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




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Abstract: This paper reviews and analyses methods used to identify neighbours in 6Dspace and estimate the corresponding phase-space density. It compares SPHmethods to 6D Delaunay tessellation on statical and dynamical realisation ofsingle halo profiles, paying attention to the unknown scaling, S G, used torelate the spatial dimensions to the velocity dimensions. The methods withlocal adaptive metric provide the best phase-space estimators. They make use ofa Shannon entropy criterion combined with a binary tree partitioning and withSPH interpolation using 10-40 neighbours. Local scaling implemented by suchmethods, which enforces local isotropy of the distribution function, can varyby about one order of magnitude in different regions within the system. Itpresents a bimodal distribution, in which one component is dominated by themain part of the halo and the other one is dominated by the substructures.While potentially better than SPH techniques, since it yields an optimalestimate of the local softening volume and the local number of neighboursrequired to perform the interpolation, the Delaunay tessellation in factpoorly 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 thatyield a good global compromise. However, the Delaunay interpolation stillremains quite sensitive to local anisotropies in the distribution. We alsocompare 6D phase-space density estimation with the proxy, Q=rho-sigma^3, whererho is the local density and 3 sigma^2 is the local 3D velocity dispersion. Weshow that Q only corresponds to a rough approximation of the true phase-spacedensity, and is not able to capture all the details of the distribution inphase-space, ignoring, in particular, filamentation and tidal streams.



Author: M. Maciejewski, S. Colombi, C. Alard, F. Bouchet, C. Pichon

Source: https://arxiv.org/







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