Radial Arc statistics: A powerful new probe of the central density profile of galaxy clusters

We show that the number ratio of radial arcs to tangential arcs in a cluster of galaxies depends sensitively on the central density profile of galaxy clusters but depends little on the lensing parameter and the threshold ellipticity of the lensed images. Based on these results, we propose a method to constrain the central density profile of clusters using radial arc statistics. A tentative comparison with the observations shows that radial arc statistics can be a powerful tool for constraining the cluster central density profile. Our results show that a systematic survey of radial and tangential arcs for an unbiased uniform cluster sample can be a promising test of the fundamental characteristics of dark matter.