An optimized correlation function estimator for galaxy surveys
Abstract
Measuring the twopoint correlation function of the galaxies in the Universe gives access to the underlying dark matter distribution, which is related to cosmological parameters and to the physics of the primordial Universe. The estimation of the correlation function for current galaxy surveys makes use of the LandySzalay estimator, which is supposed to reach minimal variance. This is only true, however, for a vanishing correlation function. We study the LandySzalay estimator when these conditions are not fulfilled and propose a new estimator that provides the smallest variance for a given survey geometry. Our estimator is a linear combination of ratios between pair counts of data and/or random catalogues (DD, RR, and DR). The optimal combination for a given geometry is determined by using lognormal mock catalogues. The resulting estimator is biased in a modeldependent way, but we propose a simple iterative procedure for obtaining an unbiased modelindependent estimator. Our method can be easily applied to any dataset and requires few extra mock catalogues compared to the standard LandySzalay analysis. Using various sets of simulated data (lognormal, secondorder LPT, and Nbody), we obtain a 2025% gain on the error bars on the twopoint correlation function for the SDSS geometry and ΛCDM correlation function. When applied to SDSS data (DR7 and DR9), we achieve a similar gain on the correlation functions, which translates into a 1015% improvement over the estimation of the densities of matter Ω_{m} and dark energy Ω_{Λ} in an open ΛCDM model. The constraints derived from DR7 data with our estimator are similar to those obtained with the DR9 data and the LandySzalay estimator, which covers a volume twice as large and has a density that is three times higher.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 June 2013
 DOI:
 10.1051/00046361/201220790
 arXiv:
 arXiv:1211.6211
 Bibcode:
 2013A&A...554A.131V
 Keywords:

 surveys;
 largescale structure of Universe;
 galaxies: statistics;
 distance scale;
 cosmology: observations;
 methods: data analysis;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 Accepted for publication A&