  Recently, Meneghetti et al. reported an excess of small-scale gravitational
lenses in galaxy clusters, compared to simulations of standard cold dark matter
(CDM). We propose a self-interacting dark matter (SIDM) scenario, where a
population of subhalos in the clusters experiences gravothermal collapse. Using
controlled N-body simulations, we show the presence of early-type galaxies in
substructures accelerates gravothermal evolution and a collapsed SIDM subhalo
has a steeper density profile than its CDM counterpart, leading to a larger
radial galaxy-galaxy strong lensing cross section and more lens images, in
better agreement with the observations. Our results indicate that strong
gravitational lensing can provide a promising test of the self-interacting
nature of dark matter.
