Phasespace structure of dark matter haloes: scaleinvariant probability density function driven by substructure
Abstract
We present a method for computing the sixdimensional coarsegrained phasespace density f(x, v) in an Nbody system, and derive its distribution function v(f). The method is based on Delaunay tessellation, where v(f) is obtained with an effective fixed smoothing window over a wide f range. The errors are estimated, and v(f) is found to be insensitive to the sampling resolution or the simulation technique. We find that in gravitationally relaxed haloes built by hierarchical clustering, v(f) is well approximated by a robust power law, v(f) ~f^{2.5+/0.05}, over more than four decades in f, from its virial level to the numerical resolution limit. This is tested to be valid in the Λ cold dark matter cosmology for haloes with masses 10^{9}10^{15} M_{solar}, indicating insensitivity to the slope of the initial fluctuation power spectrum. By mapping the phasespace density in position space, we find that the highf end of v(f) is dominated by the `cold' subhaloes rather than the parenthalo central region and its global spherical profile. The value of f in subhaloes near the virial radius is typically >100 times higher than its value at the halo centre, and it decreases gradually from the outside in toward its value at the halo centre. This seems to reflect phase mixing due to mergers and tidal effects involving puffing up and heating. The phasespace density can thus provide a sensitive tool for studying the evolution of subhaloes during the hierarchical buildup of haloes. It remains to be understood why the evolved substructure adds up to the actual universal power law of v(f) ~f^{5/2}. It seems that this behaviour results from the hierarchical clustering process and is not a general result of violent relaxation.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 September 2004
 DOI:
 10.1111/j.13652966.2004.08045.x
 arXiv:
 arXiv:astroph/0403135
 Bibcode:
 2004MNRAS.353...15A
 Keywords:

 galaxies: dwarf;
 galaxies: formation;
 galaxies: haloes;
 galaxies: kinematics and dynamics;
 cosmology: theory;
 dark matter;
 Astrophysics
 EPrint:
 16 pages, 11 figures, submitted to mnras