An optimized correlation function estimator for galaxy surveys
Abstract
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.
Origin : Publication funded by an institution
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