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

TL;DR

This paper assesses the accuracy of radial pairwise velocity measurements in large-scale N-body simulations using scale-free models, demonstrating convergence at sub-percent levels and providing insights into resolution limits over cosmic time.

Contribution

It introduces a detailed analysis of velocity convergence in high-resolution N-body simulations, comparing estimators and establishing resolution benchmarks for scale-free cosmologies.

Findings

Convergence at 1% level for mean relative pairwise velocity over a range of scales.

Down to smoothing scale, convergence reaches approximately 5% precision.

Provides estimates on resolution evolution in LCDM simulations across redshifts.

Abstract

We present a continuation of an analysis that aims to quantify resolution of $N$-body simulations by exploiting large (up to $N=4096^3$) 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-2PCF (using the pair conservation equation). We find that convergence at the $1\%$ 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 order of the smoothing parameter, convergence is obtained at $\sim5\%$ 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 $5\%$ precision) as a function of redshift.