The optimal gravitational softening length for cosmological N-body simulations

TL;DR

This study revises the optimal gravitational softening length in cosmological N-body simulations, showing that smaller lengths improve resolution but require careful calibration to avoid overprediction of inner halo densities.

Contribution

The paper proposes a modified optimal softening scheme based on Power et al. (2003), improving resolution and convergence in cosmological N-body simulations.

Findings

Smaller softening lengths yield higher spatial resolution.

Overly small softening lengths overpredict inner halo densities.

A modified scheme based on P03 improves simulation accuracy.

Abstract

Gravitational softening length is one of the key parameters to properly set up a cosmological $N$-body simulation. In this paper, we perform a large suit of high-resolution $N$-body simulations to revise the optimal softening scheme proposed by Power et al. (P03). Our finding is that P03 optimal scheme works well but is over conservative. Using smaller softening lengths than that of P03 can achieve higher spatial resolution and numerically convergent results on both circular velocity and density profiles. However using an over small softening length overpredicts matter density at the inner most region of dark matter haloes. We empirically explore a better optimal softening scheme based on P03 form and find that a small modification works well. This work will be useful for setting up cosmological simulations.