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

Context. Dark matter (DM) self-interactions alter matter distribution on galactic scales and alleviate tensions with observations. A feature of the self-interaction cross section is its angular dependence, which influences 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 within N-body simulations remains challenging. Aims. To efficiently simulate models with a realistic angle dependence, such as light mediator models, we developed, validated, and applied a novel method. Methods. We combined existing approaches to describe small- and large-angle scattering regimes within a hybrid scheme. Below a critical angle, the scheme uses the effective description of small-angle scattering via a drag force combined with transverse momentum diffusion, while above the angle, it samples the dependence explicitly. Results. We first verified the scheme using a test set-up with known analytical solutions, and we checked that our results are insensitive to the choice of the critical angle within an expected range. Next, we demonstrated that our scheme speeds up the computations by multiple orders of magnitude for realistic light mediator models. Finally, we applied the method to galaxy cluster mergers. We 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 mϕ and DM mass mχ within the range 0.1v/c ≲ mϕ/mχ ≲ 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_{\mathrm{tot}}/\sigma_{\mathrm{\widetilde{T}}}\lesssim 10 $ for the ratio of the total and momentum transfer cross sections, with the ratio being 1 (∞) in the isotropic (forward-dominated) limits.