Models of violently relaxed galaxies

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Abstract
We investigate the properties of spherical self-gravitating models derived from two distribution functions that incorporate, in a crude way, the physics of violent relaxation. The first distribution function is identical to the one discussed by Stiavelli & Bertin, except for a change in the sign of the ‘temperature’, i.e. |$e^{-aE}\rightarrow e^{+aE}$|⁠. We show that these ‘negative temperature’ models provide a much better description of the end-state of violent relaxation than ‘positive temperature’ models. The second distribution function is similar to the first except for a different dependence on angular momentum. Both distribution functions yield single-parameter families of models with surface density profiles very similar to the Rl,A law. Furthermore, the central concentration of models in both families increases monotonically with the velocity anisotropy, as expected in systems that formed through cold collapse.

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