A 2% 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 reconstruction to a galaxy redshift survey, namely, the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) luminous red galaxy (LRG) catalogue. We also introduce more careful approaches for deriving a suitable covariance matrix and fitting model for galaxy correlation functions. These all aid in obtaining a more accurate measurement of the acoustic scale and its error. We validate our reconstruction, covariance matrix and fitting 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 ~3.5% before reconstruction to ~1.9% after reconstruction. This factor of 1.8 reduction in the error is equivalent to the effect of tripling the survey volume. We also see an increase in our BAO detection confidence from ~3-sigma to ~4-sigma after reconstruction with our confidence level in measuring the correct acoustic scale increasing from ~3-sigma to ~5-sigma. Using the mean of the acoustic scale probability distributions produced from our fits, we find D_v/r_s = 8.89 +/- 0.31 before reconstruction and 8.88 +/- 0.17 after reconstruction.