  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.
