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Are cosmological N-body simulations reliable on scales below the mean separation length of particles?
Published online by Cambridge University Press: 26 May 2016
Abstract
We critically examine the reliability of clustering below the mean separation length of particles in cosmological high-resolution N-body simulations. The particle discreteness effect imposes two fundamental limitations on those scales; the lack of the initial fluctuation power and the finite mass resolution. We address this problem applying the dark matter halo approach which makes us possible to examine separately how those two limitations affect the simulation results at later epochs. We find that the reliability of the simulations on scale below the mean particle separation is primarily determined by the mass of particles. Since the small scale matter clustering is dominated by the matter in a virialized halo, it is naturally expected that the small scale clustering becomes unreliable when the characteristic nonlinear mass for gravitationally collapsed objects at that time becomes smaller than the particle mass. This is confirmed by a detailed comparison with three major cosmological simulations. The characteristic mass, MNL(z), is approximately given by the condition σ(MNL, z) = 1. This mass scale should be much larger than the simulation particle mass mpart so as to reproduce the proper amplitude of the small scale clustering. This requirement can be translated to the criterion for the critical redshift zcrit when simulations reasonably resolve the clustering on scales below the mean separation: MNL(zcrit) = nhalompart, where we introduce a fudge factor, nhalo, of around ten. We conclude that at z > zcrit high-resolution N-body simulations are not reliable on scales below the mean particle separation. Although it is not obvious if the opposite is true at z < zcrit, our detailed comparison suggests that it is indeed the case at least as far as the two-point correlation functions of the matter are concerned. The detail discussions are presented in Hamana, Yoshida & Suto (2001).
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