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

摘要

We study the uncertainty in different two-point correlation function (2PCF)estimators in currently available galaxy surveys. This is motivated by theactive subject of using the baryon acoustic oscillations (BAOs) feature in thecorrelation function as a tool to constrain cosmological parameters, whichrequires a fine analysis of the statistical significance. We discuss howestimators 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 currentlyavailable galaxy samples using simulated mock catalogues of the Sloan DigitalSky Survey (SDSS) following a lognormal model, with a Lambda-Cold Dark Matter($\Lambda\text{CDM}$) correlation function and similar properties as thesamples (number density, mean redshift for the $\Lambda\text{CDM}$ correlationfunction, survey geometry, mass-luminosity bias). Because we need extensivesimulations to quantify small statistical effects, we cannot use realisticN-body simulations and some physical effects are neglected. Our simulationsstill enable a comparison of the different estimators by looking at theirbiases and variances. We also test the reliability of the BAO detection in theSDSS samples and study the compatibility of the data results with our$\Lambda\text{CDM}$ simulations.