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.
