Discreteness effects in cosmological N-body simulations

An estimate of the convergence radius of a simulated cold dark matter halo is obtained under the assumption that the peak phase-space density in the system is set by discreteness effects that operate prior to relaxation. The predicted convergence radii are approximately a factor of 2 larger than those estimated for numerical convergence studies. A toy model is used to study the formation of sheets of the cosmic web, from which dark matter haloes form later. This model demonstrates the interplay between phase mixing and violent relaxation that must also be characteristic of spherical collapse. In the limit in which sheets contain arbitrarily many particles, it seems that power-law profiles are established in both distance and energy. When only a finite number of particles are employed, relaxation is prematurely terminated and the power laws are broken. In a given simulation, the sheets with the highest peak phase-space densities are those that form from the longest waves. Hence simulations with little small-scale power are expected to form the cuspiest haloes.