TY - JOUR

T1 - An optimized correlation function estimator for galaxy surveys

AU - Vargas-Magaña, M.

AU - Bautista, J. E.

AU - Hamilton, J. Ch

AU - Busca, N. G.

AU - Aubourg, É

AU - Labatie, A.

AU - Le Goff, J. M.

AU - Escoffier, S.

AU - Manera, M.

AU - McBride, C. K.

AU - Schneider, D. P.

AU - Willmer, Ch N.A.

N1 - Funding Information:
We would like to thank the SDSS-III collaboration for such wonderful data. We thank N. Padmanabhan, and J.K. Parejko for making their kd-tree code available. We used the “gamma” release LRG galaxy mock catalogues produced by the LasDamas projecta and we thank the LasDamas collaboration for providing us with this data. We would like to thank R. Skibba, Chia-Hsun Chuang, Lado Samushia, and Graziano Rossi for helpful suggestions and comments. This project was supported by the Agence Nationale de la Recherche under contract ANR-08-BLAN-0222. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/ . SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, University of Cambridge, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.

PY - 2013

Y1 - 2013

N2 - Measuring the two-point 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 Landy-Szalay estimator, which is supposed to reach minimal variance. This is only true, however, for a vanishing correlation function. We study the Landy-Szalay 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 model-dependent way, but we propose a simple iterative procedure for obtaining an unbiased model-independent estimator. Our method can be easily applied to any dataset and requires few extra mock catalogues compared to the standard Landy-Szalay analysis. Using various sets of simulated data (lognormal, second-order LPT, and N-body), we obtain a 20-25% gain on the error bars on the two-point 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 10-15% improvement over the estimation of the densities of matter Ωm and dark energy ΩΛ 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 Landy-Szalay estimator, which covers a volume twice as large and has a density that is three times higher.

AB - Measuring the two-point 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 Landy-Szalay estimator, which is supposed to reach minimal variance. This is only true, however, for a vanishing correlation function. We study the Landy-Szalay 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 model-dependent way, but we propose a simple iterative procedure for obtaining an unbiased model-independent estimator. Our method can be easily applied to any dataset and requires few extra mock catalogues compared to the standard Landy-Szalay analysis. Using various sets of simulated data (lognormal, second-order LPT, and N-body), we obtain a 20-25% gain on the error bars on the two-point 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 10-15% improvement over the estimation of the densities of matter Ωm and dark energy ΩΛ 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 Landy-Szalay estimator, which covers a volume twice as large and has a density that is three times higher.

KW - Cosmology: observations

KW - Distance scale

KW - Galaxies: statistics

KW - Large-scale structure of Universe

KW - Methods: data analysis

KW - Surveys

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UR - http://www.scopus.com/inward/citedby.url?scp=84879117018&partnerID=8YFLogxK

U2 - 10.1051/0004-6361/201220790

DO - 10.1051/0004-6361/201220790

M3 - Article

AN - SCOPUS:84879117018

VL - 554

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

SN - 0004-6361

M1 - A131

ER -