Simulating realistic self-interacting dark matter models including small and large-angle scattering

Dark matter (DM) self-interactions alter the matter distribution on galactic scales and alleviate tensions with observations. A feature of the self-interaction cross section is its angular dependence, influencing offsets between galaxies and DM halos in merging galaxy clusters. While algorithms for modelling mostly forward-dominated or mostly large-angle scatterings exist, incorporating realistic angular dependencies, such as light mediator models, within $N$-body simulations remains challenging. We develop, validate and apply a novel and efficient method, combining existing approaches to describe small- and large-angle scattering regimes within a hybrid scheme. Below a critical angle the effective description via a drag force combined with transverse momentum diffusion is used, while above the angle dependence is sampled explicitly. First, we verify the scheme using a test set-up with known analytical solutions, and check that our results are insensitive to the choice of the critical angle within an expected range. Next, we demonstrate that our scheme speeds up the computations by multiple orders of magnitude for realistic light mediator models. Finally, we apply the method to galaxy cluster mergers and discuss the sensitivity of the offset between galaxies and DM to the angle dependence of the cross section. Our scheme ensures accurate offsets for mediator mass $m_\phi$ and DM mass $m_\chi$ within the range $0.1v/c\lesssim m_\phi/m_\chi\lesssim v/c$, while for larger (smaller) mass ratios the offsets obtained for isotropic (forward-dominated) self-scattering are approached. Here $v$ is the typical velocity scale. Equivalently, the upper condition can be expressed as $1.1\lesssim \sigma_{\rm tot}/\sigma_{\mathrm{\widetilde{T}}}\lesssim 10$ for the ratio of the total and momentum transfer cross sections, with the ratio being $1$ ($\infty$) in the isotropic (forward-dominated) limits.