We apply the Delaunay Tessellation Field Estimator (DTFE) to reconstruct and analyze 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 o
f optimal resolution three-dimensional maps fully volume-covering of the volume-weighted velocity and density fields throughout the nearby Universe, out to a distance of 150 Mpc/h. 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 theDelaunay 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 Brachini et al. (1999), 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 cutoff in the DTFE velocity divergence pdf. We found that on the basis of this cutoff DTFE manages to consistently reproduce the value of O_m ~ 0.35 underlying the linearized velocity dataset.
