Non-radial motion and the NFW profile
Résumé
The self-similar infall model (SSIM) is normally discussed in thecontext of radial orbits in spherical symmetry. However it is possibleto retain the spherical symmetry while permitting the particles tomove in Keplerian ellipses, each having the squared angular momentumpeculiar to their 'shell'. Thespherical 'shell', defined for example by the particles turning at a given radius, thenmoves according to the radial equation of motion of a 'shell'particle. The 'shell' itself has no physical existence except as an ensemble of particles, but it is convenient to sometimes refer to the shellssince it is they that are followed by a shell code.In this note we find the distribution of squared angular momentum as afunction of radius that yields the NFW density profile for the finaldark matter halo. It transpires that this distribution is amply motivated dimensionally. An effective 'lambda' spinparameter is roughly constant over the shells. We also study the effectsof angular momentum on the relaxation of a dark matter system using a three dimensional representation of the relaxed phase space.
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