Journal Article

Phase-space consistency of stellar dynamical models determined by separable augmented densities

J. An, E. Van Hese and M. Baes

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 422, issue 1, pages 652-664
Published in print May 2012 | ISSN: 0035-8711
Published online April 2012 | e-ISSN: 1365-2966 | DOI:
Phase-space consistency of stellar dynamical models determined by separable augmented densities

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Assuming the separable augmented density, it is always possible to construct a distribution function of a spherical population with any given density and anisotropy. We consider under what conditions the distribution constructed as such is in fact non-negative everywhere in the accessible phase space. We first generalize the known necessary conditions on the augmented density using fractional calculus. The condition on the radius part R(r2) (whose logarithmic derivative is the anisotropy parameter) is equivalent to the complete monotonicity of w−1R(w−1). The condition on the potential part on the other hand is given by its derivative up to any order not greater than being non-negative where β0 is the central anisotropy parameter. We also derive a specialized inversion formula for the distribution from the separable augmented density, which leads to sufficient conditions on separable augmented densities for the non-negativity of the distribution. These last conditions are generalizations of the similar condition derived earlier for the generalized Cuddeford system to arbitrary separable systems.

Keywords: methods: analytical; galaxies: kinematics and dynamics; dark matter

Journal Article.  8320 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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