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Many models of dark matter include self-interactions beyond gravity. Avariety of astrophysical observations have previously been used to place limitson the strength of such self-interactions. However, previous works havegenerally focused either on short-range interactions resulting in individualdark matter particles scattering from one another, or on effectivelyinfinite-range interactions which sum over entire dark matter halos. In thiswork, we focus on the intermediate regime: forces with range much larger thandark matter particles' inter-particle spacing, but still shorter than thelength scales of known halos. We show that gradients in the dark matter densityof such halos would still lead to observable effects. We focus primarily oneffects in the Bullet Cluster, where finite-range forces would lead either to amodification of the collision velocity of the cluster or to a separation of thedark matter and the galaxies of each cluster after the collision. We alsoconsider constraints from the binding of ultrafaint dwarf galaxy halos, andfrom gravitational lensing of the Abell 370 cluster. Taken together, theseobservations allow us to set the strongest constraints on dark matterself-interactions over at least five orders of magnitude in range, surpassingexisting limits by many orders of magnitude throughout.

Coherent Self-Interactions of Dark Matter in the Bullet Cluster