Testing the Collisionless Nature of Dark Matter with the Radial Acceleration Relation in Galaxy Clusters

The radial acceleration relation (RAR) represents a tight empirical relation between the inferred total and baryonic centripetal accelerations, $g_{\rm{tot}}=GM_{\rm{tot}}(<r)/r^2$ and $g_{\rm{bar}}=GM_{\rm{bar}}(<r)/r^2$, observed in galaxies and galaxy clusters. The tight correlation between these two quantities can provide insight into the nature of dark matter. Here we use BAHAMAS, a state-of-the-art suite of cosmological hydrodynamical simulations, to characterize the RAR in cluster-scale halos for both cold and collisionless dark matter (CDM) and self-interacting dark matter (SIDM) models. SIDM halos generally have reduced central dark matter densities, which reduces the total acceleration in the central region when compared with CDM. We compare the RARs in galaxy clusters simulated with different dark matter models to the RAR inferred from CLASH observations. Our comparison shows that the cluster-scale RAR in the CDM model provides an excellent match to the CLASH RAR obtained by Tian et al. including the high-acceleration regime probed by the brightest cluster galaxies (BCGs). By contrast, models with a larger SIDM cross-section yield increasingly poorer matches to the CLASH RAR. Excluding the BCG regions results in a weaker but still competitive constraint on the SIDM cross-section. Using the RAR data outside the central $r<100$kpc region, an SIDM model with $\sigma/m=0.3$cm$^{2}$g$^{-1}$ is disfavored at the $3.8\sigma$ level with respect to the CDM model. This study demonstrates the power of the cluster-scale RAR for testing the collisionless nature of dark matter.