A Test of the Collisional Dark Matter Hypothesis from Cluster Lensing
  Spergel & Steinhardt proposed the possibility that the dark matter particles are self-interacting, as a solution to two discrepancies between the predictions of cold dark matter models and the observations: first, the observed dark matter distribution in some dwarf galaxies has large, constant-density cores, as opposed to the predicted central cusps; and second, small satellites of normal galaxies are much less abundant than predicted. The dark matter self-interaction would produce isothermal cores in halos, and would also expel the dark matter particles from dwarfs orbiting within large halos. However, another inevitable consequence of the model is that halos should become spherical once most particles have interacted. Here, I rule out this model by the fact that the innermost regions of dark matter halos in massive clusters of galaxies are elliptical, as shown by gravitational lensing and other observations. The absence of collisions in the lensing cores of massive clusters implies that any dark matter self-interaction is too weak to have affected the observed density profiles in the dark-matter dominated dwarf galaxies, or to have eased the destruction of dwarf satellites in galactic halos. If $s_x$ is the cross section and $m_x$ the mass of the dark matter particle, then $s_x/m_x < 10^{-25.5} \cm^2/\gev$. 
Jordi Miralda-Escude (The Ohio State University)