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Keywords:

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

ABSTRACT

This paper presents a set of new conditions on the augmented density of a spherical anisotropic system that is necessary for the underlying two-integral phase-space distribution function to be non-negative. In particular, it is shown that the partial derivatives of the Abel transformations of the augmented density must be non-negative. Applied for the separable augmented densities, this recovers the earlier result of Van Hese, Baes & Dejonghe.