Chaotic Motion Around Stellar Objects with Octupolar Deformation: Newtonian and Post Newtonian Approaches

TL;DR

This study investigates how octupolar deformations and post-Newtonian corrections influence the regularity and chaos in test particle motion around stellar objects, revealing conditions under which chaos is suppressed or enhanced.

Contribution

It demonstrates the impact of octupolar deformation and relativistic corrections on the dynamical behavior of particles in gravitational fields, highlighting a transition to integrability at large perturbations.

Findings

Octupolar terms distort KAM curves and increase chaos in Newtonian gravity.

Post-Newtonian corrections generally preserve phase-space structure, but large multipoles can suppress chaos.

Large perturbations can make a non-integrable system effectively integrable.

Abstract

Regular and chaotic test particle motion in gravitational fields due to stellar bodies with quadrupolar and octupolar deformation are studied using Poincare surfaces of section. In first instance, we analyze the purely Newtonian case and we find that the octupolar term induces a distortion in the KAM curves corresponding to regular trajectories as well as an increase in chaoticity, even in the case corresponding to oblate deformation. Then we examine the effect of the first general relativistic corrections, provided by the post Newtonian approach. For typical values of the post Newtonian multipoles we find that the phase-space structure practically remains the same as in the classical case, whereas that for certain larger values of these multipoles the chaoticity vanishes. This important fact provides an interesting example of a situation where a non-integrable dynamical system becomes integrable through the introduction of a large perturbation.