The Mass Profile of Galaxy Clusters Out to $2r_{200}$

We use the public release of ~=100,000 galaxies from the Two Degree Field Galaxy Redshift Survey (2dFGRS) to analyze the internal dynamics of galaxy clusters. We select 43 noninteracting clusters that are adequately sampled in the 2dFGRS public release. Members of these clusters are selected out to ~2 virial radii. We build an ensemble cluster by stacking together the 43 clusters, after appropriate scaling of their galaxy velocities and clustercentric distances. We solve the Jeans equation for the hydrostatic equilibrium for the member galaxies within the virial radius of the ensemble cluster, assuming isotropic orbits. We constrain the cluster mass profile within the virial radius by exploring parameterized models for the cluster mass density profile. We find that both cuspy profiles and profiles with a core are acceptable. In particular, the concentration parameter of the best-fit Navarro-Frenk-White model is as predicted from numerical simulations in a Λ cold dark matter cosmology. Density profiles with very large core radii are ruled out. Beyond the virial radius, dynamical equilibrium cannot be taken for granted, and the Jeans equation may not be applicable. In order to extend our dynamical analysis out to ~2 virial radii, we rely on the method that uses the amplitude of the caustics in the space of galaxy clustercentric distances and velocities. We find very good agreement between the mass profile determined with the caustic method and the extrapolation to ~2 virial radii of the best-fit mass profile determined by the Jeans analysis in the virialized inner region. We determine the mass-to-number density profile and find that it is fully consistent with a constant within the virial radius. The mass-to-number density profile is, however, inconsistent with a constant when the full radial range from 0 to ~2 virial radii is considered, unless the sample used to determine the number density profile is restricted to the early-type galaxies.