CLUSTERS OF GALAXIES MICHAEL J. WEST Clusters of galaxies are gravitationally bound systems of tens, hundreds, or even thousands of galaxies. They are among the largest known objects in the universe, having typical dimensions of roughly 10-20 million light years across. Observations suggest that most galaxies belong to groups of various sizes, although it is estimated that only 5-10% of all galaxies in the universe reside in richly populated clusters. Thus, while very rich clusters of galaxies are certainly impressive behemoths in the cosmic menagerie, they are relatively rare. Nevertheless, thousands of clusters have been revealed by telescopes, and there are no doubt countless others as yet undetected. The study of clusters of galaxies has yielded a wealth of astronomical information and has provided valuable insights into such diverse areas as cosmology, galaxy formation and evolution, high-energy astrophysics, and the origin of the large-scale structure of the universe. Clusters can be readily detected out to quite great distances, and hence can serve as beacons for probing the universe on large scales. For this reason, they play an essential role in astronomers' quest to determine the ultimate fate of the universe. Furthermore, because looking at greater astronomical distances means looking further back into the past, distant clusters may provide important clues as to what conditions were like in the early universe and may allow astronomers to actually observe how galaxies and clusters evolve with time. CLASSIFICATION Clusters of galaxies exhibit a wide range of properties. Just as it has proven advantageous for biologists to classify plants and animals based on certain shared characteristics or features, so too astronomers find it useful to recognize different morphological classes of clusters. A number of different schemes have been devised for classifying clusters. The richness of a cluster is a measure of how many galaxies comprise it, which is determined by counting the number of bright galaxies within a given distance of the cluster center. Thus, astronomers classify a cluster as either poor or rich depending on whether it has relatively few or many member galaxies. In addition to the observable cluster galaxies, there are no doubt also many smaller member galaxies which are too faint to be seen at the great distances of most clusters from earth. A cluster may also be classified as regular or irregular, depending on its overall appearance. Regular clusters, which are usually quite rich, show a smooth, centrally concentrated galaxy distribution and an overall symmetric shape. The closest example of a very rich, regular cluster is the Coma cluster which lies at a distance of approximately 70 Megaparsecs (1 Mpc = 3.26 million light years) from earth. Irregular clusters, on the other hand, have a generally amorphous appearance, usually showing little overall symmetry or central concentration. They are often composed of several distinct clumps of galaxies referred to as subclusters. The majority of clusters are irregular. The nearby Virgo cluster, at a distance of -15 Mpc, is a good example of this type of cluster. Clusters can also be classified according to their galaxy content. The galaxy populations of rich regular clusters tend to be composed primarily of elliptical and S0 (lenticular) galaxies, with only a small fraction of spirals. In the Coma cluster, for example, as many as 80% of the brightest galaxies may be ellipticals, with the few spirals that are found relegated to the outer regions of the cluster. Irregular clusters, on the other hand, have a more even mixture of different galaxy types. Nearly half of all galaxies in the Virgo cluster are spirals. Thus, astronomers sometimes classify clusters according to the fraction of spiral galaxies that they possess, malting a distinction between spiral-rich and spiral-poor clusters. More sophisticated cluster classification schemes have also been proposed. One example is the Rood-Sastry classification scheme, which differentiates between six basic cluster morphologies: cD- dominated (cD, see next section), binary (B), linear (L), core-halo (C), flattened (F), and irregular (I). A cluster is assigned to a particular morphological classification depending on its dominant characteristic feature. A very flattened cluster, for instance, would belong to Rood-Sastry class F, while a cluster that is dominated by two large galaxies at its center would be a B cluster in this system. There is a good deal of overlap between various classification schemes, which indicates that different cluster properties are corre- lated with one another. For instance, very rich clusters are almost always regular in appearance and spiral poor in terms of their galaxy population. It is important to emphasize, however, that cluster classification schemes are merely a crude but useful means of trying to search for gross similarities between clusters. Clusters, of course, exhibit a continuum of properties and recognize no sharp divisions between the different morphological classes proposed by astronomers. Several catalogs listing the locations and some of the basic properties of thousands of clusters have been compiled. The most widely used are those of George Abell and Fritz Zwicky, who each identified clusters using somewhat different criteria. These catalogs were compiled several decades ago from laborious searches of photographic surveys of the sky. More recent developments in cluster cataloging include the use of computers for automated cluster searches, which are faster and much less prone to observer bias. Catalogs of clusters are useful because they provide the foundations for systematic studies of clusters and their properties. Numerous detailed studies of individual clusters have been published in the astronomical literature, with more and more such studies appearing every year. STRUCTURE The number of galaxies found in a rich cluster is typically two orders of magnitude greater than the number that would be found on average in some randomly selected region of space of comparable volume. The distribution of these galaxies usually shows a clear tendency to be centrally condensed, i.e., to have a high concentration of galaxies near the cluster center which decreases further out. The central densities in rich clusters may reach 10,000 or more times the mean density of galaxies in the universe. Clusters of galaxies do not have sharp, well-defined boundaries; rather, their galaxy distributions gradually fade into the cosmic background of galaxies. Their high densities and degree of central concentration provide compelling evidence that most rich clusters are genuine gravitationally bound, dynamical systems rather than chance groupings of unrelated galaxies. Cluster shapes range from spherical to quite flattened, with most clusters showing some degree of elongation. Statistical studies suggest that clusters are intrinsically flatter on average than elliptical galaxies. There is also intriguing observational evidence that the long axes of neighboring clusters may tend to point at one another, even when the clusters are separated by quite large distances, which may be telling us something quite interesting about the way in which clusters have formed. As mentioned earlier, the galaxy population in rich clusters of galaxies appears in general to differ from that found over most of the sky. In the central regions of rich, regular clusters, elliptical and SO galaxies are by far the most common galaxy types, with only a very small fraction of spiral galaxies found. This is the converse of the situation outside of clusters, where the majority of galaxies in isolation or in small groups are spirals. why different galaxy populations are found in and out of clusters is a matter of some debate. Some astronomers interpret this difference as implying that spiral galaxies have somehow been transformed into SO or elliptical galaxies within clusters. Others argue, however, that the different galaxy populations reflect intrinsic differences between the galaxy-formation process in different environments, with conditions in rich clusters favoring the formation of elliptical and SO galaxies over spirals. Also lurking in the central regions of many rich clusters are the largest known galaxies in the universe, called cD galaxies. These supergiant galaxies are unique to the dense environments of rich clusters. A cD galaxy is characterized by a very extended envelope of diffuse stellar light surrounding what may be an otherwise normal elliptical galaxy nucleus. The visible extent of a cD galaxy may be as much as 10-100 times that of a normal galaxy. Although the densities of the cD envelopes are quite low, they extend to such great distances that the total luminosity associated with these galaxies is extremely large. Many cD galaxies exhibit more than one nucleus. Whether cD galaxies represent simply the extreme end of the normal distribution of galaxy luminosities, or are instead a unique type of galaxy which has formed or evolved under special conditions in clusters, has still not been fully resolved. The fact that many cD galaxies have multiple nuclei suggests that they may have grown through mergers of smaller galaxies. For decades, most observations of clusters of galaxies were done in the visible wavelengths of light. In recent years, however, great emphasis has also been placed on observing clusters at other wavelengths, such as x-ray and radio, as these can provide different insights into the structure and properties of clusters and their constituent galaxies. Many clusters are now known to be strong emitters of x-rays, which indicates that, in addition to the visible galaxies, they also possess an intracluster medium of hot, rarefied gas at temperatures of -10x7-10x8 K. The amount of mass in the form of gas in rich clusters is probably comparable to the total mass in the form of visible galaxies. Spectral analysis indicates that this gas contains iron and other heavy elements which must have been produced in stars, suggesting that much of the intracluster gas may have once been located within individual galaxies and was subsequently liberated. Radio observations of the hydrogen gas content of cluster galaxies also show that those galaxies in the highest density regions are systematically lower in gas, suggesting that the gas has been removed from these galaxies. DYNAMICS The smooth, centrally condensed distribution of galaxies within rich, regular clusters suggests that these clusters have reached a state of dynamical equilibrium, sometimes referred to as relaxation. Irregular clusters, on the other hand, are probably unrelaxed systems, having not yet reached a steady state. Thus, it seems likely that different cluster morphologies correspond to different stages of dynamical evolution. Computer simulations of the formation and evolution of clusters of galaxies support this notion. Galaxies in a cluster move under the influence of gravity in orbits about their common center of mass. Although it is not possible to observe the true spatial velocities of galaxies, redshift measurements make it possible to determine the radial velocities (i.e., the component of velocity along the line of sight) of galaxies in clusters. Such measurements show that the member galaxies are all moving with different speeds about the cluster. A cluster can be characterized by its velocity dispersion, which is a measure of the typical speed with which the galaxies are moving in the cluster. The velocity dispersion of a rich cluster is typically -1000 km s-1. The velocity dispersion in many clusters shows a systematic decrease as the distance from the cluster center increases. In the Coma cluster, for instance, the velocity dispersion near the outskirts of the cluster has fallen by roughly a factor of 2 from its peak value at the cluster center. Given the observed size of a cluster and the velocity dispersion of its constituent galaxies, it is straightforward to compute the crossing time of the system, which is simply the time required for a galaxy moving with a speed equal to the cluster velocity dispersion to travel from one side of the cluster to the other. Crossing times in the inner regions of rich clusters are generally on the order of 10x9 years. Assuming the age of the universe to be between 10 and 20 billion years, this means that galaxies in the cores of clusters have had sufficient time to make several traversals of the system. This suggests that clusters of galaxies are well mixed and provides further evidence that rich clusters are dynamically stable systems, since the galaxies would otherwise long ago have dispersed if the cluster was not held together by gravity. Assuming that clusters of galaxies are in dynamical equilibrium, it is possible to determine their masses using the virial theorem. The virial theorem relates the total mass of a self-gravitating system of stars or galaxies to its size and velocity dispersion, V2R M-G, where M is the total mass of the cluster, R is its characteristic size, V is the cluster velocity dispersion, and G is the gravitational constant. The essence of the virial theorem is quite simple. Galaxies in a cluster are in motion because they are accelerated by the total gravitational force that they experience from every atom that is present in the cluster. Therefore, the greater the total mass of the cluster, the greater the gravitational tug felt by each galaxy, and, consequently, the greater the speed with which the galaxies move in their orbits. Thus, by observing the velocity dispersion and characteristic size of a cluster, astronomers can infer the total mass that is present in that system. Typical masses of rich clusters of galaxies obtained using the virial theorem are -10x15 solar masses. Another way that one can determine the mass of a cluster is by simply counting the number of galaxies that it contains. Astronomers have a fairly good idea of how much mass there is in a typical galaxy, and so by adding up the contribution from each galaxy that is observed within a cluster one gets an estimate of the total cluster mass. This number should probably be doubled to also include the intracluster gas. When Fritz Zwicky used these two methods to compute the mass of the Coma cluster in a seminal study over 50 years ago, he made one of the most important discoveries in modern astronomy. What Zwicky found was that the virial mass that he had computed for the Coma cluster was some 400 times greater than the mass that could be accounted for in the form of visible galaxies! A subsequent study of the Virgo cluster by Sinclair Smith in 1936 suggested that the total mass of that cluster was roughly 200 times the amount of the observable luminous matter. Thus was born one of the great puzzles of modern astronomy, which has come to be known as the missing mass problem. This discrepancy between the virial mass and visible mass has since been found in many other clusters as well, although modern estimates are that the total cluster mass is more likely 10 times the mass contained in galaxies and gas. The missing mass problem is one of the most fascinating discoveries to come out of the study of clusters of galaxies and remains one of the major unsolved problems of modern astronomy. What it may be telling us is that as much as 90% of the matter in rich clusters (and perhaps the universe) is in a form that is invisible and can be detected only by the gravitational influence that it exerts on visible matter such as galaxies and stars. In a sense, then, the term "missing,' mass is really a misnomer-it is the light, rather than mass, that is truly missing! Virial mass determinations tell us beyond any doubt just how much mass must be present in a cluster because we can see its gravitational influence on the motions of the cluster galaxies, but the fact is that we are unable to observe this dark matter directly. What the dark matter may be is still pure speculation at present. There have been many suggestions, ranging from faint low-mass stars, to black holes, to exotic forms of matter predicted by particle physics theories. There are several interesting dynamical processes that can occur in the dense environments of clusters of galaxies. In an individual galaxy, the odds of two stars colliding are extremely small because of the vast spaces between them; the average distance between stars in a galaxy is millions of times greater than the size of a typical star. However, the situation is very different in clusters of galaxies, where the high density of galaxies means that the separation between neighboring galaxies is often only a few times greater than their sizes. Frequent collisions between galaxies are therefore very likely to occur in clusters. Such collisions can have several important consequences. If two galaxies pass near each other at relatively low speeds, their mutual gravitational attraction may cause them to merge together, resulting in a single, larger galaxy. Two galaxies can also pass right through one another, sweeping out each other's interstellar gas in the process (even though their stars will rarely collide), which may be heated to high temperatures. The large gravitational forces exerted as two galaxies pass very near one another can also remove loosely bound stars from the outer regions of each of them in a process known as tidal stripping. The halos of cD galaxies may be composed largely of tidally stripped material captured from other galaxies. It is also possible that many of the largest galaxies in clusters may have grown by devouring smaller neighboring galaxies in a process referred to as galactic cannibalism. Since gravity is a long-range force, distant encounters between galaxies in a cluster that do not involve direct contact can still have very important consequences for the overall cluster evolution. Gravitational interactions between galaxies allow energy to be exchanged between them. During such two-body interactions, more massive galaxies will tend to give up some of their energy of motion to smaller ones and as a consequence will slowly sink to the center of the cluster, while the energy gained by the less massive galaxies will cause them to move in orbits which take them further away from the cluster center. Given enough time, this mechanism can lead to mass segregation between the high-mass and low-mass galaxies. Estimates Vary, but in general the two-body relaxation time for an average galaxy in a rich cluster is expected to be quite long, roughly 10x11 years or more. A related effect is dynamical friction, which occurs when a massive galaxy moves through a background of smaller mass galaxies or dark matter. As the heavy galaxy moves through the cluster, its large gravitational tug will deflect background objects from their original orbits such that they form a wake behind the path traveled by the massive galaxy. This then sets up a sort of feedback mechanism whereby the wake that has been created by the passage of the massive galaxy now exerts a gravitational tug back on it, causing this galaxy to slow down in its orbit and eventually spiral in towards the cluster center. The efficiency of dynamical friction is proportional to galaxy mass, and thus the time scale for this process can be significantly shorter than the standard two-body relaxation time for very massive galaxies, perhaps as short as -10x9 years. Observationally, the extent to which mass segregation has already occurred in rich clusters is debated at present. Although there is no doubt that the very largest galaxies are invariably found at the centers of clusters, the overall amount of mass segregation which has already occurred appears to be marginal. The fact that more pronounced mass segregation is not observed tells us something very interesting about the distribution of the dark matter in clusters. If all the missing mass was bound to individual galaxies (in the form of dark halos, for example), then the time scale for relaxation would be much less than the age of the universe, and thus one would expect to see strong mass segregation in clusters. The fact that this is not observed indicates that most of the dark matter cannot be attached to individual galaxies, but rather must be distributed smoothly throughout the entire cluster. Additional Reading Bahcall, N.A.(1977). Clusters of galaxies. Ann. Rev. Astron. Ap. 15 505. Dressler, A.(1984). The evolution of galaxies in clusters. Ann. Rev. Astron. Ap. 22 185. Gorenstein, P. and Tucker, W.(1978). Rich clusters of galaxies. Scientific American 239(No. 5),110. Shu, F.H.(1982). The Physical Universe. University Science Books, Mill Valley. Struble, M.F. and Rood, H.J.(1988). Diversity among Galaxy Clusters. Sky and Telescope 75 16. see also Clusters of Galaxies, Component Galaxy Cbaracteristics; Clusters of Galaxies, Radio Observations; Clusters of Galaxies, X-Ray Observations; Dark Matter, Cosmological; Galaxies, Properties in Relation to Environment.