  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.
