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

1. INTRODUCTION

The study of large-scale structure is an attempt to unravel the skeleton of our universe. We try to discover how matter, or at least the luminous matter observed in the form of galaxies and clusters of galaxies, is distributed in space. Early observations suggested that while galaxies show a tendency to cluster into groups and rich clusters on small scales ( 20h^-1 Mpc), as expressed statistically by the galaxy correlation function, most of the luminous matter in the Universe is distributed randomly on large scales ( 20h^-1 Mpc). This picture of a relatively "smooth" universal skeleton has been changing quickly and drastically in recent years as new observational data have begun revealing a universe with extensive structure and motion on very large scales of ~ 100h^-1 Mpc or more. The new data on the large-scale structure have led to major changes in existing theoretical ideas on how galaxies and large-scale structure might have been formed. Several previous models have proven inadequate to explain the new observations, while some new candidate models (e.g. cold dark matter, explosions, cosmic strings) have been suggested and worked out in various degrees of detail. Still, despite the great effort and many ingenious ideas, no single theory for the formation of galaxies and large-scale structure can yet satisfactorily match all the observations.

The reason that large-scale structure is fundamental to our understanding of the Universe is because the structure evolves very slowly with time. Even for typical velocities of ~ 10³ km s^-1, objects can move only ~ 10h^-1 Mpc within the Hubble time. Therefore, large structures observed today are cosmic fossils of conditions that existed in the early Universe; these fossils record the history of galaxy and structure formation and evolution.

The cosmological principle states that the Universe is homogeneous and isotropic. Observations of galaxies and clusters, however, show inhomogeneities and structure on all scales studied so far. The Universe is clumped on the scales of galaxies (kiloparsecs), clusters (megaparsecs), and very large superclusters (tens of megaparsecs or more, comparable to the largest scale of current samples). When does the Universe become homogeneous? How does the clumpy distribution of the luminous matter fit with the highly isotropic distribution of the microwave background radiation on the largest scales? The answers are not yet known.

The classic method of investigating structure in the Universe is to observe the spatial distribution of galaxies. Extensive surveys of thousands of galaxy redshifts are needed in order to cover large enough volumes and scales. Galaxy redshift surveys have been carried out by several groups (see review papers by Oort 1983, Chincarini & Vettolani 1987, and Rood 1988; also Gregory & Thompson 1978 , Gregory et al. 1981, Davis et al. 1982; Giovanelli et al. 1986, de Lapparent et al. 1986, da Costa et al. 1988).

A different approach is emphasized in this review: using the high-density peaks of the galaxy distribution, i.e. the rich clusters of galaxies, as tracers of the large-scale structure. Much as the mountain peaks trace mountain chains on Earth, so too do the rich clusters, with their low space density - and large mean separation, serve as an efficient tracer of the largest scale structures. Recent results, summarized in this review, show that clusters do indeed provide an efficient and effective tracer of the large-scale structure of the Universe.

Galaxy and cluster maps of the Northern Hemisphere to z 0.15 are compared in Figures 1 and 2 [Shane & Wirtanen's (1967) galaxy map and Abell's (1958) rich cluster map, respectively]. The clumped distribution is apparent in both maps. While ~ 10⁶ galaxies cover the mapped volume, only ~ 500 rich clusters highlight the structure in the same volume of space.

Figure 1. A map of the galaxy distribution in the Northern Hemisphere (to 19m) from the Shane & Wirtanen (1967) counts (Soneira & Peebles 1978).

Figure 2. A map of Abell's cluster distribution in the Northern Hemisphere to distance group D 5. The inner contour indicates the completeness limit of the statistical sample (Section 2). The map is plotted to the same scale as the galaxy map of Figure 1 and corresponds approximately to the same depth. A comparison of the galaxy and cluster maps (Figures 1, 2) indicates that the clusters and galaxies generally trace the same structure.

1. Rich clusters trace the large-scale structure to ~ 100h^-1 Mpc scale, revealing strong clustering of clusters to these scales. These results are expressed in terms of superclusters of clusters, or by the cluster-cluster correlation function _cc(r), which, for Abell clusters of richness 1, is unity at approximately 25h^-1 Mpc and remains positive out to ~ 100h^-1 Mpc (e.g. Bahcall & Soneira 1983). Associated velocities of ~ 10³ km s^-1 may also be suggested (Bahcall et al. 1986).

2. On a similar scale, the recently reported "bulk motion" of ~ 600 km s^-1 relative to the microwave background of the sphere of galaxies and clusters around us within ~ 30h^-1 Mpc (Rubin et al. 1976, Burstein et al. 1986, Collins et al. 1986, Dressler et al. 1987, Aaronson & Mould 1988).

3. Galaxy redshift surveys revealing netlike or spongy structures and voids to scales of ~ 100h^-1 Mpc (Gregory & Thompson 1978, Gregory et al. 1981, Chincarini et al. 1981, Davis et al. 1982, Giovanelli & Haynes 1982, Oort 1983, Giovanelli et al. 1986, Tully 1987a, de Lapparent et al. 1986, da Costa et al. 1988, Rood 1988).

4. Upper limits to the temperature fluctuations in the microwave back-ground, T / T, on various angular scales (1° corresponding to ~ 100h^-1 Mpc) (e.g. Uson & Wilkinson 1984, Davies et al. 1987, Lasenby 1988, Readhead 1988, Strukov et al. 1988).

5. The clustering of high-redshift objects, such as quasars (Kruszewski 1986, Zhou et al. 1986, Shaver 1988), L clouds (Sargent 1988), and high-redshift galaxies (Koo & Kron 1987).

In this paper I review the current results of studies using rich clusters of galaxies to trace the large-scale structure of the Universe. I describe both general statistical analyses, such as the cluster correlation function, as well as specific studies of superclusters and their properties.

For a previous review paper on superclusters, see Oort (1983). A review paper on voids is presented in this volume by Rood (1988).

I use a Hubble constant of H₀ = 100h km s^-1 Mpc^-1 throughout this paper.