Collisionless shocks in self-interacting dark matter

Self-interacting dark matter (DM) has been proposed as a solution to small scale problems in cosmological structure formation, and hints of DM self scattering have been observed in mergers of galaxy clusters. One of the simplest models for self-interacting DM is a particle that is charged under dark electromagnetism, a new gauge interaction analogous to the usual electromagnetic force, but operating on the DM particle instead of the visible particles. In this case, the collisional behaviour of DM is primarily due to the formation of collisionless shocks, that should affect the distribution of DM in merging galaxy clusters. We evaluate the time and length scales of shock formation in cluster mergers, and discuss the implications for modelling charged DM in cosmological simulations.