Coherent self-interactions of dark matter in the Bullet Cluster

Many models of dark matter include self-interactions beyond gravity. A variety of astrophysical observations have previously been used to place limits on the strength of such self-interactions. However, previous works have generally focused either on short-range interactions resulting in individual dark matter particles scattering from one another, or on effectively infinite-range interactions which sum over entire dark matter halos. In this work, we focus on the intermediate regime: forces with range much larger than dark matter particles' inter-particle spacing, but still shorter than the length scales of known halos. We show that gradients in the dark matter density of such halos would still lead to observable effects. We focus primarily on effects in the Bullet Cluster, where finite-range forces would lead either to a modification of the collision velocity of the cluster or to a separation of the dark matter and the galaxies of each cluster after the collision. We also consider constraints from the binding of ultrafaint dwarf galaxy halos, and from gravitational lensing of the Abell 370 cluster. Taken together, these observations allow us to set the strongest constraints on dark matter self-interactions over many orders of magnitude in range below ∼10 kpc, surpassing existing limits by orders of magnitude throughout.