The Effect of Particle Noise in N-body Simulations of Gravitational Lensing

TL;DR

This paper analyzes how particle noise in N-body simulations affects gravitational lensing predictions, providing analytic expressions and empirical results to determine the resolution limits for resolving substructures.

Contribution

It introduces analytic formulas to quantify Poisson noise in simulations and assesses the resolution needed to reliably detect substructures affecting lensing.

Findings

Poisson noise scales with particle number and smoothing size.

Smallest resolvable substructures are roughly independent of lensing property.

Scaling relations connect simulation resolution to substructure detectability.

Abstract

High resolution dark matter only simulations provide a realistic and fully general means to study the theoretical predictions of cosmological structure formation models for gravitational lensing. Due to the finite number of particles, the density field only becomes smooth on scales beyond a few times the local mean interparticle separation. This introduces noise on the gravitational lensing properties such as the surface mass density, the deflection angles and the magnification. At some small-scale mass limit, the noise due to the discreteness of the N-body simulation becomes comparable to the effects of physical substructures. We present analytic expressions to quantify the Poisson noise and study its scaling with the particle number of the simulation and the Lagrangian smoothing size. We use the Phoenix set of simulations, currently the largest available dark matter simulations of clusters to study the effect of limited numerical resolution and the gravitational strong lensing effects of substructure. We quantify the smallest resolved substructure, in the sense that the effect of the substructure on any strong lensing property is significant compared to the noise, and we find that the result is roughly independent of the strong lensing property. A simple scaling relates the smallest resolved substructures in a simulation with the resolution of the N-body simulation.