The Mass and Mass-to-Light Ratio for Clusters of Galaxies at Large Radii

We construct models describing the velocity field in the infall regions of clusters. The velocity field is the superposition of a systematic component and a “noise” component accounting for the effects of small scale substructure and observational errors. This procedure results in models which resemble the observations (redshifts and angular separations of galaxies surrounding clusters) quite well. We demonstrate, on simulated data, that it is possible to estimate correctly the parameters of the systematic velocity component, knowledge of which allows determination of the mass profile of a cluster. To avoid systematic effects when analyzing real data, observations from a number of clusters should be combined. In the absence of sufficient data on other clusters we illustrate the method by applying it only to the Coma cluster. This results in mass estimates near the virial radius as well as at the turn around radius.