Motion around a Monopole + Ring system: I. Stability of Equatorial Circular Orbits vs Regularity of Three-dimensional Motion

TL;DR

This paper investigates the stability of equatorial circular orbits and the regularity of three-dimensional motion of test particles around a monopole with a surrounding ring, revealing a link between orbit stability and chaotic behavior.

Contribution

It introduces a method to analyze the stability of equatorial orbits and their relation to the regularity of 3D motion in a combined monopole-ring gravitational system.

Findings

Stable equatorial orbits correlate with regular 3D motion.

Unstable orbits tend to lead to chaotic trajectories.

System parameters significantly influence orbit stability and chaos.

Abstract

We study the motion of test particles around a center of attraction represented by a monopole (with and without spheroidal deformation) surrounded by a ring, given as a superposition of Morgan & Morgan discs. We deal with two kinds of bounded orbits: (i) Equatorial circular orbits and (ii) general three-dimensional orbits. The first case provides a method to perform a linear stability analysis of these structures by studying the behavior of vertical and epicyclic frequencies as functions of the mass ratio, the size of the ring and/or the quadrupolar deformation. In the second case, we study the influence of these parameters in the regularity or chaoticity of motion. We find that there is a close connection between linear stability (or unstability) of equatorial circular orbits and regularity (or chaoticity) of the three-dimensional motion.