We develop a statistical method to measure the interaction cross-section of dark matter, exploiting the continuous minor merger events in which small substructures fall into galaxy clusters. We find that by taking the ratio of the distances between the galaxies and dark matter, and galaxies and gas in accreting subhaloes, we form a quantity that can be statistically averaged over a large sample of systems whilst removing any inherent line-of-sight projections. To interpret this ratio as a cross-section of dark matter, we derive an analytical description of subhalo infall allowing us to constrain self-interaction models in which drag is an appropriate macroscopic treatment. We create mock observations from cosmological simulations of structure formation and find that collisionless darkmatter becomes physically separated from X-ray gas by up to similar to 20 h(-1) kpc. Adding realistic levels of noise, we are able to predict achievable constraints from observational data. Current archival data should be able to detect a difference in the dynamical behaviour of dark matter and standard model particles at 6 sigma, and measure the total interaction cross-section sigma/m with 68 per cent confidence limits of +/-1 cm(2) g(-1). We note that this method is not restricted by the limited number of major merging events and is easily extended to large samples of clusters from future surveys which could potentially push statistical errors to <0.1 cm(2) g(-1).
- dark matter