Constraints on dark matter physics from dwarf galaxies through galaxy cluster haloes

One of the predictions of the standard cold dark matter model is that dark haloes have centrally divergent density profiles. An extensive body of rota tion curve observations of dwarf and low surface brightness galaxies shows the dark haloes of those systems to be characterized by soft constant-densi ty central cores. Several physical processes have been proposed to produce soft cores in dark haloes, each one with different scaling properties. With the aim of discriminating among them we have examined the rotation curves of dark-matter-dominated dwarf and low surface brightness galaxies and the inner mass profiles of two clusters of galaxies lacking a central cD galaxy and with evidence of soft cores in the centre. The core radii and central densities of these haloes scale in a well-defined manner with the depth of their potential wells, as measured through the maximum circular velocity. A s a result of our analysis we identify self-interacting cold dark matter as a viable solution to the core problem, where a non-singular isothermal cor e is formed in the halo centre surrounded by a Navarro, Frenk & White profi le in the outer parts. We show that this particular physical situation pred icts core radii in agreement with observations. Furthermore, using the obse rved scalings, we derive an expression for the minimum cross-section (sigma ) which has an explicit dependence with the halo dispersion velocity (v). I f m(x) is the mass of the dark matter particle: sigmam(x)approximate to 4x1 0(-25) (100 km s(-1) v(-1)) cm(2) GeV-1.