Phase-Space Structure & Substructure of Dark Halos
  A method is presented for computing the 6-D phase-space density f(x,v) and its PDF v(f) in an N-body system. It is based on Delaunay tessellation, yielding v(f) with a fixed smoothing window over a wide f range, independent of the sampling resolution. It is found that in a gravitationally relaxed halo built by hierarchical clustering, v(f) is a robust power law, v(f) f^{-2.5 \pm 0.05}, over more than 4 decades in f, from its virial level to the current resolution limit. This is valid for halos of different sizes in the LCDM cosmology, indicating insensitivity to the initial-fluctuation power spectrum as long as the small-scale fluctuations were not completely suppressed. By mapping f in position space, we find that the high-f contributions to v(f) come from the "cold" subhalos within the parent halo rather than the halo central region and its global spherical profile. The f in subhalos near the halo virial radius is more than 100 times higher than at the halo center, and it decreases gradually with decreasing radius. This indicates phase mixing due to mergers and tidal effects involving puffing up and heating. The phase-space structure provides a sensitive tool for studying the evolution of subhalos during the buildup of halos. One wishes to understand why the substructure adds up to the universal power law in v(f). It seems that the f^{-2.5} behavior is related to the hierarchical clustering process and is not a general result of violent relaxation. 
Avishai Dekel & Itai Arad