A test of the collisional dark matter hypothesis from cluster lensing

Spergel & Steinhardt proposed the possibility that dark matter particles are self-interacting as a solution to two discrepancies between the predictions of cold dark matter models and 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 expel the dark matter particles from dwarfs orbiting in large halos. Another consequence of the model is that halos should become spherical once most particles have interacted. Several observations show that the mass distribution in relaxed clusters of galaxies is elliptical. Here, I discuss in particular gravitational lensing in the cluster MS 2137-23, where the ellipticity of the dark matter distribution can be measured to a small radius, r similar to 70 kpc, suggesting that most dark matter particles in clusters outside this radius do not collide during the characteristic age of clusters. If true, this implies that any dark matter self-interaction with a cross section independent of velocity is too weak to have affected the observed density profiles in the dark-matter dominated dwarf galaxies, or to have facilitated 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-1.