A review of action estimation methods for galactic dynamics

TL;DR

This review compares various methods for estimating orbital actions in galactic dynamics, introducing a new approach, and evaluates their accuracy and computational efficiency for different galactic components.

Contribution

The paper provides a comprehensive comparison of existing action estimation methods and introduces a novel method based on the adiabatic approximation.

Findings

St"ackel Fudge offers the best speed-accuracy balance for the Milky Way's disc and halo.

Orbit integration with generating functions is most accurate for stellar streams.

Non-convergent methods are less suitable for precise stream studies.

Abstract

We review the available methods for estimating actions, angles and frequencies of orbits in both axisymmetric and triaxial potentials. The methods are separated into two classes. Unless an orbit has been trapped by a resonance, convergent, or iterative, methods are able to recover the actions to arbitrarily high accuracy given sufficient computing time. Faster non-convergent methods rely on the potential being sufficiently close to a separable potential and the accuracy of the action estimate cannot be improved through further computation. We critically compare the accuracy of the methods and the required computation time for a range of orbits in an axisymmetric multi-component Galactic potential. We introduce a new method for estimating actions that builds on the adiabatic approximation of Sch\"onich & Binney (2012) and discuss the accuracy required for the actions, angles and frequencies using suitable distribution functions for the thin and thick discs, the stellar halo and a star stream. We conclude that for studies of the disc and smooth halo component of the Milky Way the most suitable compromise between speed and accuracy is the St\"ackel Fudge, whilst when studying streams the non-convergent methods do not offer sufficient accuracy and the most suitable method is computing the actions from an orbit integration via a generating function. All the software used in this study can be downloaded from https://github.com/jls713/tact.