Convergence tests of SIDM N-body simulations

Self-interacting dark matter (SIDM) theory predicts that dark matter halos experience core collapse, a process where the halo's inner region rapidly increases in density and decreases in size. The N-body simulations used to study this process can suffer from numerical errors when simulation parameters are selected incorrectly. Optimal choices for simulation parameters are well-studied for cold dark matter (CDM) but are not deeply understood when self-interactions are included. In order to perform reliable N-body simulations and model core-collapse accurately we must understand the potential numerical errors, how to diagnose them, and what parameter selections must be made to reduce them. We use the Arepo N-body code to perform convergence tests of core-collapsing SIDM halos across a range of halo concentrations and SIDM cross-sections and quantify potential numerical issues related to mass resolution, timestep size, and gravitational softening length. Our tests discover that halos with fewer than 105 simulation particles, a resolution typically not met by subhalos in N-body simulations, suffer from significant discreteness noise that leads to variation and extreme outliers in the collapse rate. At our lowest resolution of N=104 particles, this collapse time variation can reach as high as 20%. At this low resolution, we also find a bias in collapse times and a small number of extreme outliers. Additionally, we find that simulations that run far beyond the age of the Universe, which have been used to calibrate SIDM gravothermal fluid models in previous work, have a sensitivity to the timestep size that is not present in shorter simulations or simulations using only CDM. Our work shows that choices of simulation parameters that yield converged results for some halo masses and SIDM models do not necessarily yield convergence for others.

Methods
This dataset contains snapshots of simulations run in the N-body code Arepo, with the addition of a scattering interaction between dark matter particles. The snapshots are organized by simulation run and are saved as hdf5 files output by Arepo. The snapshots have not been processed, aside from the removal of some data (such as local particle density) to save space. The results of our publication can be replicated using the remaining particle data: mass, positions, velocities, potentials, number of scattering events, and ID numbers.

In addition to the N-body output, we also share reduced data files. These files contain halo central densities versus time and were computed from the N-body data using the method described in section II.D of our publication.