A 2 per cent distance to z=0.35 by reconstructing baryon acoustic oscillations - II. Fitting techniques

We present results from fitting the baryon acoustic oscillation (BAO) signal in the correlation function obtained from the first application of density-field reconstruction to a galaxy redshift survey, namely the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) luminous red galaxy (LRG) catalogue. Reconstruction works to partially remove the effects of non-linear structure growth on the BAO by reconstructing the linear matter density field from the observed galaxy density field using the continuity equation. We also introduce more careful approaches for deriving a suitable covariance matrix and fitting model for galaxy correlation functions. Our covariance matrix technique guarantees smooth diagonal and off-diagonal terms by fitting a modified Gaussian covariance matrix to that calculated from mock catalogues. Our proposed fitting model is effective at removing broad-band effects such as redshift-space distortions, scale-dependent bias and any artefacts introduced by assuming the wrong model cosmology. These all aid in obtaining a more accurate measurement of the acoustic scale and its error. We validate these techniques on 160 mock catalogues derived from the LasDamas simulations in real and redshift space. We then apply these techniques to the DR7 LRG sample and find that the error on the acoustic scale decreases from similar to 3.5 per cent before reconstruction to similar to 1.9 per cent after reconstruction. We also see an increase in our BAO detection confidence from similar to 3 sigma to similar to 4 sigma after reconstruction with our confidence level in measuring the correct acoustic scale increasing from 3s to 5s. Using the mean of the acoustic scale probability distributions produced from our fits, we find Dv/rs = 8.89 +/- 0.31 before reconstruction and 8.88 +/- 0.17 after reconstruction.