In the wake of dark giants: new signatures of dark matter self-interactions in equal-mass mergers of galaxy clusters

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.