Milking the spherical cow: on aspherical dynamics in spherical coordinates

TL;DR

This paper investigates the inaccuracies introduced by assuming spherical symmetry in modeling aspherical galaxy systems, showing that such assumptions can lead to misleading conclusions and proposing more accurate analysis methods.

Contribution

It provides a theoretical framework to quantify the impact of spherical symmetry assumptions on the dynamics of aspherical systems and highlights the limitations of idealized spherical models.

Findings

Spherical symmetry assumptions can misrepresent phase space density as ergodic.

Imposing isotropic velocity priors improves observational analysis accuracy.

Triaxial dark matter halos approach, but do not reach, the maximally-stable limit.

Abstract

Galaxies and the dark matter halos that host them are not spherically symmetric, yet spherical symmetry is a helpful simplifying approximation for idealised calculations and analysis of observational data. The assumption leads to an exact conservation of angular momentum for every particle, making the dynamics unrealistic. But how much does that inaccuracy matter in practice for analyses of stellar distribution functions, collisionless relaxation, or dark matter core-creation? We provide a general answer to this question for a wide class of aspherical systems; specifically, we consider distribution functions that are "maximally stable", i.e. that do not evolve at first order when external potentials (which arise from baryons, large scale tidal fields or infalling substructure) are applied. We show that a spherically-symmetric analysis of such systems gives rise to the false conclusion that the density of particles in phase space is ergodic (a function of energy alone). Using this idea we are able to demonstrate that: (a) observational analyses that falsely assume spherical symmetry are made more accurate by imposing a strong prior preference for near-isotropic velocity dispersions in the centre of spheroids; (b) numerical simulations that use an idealised spherically-symmetric setup can yield misleading results and should be avoided where possible; and (c) triaxial dark matter halos (formed in collisionless cosmological simulations) nearly attain our maximally-stable limit, but their evolution freezes out before reaching it.