A New Robust Constraint on the Self-interaction Cross Section of Dark Matter with Double Radio Relic Clusters

Abstract Merging galaxy clusters are a promising laboratory for measuring the self-interaction cross section (SICS) of dark matter. However, previous studies have focused on mass-galaxy offsets, which numerical simulations have shown to be intrinsically small because galaxies remain tightly coupled to the dominant dark matter potential even with significant self-interaction. Their interpretation is further complicated by unknowns of the merger phase, geometry, and initial conditions. In this paper, we overcome these obstacles by introducing the shock-to-shock distance, traced by double radio relics, as a merger chronometer that time-stamps the post-pericenter dynamical phase. Because the propagation speed of merger shocks is nearly independent of the SICS, while the halo-to-halo distance is depressed by SIDM-induced drag, the ratio of the two distances translates directly into a constraint on σ / m . Applying this method to a gold sample of 11 cluster mergers hosting symmetric double radio relics, we determine an upper limit on the SICS of σ / m < 0.22 (0.63) cm 2 g −1 at the 68% (95%) confidence level. This is the first constraint from cluster collisions that fully marginalizes over mass uncertainty, viewing angle, collision speed, merger phase, impact parameter, and gas profile slope.