Uncertainty in 2-point correlation function estimators and BAO detection in SDSS DR7

TL;DR

This paper analyzes the uncertainties in two-point correlation function estimators used in galaxy surveys, focusing on their impact on BAO detection and cosmological parameter constraints, through simulations of SDSS data.

Contribution

It provides a detailed quantification of estimator biases and variances, and assesses BAO detection reliability in SDSS using mock catalogues with a lognormal model.

Findings

Estimator biases depend on mean density and integral constraint effects.

Simulations reveal the level of statistical uncertainty in BAO detection.

Results support the compatibility of SDSS data with $ ext{Lambda}$CDM predictions.

Abstract

We study the uncertainty in different two-point correlation function (2PCF) estimators in currently available galaxy surveys. This is motivated by the active subject of using the baryon acoustic oscillations (BAOs) feature in the correlation function as a tool to constrain cosmological parameters, which requires a fine analysis of the statistical significance. We discuss how estimators are affected by both the uncertainty in the mean density $\bar{n}$ and the integral constraint $\frac{1}{V^2}\int_{V^2} \hat{\xi} (r) d^3r =0$ which necessarily causes a bias. We quantify both effects for currently available galaxy samples using simulated mock catalogues of the Sloan Digital Sky Survey (SDSS) following a lognormal model, with a Lambda-Cold Dark Matter ($\Lambda\text{CDM}$) correlation function and similar properties as the samples (number density, mean redshift for the $\Lambda\text{CDM}$ correlation function, survey geometry, mass-luminosity bias). Because we need extensive simulations to quantify small statistical effects, we cannot use realistic N-body simulations and some physical effects are neglected. Our simulations still enable a comparison of the different estimators by looking at their biases and variances. We also test the reliability of the BAO detection in the SDSS samples and study the compatibility of the data results with our $\Lambda\text{CDM}$ simulations.