Self-similarity of k-nearest neighbour distributions in scale-free simulations

ABSTRACT We use the k-nearest neighbour probability distribution function (kNN-PDF; Banerjee & Abel 2021a) to assess convergence in a scale-free N-body simulation. Compared to our previous two-point analysis, the kNN-PDF allows us to quantify our results in the language of haloes and numbers of particles, while also incorporating non-Gaussian information. We find good convergence for 32 particles and greater at densities typical of haloes, while 16 particles and fewer appear unconverged. Halving the softening length extends convergence to higher densities, but not to fewer particles. Our analysis is less sensitive to voids, but we analyse a limited range of underdensities and find evidence for convergence at 16 particles and greater even in sparse voids.