The effect of particle noise in N-body simulations of gravitational lensing

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.