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Generating pre-initial conditions (or particle loads) is the very first stepto set up a cosmological N-body simulation. In this work, we revisit thenumerical convergence of pre-initial conditions on dark matter halo propertiesusing a set of simulations which only differs in initial particle loads, i.e.grid, glass, and the newly introduced capacity constrained Voronoi tessellation(CCVT). We find that the median halo properties agree fairly well (i.e. withina convergence level of a few per cent) among simulations running from differentinitial loads. We also notice that for some individual haloes cross-matchedamong different simulations, the relative difference of their propertiessometimes can be several tens of per cent. By looking at the evolution historyof these poorly converged haloes, we find that they are usually merging haloesor haloes have experienced recent merger events, and their merging processes indifferent simulations are out-of-sync, making the convergence of haloproperties become poor temporarily. We show that, comparing to the simulationstarting with an anisotropic grid load, the simulation with an isotropic CCVTload converges slightly better to the simulation with a glass load, which isalso isotropic. Among simulations with different pre-initial conditions, haloesin higher density environments tend to have their properties converged slightlybetter. Our results confirm that CCVT loads behave as well as the widely usedgrid and glass loads at small scales, and for the first time we quantify theconvergence of two independent isotropic particle loads (i.e. glass and CCVT)on halo properties.

Numerical convergence of pre-initial conditions on dark matter halo properties