Journal Article

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

M. Maciejewski, S. Colombi, C. Alard, F. Bouchet and C. Pichon

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 393, issue 3, pages 703-722
Published in print March 2009 | ISSN: 0035-8711
Published online February 2009 | e-ISSN: 1365-2966 | DOI:
Phase-space structures – I. A comparison of 6D density estimators

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In the framework of particle-based Vlasov systems, this paper reviews and analyses different methods recently proposed in the literature to identify neighbours in 6D space and estimate the corresponding phase-space density. Specifically, it compares smoothed particle hydrodynamics (SPH) methods based on tree partitioning to 6D Delaunay tessellation. This comparison is carried out on statistical and dynamical realizations of single halo profiles, paying particular attention to the unknown scaling, SG, used to relate the spatial dimensions to the velocity dimensions.

It is found that, in practice, 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 subsequent SPH interpolation using 10–40 nearest neighbours. We note that the local scaling SG 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 of the halo.

While potentially better than SPH techniques, since it yields an optimal estimate of the local softening volume (and therefore the local number of neighbours required to perform the interpolation), the Delaunay tessellation in fact generally poorly estimates the phase-space distribution function. Indeed, it requires, prior to its implementation, the choice of a global scaling SG. We propose two simple but efficient methods to estimate SG that yield a good global compromise. However, the Delaunay interpolation still remains quite sensitive to local anisotropies in the distribution.

To emphasize the advantages of 6D analysis versus traditional 3D analysis, we also compare realistic 6D phase-space density estimation with the proxy proposed earlier in the literature, Q=ρ/σ3, where ρ is the local 3D (projected) density and 3σ2 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.

Keywords: methods: data analysis; methods: numerical; galaxies: haloes; galaxies: structure; dark matter

Journal Article.  13796 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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