FUNDAMENTAL DISCRETENESS LIMITATIONS OF COSMOLOGICAL N-BODY CLUSTERING SIMULATIONS

Fundamental physical considerations and past tests suggest that there may be a problem with discreteness error in N-body methods widely used in cosmological clustering studies. This could cause problems with ac curacy when coupled to hydrodynamics codes. We therefore investigate s ome of the effects that discreteness and two-body scattering may have on N-body simulations with ''realistic'' cosmological initial conditio ns. We use an identical subset of particles from the initial condition s for a 128(3) particle-mesh (PM) calculation as the initial condition s for a variety of particle-particle-particle mesh ((PM)-M-3) and tree code runs. The force softening length and particle number in the (PM) -M-3 and tree code runs are varied, and results are compared with thos e of the Phl run. In particular, we investigate the effect of mass res olution (or equivalently the mean interparticle separation) since most ''high-resolution'' codes only have high resolution in gravitational force, not in mass. We show the evolution of a wide variety of statist ical measures. The phase-insensitive two-point statistics, P(k) and xi (R), are affected by the number of particles when the force resolution is held constant and differ in different N-body codes with similar pa rameters and the same initial conditions. Phase-sensitive statistics s how greater differences. Results converge at the mean interparticle se paration scale of the lowest mass-resolution code. As more particles a re added but the absolute scale of the force resolution is held consta nt, the (PM)-M-3 and the tree runs agree more and more strongly with e ach other and with the PM run that had the same initial conditions, su ggesting that the time integration is converging. However, they do not particularly converge to a PM run that continued the power-law fluctu ations to small scales. This suggests high particle density is necessa ry for correct time evolution, since many different results cannot all be correct. Our results showing the effect of the presence or absence of small-scale initial power suggest that leaving it out is a conside rable source of error on comoving scales of the missing wavelengths, w hich can be resolved by putting in a high particle density. Since the codes never agree well on scales below the mean comoving interparticle separation, we find little justification to use results on these scal es to make quantitative predictions in cosmology. The range of values found for some quantities spans 50%, but others, such as the amount of mass in high-density regions, can be off by a factor of 3 or more. Ou r results have strong implications for applications such as the densit y of galaxy halos, early generation objects such as QSO absorber cloud s, etc.