Managing resonant trapped orbits in our Galaxy

TL;DR

This paper investigates how resonant trapping affects the use of angle-action coordinates in galaxy models, showing that trapping mainly occurs in thick-disc and halo orbits and proposing methods to handle these trapped orbits in computational tools.

Contribution

It extends the Torus Mapper code to effectively manipulate resonantly trapped orbits, improving galaxy modeling accuracy.

Findings

Resonant trapping occurs mainly in thick-disc and halo orbits.

The impact of trapping on velocity space structure is generally small with proper weighting.

The extended TM code allows easier manipulation of trapped orbits.

Abstract

Galaxy modelling is greatly simplified by assuming the existence of a global system of angle-action coordinates. Unfortunately, global angle-action coordinates do not exist because some orbits become trapped by resonances, especially where the radial and vertical frequencies coincide. We show that in a realistic Galactic potential such trapping occurs only on thick-disc and halo orbits (speed relative to the guiding centre >~80 km/s). We explain how the Torus Mapper code (TM) behaves in regions of phase space in which orbits are resonantly trapped, and we extend TM so trapped orbits can be manipulated as easily as untrapped ones. The impact that the resonance has on the structure of velocity space depends on the weights assigned to trapped orbits. The impact is everywhere small if each trapped orbit is assigned the phase space density equal to the time average along the orbit of the DF for untrapped orbits. The impact could be significant with a different assignment of weights to trapped orbits.