UC Davis

Merging galaxy clusters have been touted as one of the best probes for constraining selfinteracting darkmatter, but fewsimulations exist to back up this claim. We simulate equal-mass mergers of 1015 M⊙ haloes, like the El Gordo and Sausage clusters, with cosmologically motivated halo and merger parameters, and with velocity-independent dark-matter self-interactions. Although the standard lore for merging clusters is that self-interactions lead to large separations between the galaxy and dark-matter distributions, we find that maximal galaxy-dark matter offsets of ≲20 kpc form for a self-interaction cross-section of σSI/mχ = 1 cm2 g-1. This is an order of magnitude smaller than those measured in observed equal-mass and near-equalmass mergers, and is likely to be even smaller for lower mass systems. While competitive cross-section constraints are thus unlikely to emerge from offsets, we find other signatures of self-interactions that are more promising. Intriguingly, we find that after dark-matter haloes coalesce, the collisionless galaxies [and especially the brightest cluster galaxy (BCG)] oscillate around the centre of the merger remnant on stable orbits of 100 kpc for σSI/mχ =1 cm2 g-1 for at least several Gyr, well after the clusters have relaxed. If BCG miscentring in relaxed clusters remains a robust prediction of self-interacting dark matter under the addition of gas physics, substructure, merger mass ratios (e.g. 10:1 like the Bullet Cluster) and complex cosmological merger histories, the observed BCG offsets may constrain σSI/mχ to ≲0.1 cm2 g-1 - the tightest constraint yet.