Comments on the size of the simulation box in cosmological N-body simulations

Abstract

N‐body simulations are a very important tool in the study of the formation of large‐scale structures. Much of the progress in understanding the physics of the high‐redshift universe and comparison with observations would not have been possible without N‐body simulations. Given the importance of this tool, it is essential to understand its limitations, as ignoring the limitations can easily lead to interesting but unreliable results. In this paper we study the limitations arising out of the finite size of the simulation volume. This finite size implies that modes larger than the size of the simulation volume are ignored and a truncated power spectrum is simulated. If the simulation volume is large enough then the mass in collapsed haloes expected from the full power spectrum and from the truncated power spectrum should match. We propose a quantitative measure based on this approach that allows us to compute the minimum box size for an N‐body simulation. We find that the required box size for simulations of the ΛCDM model at high redshifts is much larger than is typically used. We can also use this approach to quantify the effect of perturbations at large scales for power‐law models and we find that if we fix the scale of non‐linearity, the required box size becomes very large as the index becomes small. The appropriate box size computed using this approach is also an appropriate choice for the transition scale when tools like MAP, which add the contribution of the missing power, are used.

The effect of large-scale power on simulated spectra of the Lyα forest

“…We also see higher power because we use longer sightlines in the larger boxes. As Bagla & Ray (2005) showed, there is some effect from having longer modes in the larger boxes. Figs 1 and 2 showed only small changes in the frequencies of different densities per cell, which suggest that the extra long modes have a small effect on the quantities that we are evaluating.…”

“…Bagla & Ray (2005) have explored how the frequency of high‐density CDM collapsed structures changes with effective box size. They use simulations with N = 256 CDM particles in 300 h −1 Mpc boxes with a softening length of 0.47 h −1 Mpc.…”

“…Numerical simulations have often found too few systems with high N H i values (Katz et al 1996; Gnedin 1998; Gardner et al 2001; D'Odorico et al 2006). Simulations need both sufficient volume to contain the long‐wavelength modes to get enough CDM haloes (Bagla & Ray 2005), and they need high enough resolution to make the clumps of gas that cause Lyman limit systems (LLS). In recent work, Kohler & Gnedin (2007) are able to reproduce both the mean flux in the forest and the column density distribution of LLS at z = 4 in 4 h −1 Mpc boxes with 2 h −1 kpc resolution.…”

“…Meiksin & White (2004), for example, study the convergence properties of the flux power spectrum and autocorrelation function and recommend a box size of 25 h −1 Mpc but only for high redshifts ( z > 3) and even then they do not find convergence to better than 10 per cent. Similarly, (Bagla & Ray 2005) study the effects of box size on halo mass functions and indicate that a minimum box size of several 100 h −1 Mpc is needed.…”

Small-scale galaxy clustering in the eagle simulation

“…Bagla & Ray 2005;Bagla & Prasad 2006;Trenti & Stiavelli 2008). To estimate the severity of this, we compare the clustering of haloes in a DMO version of the EAGLE volume to that in a much larger volume, simulated with the same cosmological parameters.…”