Unequal-mass mergers of dark matter haloes with rare and frequent self-interactions

Dark matter (DM) self-interactions have been proposed to solve problems on small length scales within the standard cold DM cosmology. Here, we investigate the effects of DM self-interactions in merging systems of galaxies and galaxy clusters with equal and unequal mass ratios. We perform N-body DM-only simulations of idealized setups to study the effects of DM self-interactions that are elastic and velocity-independent. We go beyond the commonly adopted assumption of large-angle (rare) DM scatterings, paying attention to the impact of small-angle (frequent) scatterings on astrophysical observables and related quantities. Specifically, we focus on DM-galaxy offsets, galaxy--galaxy distances, halo shapes, morphology, and the phase--space distribution. Moreover, we compare two methods to identify peaks: one based on the gravitational potential and one based on isodensity contours. We find that the results are sensitive to the peak finding method, which poses a challenge for the analysis of merging systems in simulations and observations, especially for minor mergers. Large DM-galaxy offsets can occur in minor mergers, especially with frequent self-interactions. The subhalo tends to dissolve quickly for these cases. While clusters in late merger phases lead to potentially large differences between rare and frequent scatterings, we believe that these differences are non-trivial to extract from observations. We therefore study the galaxy/star populations which remain distinct even after the DM haloes have coalesced. We find that these collisionless tracers behave differently for rare and frequent scatterings, potentially giving a handle to learn about the micro-physics of DM.