Towards an improved model of self-interacting dark matter haloes

We discuss the relation between the strength of the self-interaction of dark matter particles and the predicted properties of the inner density distributions of dark matter haloes. We present the results of N-body simulations for 28 galaxy cluster sized haloes performed with the same initial conditions for cold dark matter and for self-interacting dark matter with cross-sections ranging from 0.1 to 10 cm²/g. We provide a simple phenomenological description of these results and compare them to the semi-analytical model typically used in the literature. We find that some of the assumptions made in this model are not satisfied in the simulations. We identify the reasons for this disagreement and improve the semi-analytical model correspondingly. We discuss how simulation results can be properly compared with observations and in particular how quantities like the core radius and the inner dark matter surface density depend on the self-interaction cross-section.