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

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 {sup 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 {sup 2}). Instead, we require that when integrating N(E, L {sup 2}) over squared angular momenta one retrieves the DARKexp N(E). Starting with a general expression for N(E, L {sup 2}) we show how the distribution of particles in L {sup 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 {sup 2}, for each separate energy bin. The distribution in energy ofmore » 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 toward deriving the full distribution function for spherically symmetric dark matter halos.« less
Authors:
 [1] ; ;  [2]
  1. School of Physics and Astronomy, University of Minnesota, 116 Church Street SE, Minneapolis, MN 55455 (United States)
  2. Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, DK-2100 Copenhagen Ø (Denmark)
Publication Date:
OSTI Identifier:
22351376
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 783; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANGULAR MOMENTUM; ASTROPHYSICS; COMPUTERIZED SIMULATION; DENSITY; DISTRIBUTION; DISTRIBUTION FUNCTIONS; ENERGY SPECTRA; ENTROPY; GALAXIES; NONLUMINOUS MATTER; SPHERICAL CONFIGURATION; SYMMETRY