Open AccessOn stationary self-similar distributions of a collisionless self-gravitating gas
Author(s) -
R. N. Henriksen,
Lawrence M. Widrow
Publication year - 1995
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-8711
pISSN - 0035-8711
DOI - 10.1093/mnras/276.2.679
Subject(s) - physics , classical mechanics , gravitational potential , circular symmetry , symmetry (geometry) , isotropy , gravitation , distribution (mathematics) , power law , phase space , space (punctuation) , distribution function , mass distribution , poisson's equation , statistical physics , mathematical analysis , galaxy , quantum mechanics , geometry , linguistics , statistics , mathematics , philosophy
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
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