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In this paper we study the density profiles of self-interacting dark matter(SIDM) haloes spanning the full observable mass range, from dwarf galaxies togalaxy clusters. Using realistic simulations that model the baryonic physicsrelevant for galaxy formation, we compare the density profiles of haloessimulated with either SIDM or cold and collisionless dark matter (CDM) to thoseinferred from observations of stellar velocity dispersion, gas rotation curves,weak and strong gravitational lensing, and/or X-ray maps. We make ourcomparison in terms of the maximal surface density of haloes, circumventing theneed 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 wellreproduced by CDM simulations that include baryons, while for SIDM with avelocity-independent cross-section of 1 cm$^2/$g, the simulated galaxy clustershave mean maximal surface densities that are below those of observed systems byan amount greater than the standard deviation of the observed maximal surfacedensity at fixed mass. For less massive systems both CDM and SIDM agree withthe observation equally well.

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