Mergers of galaxy clusters, the largest bound structures in the universe, act as cosmic particle colliders, and are thus prime testbeds for dark sector physics. In particular, they are a unique probe of dark matter collisionality (i.e. momentum-transfer inducing self-interactions). After two galaxy clusters collide, each cluster component---the gas, galaxies, and dark matter---separate with post-impact speeds that depend on their collisionality. This causes the effectively collisonless galaxies to lead, while the highly collisional gas lags behind. An offset between the dark matter and the galaxies can thus provide a measure of the strength of dark matter self-interactions, quantified by the self-interaction cross section. However, the mapping between dark matter-galaxy offsets and the cross section had hitherto not been well studied.
I simulated a suite of equal mass cluster mergers to study this mapping. Given current cross section limits ~1 cm^2/g, I found that offsets are small---at most ~20 kpc. This is smaller than the measurement uncertainties, which are as large as several 10s to 100 kpc due in large part to the uncertainty in measuring the centroid of a poorly sampled galaxy distribution. Furthermore, offsets are short lived, peaking during the cluster collision and decaying quickly after due to the restorative gravitational pull of the dark matter on the galaxies. This contradicted the prevailing assumption that offsets continually grew after collision. Observed offsets, which have been measured to be as large as a few 100 kpc, are likely to be a product of measurement uncertainties rather than dark matter self-interactions.
Although competitive cross-section constraints are thus unlikely to emerge from offsets, I identified a more promising constraint. I showed that after a cluster merger, the brightest cluster galaxies (BCGs) oscillate in the remnant core with orbital amplitudes that depend sensitively on how strongly dark matter self-interacts. This implies that we should see miscentered BCGs in relaxed, post-merger clusters. Observed miscenterings are fairly small---BCGs are in fact considered the best measure of the cluster center in some studies---which indicates that this could provide one of the strongest constraints on the self-interaction cross section to date.
For more details, check out our paper In the Wake of Dark Giants: New Signatures of Dark Matter Self-Interactions in Equal Mass Mergers of Galaxy Clusters.
You can also check out a video summary I made of our results on Youtube here.