Affordable Access

deepdyve-link deepdyve-link
Publisher Website

On Stationary, Self-Similar Distributions of a Collisionless, Self-Gravitating, Gas

Authors
Type
Preprint
Publication Date
Submission Date
Identifiers
DOI: 10.1093/mnras/276.2.679
arXiv ID: astro-ph/9412047
Source
arXiv
License
Unknown
External links

Abstract

We study systematically stationary solutions to the coupled Vlasov and Poisson equations which have `self-similar' or scaling symmetry in phase space. In particular, we find analytically {\it all} spherically symmetric distribution functions where the mass density and gravitational potential are strict power laws in $r$, the distance from the symmetry point. We treat as special cases, systems built from purely radial orbits and systems that are isotropic in velocity space. We then discuss systems with arbitrary velocity space anisotropy finding a new and very general class of distribution functions. These distributions may prove useful in modelling galaxies. Distribution functions in cylindrical and planar geometries are also discussed. Finally, we study spatially spheroidal systems that again exhibit strict power-law behaviour for the density and potential and find results in agreement with results published recently.

Statistics

Seen <100 times