The fundamental properties of the postulated dark matter (DM) affect the internal structure of gravitationally bound structures. In the cold dark matter paradigm, DM particles interact only via... Show moreThe fundamental properties of the postulated dark matter (DM) affect the internal structure of gravitationally bound structures. In the cold dark matter paradigm, DM particles interact only via gravity. Their distribution is well represented by an Einasto profile with shape parameter alpha approximate to 0.18 in the smallest dwarf galaxies or the most massive galaxy clusters alike. Conversely, if DM particles self-interact via additional forces, we expect the mass density profiles of DM halos to flatten in their central regions, thereby increasing the Einasto shape parameter. We measured the structural properties of 12 massive galaxy clusters from observations of their hot gaseous atmosphere, using the X-ray observatory XMM-Newton, and of the Sunyaev-Zel'dovich effect using the Planck all-sky survey. After removing morphologically disturbed systems, we measured Einasto shape parameters with mean =0.19 +/- 0.03 and intrinsic scatter sigma(alpha)=0.06, which is in close agreement with the prediction of the cold dark matter paradigm. We used cosmological hydrodynamical simulations of cluster formation with self-interacting DM (BAHAMAS-SIDM) to determine how the Einasto shape parameter depends on the self-interaction cross section. We used the fitted relation to turn our measurements of alpha into constraints on the self-interaction cross section, which imply sigma/m< 0.19 cm(2) g(-1) (95% confidence level) at collision velocity v(DM - DM)similar to 1000 km s(-1). This is lower than the interaction cross section required for DM self-interactions to solve the core-cusp problem in dwarf spheroidal galaxies, unless the cross section is a strong function of velocity. Show less
