The Dark Matter Distribution in the Central Regions of Galaxy Clusters: Implications for Cold Dark Matter

We have undertaken a spectroscopic survey of gravitational arcs in a carefully chosen sample of six clusters, each containing a dominant brightest cluster galaxy. We use these systems to study the relative distributions of dark and baryonic material in the central regions. Three clusters present both radial and tangential arcs and provide particularly strong constraints on the mass profiles, whereas the other three display only tangential arcs and act as a control set. Following Sand, Treu, & Ellis, we analyze stellar velocity dispersion data for the brightest cluster galaxies in conjunction with the arc redshifts and lens models to constrain the dark and baryonic mass profiles jointly. For the systems containing radial arcs we find that the inner dark matter density profile is consistent with a three-dimensional distribution, ρ_DM~r^-β, with logarithmic slope <β>=0.52^+0.05_-0.05 (68% CL). Similarly, we find that the tangential arc sample gives an upper limit, β<0.57 (99% CL). Taking the six clusters together, the mean dark matter distribution is inconsistent with the standard NFW value, β=1.0, at greater than 99% confidence. In addition, we find considerable cosmic scatter in the β (Δβ~0.3) values of the radial arc sample. We find no evidence that systems with radial arcs preferentially yield flatter dark matter profiles as might be expected if they were a biased subset. We discuss the validity of our one-dimensional mass reconstruction method and verify its conclusions by comparing with results of a more rigorous ray-tracing code that does not assume axial symmetry. Our results extend and considerably strengthen the earlier conclusions presented by Sand and coworkers and suggest that the relationship between dark and visible matter in the cores of clusters is much more complex than anticipated from recent simulations.