Annu. Rev. Astron. Astrophys. 1979. 17: 135-87
Copyright © 1979 by . All rights reserved

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7.3 Uncertainties

Adopting the mass-to-light ratio of Coma as typical of great clusters, we have M / LV approx 250 and M / LB approx 325, much larger than those of individual galaxies and significantly larger than those of binaries and small groups. Without doubt, the single aspect of the data that contributes most to the large M / L in clusters is their large velocity dispersions. We must therefore consider the possible effects of contamination and subclustering on this parameter.

To assess contamination, the cluster must be viewed in the context of its environment. The N-body calculations of Aarseth et al. (1979) are appropriate here since they model a representative volume of space rather than an isolated cluster. For their model with Omega = 0.1, the largest cluster has M / LB = 320, much larger than the model value of 70 (Turner et al. 1979). This discrepancy is entirely a result of contamination. Turner et al. point out that substantial contamination is to be expected in rich clusters because of their large angular extent, and on this basis question the belief that the great clusters provide a reliable estimate of masses of galaxies. They also show that because of the high intrinsic velocity dispersions in clusters, noncluster members in a large volume of the Hubble flow can cause confusion. Because of this effect, Turner et al. suggest that velocity sampling alone cannot eliminate contamination. L. Thompson (private communication) has likewise speculated that the traditional Coma sample is contaminated by unbound members of the Coma supercluster.

To assess the severity of this effect, we need better dynamical models of clusters and their environs, plus a very deep and complete survey of radial velocities in several cluster complexes. Unfortunately this material is not yet available. For the present, however, we are inclined to think that contamination is not solely responsible for large cluster dispersions. Our belief rests principally on the core properties of such clusters, where the density contrast is large and the contamination therefore smaller. As we have seen, the core fitting procedures yield mass-to-light ratios just as high as those from global methods. Furthermore, in Coma the velocity dispersion declines markedly outside the core region, whereas one would in general expect the reverse if contamination were significant. Finally, virtually all the galaxies in the Coma core are of early morphological type, a much larger fraction than those either in small groups or in the extended supercluster (Gregory & Thompson 1978). These galaxies therefore appear to be a distinct population physically located in the core itself.

Holmberg (1961) suggested that cluster velocity dispersions might be spuriously inflated through the inclusion of binaries and subclusters. However, since binaries and small groups generally have dispersions leq 300 km s-1, this effect cannot produce the large dispersions of several hundred km s-1 typical of great clusters.

X-ray observations of clusters may soon provide an independent check on cluster potential and kinetic energies. With the discovery of iron-line emission in clusters of galaxies (Mitchell et al. 1976, Serlemitsos et al. 1977), the probability that cluster X rays originate from thermal bremsstrahlung in a hot intracluster medium (ICM) has greatly increased. If the emission is thermal, the X-ray temperature is determined by the cluster potential. For gas in equilibrium, the X-ray temperature should follow T propto V2, (or sigma2) (Mushotzky et al. 1978, Jones & Forman 1978). Although the current data are limited, there is a good correlation between the observed X-ray temperatures and sigma2 in X-ray clusters (Mitchell et al. 1977, Jones & Forman 1978, Mushotzky et al. 1978). A strong statement would be premature, but the currently available data are consistent with the relation V2 = 3 sigma2, where sigma is the usual line-of-sight velocity dispersion. With more observations, we expect that modelling of the ICM will provide an accurate measurement of cluster potentials and thus of cluster masses.

Finally, the considerable range in M / LV among large clusters themselves suggests that the amount of unseen matter might vary significantly from cluster to cluster. Rood (1974) and Rood & Dickel (1978a) have emphasized this possibility and noted that the virial mass discrepancy is strongly correlated with the velocity dispersion for both small groups and large clusters.

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