Constraints on velocity anisotropy of spherical systems with separable
  augmented densities
  If the augmented density of a spherical anisotropic system is assumed to be
multiplicatively separable to functions of the potential and the radius, the
radial function, which can be completely specified by the behavior of the
anisotropy parameter alone, also fixes the anisotropic ratios of every
higher-order velocity moment. It is inferred from this that the non-negativity
of the distribution function necessarily limits the allowed behaviors of the
radial function. This restriction is translated into the constraints on the
behavior of the anisotropy parameter. We find that not all radial variations of
the anisotropy parameter satisfy these constraints and thus that there exist
anisotropy profiles that cannot be consistent with any separable augmented
density.
