Annu. Rev. Astron. Astrophys. 1988. 26: 631-86
Copyright © 1988 by . All rights reserved

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In order to use rich galaxy clusters as tracers of the large-scale structure in the Universe, a complete sample of clusters over a large volume of space is required. I describe below the available catalogs of rich clusters of galaxies. The clusters in these catalogs were used as tracers, with different techniques employed, as discussed in the sections that follow.

Three extensive catalogs of rich clusters of galaxies are available: The Abell (1958) catalog of rich clusters; the "Catalog of Galaxies and Clusters of Galaxies" by Zwicky et al. (1961-1968); and the catalog of clusters by Shectman (1985) determined from the Shane & Wirtanen (1967) galaxy counts. Abell and Zwicky both identified clusters as density enhancements on the Palomar Sky Survey plates, but they used quite different selection criteria for the inclusion of clusters in their catalogs. Shectman (1985) identified clusters from the Shane & Wirtanen (1967) galaxy counts, using still another selection algorithm of density enhancement. I summarize below the selection algorithms and the main properties of these catalogs.

The obvious next step is to use a completely automated procedure of identifying clusters by computer algorithms that search data tapes of computer-scanned images. Such "objective" catalogs are being prepared by several groups (e.g. Maddox et al. 1988). A complete sample of X-ray - selected rich clusters of galaxies. which will be available in a few years from new X-ray surveys, will provide another objective sample of clusters that can be used to trace the large-scale structure.

2.1. The Abell Catalog

The Abell (1958) catalog of rich clusters of galaxies contains a total of 2712 clusters that are the richest, densest clusters found on the Palomar Sky Survey plates and are identified by a well-defined set of selection criteria. Of these rich clusters, 1682 constitute Abell's complete statistical sample; they are distributed over 4.26 steradians of the sky and satisfy restrictive selection criteria. The Abell criteria are summarized as follows: (a) A cluster must contain at least 50 members, after proper correction for background, in the magnitude range m3 to m3 + 2, where m3 is the magnitude of the third brightest galaxy; (b) the gtapprox 50 members should be contained within a circle of radius 1.5h-1 Mpc around the center of the cluster (corresponding to the Abell radius RA = 1.7' / z = 1.5h-1 Mpc, where z is the cluster redshift); (c) the cluster redshift z should be in the range 0.02 ltapprox z ltapprox 0.20; and (d) the cluster should lie north of declination -27° and within the region of complete identification given in Table 1 of Abell (1958). The clusters' redshifts are estimated by Abell from the magnitude of the tenth brightest galaxy in the cluster, m10. For each cluster the catalog lists the cluster position on the sky; m10; the distance group D (estimated from m10); and the richness classification R. (The latter is related to the number of member galaxies brighter than m3 + 2 and located within RA = 1.5h-1 Mpc around the cluster center. This population is corrected for a background count in a nearby field.)

The 1682 rich clusters in the statistical sample belong to distance D = 1 through 6 and have richness classes of R = 1 through 5. These richness classes correspond to galaxy richness counts that range from 50 to over 300 members (as defined above); the less populated (poorer) clusters are much more numerous than the more richly populated ones. The distribution of clusters in the statistical sample among distance groups and richness classes is shown in Table 1.

The full list of 2712 clusters is larger than the 1682 clusters in the statistical sample mostly because of the poorer R = 0 clusters (with 30 to 49 members), which are not part of the statistical sample. (They are more easily missed at large distances and are therefore incomplete.) In addition the full list includes some clusters at lower latitude than the boundary of the statistical sample, as well as clusters with estimated redshifts outside the range of the statistical sample.

Table 1. Distribution of Abell clusters with distance and richness a

Distance distribution | Richness distribution

D <zest> Ncl(R geq 1) | R Ngl Ncl
1 0.0283 9 | (0) (30-49) (gtapprox 103)b
2 0.0400 2 | 1 50-79 1224
3 0.0577 33 | 2 80-129 383
4 0.0787 60 | 3 130-199 68
5 0.131 657 | 4 200-299 6
6 0.198 921 | 5 geq 300 1


Total 1682 | Total (R geq 1) 1682

Complete redshift sample | Distant projected sample
(see Section 3) | (see Section 3)

D leq 4 | D = 5 + 6
Ncl (total) 104 | 1547
Ncl (b geq 30°) 71 | 984
Ncl (b leq - 30°) 33 | 563
Ncl (R = 1) 82 | 1125
Ncl (R geq 2) 22 | 422

a Notation: D = distance group; <zest> = estimated redshift; Ncl = number of clusters; R = richness class; Ncl = number of galaxies (cluster population).
bR = 0 clusters are not part of the statistical sample.

Redshifts for all clusters in Abell's statistical nearby sample of distance class D leq 4 (z ltapprox 0.1) were recently measured by Hoessel et al. (1980). This complete redshift sample includes 104 clusters at D leq 4 that are of richness class R geq 1 and are located at high Galactic latitude (as specified in Abell's Table 1 plus the requirement of |b| geq 30°). This complete nearby redshift sample was used extensively in tracing the large-scale structure in space (Sections 3.2.1, 6, and 8). A somewhat larger sample of 175 clusters that include R = 0 clusters with measured redshifts, for the same distance groups D leq 4, was also used in several studies. Two selection effects within this bright nearby sample were observed and quantified by Bahcall & Soneira (1983) : an observed decrease of cluster density at low latitudes (to b ~ 30°), arising probably from obscuration and confusion with high-density regions of stars; and a decrease of cluster spatial density near the redshift limit of the sample, as expected from the uncertainties in the magnitude limit of the Abell distance group. Both of these selection effects, however, can be easily corrected for when using the sample for statistical purposes.

An estimate of the completeness limit of this nearby sample obtained by comparison with X-ray emission from the clusters suggests a reasonably high level of completeness (see Section 3.3).

The mean space density of rich clusters (R geq 1) is observed to be 6 × 10-6 h3 Mpc-3, uncorrected for obscuration. When corrected for the latter, the spatial density of R geq 1 clusters increases to ~ 10-5h3 Mpc-3. The density decreases rapidly with increasing richness. The luminosity function of clusters was determined by Bahcall (1979).

A map showing the surface distribution of Abell clusters (Northern Hemisphere, D leq 5) is shown in Figure 2. The distribution is similar to that seen in comparable galaxy maps and shows a highly clumped distribution of clusters. The clumped distribution, and analyzed quantitatively in Sections 3 and 6, reflects the large-scale structure of the Universe as traced by galaxy clusters.

An extension of the Abell catalog to the Southern Hemisphere, which was started by Abell before his death, was recently completed by Abell et al. (1988).

2.2. The Zwicky Catalog

The Zwicky et al. (1961-68) "Catalog of Galaxies and Clusters of Galaxies" contains over 30,000 galaxies brighter than 15.7m identified on the Palomar Sky Survey plates and 9700 clusters of galaxies visible to the limit of the plates (m appeq 20). The criteria for including a cluster in the Zwicky catalog are less strict than Abell's. These criteria are the following: (a) The cluster must contain at least 50 galaxies in the magnitude range m1 to m1 + 3, where m1 is the magnitude of the brightest galaxy; (b) these galaxies must lie within the cluster's contour, defined as the isopleth where the projected density of galaxies is about twice that of the neighboring field; (c) no limit on the cluster redshift is specified, but aggregates such as the Virgo cluster (which cover very large areas of the sky) are not included in the contour maps; and (d) the clusters must lie north of declination -3° and within the areas given in the introduction to Volume 6 of the catalog.

Zwicky classifies cluster distances according to estimated redshifts (from brightness and apparent size of member galaxies): near clusters (z ltapprox 0.05), medium distant (z appeq 0.05 - 0.10), distant (z appeq 0.10 - 0.15), very distant (z appeq 0.15 - 0.2), and extremely distant (z gtapprox 0.2).

Cluster population (or richness) is defined by Zwicky as the number of galaxies visible on the red Palomar Sky Survey plate, corrected for the mean field count, that are located within the isopleth of twice the field density. Because of the boundary at twice the field density, and the count to the plate limit. Zwicky's populations depend systematically on the cluster redshift (unlike the absolute intrinsic richness classification of Abell).

The Zwicky catalog contains systems that are less rich than those of Abell, and hence it has many more clusters. Zwicky clusters also differ in size from Abell's; Zwicky clusters are mostly larger, lower density systems that may contain multiple dense clumps within them. These differences in cluster properties for the two catalogs arise mainly from the different criteria used in the identification process.

2.3. The Shectman Catalog

The Shane & Wirtanen (1967) counts of galaxies using the Lick Observatory astrographic survey include about 106 galaxies brighter than 19m at declinations delta > - 22.5°. A large number of clusters, i.e. high-density regions of galaxies, are easily recognized in these counts (see Figure 1). Shectman (1985), using an automated procedure, has identified a sample of 646 clusters of galaxies based on the Shane-Wirtanen counts in 10' bins. The clusters are located at Galactic latitudes |b| geq 40° and declinations delta > - 22.5°. The selection was based on local density maxima above a given threshold value, after lightly smoothing the data to reduce the effect of the sampling grid.

A selected threshold value of five galaxy counts per bin was used by Shectman for the catalog; this threshold is considerably higher than the tail of the random (background) distribution of galaxy counts, which has a median of 1.3 galaxies per bin. Because of the smoothing, a minimum of 20 galaxies must be counted by Shane & Wirtanen to 19m in order to result in a detection of a cluster. The above threshold of five galaxies succeeds in detecting 70% of Abell's D leq 4 clusters and 10% of the D = 5 clusters. A threshold of about 3.5-4 galaxy counts per bin appears to identify all of Abell's D leq 4 clusters and still be well out on the tail of the random distribution.

The Shectman procedure selects clusters that are considerably poorer than the Abell R geq 1 cluster (the latter having geq 50 members brighter than m3 + 2). The mean number density of the Shectman clusters is thus much higher than the density of the Abell clusters (see below). It is therefore expected that only a fraction of the Shectman clusters will also be clusters in the Abell catalog. Shectman finds that 40% of his clusters are members of the Abell catalog.

Redshift measurements of a complete subsample of 112 Shectman clusters in the south yield a redshift distribution (and thus depth) similar to the clusters in the D leq 4 Abell sample. The implied space density of the Shectman clusters is therefore about 6 times higher than the space density of the Abell R geq 1 clusters.

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