  Mergers of galaxy clusters are promising probes of dark matter (DM) physics.
For example, an offset between the DM component and the galaxy distribution can
constrain DM self-interactions. We investigate the role of the intracluster
medium (ICM) and its influence on DM-galaxy offsets in self-interacting dark
matter models. To this end, we employ Smoothed Particle Hydrodynamics + N-body
simulations to study idealized setups of equal- and unequal-mass mergers with
head-on collisions. Our simulations show that the ICM hardly affects the
offsets arising shortly after the first pericentre passage compared to DM-only
simulations. But later on, e.g. at the first apocentre, the offsets can be
amplified by the presence of the ICM. Furthermore, we find that cross-sections
small enough not to be excluded by measurements of the core sizes of relaxed
galaxy clusters have a chance to produce observable offsets. We found that
different DM models affect the DM distribution and also the galaxy and ICM
distribution, including its temperature. Potentially, the position of the shock
fronts, combined with the brightest cluster galaxies, provides further clues to
the properties of DM. Overall our results demonstrate that mergers of galaxy
clusters at stages about the first apocentre passage could be more interesting
in terms of DM physics than those shortly after the first pericentre passage.
This may motivate further studies of mergers at later evolutionary stages.
