Phase-space structures I: A comparison of 6D density estimators

Abstract

This paper reviews and analyses methods used to identify neighbours in 6D space and estimate the corresponding phase-space density. It compares SPH methods to 6D Delaunay tessellation on statical and dynamical realisation of single halo profiles, paying attention to the unknown scaling, S_G, used to relate the spatial dimensions to the velocity dimensions. The methods with local adaptive metric provide the best phase-space estimators. They make use of a Shannon entropy criterion combined with a binary tree partitioning and with SPH interpolation using 10-40 neighbours. Local scaling implemented by such methods, which enforces local isotropy of the distribution function, can vary by about one order of magnitude in different regions within the system. It presents a bimodal distribution, in which one component is dominated by the main part of the halo and the other one is dominated by the substructures. While potentially better than SPH techniques, since it yields an optimal estimate of the local softening volume (and the local number of neighbours required to perform the interpolation), the Delaunay tessellation in fact poorly estimates the phase-space distribution function. Indeed, it requires, the choice of a global scaling S_G. We propose two methods to estimate S_G that yield a good global compromise. However, the Delaunay interpolation still remains quite sensitive to local anisotropies in the distribution. We also compare 6D phase-space density estimation with the proxy, Q=rho/sigma^3, where rho is the local density and 3 sigma^2 is the local 3D velocity dispersion. We show that Q only corresponds to a rough approximation of the true phase-space density, and is not able to capture all the details of the distribution in phase-space, ignoring, in particular, filamentation and tidal streams.

Submitted to MNRAS, 22 pages, 18 figures

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• Evolution of the Dark Matter Phase-Space Density Distributions of LCDM Halos
• Non--power law behavior of the radial profile of phase--space density of halos
• Bound and unbound substructures in Galaxy-scale Dark Matter haloes
• A Two-Point Correlation Function For Galactic Halo Stars
• Estimating multidimensional probability fields using the Field Estimator for Arbitrary Spaces (FiEstAS) with applications to astrophysics
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• Voronoi Tessellation and Non-parametric Halo Concentration
• Dirichlet process mixtures under affine transformations of the data
• A Data-Driven Statistical Description for the Hydrodynamics of Active Matter
• The Non-universal Pseudo Phase-Space Density Profiles of Symphony Host Halos