2015/02/25 by Andrew Pontzen, Justin I. Read, Justin Read +5
Physics and Astronomy · #Angular momentum #Astrophysics #Circular symmetry #Classical mechanics #Cosmology and Gravitation Theories #Dark Matter and Cosmic Phenomena #Dark matter #Galaxies: Formation, Evolution, Phenomena #Galaxy #Geometry #Isotropy #Physics #Quantum mechanics #Spherical geometry #astro-ph.CO #astro-ph.GA
paper · pdf · doi:10.1093/mnras/stv1032
published as MNRAS, 2015, 451: 1366-1379 · Submitted to MNRAS. Comments welcome
arxiv created 2015/02/25 · openalex publication_date 2015/06/04 · arxiv updated 2016/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Galaxies and the dark matter haloes that host them are not spherically symmetric, yet spherical symmetry is a helpful simplifying approximation for idealized 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 idealized spherically symmetric setup can yield misleading results and should be avoided where possible; and (c) triaxial dark matter haloes (formed in collisionless cosmological simulations) nearly attain our maximally stable limit, but their evolution freezes out before reaching it.