Self-consistent dynamical models with a finite extent -- II. Radially truncated models

TL;DR

This paper explores the construction of finite-extent spherical dynamical models with preset density profiles, finding that models with discontinuous truncation are unsupported by ergodic orbits, but tangential orbital structures can support certain truncated models.

Contribution

It demonstrates that radially truncated models with discontinuous density are unsupported by ergodic orbits, and proposes tangential Osipkov-Merritt orbital structures as a solution.

Findings

Discontinuous density truncations cannot be supported by ergodic orbital structures.

Tangential Osipkov-Merritt models can support radially truncated density profiles.

Numerical exploration confirms the viability of tangential orbital structures for finite models.

Abstract

Galaxies, dark matter haloes, and star clusters have a finite extent, yet most simple dynamical models have an infinite extent. The default method to generate dynamical models with a finite extent is to apply an energy truncation to the distribution function, but this approach is not suited to construct models with a preset density profile and it imposes unphysical constraints on the orbit population. We investigate whether it is possible to construct simple dynamical models for spherical systems with a preset density profile with a finite extent, and ideally with a different range of orbital structures. We systematically investigate the consistency of radially truncated dynamical models, and demonstrate that no spherical models with a discontinuous density truncation can be supported by an ergodic orbital structure. On the other hand, we argue that many radially truncated models can be supported by a tangential Osipkov-Merritt orbital structure that becomes completely tangential at the truncation radius. We formulate a consistency hypothesis for radially truncated models with such an orbital structure, and test it using an analytical example and the numerical exploration of a large model parameter space using the SpheCow code. We physically interpret our results in terms of the occupancy of bound orbits, and we discuss possible extensions of the tangential Osipkov-Merritt orbital structure that can support radially truncated models.