Milking the spherical cow - on aspherical dynamics in spherical coordinates

Andrew Pontzen, Justin I. Read, Romain Teyssier, Fabio Governato, Alessia Gualandris, Nina Roth, Julien Devriendt

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1366-1379
Number of pages14
JournalMonthly Notices of the Royal Astronomical Society
Issue number2
StatePublished - May 1 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Galaxies: evolution
  • Galaxies: formation
  • Galaxies: haloes


Dive into the research topics of 'Milking the spherical cow - on aspherical dynamics in spherical coordinates'. Together they form a unique fingerprint.

Cite this