Observable tests of self-interacting dark matter in galaxy clusters: BCG
  wobbles in a constant density core
  Models of Cold Dark Matter predict that the distribution of dark matter in
galaxy clusters should be cuspy, centrally concentrated. Constant density cores
would be strong evidence for beyond-CDM physics, such as Self-Interacting Dark
Matter (SIDM). An observable consequence would be oscillations of the Brightest
Cluster Galaxy (BCG) in otherwise relaxed galaxy clusters. Offset BCGs have
indeed been observed - but only interpreted via a simplified, analytic model of
oscillations. We compare these observations to the BAHAMAS-SIDM suite of
cosmological simulations, which include SIDM and a fully hydrodynamical
treatment of star formation and feedback. We predict that the median offset of
BCGs increases with the SIDM cross-section, cluster mass and the amount of
stellar mass within 10kpc, while CDM exhibits no trend in mass. Interpolating
between the simulated cross-sections, we find that the observations (of 10
clusters) is consistent with CDM at the ~1.5$\sigma$ level, and prefer
cross-section $\sigma$/m < 0.12(0.39)cm$^2$/g at 68% (95%) confidence level.
This is on the verge of ruling out velocity-independent dark matter
self-interactions as the solution to discrepancies between the predicted and
observed behaviour of dwarf galaxies, and will be improved by larger surveys by
Euclid or SuperBIT.
