Halo abundance matching: accuracy and conditions for numerical convergence

Accurate predictions of the abundance and clustering of dark matter haloes play a key role in testing the standard cosmological model. Here, we investigate the accuracy of one of the leading methods of connecting the simulated dark matter haloes with observed galaxies- the halo abundance matching (HAM) technique. We show how to choose the optimal values of the mass and force resolution in large volume N-body simulations so that they provide accurate estimates for correlation functions and circular velocities for haloes and their subhaloes - crucial ingredients of the HAM method. At the 10 per cent accuracy, results converge for ∼50 particles for haloes and ∼150 particles for progenitors of subhaloes. In order to achieve this level of accuracy a number of conditions should be satisfied. The force resolution for the smallest resolved (sub)haloes should be in the range (0.1-0.3)r_s, where r_s is the scale radius of (sub)haloes. The number of particles for progenitors of subhaloes should be ∼150. We also demonstrate that the two-body scattering plays a minor role for the accuracy of N-body simulations thanks to the relatively small number of crossing-times of dark matter in haloes, and the limited force resolution of cosmological simulations.