Comment on 'Discreteness Effects in Simulations of Hot/Warm Dark Matter' by J. Wang & S.D.M. White

TL;DR

This paper highlights a fundamental issue in dark matter N-body simulations, showing that particle discreteness causes spurious fluctuations that limit the accuracy of small-scale results, challenging previous conclusions in the field.

Contribution

It reveals that small-scale simulation results are limited by particle discreteness effects, not just force softening, and this problem has been largely unacknowledged for 25 years.

Findings

Spurious fluctuations grow rapidly due to particle discreteness.

Small-scale results are limited by N^-1/3, not force softening.

Many past small-scale dark matter simulation results are questionable.

Abstract

Wang and White (2007) have discussed some problems with N-body simulation methods. These problems are a special case of a more general problem which has been largely unacknowledged for approximately 25 years, and affects results of all dark matter simulations on small scales (the definition of 'small' varying with time). Extensive numerical experiments with multiple types of N-body codes have demonstrated that spurious fluctuations due to particle discreteness grow rapidly even in the presence of substantial small-scale power from the intended model spectrum, and modify the results on scales smaller than the mean comoving interparticle separation. This implies that the spatial resolution of such simulations is typically limited not by the force softening length, often referred to as the 'resolution', and not by the particle density in halos. Instead it is approximately N^-1/3, where N is the mean particle density, and of course depends on and improves very slowly with increased number of particles. This calls into question many results on smaller scales over more than two decades.