Structural Analysis of the SDSS Cosmic Web I.Nonlinear Density Field Reconstructions

TL;DR

This study compares three reconstruction techniques—DTFE, NNFE, and Kriging—for analyzing the cosmic web's structure in galaxy surveys, finding that DTFE offers better quantitative performance despite similar error behaviors to the others.

Contribution

The paper provides a comprehensive comparison of three density field reconstruction methods applied to SDSS data, highlighting DTFE's superior quantitative accuracy and computational efficiency.

Findings

DTFE outperforms NNFE and Kriging in quantitative density and topology accuracy.

Higher order NNFE and Kriging produce more visually appealing reconstructions.

Void recovery is effective on scales larger than 3 h-1Mpc, limiting small-scale void studies to the local Universe.

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.