A fast algorithm for estimating actions in triaxial potentials

TL;DR

This paper introduces a rapid approximation method for calculating actions in triaxial potentials, extending previous axisymmetric techniques, with applications in galaxy modeling despite some accuracy trade-offs.

Contribution

The paper develops a new fast algorithm for estimating actions in triaxial potentials by locally approximating the potential with Stäckel potentials, enabling efficient modeling of galaxy systems.

Findings

The method provides quick action estimates with acceptable accuracy for certain applications.

It can recover observable properties of triaxial systems sufficiently well for Jeans modeling.

Combining with torus mapping improves accuracy for detailed studies.

Abstract

We present an approach to approximating rapidly the actions in a general triaxial potential. The method is an extension of the axisymmetric approach presented by Binney (2012), and operates by assuming that the true potential is locally sufficiently close to some St\"ackel potential. The choice of St\"ackel potential and associated ellipsoidal coordinates is tailored to each individual input phase-space point. We investigate the accuracy of the method when computing actions in a triaxial Navarro-Frenk-White potential. The speed of the algorithm comes at the expense of large errors in the actions, particularly for the box orbits. However, we show that the method can be used to recover the observables of triaxial systems from given distribution functions to sufficient accuracy for the Jeans equations to be satisfied. Consequently, such models could be used to build models of external galaxies as well as triaxial components of our own Galaxy. When more accurate actions are required, this procedure can be combined with torus mapping to produce a fast convergent scheme for action estimation.