2007MNRAS.382....2R

We apply the Delaunay Tessellation Field Estimator (DTFE) to reconstruct and analyse the matter distribution and cosmic velocity flows in the local Universe on the basis of the PSCz galaxy survey. The prime objective of this study is the production of optimal resolution 3D maps of the volume-weighted velocity and density fields throughout the nearby universe, the basis for a detailed study of the structure and dynamics of the cosmic web at each level probed by underlying galaxy sample. Fully volume-covering 3D maps of the density and (volume-weighted) velocity fields in the cosmic vicinity, out to a distance of 150h^–1Mpc, are presented. Based on the Voronoi and Delaunay tessellation defined by the spatial galaxy sample, DTFE involves the estimate of density values on the basis of the volume of the related Delaunay tetrahedra and the subsequent use of the Delaunay tessellation as natural multidimensional (linear) interpolation grid for the corresponding density and velocity fields throughout the sample volume. The linearized model of the spatial galaxy distribution and the corresponding peculiar velocities of the PSCz galaxy sample, produced by Branchini et al., forms the input sample for the DTFE study. The DTFE maps reproduce the high-density supercluster regions in optimal detail, both their internal structure as well as their elongated or flattened shape. The corresponding velocity flows trace the bulk and shear flows marking the region extending from the Pisces-Perseus supercluster, via the Local Superclusters, towards the Hydra-Centaurus and the Shapley concentration. The most outstanding and unique feature of the DTFE maps is the sharply defined radial outflow regions in and around underdense voids, marking the dynamical importance of voids in the local Universe. The maximum expansion rate of voids defines a sharp cut-off in the DTFE velocity divergence probability distribution function. We found that on the basis of this cut-off DTFE manages to consistently reproduce the value of Ω_m~ 0.35 underlying the linearized velocity data set.