Annu. Rev. Astron. Astrophys. 1982. 20: 547-85
Copyright © 1982 by . All rights reserved

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1.2 Cluster Dynamical Evolution

In this article we assume that the differences between regular and irregular clusters can be described in an evolutionary framework. Abell (1975) characterized regular clusters as having marked spherical symmetry, a high central concentration, a galaxy population dominated by S0s and ellipticals, little (if any) subclustering, a high velocity dispersion (~ 1000 km s-1), and a large number of member galaxies (~ 1000 or more galaxies within 7 mag of the brightest galaxy). At the other extreme are the irregular clusters characterized by little spherical symmetry, an absence of central condensation, a galaxy population containing all types, significant subclustering, a lower velocity dispersion, and fewer member galaxies. In this evolutionary scenario as the cluster collapses, galactic halos are stripped, central galaxies cannibalize their neighbors, the velocity dispersion increases, and the X-ray gas is heated and its luminosity increases. Although future observations and theoretical calculations may modify or invalidate some of the details, this framework allows us to synthesize the increasing wealth of observational material into a coherent structure, permitting the comparison of many cluster properties.

The evolutionary sequence of clusters is delineated by cluster properties that can be related to processes occurring during the collapse and relaxation of a cluster - violent relaxation, equipartition, galaxy collisions, and dynamical friction. However, since the timescales for these processes depend on different parameters, they will not necessarily all behave in the same way from cluster to cluster. Therefore the evolutionary sequence should not be interpreted as one in which younger clusters become the precise replicas of evolved ones.

The timescales for the processes occurring during the dynamical relaxation of a cluster are interrelated (see Lightman & Shapiro 1978, Bahcall 1977a, and Ostriker 1978). The shortest cluster timescale is that for the violent relaxation. On this timescale, gross departures from equilibrium in the cluster potential will be reduced and the galaxies in the core will exhibit a Maxwellian distribution with little equipartition. This timescale is approximately the crossing time

Equation 1

where R is the cluster radius, V the velocity dispersion, G the gravitational constant, and rhobar the mean density. Thus, clusters of high mean density relax rapidly. The two-body relaxation timescale is

Equation 2

where M is the mass of a galaxy, n the galaxy density, and N the total number of galaxies in the cluster. For typical values of the parameters

Equation 3

where VR is the radial component of the velocity dispersion and Mgal is the mass of a galaxy. The dynamical and two-body timescales are related by

Equation 4

Therefore for a given mean density, poorer clusters have shorter two-body relaxation times than rich clusters.

The equipartition and dynamical friction timescales are related to the relaxation time by tauF propto (Mbar/MH) tauR, where Mbar is the mass of the average galaxy and MH that of a heavier one. Thus, on a timescale less than tauR a heavy galaxy will settle to the cluster center.

Some cluster evolutionary indicators are tied directly to dynamical processes. For example, the increases in central galaxy density and X-ray luminosity are related to the deepening of the gravitational potential during the cluster collapse and relaxation. With regard to galactic content as an evolutionary indicator, Dressler (1980a) argued that the cluster population depends not only on changes that occur during the cluster's evolution (e.g., ram-pressure stripping and evaporation) but also on the fact that S0s are born preferentially in denser regions. However, since denser regions have shorter dynamical timescales, regions dominated by S0s would tend to have undergone more relaxation. In this sense, spiral fraction remains an evolutionary indicator, although galaxy density is probably a more fundamental parameter.

The X-ray morphology shown by imaging observations has been related to the evolutionary sequence of clusters. Irregular, clumped emission is associated with dynamically young (irregular) clusters (Jones et al. 1979, Bechtold et al. 1983). Smooth, symmetrical emission is observed in relaxed (regular) clusters (Jones et al. 1979, Helfand et al. 1980), while a possible intermediate state exhibits a biomodal X-ray surface brightness distribution (Forman et al. 1981a, Henry et al. 1981).

The X-ray images also suggest that the evolutionary sequence is divided into two parallel sequences corresponding to clusters with and without dominant, central, galaxies. Clusters that have a core radius of less than ~ 300 kpc have emission peaked on a central, dominant galaxy; those with a core radius of ~ 400-700 kpc lack a central, dominant galaxy (Jones et al. 1979). Although exceptions or new families of clusters may be discovered in future analyses, the present observations can be organized in this rudimentary system. Figure 1 graphically illustrates this two-family classification with X-ray isointensity contours of six clusters. The X-ray and optical dynamical indicators span the full range for clusters in both families.

Figure 1

Figure 1. X-ray isointensity contours for 6 clusters from 0.5-3.0 keV IPC images. Before contours were drawn, the images (and all other IPC images shown in this article) were smoothed with a Gaussian (sigma = 32") whose width corresponds to that of the instrumental response. The clusters on the left represent those from the family having large X-ray core radii and no central, dominant galaxy. Those on the right have smaller X-ray core radii and contain central, dominant galaxies. The clusters at the top of the figure are less dynamically evolved than those at the bottom. These clusters are discussed in detail in Sections 3 and 4, and their properties are summarized in Table 3.

X-ray observations of individual clusters from the family without dominant galaxies (nXD) are discussed in Section 3 beginning with the irregular clusters Abell 1367 and Abell 194 and ending with evolved Coma-type systems. In a parallel structure, the X-ray images of clusters with dominant galaxies (XD) are described in Section 4 beginning with Virgo and ending with the cD clusters and Perseus.

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