Dark Matter Caustics in Galaxy Clusters

We interpret the recent gravitational lensing observations of Jee et al. \cite{Jee} as first evidence for a {\it caustic} ring of dark matter in a galaxy cluster. A caustic ring unavoidably forms when a cold collisionless flow falls with net overall rotation in and out of a gravitational potential well. Evidence for caustic rings of dark matter was previously found in the Milky Way and other isolated spiral galaxies. We argue that galaxy clusters have at least one and possibly two or three caustic rings. We calculate the column density profile of a caustic ring in a cluster and show that it is consistent with the observations of Jee et al.