Accurately simulating core-collapse self-interacting dark matter halos

Context . The properties of satellite halos provide a promising probe for dark matter (DM) physics. Observations have motivated current efforts to explain surprisingly compact DM halos. If DM is not collisionless, but has strong self-interactions, halos can undergo gravothermal collapse, leading to higher densities in the central region of the halo. However, it is challenging to model this collapse phase from first principles. Aims . To improve on this, we sought to better understand the numerical challenges and convergence properties of self-interacting dark matter (SIDM) N -body simulations in the collapse phase. Especially, our aim was to better understand the evolution of satellite halos. Methods . To do so, we ran SIDM N -body simulations of a low-mass halo in isolation and within an external gravitational potential. The simulation set-up was motivated by the perturber of the stellar stream GD-1. Results . We find that the halo evolution is very sensitive to energy conservation errors, and a SIDM kernel size that is too large can artificially speed up the collapse. Moreover, we demonstrate that the King model can describe the density profile at small radii for the late stages that we have simulated. Furthermore, for our most highly resolved simulation ( N = 5 × 10 7 ) we have made the data public. It can serve as a benchmark. Conclusions . Overall, we find that the current numerical methods do not suffer from convergence problems in the late collapse phase and provide guidance on how to choose numerical parameters, for example that the energy conservation error is better kept well below 1%. This allows simulations to be run of halos that become concentrated enough to explain observations of GD-1-like stellar streams or strong gravitational lensing systems.