Galaxies are not distributed randomly on the sky . There are clear gaps where the plane of the Galaxy obscures our line of sight. It can be shown without doubt that the probability of obtaining by chance the observed distribution of galaxies on the sky is negligible. Studies of the clumping for galaxies of different brightnesses and distances show that the clustering cannot be due solely to galactic obscuration. Such an effect would presumably cause clumps of near and far galaxies to occur in the same direction, which is contrary to observation.

A detailed investigation requires the application of statistical methods. The Universe presumably consists of galaxies scattered throughout three-dimensional space. These galaxies are inter¬related and clumped in some manner reflecting their origin, formation and interactions. We have to discover the nature and under¬lying form of these groupings in order that we can unwind the past and understand the evolution of galaxies. Unfortunately, however, we see these galaxies from only one vantage point through a relatively dirty window. More important, we see only a two-dimensional projection of these galaxies. Exact distances are not available for a sufficiently large number of galaxies for this projection to be reconstructed as a true image of space. Workers minimize distance spread by restricting their attention at any one time to narrow bands of galactic magnitudes. The results of such work rely upon the dispersion in galaxy luminosities: the LUMINOSITY FUNCTION of galaxies
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We are presented with a classical observational problem : plenty of data (in the form of catalogues), but a lack of knowledge of what to look for. Aggregations such as the Coma cluster are not too difficult to pick out, but how do we define weaker clusters ? We have already stressed in the introduction that there is a difference between groups of galaxies that are gravitationally bound together, and groups which appear by chance, or birth. There are two fairly well-defined approaches that we can make to this problem. One is to think up some models for the clustering and fit them to the data. The other is to apply many unbiased tests and interpretations to the data before drawing any conclusion. In practice a combination of the two is used. Certain properties may be plotted against each other in a search for correlations. For example, a comparison of the absolute brightness of stars with their spectral types reveals a striking correlation (the Hertzsprung- Russell diagram). There is no such definitive case for galaxies, or their distributions, although an interesting limit was published by E.F Carpenter in 1938 carpenter plotted the number density of galaxies in well-defined clusters and groups against the diameter of that group or cluster. A distinct upper limit emerged . This was interpreted to mean that a cluster of given extent may have no more than a certain limited density which is larger for smaller clusters. Smaller clusters must therefore be more densely populated than larger ones, although in total the larger ones contain far more galaxies. A similar limit does not show up if the same parameters are plotted for galactic star clusters. This is clearly an important result, and the population densities in all clusters and groups strongly suggest that they are all members of a more universal distribution. The distinction between groups and clusters becomes arbitrary and only based upon convenience!

This has not taken us far in finding out the distribution of all galaxies however. We must avoid splitting off the richest groups and clusters and discussing them only for they may merely be extreme cases: what models shall we try ? Hubble and his contemporaries favoured a relatively random distribution of field galaxies dotted here and there with clusters. More recent studies suggest that the percentage of real field galaxies is in fact small. A powerful statistical approach to our problem can be found by studying the frequency with which various angular separations occur between randomly selected galaxies. We are, of course, interested in how such a frequency distribution differs from one compiled from a chance arrangement of galaxies. The initial results for pairs and triplets of galaxies indicate that excess small separations are more likely than large ones. Significant excesses are found even out to separations of 10° or more, depending upon the magnitude limit of the sample. This indicates that most galaxies are correlated on linear scales up to about 30Mpc. The frequency distribution is fairly smooth and is similar in form to Carpenter’s limit, which involved the richer clumps only

There may be some weakly preferred scales for clustering, the evidence for which is lost in the partial smearing inherent in re-constructing the three-dimensional image from the observed flat projection. The results do appear inconsistent with Bubble’s picture of clusters embedded in a relatively smooth distribution of field galaxies. The behaviour observed is common on all scales up to about 30 Mpc and it strongly suggests that the same mechanism that has produced the dumpiness, or caused it to evolve, applies both to the distribution of galaxies on the scale of-a small group and to superclusters extending tens of megaparsecs.

We now describe some specific examples of well-studied clusters; those in the constellations of Coma, Perseus, Virgo and Centaurus. Remember that these are clear enhancements in the observed sur¬face densities of galaxies and can be isolated and discussed as such. Surrounding them is a complete spectrum of matter clumping from pairs of galaxies, through sparsely populated groups to the rich clusters. Clusters of galaxies have best been studied at present by optical means. X-ray observations are making it clear that not all matter is optically visible and the detection of extended X-ray omission from clusters suggests that observations will be more varied in the future. The advent of fast computerized plate scanners that can recognize galaxies will also considerably speed up our knowledge of their distribution.

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