Reflection symmetries of Isolated Self-consistent Stellar Systems

Abstract

Isolated, steady-state galaxies correspond to equilibrium solutions of the Poisson--Vlasov system. We show that (i) all galaxies with a distribution function depending on energy alone must be spherically symmetric and (ii) all axisymmetric galaxies with a distribution function depending on energy and the angular momentum component parallel to the symmetry axis must also be reflection-symmetric about the plane $z=0$. The former result is Lichtenstein's Theorem, derived here by a method exploiting symmetries of solutions of elliptic partial differential equations, while the latter result is new. These results are subsumed into the Symmetry Theorem, which specifies how the symmetries of the distribution function in configuration or velocity space can control the planes of reflection symmetries of the ensuing stellar system.

arXiv commentMNRAS, in press

Cited by in corpus (4)

• Charting Galactic Accelerations: When and How to Extract a Unique Potential from the Distribution Function
• Applying Noether's theorem to matter in the Milky Way: evidence for external perturbations and non-steady-state effects from Gaia Data Release 2
• Two-point correlation function studies for the Milky Way: discovery of spatial clustering from disk excitations and substructure
• A Wave-Corrected Assessment of the Local Midplane