Core or Cusps: The Central Dark Matter Profile of a Strong Lensing Cluster with a Bright Central Image at Redshift 1

We report on SPT-CLJ2011-5228, a giant system of arcs created by a cluster at z = 1.06. The arc system is notable for the presence of a bright central image. The source is a Lyman break galaxy at z _s = 2.39 and the mass enclosed within the Einstein ring of radius 14 arcsec is . We perform a full reconstruction of the light profile of the lensed images to precisely infer the parameters of the mass distribution. The brightness of the central image demands that the central total density profile of the lens be shallow. By fitting the dark matter as a generalized Navarro-Frenk-White profile - with a free parameter for the inner density slope - we find that the break radius is kpc, and that the inner density falls with radius to the power -0.38 ±0.04 at 68% confidence. Such a shallow profile is in strong tension with our understanding of relaxed cold dark matter halos; dark matter-only simulations predict that the inner density should fall as . The tension can be alleviated if this cluster is in fact a merger; a two-halo model can also reconstruct the data, with both clumps (density varying as and ) much more consistent with predictions from dark matter-only simulations. At the resolution of our Dark Energy Survey imaging, we are unable to choose between these two models, but we make predictions for forthcoming Hubble Space Telescope imaging that will decisively distinguish between them.