Testing self-interacting dark matter with galaxy warps

Self-interacting dark matter (SIDM) is an able alternative to collisionless dark matter. If dark matter does have self-interactions, we would expect this to cause a separation between the collisionless stars and the dark matter halo of a galaxy as it falls through a dark matter medium. For stars arranged in a disk, this would generate a U-shaped warp. The magnitude of this warping depends on the SIDM cross section, type of self-interaction, relative velocity of galaxy and background, halo structure, and density of the dark matter medium. In this paper we set constraints on long-range (light mediator) dark matter self-interaction by means of this signal. We begin by measuring U-shaped warps in 3,213 edge-on disk galaxies within the Sloan Digital Sky Survey. We then forward-model the expected warp from SIDM on a galaxy-by-galaxy basis by combining models of halo structure, density and velocity field reconstructions, and models for the dark matter interactions. We find no evidence for a contribution to the warps from SIDM. Our constraints are highly dependent on the uncertain velocities of our galaxies: we find (sigma) over tilde /m(DM) less than or similar to 3 x 10(-13) cm(2)/g at fixed velocity v = 300 km/s, a bound that scales roughly linearly with increasing v. We also consider galaxy velocities from the CosmicFlows-3 catalogue. These limits are stronger than those from dwarf galaxy evaporation, and we show that they scale well with additional data from the next generation of photometric galaxy surveys. Finally, we forecast constraints for contact and intermediate-range interactions that could be achieved with a similar sample of galaxies in cluster environments, where multistreaming and the fluid approximation are satisfied.