Core or cusps: The central dark matter profile of a redshift one strong lensing cluster with a bright central image

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 14 arc second radius Einstein ring is $10^{14.2}$ solar masses. We perform a full light profile reconstruction 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 $270^{+48}_{-76}$ kpc, and that the inner density falls with radius to the power $-0.38\pm0.04$ at 68 percent confidence. Such a shallow profile is in strong tension with our understanding of relaxed cold dark matter halos; dark matter only simulations predict the inner density should fall as $r^{-1}$. 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 going as $r^{-0.8}$ and $r^{-1.0}$) 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.