Cosmological simulations with self-interacting dark matter - II. Halo shapes versus observations

If dark matter has a large self-interaction scattering cross-section, then interactions among dark-matter particles will drive galaxy and cluster haloes to become spherical in their centres. Work in the past has used this effect to rule out velocity-independent, elastic cross-sections larger than σ/m ≃ 0.02 cm² g^-1 based on comparisons to the shapes of galaxy cluster lensing potentials and X-ray isophotes. In this paper, we use cosmological simulations to show that these constraints were off by more than an order of magnitude because (a) they did not properly account for the fact that the observed ellipticity gets contributions from the triaxial mass distribution outside the core set by scatterings, (b) the scatter in axis ratios is large and (c) the core region retains more of its triaxial nature than estimated before. Including these effects properly shows that the same observations now allow dark matter self-interaction cross-sections at least as large as σ/m = 0.1 cm² g^-1. We show that constraints on self-interacting dark matter from strong-lensing clusters are likely to improve significantly in the near future, but possibly more via central densities and core sizes than halo shapes.