A&A 368, 776–786 (2001)DOI: 10.1051/0004-6361:20010071c ESO 2001Astronomy&AstrophysicsFinding galaxy clusters using Voronoi tessellationsM. Ramella1,W.Boschin2, D. Fadda3, and M. Nonino11Osservatorio Astronomico di Trieste, Via Tiepolo 11, 34100 Trieste, Italye-mail: [email protected] di Astronomia, Universit`a degli Studi di Trieste, Via Tiepolo 11, 34100 Trieste, Italye-mail: [email protected] de Astrofisica de Canarias, Via Lactea S/N, 38200 La Laguna (Tenerife), Spaine-mail: [email protected] 30 November 2000 / Accepted 22 December 2000Abstract. We present an objective and automated procedure for detecting clusters of galaxies in imaging galaxysurveys?. Our Voronoi Galaxy Cluster Finder (VGCF) uses galaxy positions and magnitudes to find clusters anddetermine their main features: size, richness and contrast above the background. The VGCF uses the Voronoitessellation to evaluate the local density and to identify clusters as significative density fluctuations above thebackground. The significance threshold needs to be set by the user, but experimenting with different choices isvery easy since it does not require a whole new run of the algorithm. The VGCF is non-parametric and doesnot smooth the data. As a consequence, clusters are identified irrespective of their shape and their identificationis only slightly affected by border effects and by holes in the galaxy distribution on the sky. The algorithm isfast, and automatically assigns members to structures. A test run of the VGCF on the PDCS field centered atα =13h26mand δ =+29◦520(J2000) produces 37 clusters. Of these clusters, 12 are VGCF counterparts of the13 PDCS clusters detected at the 3σ level and with estimated redshifts from z =0.2toz =0.6. Of the remaining25 systems, 2 are PDCS clusters with confidence level < 3σ and redshift z ≤ 0.6. Inspection of the 23 new VGCFclusters indicates that several of these clusters may have been missed by the matched filter algorithm for one ormore of the following reasons: a) they are very poor, b) they are extremely elongated, c) they lie too close to arich and/or low redshift cluster.Key words. cosmology: large-scale structure of Universe – galaxies: clusters: general – galaxies: statistics1. IntroductionWide field imaging is becoming increasingly common sincenew large format CCD cameras are, or soon will be avail-able at several telescope (see e.g. MEGACAM, Boulade1998; Boulade et al. 1998; WFI, Baade 1999; etc.). Thepossibility to perform wide field imaging of the extragalac-tic sky allows a systematic search of medium-high redshiftgalaxy clusters in two-dimensional photometric catalogs ofgalaxies. These candidate clusters are of cosmological in-terest and are primary targets for subsequent follow-upspectroscopical observations (see, e.g., Holden et al. 1999;Ramella et al. 2000).Several automated algorithms have already been de-veloped for the detection of clusters within two dimen-sional galaxy catalogs. The classical techniques used forthis task are the “box count” (Lidman & Peterson 1996)Send offprint requests to:M.Ramella,e-mail: [email protected]?The code described in this paper is available on request.and the “matched filter” algorithm proposed by Postmanet al. (1996, hereafter P96) and its recent refinements (seeKepner et al. 1999; Kawasaki et al. 1998; Lobo et al. 1999).The box-counting method uses sliding windows (usu-ally squares) which are moved across the point distribu-tion marking the positions where the count rate in thecentral part of the window exceeds the value expectedfrom the background determined in the outermost regionsof the window. The main drawbacks of the method arethe introduction of a binning to determine the local back-ground, which improves count statistics at the expenseof spatial accuracy, and the dependence on artificial pa-rameters like bin sizes and positions or window size andgeometry.The “matched filter” is a maximum-likelihood (ML)algorithm which analyzes the galaxy distribution with theassumption of some model profiles to fit the data (e.g.a density distribution profile and a luminosity function).This last technique has been used to build the PalomarDistant Cluster Survey (PDCS, see P96) catalog and theM. Ramella et al.: Finding galaxy clusters using Voronoi tessellations 777EIS cluster catalog (Olsen et al. 1999; Scodeggio et al.1999). These two catalogs are two of the largest presentlyavailable sets of distant clusters, with 79 and 302 candi-date clusters respectively.However, the main drawback of the matched filtermethod is that it can miss clusters that are not symmet-ric or that differ significantly from the assumed profile.This can be a serious problem since we know that a largefraction of clusters have a pronounced ellipticity (see e.g.Plionis et al. 1991; Struble & Ftaclas 1994; Wang & Ulmer1997; Basilakos et al. 2000). Furthermore, the matched fil-ter technique is sensitive to border effects because the MLis computed on a circular area. This is a problem becausereal galaxy catalogs are finite and usually present holes inregions corresponding to camera defects or bright stars.Other interesting methods to detect overdensities in agalaxy catalog are the LRCF method (Cocco & Scaramella1999), kernel based techniques (Silvermann 1986; Pisani1996), and wavelet transforms (Bijaoui 1993; Fadda et al.1997). In general, all these techniques are very sensitiveto symmetric structures and suffer from border effects.Ebeling & Wiedenmann (1993) develop a methodbased on Voronoi tessellation (VTP) in order to identifyoverdensities in a Poissonian distribution of photon events.Their goal is to detect sources in ROSAT X-ray images.The VTP does not sort points into artificial bins and doesnot assume any particular source geometry for the de-tection process. These interesting properties are also veryattractive for other applications. For example, Meurs &Wilkinson (1999) present an application of VTP to a sliceof the CfA redshift survey with the purpose of isolating thebubbly and filamentary structure of the galaxy distribu-tion. Several other applications of the Voronoi tessellationto astronomical problems have been published (see, e.g.,van de Weygaert 2000; El-Ad & Piran 1996, 1997; Ryden1995; Goldwirth et al. 1995; Zaninetti 1995; Doroshkevichet al. 1997; Ikeuchi & Turner 1991; Icke & van de Weygaert1991). Clearly, Voronoi tessellation is also interesting forthe search of galaxy clusters