Glass-Like Random Catalogues for Two-Point Estimates on the Light Cone

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. Utilising 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 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 $\sigma$ 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 $N_R$ in the random catalogue; we find a power law $\sigma \propto N_R^{-0.9}$ for glass-like random catalogues as opposed to $\sigma \propto N_R^{-0.48}$ using Poisson-sampled random catalogues. Given a required precision, this allows for a much reduced number of objects in the glass-like random catalogues used for the LS estimate of the 2PCF multipoles, significantly reducing the computational costs of each estimate.

16 pages, 14 figures

References in corpus (15)

• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological Implications from two Decades of Spectroscopic Surveys at the Apache Point observatory
• Cosmological Constraints from the SDSS Luminous Red Galaxies
• The DESI Experiment Part I: Science,Targeting, and Survey Design
• A test of the nature of cosmic acceleration using galaxy redshift distortions
• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the luminous red galaxy sample from the anisotropic correlation function between redshifts 0.6 and 1
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological implications of the configuration-space clustering wedges
• Magnification and evolution biases in large-scale structure surveys
• Towards quantitative control on discreteness error in the non-linear regime of cosmological N body simulations
• Improving the modelling of redshift-space distortions: I. A bivariate Gaussian description for the galaxy pairwise velocity distributions
• Mapping the real space distributions of galaxies in SDSS DR7: I. Two Point Correlation Functions
• An alternative to grids and glasses: Quaquaversal pre-initial conditions for N-body simulations
• The halo bias for number counts on the light cone from relativistic N-body simulations
• Fast analytical calculation of the random pair counts for realistic survey geometry
• Nonlinear Behavior of Baryon Acoustic Oscillations in Redshift Space from the Zel'dovich Approximation
• Improved two-point correlation function estimates using glass-like distributions as a reference sample

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