Probing the Core Structure of Dark Halos with Tangential and Radial Arc Statistics

We study the arc statistics of gravitational lensing generated by dark matter halos in order to probe their density profile. We characterize the halo profile by two parameters, the inner slope of the central cusp α and the median amplitude of the concentration parameter, c_norm, for a halo of mass 10¹⁴ h^-1 M_☉ at z = 0 and compute the numbers of tangential and radial arcs produced by gravitational lensing of galaxy clusters. We find that the number of arcs divided by the number of halos is a good statistic that is sensitive to both c_norm and α with very weak dependence on the cosmological parameters. If arc samples with well-defined selection criteria for the clusters become available, one can strongly constrain both c_norm and α. While our tentative comparison with the existing observational data indicates that the inner density profile of dark halos is indeed as steep as predicted by recent simulations (α ~ 1.5), homogeneous samples of tangential and radial arcs are required for more quantitative discussions.