What does the Bullet Cluster tell us about self-interacting dark matter?

We perform numerical simulations of the merging galaxy cluster 1E 0657-56 (the Bullet Cluster), including the effects of elastic dark matter scattering. In a similar manner to the stripping of gas by ram pressure, dark matter self-interactions would transfer momentum between the two galaxy-cluster dark matter haloes, causing them to lag behind the collisionless galaxies. The absence of an observed separation between the dark matter and stellar components in the Bullet Cluster has been used to place upper limits on the cross-section for dark matter scattering. We emphasize the importance of analysing simulations in an observationally motivated manner, finding that the way in which the positions of the various components are measured can have a larger impact on derived constraints on dark matter's self-interaction cross-section than reasonable changes to the initial conditions for the merger. In particular, we find that the methods used in previous studies to place some of the tightest constraints on this cross-section do not reflect what is done observationally, and overstate the Bullet Cluster's ability to constrain the particle properties of dark matter. We introduce the first simulations of the Bullet Cluster including both self-interacting dark matter and gas. We find that as the gas is stripped it introduces radially dependent asymmetries into the stellar and dark matter distributions. As the techniques used to determine the positions of the dark matter and galaxies are sensitive to different radial scales, these asymmetries can lead to erroneously measured offsets between dark matter and galaxies even when they are spatially coincident.