Three-dimensional Identification and Reconstruction of Galaxy Systems within Deep Redshift Surveys

We have developed a new geometrical method for identifying and reconstructing a homogeneous and highly complete set of galaxy groups in the next generation of deep, flux-limited redshift surveys. Our method combines information from the three-dimensional Voronoi diagram and its dual, the Delaunay triangulation, to obtain group and cluster catalogs that are remarkably robust over wide ranges in redshift and degree of density enhancement. As free byproducts, this Voronoi-Delaunay method (VDM) provides a non-parametric measurement of the galaxy density around each object observed and a quantitative measure of the distribution of cosmological voids in the survey volume. In this paper, we describe the VDM algorithm in detail and test its effectiveness using a family of mock catalogs that simulate the DEEP2 Redshift Survey. We show that this survey will be quite suitable for optically selecting distant clusters at z ∼ 1 over a wide range of richness. Using the mock DEEP2 catalogs, we demonstrate that the VDM algorithm can be used to identify a homogeneous set of groups in a magnitude-limited sample (IAB ≤ 23.5) throughout the survey redshift window 0.7 < z < 1.2. The actual group membership can be effectively reconstructed even in the distorted redshift space environment for systems with line of sight velocity dispersion σlos greater than ≈ 200 km s. By applying the sampling rate and the instrument-imposed target selection biases expected for DEEP2, we show that we can construct a homogeneous sample of systems which reproduces major properties of the “real” cluster parent population down to ≈ 200 km s for systems with at least 5 members. In a ΛCDM cosmology this translates into an identification rate of ∼ 270 systems per square degree and a total of more than 1000 groups within the full DEEP2 survey volume. By comparing the galaxy cluster catalog derived from the mock DEEP2 observations to the underlying distribution of clusters found in real space with much fainter galaxies included (which should more closely trace mass in the cluster), we can assess completeness in velocity dispersion directly. We conclude that the recovered DEEP2 group and cluster sample should be statistically complete for σlos ∼> 400 km s . Finally, we argue that the reconstructed bivariate distribution of systems as a function of redshift and velocity dispersion reproduces with high fidelity the underlying real space distribution and can thus be used robustly to constrain cosmological parameters. Subject headings: galaxies: high-redshift – galaxies: clusters: general – cosmology: large–scale structure of the universe – methods: data analysis