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 self-interacting dark matter, but few simulations exist to back up this claim. We simulate equal-mass mergers of 10(15) M-circle dot 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 less than or similar to 20 kpc form for a self-interaction cross-section of sigma(SI)/m(chi) = 1 cm(2) g(-1). This is an order of magnitude smaller than those measured in observed equal-mass and near-equal-mass 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 sigma(SI)/m(chi) = 1 cm(2) 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 sigma(SI)/m(chi) to less than or similar to 0.1 cm(2) g(-1) - the tightest constraint yet.