1 Introduction

Studies on clusters of galaxies provide us with valuable information on cosmology and extragalactic astronomy. It is a common way in most of the studies to collect samples from available catalogs. For example, Bahcall (1988) compiled the previous work on two-point angular cluster-cluster correlation function based on published cluster catalogs. Rhoads et al. (1994) measured a genus curve of Abell clusters for topological studies on the large-scale structure of the Universe. Struble & Ftaclas (1994) studied correlations amongst richness, flattening, and velocity dispersion of 350 Abell clusters. A large number of reports have also been made on the relations between various properties of clusters (Henry & Tucker 1979; Edge & Stewart 1991; Lubin & Bahcall 1993; Annis 1996; and references therein). Multicolor photometry reveals the color evolution of individual galaxies in clusters: Butcher & Oemler (1978, 1984) reported an increasing fraction of "blue'' galaxies in clusters with redshift. This is known as "Butcher-Oemler effect'' and thought to be some sign of galaxy evolution (see also Rakos & Schombert 1995). Anyhow, it is indispensable to use large and statistically complete catalogs of clusters for statistical investigations.

Clusters of galaxies are identified not only as "clusters of galaxies'' as it is but also as hot plasma balls. Accordingly, both optically- and X-ray-selected cluster catalogs have been constructed so far. A number of X-ray clusters were detected by Extended Medium Sensitivity Survey with Einstein Observatory (Gioia et al. 1990) and ROSAT All-Sky Survey (Voges et al. 1996). X-ray surveys enable one to produce almost complete catalogs of nearby ( 0.2) clusters since it is easy to detect clusters as they are extended X-ray sources. At present, however, it is quite difficult to execute a deep X-ray survey over a wide area in the sky to assemble a sufficiently large and complete sample of distant X-ray clusters whereas searching with optical data can reach even more distant clusters.

Let us outline the development of optical cluster-finding techniques and the optically-selected cluster catalogs themselves in approximately historical sequence. Catalogs of nearby ( 0.2) clusters include those compiled by Abell (1958); Zwicky et al. (1961-68); Shectman (1985, hereafter S85); Abell et al. (1989, hereafter ACO); Lumsden et al. (1992, hereafter L92), and Dalton et al. (1994, hereafter D94). For more distant (0.2 < z < 0.9) ones, there exist four catalogs; Gunn et al. (1986); Couch et al. (1991); Postman et al. (1996, hereafter P96), and Lidman & Peterson (1996, hereafter LP96). The catalogs compiled by Abell (1958), Zwicky et al. (1961-1968), ACO, and Gunn et al. (1986) were constructed by eye selection of clusters on photographic plates. We can easily imagine that large efforts were required to assemble these catalogs. However, these catalogs are claimed to suffer from inhomogeneity and contamination: a significant fraction of clusters may be missed (for Abell/ACO catalog, see Gunn et al. 1986; Sutherland 1988; Ebeling et al. 1993) while some of the cataloged clusters may be spurious (Lucey 1983). These effects become much more critical for fainter (namely, more distant and/or poorer) ones.

S85, L92, and D94 detected clusters semi-objectively (L92 and D94 did it also automatically): S85 and L92 employed count-in-cells technique while D94 adopted percolation technique. Yet, both techniques use only projected positions of galaxies and simply pick up overdensities in the two-dimensional distribution of galaxies. Consequently they cannot quantify the detection rate of spurious clusters due to chance coincidence of galaxies on the sky. Collins et al. (1995) and Ebeling & Maddox (1995) reported the significant amounts of contamination in the catalogs compiled by L92 and D94, respectively. Furthermore, they pick up overdensities of galaxies within the area of a fixed apparent angular size, despite that the actual angular extension of clusters undoubtedly changes with distance. This means that cluster-finding criteria in these methods do change with redshift. Thus these catalogs may not be regarded as far more objective than the "classical'' ones such as Abell/ACO catalog.

Escalera & MacGillivray (1995, 1996) have searched for structures of various scales, from groups up to superclusters, using wavelet transform. Wavelet transform does not stick to a certain apparent size of structures and enables one to execute a "multi-scale'' analysis. However, using only galaxy positions on the sky, wavelet transform also cannot quantify spurious detection rate. Dividing the total sample into subsamples with small ranges of magnitude, as Escalera & MacGillivray (1996) did, may somewhat suppress spurious detections in such methods as count-in-cells, percolation, and wavelet transform, but at the same time, it may also reduce real signal.

P96 developed and employed an innovative cluster-finding method based on "matched-filter'' technique. The point of their method is to use both projected positions and apparent magnitudes of galaxies simultaneously. This enables one to obtain rough estimates of redshifts and richnesses for detected clusters without any spectroscopic information. We need only one broad band images, while obtaining photometric redshift requires more than three bands. The catalog by P96 contains 79 distant clusters (0.2<z<1.2) from V and I band data over 5 deg² obtained with 4-Shooter CCD camera (Gunn et al. 1987) attached to Palomar 5 m Hale telescope. It is noted here that all the above cluster catalogs except for the one by P96 were based on photographic plates. Although CCDs appeared as new optical detectors taking the place of photographic plates in 1980s, it was extremely time consuming to make use of them for survey observations because of their small sizes. However, recent developments of large-format CCDs and of CCD mosaic cameras made it possible to quickly survey over a wide area ($\sim$some deg²) on the sky and to obtain large amount of data of good quality. The cluster catalog compiled by P96 is also the first CCD-based cluster catalog. Using similar methods, LP96 conducted a search for distant clusters and built a catalog of 105 candidates from I band CCD data covering 13 deg², obtained with Anglo-Australian Telescope.

Prompted by the work of P96, we developed a variant method for automatic and objective cluster-finding with optical imaging data. Our method has some nontrivial differences from the one by P96 in the details of detection process, such as binning the input data and employing Poisson statistics. These differences have made apparent improvements in processing time and in accuracies in estimating redshift. In particular, the systematic discrepancy between true and estimated values found in P96 has been largely reduced.

In Sect. 2, we discuss the principle of the cluster-finding method. Detailed performance tests of the method are described in Sect. 3. In Sect. 4, as a performance verification test with real data, we perform a cluster survey using the B band galaxy samples within the 4.9 deg² region around the North Galactic Pole (NGP), obtained with our Mosaic CCD Camera attached to 1.05 m Schmidt Telescope at Kiso Observatory, Japan.

Throughout this paper, we assume H₀ = 80 km s^-1 Mpc^-1 and q₀=0.5.