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

Merging galaxy clusters are a promising laboratory for measuring the self-interaction cross-section (SICS) of dark matter. However, previous studies have focused on galaxy-mass 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 sigma/m. Applying this method to a gold sample of eleven cluster mergers hosting symmetric double radio relics, we determine a 68% upper limit on the SICS of sigma/m < 0.22 cm^2/g. 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.