Self-Similarity of $k$-Nearest Neighbor Distributions in Scale-Free Simulations

TL;DR

This paper evaluates the convergence of scale-free N-body simulations using the $k$NN-PDF, revealing that halos with 32 or more particles show good convergence, while fewer particles do not.

Contribution

It introduces the use of the $k$NN-PDF for assessing convergence in N-body simulations, incorporating non-Gaussian information and halo-based analysis.

Findings

Good convergence for halos with 32+ particles.

Halving softening length improves convergence at higher densities.

Limited sensitivity to voids, but convergence observed at 16+ particles in voids.

Abstract

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