A new method for the determination of action integrals in the study of galactic dynamics

TL;DR

This paper introduces a novel method for calculating action integrals in galactic dynamics that does not require prior knowledge of generating functions, using phase space data and fitting potentials with a Levenberg-Marquardt routine.

Contribution

The paper presents a new, general approach to determine actions in arbitrary potentials without needing specific generating functions, enhancing analysis of stellar orbits.

Findings

Method accurately recovers actions within 1% for test potentials.

Uses phase space points and potential fitting to compute actions.

Discusses error minimization and noise sources in data.

Abstract

Action-angle coordinates are an essential tool for understanding the properties of the six dimensional phase space involved in orbits of stars in galactic potentials. A new method, which does not require specific knowledge of a generating function, is described, implemented and tested that calculates the actions of an orbit in an arbitrary potential of an integrable Hamiltonian given a set of Cartesian phase space points. The method chooses between the simple harmonic oscillator and isochrone potentials to fit the data using a Levenberg-Marquardt routine. An average is taken over the angle coordinates by calculating volumes in phase space using the metric free FiEstAS algorithm. The perfect ellipsoidal potential, with actions chosen a priori, is used to test the output of the algorithm, giving some results that agree within 1%. Minimisation of a sampling error is discussed along with an identification of a source of noise in the data.