Good and proper: self-similarity of N-body simulations with proper force softening

Analysis of self-similarity in scale-free N-body simulations reveals the spatial and temporal scales for which statistics measured in cosmological simulations are converged to the physical continuum limit. We examine how the range of scales in which the two-point correlation function is converged depends on the force softening length and whether it is held constant in comoving or proper coordinates. We find that a proper softening that reaches roughly 1/30th of the inter-particle spacing by the end of the simulation resolves the same spatial and temporal scales as a comoving softening of the same length while using a third fewer time-steps, for a range of scale factors typical to Lambda cold dark matter (Lambda CDM) simulations. We additionally infer an inherent resolution limit, set by the particle mass and scaling as a(-1/2), beyond which reducing the softening does not improve the resolution. We postulate a mapping of these results with spectral index n = -2 to Lambda CDM simulations.

Automated summary

Self-similarity analysis in scale-free N-body simulations helps determine the spatial and temporal scales at which statistics converge to the physical continuum limit. Proper softening reaching 1/30th of inter-particle spacing by the end of the simulation can resolve similar scales as comoving softening of the same length with fewer time steps in Lambda CDM simulations. Additionally, there is an inherent resolution limit set by particle mass, beyond which reducing softening does not improve resolution, suggesting a relationship with spectral index n = -2 in Lambda CDM simulations.