Glass-like random catalogues for two-point estimates on the light-cone

Abstract

ABSTRACT We introduce grlic, a publicly available Python tool for generating glass-like point distributions with a radial density profile n(r) as it is observed in large-scale surveys of galaxy distributions on the past light-cone. Utilizing these glass-like catalogues, we assess the bias and variance of the Landy–Szalay (LS) estimator of the first three two-point correlation function (2PCF) multipoles in halo and particle catalogues created with the cosmological N-body code gevolution. Our results demonstrate that the LS estimator calculated with the glass-like catalogues is biased by less than 10−4 with respect to the estimate derived from Poisson-sampled random catalogues, for all multipoles considered and on all but the smallest scales. Additionally, the estimates derived from glass-like catalogues exhibit significantly smaller standard deviation σ than estimates based on commonly used Poisson-sampled random catalogues of comparable size. The standard deviation of the estimate depends on a power of the number of objects NR in the random catalogue; we find a power law $\sigma \propto N_\mathit{R}^{-0.9}$ for glass-like catalogues as opposed to $\sigma \propto N_\mathit{R}^{-0.48}$ using Poisson-sampled random catalogues. Given a required precision, this allows for a much reduced number of objects in the glass-like catalogues used for the LS estimate of the 2PCF multipoles, significantly reducing the computational costs of each estimate.