On the effects of resolution in dissipationless cosmological simulations

We present a study of numerical effects in dissipationless cosmological sim ulations. The numerical effects are evaluated and studied by comparing the results of a series of 64(3)-particle simulations of varying force resoluti on and number of time-steps, performed using three of the N-body techniques currently used for cosmological simulations: the Particle-Mesh (PM), the A daptive Particle-Particle-Particle-Mesh (AP(3)M) and the newer Adaptive Ref inement Tree (ART) codes, This study can therefore be interesting both as a n analysis of numerical effects and as a systematic comparison of different codes. We find that the AP(3)M and the ART codes produce similar results given tha t convergence is reached within the code type. We also find that numerical effects may affect the high-resolution simulations in ways that have not be en discussed before. In particular, our study revealed the presence of two- body scattering, the effects of which can be greatly amplified by inaccurac ies in time integration. This process appears to affect the correlation fun ction of matter, the mass function, the inner density of dark matter haloes and other statistics at scales much larger than the force resolution, alth ough different statistics may be affected in a different fashion. We discus s the conditions for which strong two-body scattering is possible and discu ss the choice of the force resolution and integration time-step. Furthermor e, we discuss recent claims that simulations with force softening smaller t han the mean interparticle separation are not trustworthy and argue that th is claim is incorrect in general, and applies only to the phase-sensitive s tatistics. Our conclusion is that, depending on the choice of mass and forc e resolution and the integration time-step, a force resolution as small as 0.01 of the mean interparticle separation can be justified.