Abstract
We investigate the ability of three reconstruction techniques to analyze and investigate weblike features and geometries in a discrete distribution of objects. The three methods are the linear Delaunay Tessellation Field Estimator (DTFE), its higher order equivalent Natural Neighbour Field Estimator (NNFE) and a version of Kriging interpolation adapted to the specific circumstances encountered in galaxy redshift surveys, the Natural Lognormal Kriging technique. DTFE and NNFE are based on the local geometry defined by the Voronoi and Delaunay tessellations of the galaxy distribution. The three reconstruction methods are analysed and compared using mock magnitude-limited and volume-limited SDSS redshift surveys, obtained on the basis of the Millennium simulation. We investigate error trends, biases and the topological structure of the resulting fields, concentrating on the void population identified by the Watershed Void Finder. Environmental effects are addressed by evaluating the density fields on a range of Gaussian filter scales. Comparison with the void population in the original simulation yields the fraction of false void mergers and false void splits. In most tests DTFE, NNFE and Kriging have largely similar density and topology error behaviour. Cosmetically, higher order NNFE and Kriging methods produce more visually appealing reconstructions. Quantitatively, however, DTFE performs better, even while computationally far less demanding. A successful recovery of the void population on small scales appears to be difficult, while the void recovery rate improves significantly on scales > 3 h-1Mpc. A study of small scale voids and the void galaxy population should therefore be restricted to the local Universe, out to at most 100 h-1Mpc.
Highlights
Over the past 30 yr, a clear paradigm has emerged as large redshift surveys opened the window on to the distribution of matter in our Local Universe: galaxies, intergalactic gas and dark matter exist in a wispy web-like spatial arrangement consisting of dense compactC 2011 The Authors Monthly Notices of the Royal Astronomical Society C 2011 RASSky Survey (SDSS) and the two-micron all-sky survey redshift surveys (Colless et al 2003; Tegmark et al 2004; Huchra et al 2005).According to the standard lore of structure formation, structures emerged from small perturbations in the primordial field of Gaussian density and velocity perturbations
It involves a systematic program in which we explore the cosmography of the Local Universe, assess the statistical characteristics of the density field, identify and categorize the voids and filaments within the Sloan Digital Sky Survey (SDSS) galaxy redshift sample, and study the biasing of the galaxy population with respect to the mass distribution and the dependence of galaxy properties on the large-scale environment
By means of an extensive comparison we evaluate which aspects of the density field are best reproduced by either Delaunay Tessellation Field Estimator (DTFE), Natural Neighbour Field Estimator (NNFE) or Natural Lognormal Kriging, and which of these methods is best suited to function for further structural analysis
Summary
Over the past 30 yr, a clear paradigm has emerged as large redshift surveys opened the window on to the distribution of matter in our Local Universe: galaxies, intergalactic gas and dark matter exist in a wispy web-like spatial arrangement consisting of dense compact. Prominent probes are the clustering of galaxies, which has been used to infer the underlying primordial power spectrum of density fluctuations (Peebles 1980; Percival et al 2001; Tegmark et al 2004), the temperature and polarization anisotropies in the cosmic microwave background (e.g. Smoot et al 1992; Spergel et al 2003) and the shearing of galaxy images by the gravitationally lensed photon paths through the inhomogeneous matter distribution (Mellier 1999; Massey et al 2007; Hoekstra & Jain 2008) While these (quasi-)linear cosmological probes have yielded an impressive amount of cosmological information, the exploitation of the pronounced non-linear patterns of the Cosmic Web towards probing cosmological parameters and cosmic structure formation has been less fortuitous. Even though survey limits and scales are different from that of the SDSS, it will be straightforward to carry over the results to other redshift surveys
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