deletions | additions       diff --git a/reconstructed_wedges.tex b/reconstructed_wedges.tex  index e801014..28c3802 100644  --- a/reconstructed_wedges.tex  +++ b/reconstructed_wedges.tex 
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We now use the baroynic acoustic feature as a standardized sphere to determine $D_{\rm A}/r_{\rm s}$ and $1/H/r_{\rm s}$. To obtain model-independent constraints we focus on the information contained the peak positions in $\xi_{||, \ \perp}$ and marginalize over the broad shape. This is performed by using a template based on $\Lambda$CDM based and using slight peak damping as due to coupling of $k-$modes, and described in the rernomalized perturbation theory of \citet{Crocce_2008}. For simplicity we assume reconstruction perfectly corrects for linear anisotropies, by setting all \xi multipoles except for the monopole to be zero. We run MC-Markov chain when fitting the models to the data while varying $D_{\rm A}/r_{\rm s}$ and $1/H/r_{\rm s}$ with flat prior between [0.5,1.5] of their fiducial cosmology values. In addition we vary for each clustering wedge and amplitude parameter and three polynomial terms each, yielding 10 parameters in total (2+2+2X3). In the results presented here we marginalize over these last eight parameters. A full detailed description of the procedure is given in our previous analysis of the SDSS DR9 CMASS galaxies \citet{Kazin_2013} (see \S 5.3).   Figures \ref{fig:HDA_z60_epsilon0.15}-\ref{fig:HDA_z26_epsilon0.15} display the obtained posteriors of $cz/H/r_{\rm s}$ and $D_{\rm A}/r_{\rm s}$ marginazlied to 2D and 1D. In the 2D panels the even contour solid red lines are the 68, 95\% confidence level regions, and we add a Gaussian approximation in each panel based on the mode values, the median values of the 68\% CL region widths and the covariance $r$ between the two parameters. It is apparent that the BAO-only analysis of the $\Delta z^{\rm Far}$ and $\Delta z^{\rm Mid}$ samples yield moderate constraints on these parameters and $\Delta z^{\rm Near}$ does not.  Due to these  limitations of the data to constrain the parameter space, here we present results with a top-hat  prior of 15\% on $\epsilon$ ($\epsilon \sim 1/H/D_{\rm A}$). We find that a broad top-hat prior of 25\% on $\alpha$ does not improve our results ($\alpha \sim D_{\rm A}^2/H$).  Similar results without the prior on $\epsilon$ are presented in \S (refer to Appendix)  To assess reasonable priors on $\epsilon$, $\epsilon$ and $\alpha$,  we exmamine predicted results predictions  according to the Planck data (cite Planck). We analyze propositions of MCMC obtained when using cosmomc (cite and explain cosmomc). Fitting models to Planck temperature anisotropies and WMAP polarization (cite) we investigate predications for $\alpha$($\alpha \sim D_{\rm A}^2/H$)  and $\epsilon$ at our redshifts of interest ($0.44,0.6,0.73$). Assuming an $ow$CDM model, we obtain a 68\% CL region of $22\%$ for $\alpha$ and $\sim 2.5\%$ for $\epsilon$. Examining a more restrictive flat-$\Lambda$CDM model we find a 68\% CL region of $2\%$ for $\alpha$ and similar for $\epsilon$. We argue that the reason the $\alpha$ of Planck are sensitive to assumption of flatness and $w$ and $\epsilon$ is not is due to the capability of Planck to constrain $H_{\rm 0}$, which $\alpha$ is sensitive to, but $\epsilon$ is not. We clearly see that the 1$\sigma$ CL region engulfs the fiducial value use for analysis. The 2$\sigma$ region is ill-constrained.