We build an `ensemble cluster' from the individual clusters under the assumption that they form a homologous sequence; if clusters are not homologous then our results are probably still valid in an average sense. To interpret the data we study a one-parameter family of spherical models with different constant velocity dispersion anisotropy, chosen to all provide the same acceptable fit to the projected velocity dispersion profile. The best-fit model is sought using a variety of statistics, including the likelihood of the dataset, and the shape and Gauss-Hermite moments of the grand-total velocity histogram. The confidence regions and goodness-of-fit for the best-fit model are determined using Monte-Carlo simulations. Although the results of our analysis depend slightly on which statistic is used to judge the models, all statistics agree that the best-fit model is close to isotropic. For none of the statistics does the 1-sigma confidence region extend below sigma_r / sigma_t = 0.74, or above sigma_r / sigma_t = 1.05. This result derives primarily from the fact that the observed grand-total velocity histogram is close to Gaussian, which is not expected to be the case for a strongly anisotropic model.
The best-fitting models have a mass-to-number-density ratio that is approximately independent of radius over the range constrained by the data. They also have a mass-density profile that is consistent with the dark matter halo profile advocated by Navarro, Frenk & White, in terms of both the profile shape and the characteristic scale length. This adds important new weight to the evidence that clusters do indeed follow this proposed universal mass density profile.
We present a detailed discussion of a number of possible uncertainties
in our analysis, including our treatment of interlopers and brightest
cluster galaxies, our use of a restricted one-parameter family of
distribution functions, our use of spherical models for what is in
reality an ensemble of non-spherical clusters, and our assumption that
clusters form a homologous set. These issues all constitute important
approximations in our analysis. However, none of the tests that we
have done indicates that these approximations influence our results at
a significant level.