Clusters of galaxies are the largest entities known and studied in the Universe. They are also very luminous, with integrated brightnesses rivalling those of quasars. This property, along with their radio and X-ray emission, enables them to be discovered and investigated at large distances. It is generally hoped that this will lead to the use of clusters of galaxies in testing models of the Universe. No outstanding results have as yet been obtained, nor are they likely to be gained until far more is known about the forms, populations, luminosity functions, and other properties of a large sample of clusters. Computer analyses of large-field photo¬graphs should gradually change this situation, as this is the only reasonable way of processing the quantity of data involved.

One obvious cosmological use for clusters is in defining the cosmic constants for expansion of the Universe. Here the useful distance criterion is the apparent magnitude of the first, or third, or tenth brightest member. The behaviour of the brighter end of the galaxy luminosity function means that there is only a small spread hi the absolute magnitudes of such galaxies. Selection effects cloud the usefulness of this: for example, very distant clusters may be selected because they are richer than average or contain some exceptionally bright or unusual galaxy or emission property. Obviously if a cluster of galaxies contains an unusually luminous galaxy or galaxies, then any distance assigned on the basis of the mean magnitude of other brighter cluster galaxies will be underestimated. Such effects are really important when deciding whether the universal expansion is slowing down or speeding up. If the rate of expansion was greater in the past than it is now, then a distant galaxy or cluster will have a greater redshift than if no change in expansion rate occurred. Consequently underestimating the distance to a cluster mimics overestimating the amount of deceleration.

The evolution of the overall brightnesses and spectra of galaxies is largely unknown. Consequently it is not safe to assume that the luminosity function for galaxies has always been the same as it is now. It is not even known which way to correct the magnitudes of the brighter and more massive galaxies. Although earlier they contained bright young stars which have since dimmed, the individual massive galaxies within the cores of clusters may have grown in mass. This they can do at the expense of their neighbours, by tidal disruption. Intracluster gas may also be accreted into such galaxies, whilst interstellar gas can be expelled by violent events. The red-shift of distant galaxies means that radiation emitted in the ultra¬violet now becomes visible.

Another, way in which clusters may be instrumental in deter¬mining the deceleration of the Universe is the so-called angular diameter-redshift test. An extended object of fixed size should appear smaller when viewed from increasing distances. The curvature of space may cause it to pass through a minimum angular size and then get bigger again. Clusters of galaxies are extended and they should show this effect although clusters at redshift of unity or more may be needed in order to observe a minimum. Difficulties arise in assigning some characteristic length to a cluster, especially for those of high redshift, and hence distance. Clusters probably also evolve in diameter thereby introducing further uncertainties.

Clusters of galaxies must have formed at large redshifts and studies of them now may give clues to the formation and evolution of galaxies. It is not clear whether the clusters formed first and then the galaxies, or whether it happened the other way round. Computer models reproduce details of the Coma cluster if it is assumed that the galaxies formed and then clustered. This is consistent with a picture in which gravitational instabilities gave rise to the large-scale features in the Universe in the periods after recombination of the helium and hydrogen atoms.

The discovery of intracluster gas is important in showing us another constituent of the Universe, hitherto undetectable. Such gas may be the remnant of infall into clusters from some all pervading intergalactic medium, leftovers from the process of galaxy formation, or gas expelled from individual galaxies. The diffuse X-ray background at kilovolt energies may partly originate in a hot intergalactic medium. The spatial structure of this radiation may thus be instructive in mapping further details of the large-scale matter distribution in the Universe.

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