Angle-action variables for orbits trapped at a Lindblad resonance

TL;DR

This paper develops a method using angle-action variables and torus mapping to accurately model orbits trapped at Lindblad resonances in the Galaxy, especially addressing issues with circular orbits where traditional pendulum models fail.

Contribution

It introduces a novel approach combining torus mapping with resonance analysis to model trapped orbits in realistic galactic potentials, improving over traditional pendulum models.

Findings

Outer Lindblad resonance orbits are quasiperiodic and well-fitted by torus mapping.

Inner Lindblad resonance orbits are chaotic but confined to small tori.

The method successfully models trapped orbits in a realistic Galaxy potential.

Abstract

The conventional approach to orbit trapping at Lindblad resonances via a pendulum equation fails when the parent of the trapped orbits is too circular. The problem is explained and resolved in the context of the Torus Mapper and a realistic Galaxy model. Tori are computed for orbits trapped at both the inner and outer Lindblad resonances of our Galaxy. At the outer Lindblad resonance, orbits are quasiperiodic and can be accurately fitted by torus mapping. At the inner Lindblad resonance, orbits are significantly chaotic although far from ergodic, and each orbit explores a small range of tori obtained by torus mapping.