deletions | additions       diff --git a/reconstructed_wedges.tex b/reconstructed_wedges.tex  index 3ac9e32..57b5c88 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 results with a prior of 15\% on $\epsilon$.  InFigure \ref{fig:HDA_z60_nopriors} we present  the results for $0.6 2D panels  theplots will be neater). The  even contour solid red  lines are the 1,2,3$\sigma$ 68, 95\%  confidence regions. level regions, and we add a Gaussian approximation in each panel based on the mode value, the median value of the 68\% CL region width and the covariance $r$ between the two parameters.   To assess reasonable priors on $\epsilon$, we examine propositions of MCMC when analyzing the Planck temperature anisotropies and examine predictions for $\alpha$ 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. For comparison, in Figure \ref{fig:HDA_z60_nopriors} we present these results without the prior on $\epsilon$. For  better assessing we apply priors on the parameter constraints $\alpha \sim D_{\rm A}^2/H$ and $\epsilon \sim 1/H/D_{\rm A}$. To assess reasonable priors on $\alpha$ and $\epsilon$, we examine propositions of MCMC when analyzing the Planck temperature anisotropies and examine predictions for $\alpha$ 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.   Figures \ref{fig:HDA_z60_epsilon0.15}-\ref{fig:HDA_z26_epsilon0.15} display results with a prior of 15% on $\epsilon$.  %25\% on $\alpha$. It shows no substantial difference. Figure \ref{fig:HDA_z60_alpha0.25_epsilon0.15} shows when %#also adding a constraint of 15\% on $\epsilon$. Here we see that the second apparrent mode in $1/H/r_{\rm s}$ is %substantially reduced.