Structure of cosmic web in non-linear regime: the nearest neighbour and spherical contact distributions

TL;DR

This paper compares spherical contact and nearest neighbour distribution functions in non-linear cosmic web structures using simulations and galaxy catalogues, revealing their scale sensitivities and potential for cosmological insights.

Contribution

It introduces a detailed comparison of these two statistical tools in non-linear regimes and explores their dependence on redshift, mass, and sample magnitude.

Findings

Spherical contact distribution is nearly skew-normal, probing larger scales.

Nearest neighbour distribution is nearly log-normal, sensitive to small-scale structures.

A linear relation between mean and variance of spherical contact distribution could distinguish cosmological models.

Abstract

In non-linear scales, the matter density distribution is not Gaussian. Consequently, the widely used two-point correlation function is not adequate anymore to capture the matter density field's entire behaviour. Among all statistics beyond correlation functions, the spherical contact (or equivalently void function), and nearest neighbour distribution function seem promising tools to probe matter distribution in non-linear regime. In this work, we use halos from cosmological N-body simulations, galaxy groups from the volume-limited galaxy group and central galaxies from mock galaxy catalogues, to compare the spherical contact with the nearest neighbour distribution functions. We also calculate the J-function (or equivalently the first conditional correlation function), for different samples. Moreover, we consider the redshift evolution and mass-scale dependence of statistics in the simulations and dependence on the magnitude of volume-limited samples in group catalogues as well as the mock central galaxies. The shape of the spherical contact probability distribution function is nearly skew-normal, with skewness and kurtosis being approximately 0.5 and 3, respectively. On the other hand, the nearest neighbour probability distribution function is nearly log-normal, with logarithmic skewness and kurtosis being approximately 0.1 and 2.5, respectively. Accordingly, the spherical contact distribution function probes larger scales compared to the nearest neighbour distribution function, which is influenced by details of structures. We also find a linear relation between the mean and variance of the spherical contact probability distribution function in simulations and mock galaxies, which could be used as a distinguishing probe of cosmological models.