The distribution of galaxies in the sky is far from uniform. The Herschels remarked on the unevenness of the distribution of nebulae on the celestial sphere in the nineteenth century. Part of the variation is due to the uneven distribution of obscuring matter in our Galaxy, and there is a ZONE OF AVOIDANCE at low galactic latitudes within WHICH FEW galaxies are found. Even in the two windows that are available however. one centred over the north galactic pole and one over the south, the galaxies follow a patchy distribution .

Statistical studies of the distribution of galaxies show that they tend to clump and cluster together. Few galaxies are really single or isolated: most are members of binary, triplet or multiplet systems of galaxies. Our own Galaxy is a member of the Local Group which extends over a few megaparsecs and contains several tens of galaxies,called CLUSTERS OF GALAXIES , which occupy a similar volume to the Local Group, but which are composed of as many as several thousand galaxies. There appears to be a complete, and contiuous, range for clumping of galaxies from binaries, through clusters, up to the largest entities known as SUPERCLUSTERS.

This introduces us to the concept of a HIERARCHICAL UNIVERSE in which galaxies are grouped together to form clusters, and clusters constitute superclusters, and so on. There is at present no evidence for clustering of superclusters, but such a statement is really a measure of our ignorance. It is usually assumed in cosmology that the Universe is quite uniform (homogeneous), a view that may appear contrary to the clustering discussed here. The discrepancy is overcome when it is realized that cosmologists are generally unconcerned with the detailed structure of the Universe on length scales of much less than l00Mpc. At least this is the case when models for the complete Universe are being studied, although of course it is hoped that cosmological theory will eventually explain clusters, galaxies and smaller-scale phenomena.

Counts of galaxies down to various limiting magnitudes in given regions of sky have been used to support the concept of homogeneity on a large scale. This technique is widely used throughout astronomy and appears under different guises depending upon the wavelength range and nature of the objects counted. For the present we shall assume that the objects are of the same intrinsic luminosity. Counting objects down to some limiting brightness is then the same process as counting all the objects within a sphere surrounding the observer. The radius of this sphere is proportional to the square root of the limiting brightness (since brightness varies as distance squared). If the density of objects is uniform, then the number in t he sphere varies as the radius cubed, or limiting brightness to the three halves power. Deviations from this proportionality then tell us about the homogeneity of the objects. Galaxies do have differing luminosities, but the principle still applies, and the same proportionality results, although it then becomes more difficult to interpret discrepancies. The beauty of this test for homogeneity lies in its simple observable requirements: number and magnitude. E. Hubble, and later other astronomers, have used this method to show the approximate uniformity (to within a factor of 2), of the visible Universe out to redshifts of approximately 0.5, or distances of about 2000 Mpc. Radio and X-ray astronomers find similar evidence for homogeneity.

On scales much less than 100 Mpc inhomogeneities are quite evident, and the more extreme examples of these are the subject of much of this chapter. Before discussing them in more detail, how¬ever, it is worth stressing that it is not yet clear which clumps of galaxies are dynamically associated and which are not. By a dynamical association we mean a clump within which the inter¬actions (mostly gravitational) are large and long-lived enough to affect significantly the evolution of that clump. It is possible that galaxies appear clustered on some scale, but do not really influence each other. Some clumps may result from purely random motions; others perhaps from an oddity related to the formation of the galaxies. This situation is perhaps most serious in the case of
Superclusters. It is generally assumed that galaxies are dynamically associated within clusters. The rich clusters are Indeed considered to be gravitationally bound, meaning that the individual members do not have sufficient velocities to escape from the cluster by over¬coming the combined gravitational pull of all the other members. As we shall see, there are problems in establishing the validity of this assumption. One simple way of testing the physical influences between galaxies on large scales is provided by the velocity-distance relation ( Hubble’s law). Deviations from this may reflect the overall gravitational interaction existing within, say the local supercluster

Clusters of galaxies consist of hundreds or thousands of galaxies within a volume of diameter a few megaparsecs. They can be roughly classified into two types: regular and irregular. The REGULAR CLUSTERS have a high central concentration and appear spherically symmetrical: they resemble globular clusters of stars. Elliptical galaxies predominate, especially in the core of the cluster, and giant spirals are rare. A typical example of a, regular cluster is that in the constellation of Coma. IRREGULAR CLUSTERS are similar to open star clusters, and show no marked central concentration or symmetrytry. They may contain galaxies of all types and range from being very richly populated down to much sparser groupings such as the Local Group. The Virgo cluster is an irregular cluster.

Various catalogues of galaxies have been used to compile lists of clusters of galaxies. Early catalogues of bright galaxies such as that of Shapley and Ames clearly show the Virgo cluster, some 20Mpc distant. G. Abell has studied the National Geographic Society Palomar Observatory Sky Survey plates and catalogued 2712 rich clusters of galaxies. Part of these data are sufficiently homogeneous that they can be used for statistical purposes. F. Zwicky and his colleagues have made lists of thousands of clusters and galaxies.

Radio observations have detected emission from clusters of galaxies. Very extended radio sources have been mapped over several of the nearer clusters. Many of the rich clusters also appear to be source* of X-ray emission. The cores of these clusters are thought to contain gas at temperatures of 107-108K

Clusters of galaxies are clear landmarks that can be traced out to large distances. It is generally hoped that they will be of great use in surveying the universe and testing cosmological models. The brightest galaxies in clusters seem to fall within a narrow enough range in brightness for them to be used in determining the cosmic constants for universal expansion. Clusters of galaxies should also be instructive in teaching us about the formation of galaxies and revealing what large-scale density enhancements survived the early phases of the Universe. Most of the observational sides of these issues are clouded with uncertainties and a lack of sufficient data. Future studies will hopefully resolve these problems and throw up new questions. For the present, however, we define what we mean by a cluster of galaxies and attempt to outline some of its properties.

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