Astronomy and Astrophysics – Astrophysics – Cosmology and Extragalactic Astrophysics
Scientific paper
2011-03-31
The Astrophysical Journal, 736, 151 (2011)
Astronomy and Astrophysics
Astrophysics
Cosmology and Extragalactic Astrophysics
accepted version for the publication in ApJ; title changed adopting the referee's suggestion
Scientific paper
10.1088/0004-637X/736/2/151
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.
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