Effects of the size of cosmological N-Body simulations on physical quantities - III: Skewness

TL;DR

This paper investigates how the finite size of cosmological N-Body simulations affects higher-order statistical measures like skewness and kurtosis, extending previous work and validating models with simulations.

Contribution

It extends the formalism for finite box-size effects to skewness and kurtosis, providing analytical predictions and validating them against simulations.

Findings

Good agreement between models and simulations for skewness and two-point correlation

Finite box size impacts on relative velocity statistics scale with the correlation function

Analytical models reliably predict the effects of simulation volume limitations

Abstract

N-Body simulations are an important tool in the study of formation of large scale structures. Much of the progress in understanding the physics of galaxy clustering 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 these can easily lead to interesting but unreliable results. In this paper we study the limitations due to the finite size of the simulation volume. In an earlier work we proposed a formalism for estimating the effects of a finite box-size on physical quantities and applied it to estimate the effect on the amplitude of clustering, mass function. Here, we extend the same analysis and estimate the effect on skewness and kurtosis in the perturbative regime. We also test the analytical predictions from the earlier work as well as those presented in this paper. We find good agreement between the analytical models and simulations for the two point correlation function and skewness. We also discuss the effect of a finite box size on relative velocity statistics and find the effects for these quantities scale in a manner that retains the dependence on the averaged correlation function.