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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

OnStationary,Self-SimilarDistributions

ofaCollisionless,Self-Gravitating,Gas

R.N.HenriksenandLawrenceM.Widrow

arXiv:astro-ph/9412047v1 14 Dec 1994DepartmentofPhysicsQueen’sUniversity,Kingston,CanadaDecember14,1994AbstractWestudysystematicallystationarysolutionstothecoupledVlasovandPoissonequa-tionswhichhave‘self-similar’orscalingsymmetryinphasespace.Inparticular,we ndanalyticallyallsphericallysymmetricdistributionfunctionswherethemassdensityandgravitationalpotentialarestrictpowerlawsinr,thedistancefromthesymmetrypoint.Wetreatasspecialcases,systemsbuiltfrompurelyradialorbitsandsystemsthatareisotropicinvelocityspace.Wethendiscusssystemswitharbitraryvelocityspaceanisotropy ndinganewandverygeneralclassofdistributionfunctions.Thesedistributionsmayproveusefulinmodellinggalaxies.Distributionfunctionsincylin-dricalandplanargeometriesarealsodiscussed.Finally,westudyspatiallyspheroidalsystemsthatagainexhibitstrictpower-lawbehaviourforthedensityandpotentialand

ndresultsinagreementwithresultspublishedrecently.

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