Constraining accuracy of the pairwise velocities in N-body simulations using scale-free models

We present a continuation of an analysis that aims to quantify resolution of N-body simulations by exploiting large (up to N = 4096³) simulations of scale-free cosmologies run using ABACUS. Here, we focus on radial pairwise velocities of the matter field, both by direct estimation and through the cumulative two-point correlation function (using the pair conservation equation). We find that convergence at the 1 per cent level of the mean relative pairwise velocity can be demonstrated over a range of scales, evolving from a few times the grid spacing at early times to slightly below this scale at late times. We show the analysis of two different box sizes as well as from averaging results from the smaller boxes, and compare the power of the two aforementioned estimators in constraining accuracy at each scale. Down to scales of the order of the smoothing parameter, convergence is obtained at ~$5~{{\rm per\, cent}}$ precision, and shows a behaviour indicating asymptotic stable clustering. We also infer for LCDM simulations conservative estimates on the evolution of the lower cut-off to resolution (at 1 and 5 per cent precision) as a function of redshift.