Demonstrating Discreteness and Collision Error in Cosmological N-body Simulations of Dark Matter Gravitational Clustering

Abstract

Two-body scattering and other discreteness effects are unimportant in cosmological gravitational clustering in most scenarios, since the dark matter has a small particle mass. The collective field should determine evolution: Two-body scattering in simulations violates the Poisson-Vlasov equations. We test this in PM, P$^3$M, Tree, and NGPM codes, noting that a collisionless code will preserve the one-dimensional character of plane wave collapse. We find collisionality vanishing as the softening parameter approaches the mean interparticle separation. Solutions for the problem are suggested, involving greater computer power, PM-based nested grid codes, and a more conservative approach to resolution claims.

Final version accepted for ApJ Letters. Minor revisions, including due to bug fix in tree code. Uses aasms4.sty. 15 pages. Higher resolution figures available at ftp://kusmos.phsx.ukans.edu/preprints/discrete