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Weakly Self-Interacting Dark Matter and the Structure of Dark Halos

We study the formation of dark halos in a $Λ$CDM universe under the assumption that Cold Dark Matter particles have a finite cross-section for elastic collisions. We compare evolution when CDM mean free paths are comparable to halo sizes with the collisionless and fluid limits. We show that a few collisions per particle per Hubble time at halo centre can substantially affect the central density profile. Cross-sections an order of magnitude larger produce sufficient relaxation for rich clusters to develop core radii in the range 100-200 $h^{-1}$kpc. The structural evolution of halos is a competition between collisional relaxation caused by individual particle interactions and violent relaxation resulting from the infall and merging processes by which clusters grow. Although our simulations concentrate on systems of cluster size, we can scale our results to address the halo structure expected for dwarf galaxies. We find that collision cross-sections sufficiently large to significantly modify the cores of such galaxies produce cluster cores which are too large and/or too round to be consistent with observation. Thus the simplest model for self-interacting dark matter is unable to improve fits to published dwarf galaxy rotation curves without violating other observational constraints.