Finding galaxy clusters using Voronoi tessellations

We present an objective and automated procedure for detecting clusters of galaxies in imaging galaxy surveys. Our Voronoi Galaxy Cluster Finder (VGCF) uses galaxy positions and magnitudes to find clusters and determine their main features: size, richness and contrast above the background. The VGCF uses the Voronoi tessellation to evaluate the local density and to identify clusters as significative density fluctuations above the background. The significance threshold needs to be set by the user, but experimenting with different choices is very easy since it does not require a whole new run of the algorithm. The VGCF is non-parametric and does not smooth the data. As a consequence, clusters are identified irrespective of their shape and their identification is only slightly affected by border effects and by holes in the galaxy distribution on the sky. The algorithm is fast, and automatically assigns members to structures. A test run of the VGCF on the PDCS field centered at $\alpha = 13^{\rm h}26^{\rm m}$ and δ = +$29\degr$52´(J2000) produces 37 clusters. Of these clusters, 12 are VGCF counterparts of the 13 PDCS clusters detected at the 3 σ level and with estimated redshifts from $z=0.2$ to $z=0.6$. Of the remaining 25 systems, 2 are PDCS clusters with confidence level $< 3\sigma$ and redshift $z \leq 0.6$. Inspection of the 23 new VGCF clusters indicates that several of these clusters may have been missed by the matched filter algorithm for one or more of the following reasons: a) they are very poor, b) they are extremely elongated, c) they lie too close to a rich and/or low redshift cluster.