A 3D Voronoi+Gapper Galaxy Cluster Finder in Redshift Space to z ∼ 0.2 I: an Algorithm Optimized for the 2dFGRS

This paper is the first in a series, presenting a new galaxy cluster finder based on a three-dimensional Voronoi Tesselation plus a maximum likelihood estimator, followed by gapping-filtering in radial velocity(VoML+G). The scientific aim of the series is a reassessment of the diversity of optical clusters in the local universe. A mock galaxy database mimicking the southern strip of the magnitude(blue)-limited 2dF Galaxy Redshift Survey (2dFGRS), for the redshift range 0.009 < z < 0.22, is built on the basis of the Millennium Simulation of the LCDM cosmology and a reference catalog of "Millennium clusters," spannning across the 1.0 x. 10(12) -1.0 x 10(15)M(circle dot)h(-1) dark matter (DM) halo mass range, is recorded. The validation of VoML+G is performed through its application to the mock data and the ensuing determination of the completeness and purity of the cluster detections by comparison with the reference catalog. The execution of VoML+G over the 2dFGRS mock data identified 1614 clusters, 22% with Ng >= 10, 64 percent with 10 > Ng >= 5, and 14% with Ng < 5 The ensemble of VoML+G clusters has a similar to 59% completeness and a similar to 66% purity, whereas the subsample with Ng >= 10, to z similar to 0.14, has greatly improved mean rates of similar to 75% and similar to 90%, respectively. The VoML+G cluster velocity dispersions are found to be compatible with those corresponding to "Millennium clusters" over the 300-1000 km s(-1) interval, i.e., for cluster halo masses in excess of similar to 3.0 x. 10(13)M(circle dot)h(-1)