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Accurate predictions of the abundance and clustering of dark matter haloesplay a key role in testing the standard cosmological model. Here, weinvestigate the accuracy of one of the leading methods of connecting thesimulated dark matter haloes with observed galaxies -- the Halo AbundanceMatching (HAM) technique. We show how to choose the optimal values of the massand force resolution in large-volume N-body simulations so that they provideaccurate estimates for correlation functions and circular velocities for haloesand their subhaloes -- crucial ingredients of the HAM method. At the 10%accuracy, results converge for 50 particles for haloes and 150 particles forprogenitors subhaloes. In order to achieve this level of accuracy a number ofconditions should be satisfied. The force resolution for the smallest resolved(sub)haloes should be in the range (0.1-0.3)rs, where rs is the scale radius of(sub)haloes. The number of particles for progenitors of subhaloes should be150. We also demonstrate that the two-body scattering plays a minor role forthe accuracy of N-body simulations thanks to the relatively small number ofcrossing-times of dark matter in haloes, and the limited force resolution ofcosmological simulations.

Halo Abundance Matching: accuracy and conditions for numerical convergence