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Rich clusters of galaxies are powerful tracers of the large-scale structure of the universe (Bahcall 1988, Peebles 1993). I summarize in the sections below the use of clusters in tracing the large-scale structure; I include superclusters (Section 9), statistics of the cluster correlation function (Section 10), and peculiar motions on large scales (Section 11).

9.1. Supercluster Properties

Redshift surveys of galaxies reveal that superclusters are very large, high-density systems of galaxies that are flattened or filamentary in shape, extending to tens of Mpc. The superclusters appear to surround large under-dense regions ("voids") of comparable sizes creating a "cellular-like" morphology of the universe on large scales (Gregory and Thompson 1978; Gregory et al. 1981; Chincarini et al. 1981; Giovanelli et al. 1986; de-Lapparent et al. 1986; da Costa et al. 1988; Rood 1988; Schectman et al. 1996; Landy et al. 1996).

Large scale superclusters have been identified very effectively by rich clusters of galaxies (Bahcall and Soneira 1984), like high mountain peaks tracing mountain chains. Superclusters are generally defined as clusters of rich clusters of galaxies above a given spatial density enhancement f. Here f ident nc(SC)/nc, where nc(SC) is the number density of clusters in a supercluster and nc is the mean number density of clusters. The observed superclusters are large flattened systems, extending to ~ 150h-1 Mpc in size. The superclusters typically contain several clusters. The high-density superclusters generally surround low-density regions.

A complete catalog of superclusters was constructed by Bahcall and Soneira (1984) to z ltapprox 0.08. The catalog identifies all superclusters that have a spatial density enhancement f geq 20. The mean number density of the Bahcall-Soneira superclusters is ~ 10-6h3 Mpc-3, with a mean separation between superclusters of ~ 100h-1 Mpc. A summary of the main properties of the superclusters is presented in Table 8.

The superclusters trace well the structure observed in the more detailed, but smaller, galaxy redshift surveys.

Table 8. Global Properties of Bahcall-Soneira Superclusters.

Property f = 20 superclusters

Number density of SCs ~ 10-6h3 Mpc-3
Number of clusters per SC 2-15 clusters
Fraction of clusters in SCs 54%
Size of largest SC ~ 150h-1 Mpc
SC shape Flattened
Volume of space occupied by SCs ~ 3%

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