Statistical mechanics of collisionless orbits. IV. Distribution of angular momentum

Abstract

It has been shown in previous work that DARKexp, which is a theoretically derived, maximum entropy, one shape parameter model for isotropic collisionless systems, provides very good fits to simulated and observed dark-matter halos. Specifically, it fits the energy distribution, N(E), and the density profiles, including the central cusp. Here, we extend DARKexp N(E) to include the distribution in angular momentum, L^2, for spherically symmetric systems. First, we argue, based on theoretical, semi-analytical, and simulation results, that while dark-matter halos are relaxed in energy, they are not nearly as relaxed in angular momentum, which precludes using maximum entropy to uniquely derive N(E,L^2). Instead, we require that when integrating N(E,L^2) over squared angular momenta one retrieves the DARKexp N(E). Starting with a general expression for N(E,L^2) we show how the distribution of particles in L^2 is related to the shape of the velocity distribution function, VDF, and velocity anisotropy profile, β(r). We then demonstrate that astrophysically realistic halos, as judged by the VDF shape and β(r), must have linear or convex distributions in L^2, for each separate energy bin. The distribution in energy of the most bound particles must be nearly flat, and become more tilted in favor of radial orbits for less bound particles. These results are consistent with numerical simulations and represent an important step towards deriving the full distribution function for spherically symmetric dark-matter halos.

17 pages, 10 figures, accepted to ApJ. The first three in this series are: Paper I: arXiv:1010.0265, Paper II: arXiv:1010.0266, Paper III: arXiv:1010.0267

References in corpus (9)

• CLASH-VLT: The mass, velocity-anisotropy, and pseudo-phase-space density profiles of the z=0.44 galaxy cluster MACS 1206.2-0847
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• The distribution function of dark matter in massive haloes
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• Secondary infall and dark matter haloes
• The nature of dark matter and the density profile and central behavior of relaxed halos
• Measurement of the dark matter velocity anisotropy in galaxy clusters
• Statistical mechanics of collisionless orbits. III. Comparison with N-body simulations
• Collisionless dynamics in Globular Clusters

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