Orbital tori for non-axisymmetric galaxies

TL;DR

This paper develops a method using orbital tori to analyze the effects of non-axisymmetry, such as galactic bars, on stellar orbits, enabling detailed modeling of galaxy dynamics including resonances and velocity structures.

Contribution

It introduces an extension of the TorusModeller library to efficiently compute and manipulate non-axisymmetric orbital tori, including trapped and untrapped orbits, with applications to galactic dynamics.

Findings

Thick-disc orbits are as likely to be trapped as thin-disc orbits.

The method accurately recovers trapped and untrapped orbits.

The technique can model the velocity structure of the solar neighborhood for different bar pattern speeds.

Abstract

Our Galaxy's bar makes the Galaxy's potential distinctly non-axisymmetric. All orbits are affected by non-axisymmetry, and significant numbers are qualitatively changed by being trapped at a resonance with the bar. Orbital tori are used to compute these effects. Thick-disc orbits are no less likely to be trapped by corotation or a Lindblad resonance than thin-disc orbits. Perturbation theory is used to create non-axisymmetric orbital tori from standard axisymmetric tori, and both trapped and untrapped orbits are recovered to surprising accuracy. Code is added to the TorusModeller library that makes it as easy to manipulate non-axisymmetric tori as axisymmetric ones. The augmented TorusModeller is used to compute the velocity structure of the solar neighbourhood for bars of different pattern speeds and a simple action-based distribution function. The technique developed here can be applied to any non-axisymmetric potential that is stationary in a rotating from - hence also to classical spiral structure.