On the effects of resolution in dissipationless cosmological simulations

We present a study of numerical effects in dissipationless cosmological simulations. The numerical effects are evaluated and studied by comparing the results of a series of 64³-particle simulations of varying force resolution and number of time-steps, performed using three of the N-body techniques currently used for cosmological simulations: the Particle-Mesh (PM), the Adaptive Particle-Particle-Particle-Mesh (AP³M) and the newer Adaptive Refinement Tree (ART) codes. This study can therefore be interesting both as an analysis of numerical effects and as a systematic comparison of different codes. We find that the AP³M and the ART codes produce similar results given that convergence is reached within the code type. We also find that numerical effects may affect the high-resolution simulations in ways that have not been discussed before. In particular, our study revealed the presence of two-body scattering, the effects of which can be greatly amplified by inaccuracies in time integration. This process appears to affect the correlation function of matter, the mass function, the inner density of dark matter haloes and other statistics at scales much larger than the force resolution, although different statistics may be affected in a different fashion. We discuss the conditions for which strong two-body scattering is possible and discuss the choice of the force resolution and integration time-step. Furthermore, we discuss recent claims that simulations with force softening smaller than the mean interparticle separation are not trustworthy and argue that this claim is incorrect in general, and applies only to the phase-sensitive statistics. Our conclusion is that, depending on the choice of mass and force resolution and the integration time-step, a force resolution as small as 0.01 of the mean interparticle separation can be justified.