarify chaos in spinning compact binaries, showing that chaos depends on complex parameter combinations rather than single factors, challenging previous assumptions.

Contribution

It applies a fast invariant Lyapunov indicator to resolve conflicting results about chaos in spinning binaries at second-order post-Newtonian approximation.

Findings

Chaos depends on complex parameter combinations.

No single parameter solely causes chaos.

Chaos is not solely dependent on mass ratio or spin alignment.

Abstract

This paper is mainly devoted to applying the invariant, fast, Lyapunov indicator to clarify some doubt regarding the apparently conflicting results of chaos in spinning compact binaries at the second-order post-Newtonian approximation of general relativity from previous literatures. It is shown with a number of examples that no single physical parameter or initial condition can be described as responsible for causing chaos, but a complicated combination of all parameters and initial conditions is responsible. In other words, a universal rule for the dependence of chaos on each parameter or initial condition cannot be found in general. Chaos does not depend only on the mass ratio, and the maximal spins do not necessarily bring the strongest effect of chaos. Additionally, chaos does not always become drastic when the initial spin vectors are nearly perpendicular to the orbital plane, and the alignment of spins cannot trigger chaos by itself.