Probing the core structure of dark halos with tangential and radial Arc statistics

We study the arc statistics of gravitational lensing generated by dark matt er halos in order to probe their density profile. We characterize the halo profile by two parameters, the inner slope of the central cusp alpha and th e median amplitude of the concentration parameter, c(norm), for a halo of m ass 10(14) h(-1) M-circle dot at z = 0 and compute the numbers of tangentia l 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 stati stic that is sensitive to both c(norm) and alpha 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 alpha. While our tentative comparison with the existing observ ational data indicates that the inner density profile of dark halos is inde ed as steep as predicted by recent simulations (alpha similar to 1.5), homo geneous samples of tangential and radial arcs are required for more quantit ative discussions.