Annu. Rev. Astron. Astrophys. 1982. 20: 547-85
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5.2 The Dynamical Stages of Clusters

Table 3 summarizes the characteristics and dynamical indicators for the two cluster families defined by X-ray core radius and dominance of the central galaxy. Details of these observations were reviewed in Sections 3 and 4 (also see Figure 1). The nXD clusters exhibit a range in dynamical indicators between those of Abell 1367 and Coma-like systems. The X-ray double clusters are classed as intermediate based on analogy to the numerical simulations, but they may represent only one of many channels through which relaxing clusters pass. Unevolved XD clusters are typified by Virgo and Abell 262, while the evolved systems include Abell 85, Abell 1795, and Perseus. The intermediate stage in this class is represented by clusters that have cool X-ray gas and intermediate-to-high spiral fractions and galaxy densities. X-ray doubles may also occur in this class although none have been reported. The evolutionary sequence in each family should be viewed as resulting from a smooth continuous process and not as discrete stages.

Table 3. Cluster classification

Clusters without a central, dominant galaxy Clusters with a central, dominant galaxy
    ~ 500 kpc X-ray core radius     ltapprox 300 kpc X-ray core radius

Early systems - Abell 1367 Early systems - Virgo, Abell 262
    Low X-ray luminosity (< 1044 erg s-1)     Low X-ray luminosity (< 1044 erg s-1)
    Cool X-ray gas (1-4 keV)     Cool X-ray gas (1-4 KeV)
    X-ray emission around galaxies     X-ray emission from halo of single galaxy
    High spiral fraction (geq 40%)     High spiral fraction (geq 40%)
    Low central galaxy density     Low central galaxy density
    Irregular X-ray and optical cluster structure
Intermediate systems - X-ray "doubles" Intermediate systems - Abell 400, Abell 1991,
    (placed based on X-ray structure)     Abell 2063, Abell 2199
    Predominantly cool X-ray gas (1-4 keV)
    Multiple nuclei often in dominant galaxy
    Intermediate-high spiral fraction (25-60%)
Evolved systems - Coma, Abell 2256, Abell 2255 Evolved systems - Abell 85, Abell 1795, Perseus
    High X-ray luminosity (> 1044 erg s-1)     High X-ray luminosity (> 3 x 1044 erg s-1)
   Hot X-ray gas (geq 6 keV)     Hot X-ray gas (geq 6 keV)
   No central cooling     Cooling accretion flows onto central dominant galaxy
    High velocity dispersion     High velocity dispersion
   Low spiral fraction (ltapprox 20%)     Low spiral fraction (ltapprox 20%)
    High central galaxy density     High central galaxy density
   Regular, relaxed, symmetric cluster structure

The sequence originates through the dynamical evolution of clusters, which formed from a range of initial conditions. Since the cluster galaxies as well as the cluster are evolving, the conditions in presently unevolved clusters may be very different from the conditions that existed during an earlier epoch in the early dynamical phases of evolved clusters. Therefore while clusters are classified along an evolutionary sequence, a specific cluster may not evolve precisely along that sequence. For example, if some fraction of S0s form initially in high-density regions, then a cluster with a smaller initial density may never have the same population distribution as an initially denser system. Although galaxies may evolve differently from cluster to cluster and the galaxy morphology may depend on initial conditions, the general cluster evolutionary trends should persist for the present epoch.

5.2.1 FRACTIONS OF EVOLVEO AND UNEVOLVED CLUSTERS     Based on the dynamical indicators, one can estimate the percentage of young and evolved clusters. Cluster samples drawn from Abell's (1958) catalog of rich clusters have cluster densities about ten times that of the field. This bias toward high-density systems also tends to be a bias toward clusters in relatively advanced evolutionary states. Therefore the following estimated fraction of unevolved clusters is probably a lower limit.

The only evolutionary indicator now available for a considerable number of clusters is X-ray luminosity. Fortunately, X-ray luminosity appears to be correlated with other dynamical indicators such as central galaxy density, cluster velocity dispersion, and X-ray temperature. A 2-10 keV luminosity threshold dividing cool (2-4 keV) from hot (> 5 keV) clusters of 3 x 1044 erg s-1 is obtained from the spectral summary of Mushotzky & Smith (1980). If the correlation of X-ray temperature and luminosity holds for all clusters, such that clusters with luminosities above 3 x 1044 erg s-1 are hot and therefore evolved, one finds from the cluster X-ray luminosity function (McKee et al. 1980) that only 9% of Abell clusters exceed this threshold and thus would be considered evolved systems. Forman & Jones (in preparation) performed a similar analysis on a sample of nearby (z leq 0.08) Abell clusters observed with Einstein. Again, based on X-ray temperatures, an X-ray luminosity threshold of 1044 erg s-1 was chosen for the 0.5-3.0 keV band. Two thirds of the sample fell below this threshold and therefore were suggested to be in early evolutionary stages. For the Einstein survey, this fraction is a lower limit since several of the clusters with higher luminosities are observed to have low temperatures. In support of the unevolved nature of most clusters, Dressler (1980b) found that the majority of the 55 rich clusters in his sample had low concentrations of galaxies, and he estimated that only ~ 20-30% had completed the violent relaxation phase and were virialized. From these observations we conclude that most rich clusters are in early stages of their dynamical evolution. The distinction of rich clusters is important in this conclusion, since some properties of evolved poor clusters and groups (high spiral fractions, low velocity dispersion, and low X-ray temperature) would be interpreted as indicating an unevolved system if these systems are mistaken for rich clusters.

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