The Velocity and Mass Distribution of Clusters of Galaxies from the CNOC1 Cluster Redshift Survey

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Abstract
In the context of the CNOC1 cluster survey, redshifts were obtained for galaxies in 16 clusters. The resulting sample is ideally suited for an analysis of the internal velocity and mass distribution of clusters. Previous analyses of this data set used the Jeans equation to model the projected velocity dispersion profile. However, the results of such an analysis always yield a strong degeneracy between the mass density profile and the velocity dispersion anisotropy profile. Here we analyze the full (R,v) data set of galaxy positions and velocities in an attempt to break this degeneracy. 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 data set 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 σ confidence region extend below σr/σt = 0.74, or above σr/σt = 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 nonspherical 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.

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