Models for spherical stellar systems with isotropic cores and anisotropic haloes

Statistics – Applications

Scientific paper

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Astronomical Models, Celestial Mechanics, Stellar Orbits, Stellar Systems, Anisotropic Media, Cores, Distribution Functions, Halos

Scientific paper

We discuss one particular class of anisotropic distribution functions for spherical stellar systems. These are separable functions of the binding energy epsilon is identical to psi(r)-v-squared/2, where the positive potential psi(r) is defined to be zero at the outer boundary, and the dimensionless quantity kappa is identical to L-squared/2r-squared(a)epsilon, where L is the angular momentum and the parameter r(a) is the anisotropy radius. In general, these models have regular cores, are isotropic for r is much less than r(a), become increasingly anisotropic for r is much greater than r(a), and reach maximum, but finite, anisotropy at the outer boundary. We study in detail self-consistent models with distribution functions of the form f = epsilon exp (nu-3/2)(1 + kappa)mu. These models resemble isotropic polytropes in the inner parts and anisotropic polytropes in the outer parts. The three parameters nu, mu, and r(a) which determine the central concentration, the degree of anisotropy and the transition region, respectively, can be chosen arbitrarily within certain bounds. The density, velocity dispersions, anisotropy etc. can be worked out analytically and are separable functions of potential and radius. Some applications of these models are briefly discussed.

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