Actions for axisymmetric potentials

TL;DR

This paper presents an efficient algorithm for calculating actions and angles in axisymmetric potentials, validated on Galactic models, with a scheme to accelerate observable computations from distribution functions.

Contribution

Introduces a novel, computationally efficient algorithm for actions and angles in axisymmetric potentials, including an interpolation scheme for faster observable calculations.

Findings

Errors in actions are typically below 2% for thick-disc star orbits.

The interpolation scheme significantly speeds up calculations of density and velocity moments.

The algorithm is validated on a realistic Galactic potential model.

Abstract

We give an algorithm for the economical calculation of angles and actions for stars in axisymmetric potentials. We test the algorithm by integrating orbits in a realistic model of the Galactic potential, and find that, even for orbits characteristic of thick-disc stars, the errors in the actions are typically smaller than 2 percent. We describe a scheme for obtaining actions by interpolation on tabulated values that significantly accelerates the process of calculating observables quantities, such as density and velocity moments, from a distribution function.