2008MNRAS.390.1647B

The Einstein radius of a cluster provides a relatively model-independent measure of the mass density of a cluster within a projected radius of ∼150kpc, large enough to be relatively unaffected by gas physics. We show that the observed Einstein radii of four well-studied massive clusters, for which reliable virial masses are measured, lie well beyond the predicted distribution of Einstein radii in the standard Λ cold dark matter (ΛCDM) model. Based on large samples of numerically simulated cluster-sized objects with virial masses ∼10¹⁵M_☉, the predicted Einstein radii are only 15-25arcsec, a factor of 2 below the observed Einstein radii of these four clusters. This is because the predicted mass profile is too shallow to exceed the critical surface density for lensing at a sizable projected radius. After carefully accounting for measurement errors as well as the biases inherent in the selection of clusters and the projection of mass measured by lensing, we find that the theoretical predictions are excluded at a 4σ significance. Since most of the free parameters of the ΛCDM model now rest on firm empirical ground, this discrepancy may point to an additional mechanism that promotes the collapse of clusters at an earlier time thereby enhancing their central mass density.