  The density field reconstruction technique, which was developed to partially
reverse the nonlinear degradation of the Baryon Acoustic Oscillation (BAO)
feature in the galaxy redshift surveys, has been successful in substantially
improving the cosmology constraints from recent galaxy surveys such as Baryon
Oscillation Spectroscopic Survey (BOSS). We estimate the efficiency of the
reconstruction method as a function of various reconstruction details. To
directly quantify the BAO information in nonlinear density fields before and
after reconstruction, we calculate the cross-correlations (i.e., propagators)
of the pre(post)-reconstructed density field with the initial linear field
using a mock galaxy sample that is designed to mimic the clustering of the BOSS
CMASS galaxies. The results directly provide the BAO damping as a function of
wavenumber that can be implemented into the Fisher matrix analysis. We focus on
investigating the dependence of the propagator on a choice of smoothing filters
and on two major different conventions of the redshift-space density field
reconstruction that have been used in literature. By estimating the BAO
signal-to-noise for each case, we predict constraints on the angular diameter
distance and Hubble parameter using the Fisher matrix analysis. We thus
determine an optimal Gaussian smoothing filter scale for the signal-to-noise
level of the BOSS CMASS. We also present appropriate BAO fitting models for
different reconstruction methods based on the first and second order Lagrangian
perturbation theory in Fourier space. Using the mock data, we show that the
modified BAO fitting model can substantially improve the accuracy of the BAO
position in the best fits as well as the goodness of the fits.
