Self-Interacting Dark Matter and Small-Scale Gravitational Lenses in
  Galaxy Clusters
  Recently, Meneghetti et al. reported an excess of small-scale gravitational
lenses in galaxy clusters. We study its implications for self-interacting dark
matter (SIDM), compared with standard cold dark matter (CDM). We design
controlled N-body simulations that incorporate observational constraints. The
presence of early-type galaxies in cluster substructures can deepen
gravitational potential and reduce tidal mass loss. Both scenarios require a
relatively high baryon concentration in the substructure to accommodate the
lensing measurements, and their tangential caustics are similar. The SIDM
substructure can experience gravothermal collapse and produce a steeper density
profile than its CDM counterpart, leading to a larger radial galaxy-galaxy
strong lensing cross section, although this effect is hard to observe. Our
results indicate SIDM can provide a unified explanation to small-scale lenses
in galaxy clusters and stellar motions in dwarf galaxies.
