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Self-Interacting Dark Matter is an attractive alternative to the Cold DarkMatter paradigm only if it is able to substantially reduce the centraldensities of dwarf-size haloes while keeping the densities and shapes ofcluster-size haloes within current constraints. Given the seemingly stringentnature of the latter, it was thought for nearly a decade that SIDM would beviable only if the cross section for self-scattering was stronglyvelocity-dependent. However, it has recently been suggested that a constantcross section per unit mass of sigma_T/m~0.1cm^2/g is sufficient to accomplishthe desired effect. We explicitly investigate this claim using high resolutioncosmological simulations of a Milky-Way size halo and find that, similarly tothe Cold Dark Matter case, such cross section produces a population of massivesubhaloes that is inconsistent with the kinematics of the classical dwarfspheroidals, in particular with the inferred slopes of the mass profiles ofFornax and Sculptor. This problem is resolved if sigma_T/m~1cm^2/g at the dwarfspheroidal scales. Since this value is likely inconsistent with the halo shapesof several clusters, our results leave only a small window open for avelocity-independent Self-Interacting Dark Matter model to work as a distinctalternative to Cold Dark Matter.

Constraining Self-Interacting Dark Matter with the Milky Way's dwarf spheroidals