Simulations of core formation for frequent dark matter self-interactions

We present the first $N$-body simulations that adapt the equations of smoothed particle hydrodynamics to capture the effect of dark matter self-interactions which are too frequent to be resolved explicitly. The relevant energy transfer equations are derived, the appropriate thermal conductivity is determined and the effects of different smoothing kernels are studied. We apply our framework to simulate the formation of isothermal cores in isolated dark matter haloes and determine the core growth rate as a function of the self-scattering cross section. Our approach may be combined with explicit simulations of rare scatterings in order to simulate accurately the effects of arbitrary dark matter self-interactions in future cosmological simulations.