On the Determination of Velocity Dispersions for CD Clusters of Galaxies

Abstract

The widely held belief that cD galaxies lie at the kinematical centers of their parent clusters is examined in detail. We find this assumption to be supported by a statistical analysis of all available velocity data. Such an assumption enables us to obtain a direct measure of the true mean velocity of the cluster. The difference between the cD velocity and the mean velocity of the galaxy sample provides a good statistical indication of how well a particular sample represents its parent cluster. For small galaxy samples which poorly represent their parent clusters, we show that the uncertainties in the velocity dispersion have been previously underestimated. A new estimate of the velocity dispersion can be made using the available galaxy sample, but with the cD velocity taken to be the true cluster mean. However, for those clusters with highly unrepresentative samples, this procedure is unlikely to result in an improved estimate of the velocity dispersion. We discuss some individual clusters and consider the extension of the above hypothesis to clusters which contain dumbbell galaxies, D galaxies, or dominant binary galaxies. We show that dumbbell clusters are also dynamically dominated by the corresponding central galaxies. However, for D or binary clusters the evidence is less conclusive.