The impact of box size on the properties of dark matter haloes in cosmological simulations

We investigate the impact finite simulation box size has on the structural and kinematic properties of cold dark matter (CDM) haloes forming in cosmological simulations. Our approach involves generating a single realization of the initial power spectrum of density perturbations and studying how truncation of this power spectrum on scales larger than L-cut = 2 pi/k(cut) affects the structure of dark matter haloes at z = 0. In particular, we have examined the cases of L-cut = f(cut) L-box with f(cut) = 1 (i.e. no truncation), 1/2, 1/3 and 1/4. In common with previous studies, we find that the suppression of long wavelength perturbations reduces the strength of clustering, as measured by a suppression of the two-point correlation function xi(r), and reduces the numbers of the most massive haloes, as reflected in the depletion of the high-mass end of the mass function n(M). However, we note that the number density of 'intermediate'-mass haloes (M similar to 10(13) h(-1) M-circle dot) is enhanced by the suppression of long wavelength perturbations - by as much as similar to 20 per cent for f(cut) = 1/4 - and that this effect becomes more pronounced as f(cut) is decreased. Such a trend is in good agreement with the predictions of the Sheth-Tormen prescription. Interestingly, we find that truncation of the initial power spectrum has little impact on the internal properties of haloes. The masses of high-mass haloes decrease in a systematic manner as L-cut is reduced, but the distribution of concentrations is unaffected. On the other hand, the median spin parameter is similar to 15 per cent lower in runs with f(cut) < 1. We argue that this is an imprint of the linear growth phase of the halo's angular momentum by tidal torquing, and that the absence of any measurable trend in concentration or halo shape reflects the importance of virialization and complex mass-accretion histories for these quantities. These results are of interest for studies that require high-mass resolution and statistical samples of simulated haloes, such as simulations of the population of first stars. Our analysis shows that large-scale tidal fields have relatively little effect on the internal properties of CDM haloes and hence may be ignored in these studies.