Three-dimensional identification and reconstruction of galaxy systems within flux-limited redshift surveys

We have developed a new geometrical method for identifying and reconstructing a homogeneous and highly complete set of galaxy groups within 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 by-products, this Voronoi-Delaunay method (VDM) provides a nonparametric 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 Deep Extragalactic Evolutionary Probe (DEEP2) Redshift Survey, which should present at least as much challenge to cluster reconstruction methods as any other near future survey that is capable of resolving their velocity dispersions. Using these mock DEEP2 catalogs, we demonstrate that the VDM algorithm can be used to identify a homogeneous set of groups in a magnitude-limited sample throughout the survey redshift window 0.7<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 sigma(los) greater than approximate to200 km s(-1). By applying the sampling rate and the instrument-imposed target selection biases expected for DEEP2, we show that even in a worst-case scenario our VDM method can construct a homogeneous sample of systems that reproduces major properties of the real'' cluster parent population down to approximate to200 km s(-1) for systems with at least five members (and down to approximate to400 km s(-1) for clusters as a whole). In a Lambda cold dark matter cosmology, that limit translates into an identification rate of similar to270 systems per square degree with 0.7<1.2 and a total of more than 1000 groups within the full DEEP2 survey volume. By comparing the galaxy cluster catalogs derived from mock observations to the underlying distribution of clusters as 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 if our VDM algorithm is used, the recovered DEEP2 group and cluster sample should be statistically complete for sigma(los)greater than or similar to400 km s(-1). Finally, we argue that the bivariate distribution of systems as a function of redshift and velocity dispersion reconstructed with these techniques reproduces with high fidelity the underlying real space distribution and can thus be used robustly to constrain cosmological parameters. We expect that the VDM algorithm, which has performed so well when faced with the challenges posed by the DEEP2 survey, should only be more effective when applied to the better sampled, larger surveys of the local universe now underway.