A Test of the Collisional Dark Matter Hypothesis from Cluster Lensing

Spergel & Steinhardt proposed the possibility that the dark matter particlesare self-interacting, as a solution to two discrepancies between thepredictions of cold dark matter models and the observations: first, theobserved 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. Thedark matter self-interaction would produce isothermal cores in halos, and wouldalso expel the dark matter particles from dwarfs orbiting within large halos.However, another inevitable consequence of the model is that halos shouldbecome spherical once most particles have interacted. Here, I rule out thismodel by the fact that the innermost regions of dark matter halos in massiveclusters of galaxies are elliptical, as shown by gravitational lensing andother observations. The absence of collisions in the lensing cores of massiveclusters implies that any dark matter self-interaction is too weak to haveaffected the observed density profiles in the dark-matter dominated dwarfgalaxies, or to have eased the destruction of dwarf satellites in galactichalos. If $s_x$ is the cross section and $m_x$ the mass of the dark matterparticle, then $s_x/m_x < 10^{-25.5} \cm^2/\gev$