Torus mapper: a code for dynamical models of galaxies

TL;DR

The paper introduces the Torus Mapper software for galaxy dynamics, enabling precise orbital modeling through torus mapping, which improves over traditional methods by allowing accurate orbit predictions and phase space analysis.

Contribution

The paper presents a new software package that implements non-perturbative torus mapping for galaxy dynamics, offering a novel tool for orbital modeling and phase space analysis.

Findings

TM accurately constructs orbital tori with high precision.

TM effectively handles resonant trapping scenarios.

The software facilitates initial condition setup for N-body simulations.

Abstract

We present a freely downloadable software package for modelling the dynamics of galaxies, which we call the Torus Mapper (TM). The package is based around `torus mapping', which is a non-perturbative technique for creating orbital tori for specified values of the action integrals. Given an orbital torus and a star's position at a reference time, one can compute its position at any other time, no matter how remote. One can also compute the velocities with which the star will pass through any given point and the contribution it will make to the time-averaged density there. A system of angle-action coordinates for the given potential can be created by foliating phase space with orbital tori. Such a foliation is facilitated by the ability of TM to create tori by interpolating on a grid of tori. We summarise the advantages of using TM rather than a standard time-stepper to create orbits, and give segments of code that illustrate applications of TM in several contexts, including setting up initial conditions for an N-body simulation. We examine the precision of the orbital tori created by TM and the behaviour of the code when orbits become trapped by a resonance.