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Effective description of dark matter self-interactions in small dark matter haloes

Self-interacting dark matter may have striking astrophysical signatures, such as observable offsets between galaxies and dark matter in merging galaxy clusters. Numerical N-body simulations used to predict such observables typically treat the galaxies as collisionless test particles, a questionable assumption given that each galaxy is embedded in its own dark matter halo. To enable a more accurate treatment we develop an effective description of small dark matter haloes taking into account the two major effects due to dark matter self-scatterings: deceleration and evaporation. We point out that self-scatterings can have a sizeable impact on the trajectories of galaxies, diminishing the separation between galaxies and dark matter in merging clusters. This effect depends sensitively on the underlying particle physics, in particular the angular dependence of the self-scattering cross section, and cannot be predicted from the momentum transfer cross section alone.