From dwarf galaxies to galaxy clusters: Self-Interacting Dark Matter over 7 orders of magnitude in halo mass

In this paper we study the density profiles of self-interacting dark matter (SIDM) haloes spanning the full observable mass range, from dwarf galaxies to galaxy clusters. Using realistic simulations that model the baryonic physics relevant for galaxy formation, we compare the density profiles of haloes simulated with either SIDM or cold and collisionless dark matter (CDM) to those inferred from observations of stellar velocity dispersion, gas rotation curves, weak and strong gravitational lensing, and/or X-ray maps. We make our comparison in terms of the maximal surface density of haloes, circumventing the need for semi-analytic or parametric models for dark matter density profiles. We find that the maximal surface density as a function of halo mass is well reproduced by simulations of CDM that include baryons, and that a SIDM cross-section of 1 cm$^2/$g is marginally excluded. This constraint is driven mainly by galaxy clusters, with less massive systems being relatively less affected by DM self-interactions with velocity-independent cross-section.