Modeling the reconstructed BAO in Fourier space

TL;DR

This work analyzes Fourier-space BAO reconstruction by comparing isotropic and anisotropic redshift-space conventions, using propagators to quantify BAO damping and a CMASS-like mock to assess signal and noise across smoothing scales. It introduces a modified Gaussian damping model derived from LPT for isotropic reconstruction, demonstrating improved fits and reduced biases in BAO measurements. Through Fisher-matrix forecasts, it shows that smaller smoothing scales (∼7–10 h^-1 Mpc) substantially enhance distance constraints, with notable gains in D_A and H for BOSS CMASS DR12, while validating the need for the modified model to avoid biased inferences. Overall, the paper provides practical guidance on reconstruction choices and modeling improvements to optimize BAO-based cosmological constraints.

Abstract

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.

Figures (7)

• Figure 1: Propagators of mock CMASS galaxy density field using different conventions for how RSD-induced anisotropy is treated in the reconstruction, for a fixed smoothing length $\Sigma_{\rm sm} = 14h^{-1}{\rm\;Mpc}$. The black line shows the pre-reconstructed density field; the red lines show the post-reconstructed field with the isotropic reconstruction (corresponds to the magenta lines in Figure \ref{['fig:figSm']}) and blue dashed lines show the anisotropic reconstruction. The left panels show propagators for $\delta_{\rm rec}$ and the right panels show the individual density fields, i.e., the negative of the displaced random field ($-\delta_s$, the two thinner curves peaking at low k) and displaced galaxy density field ($\delta_d$, the two thicker curves peaking at high k) that forms the reconstructed density field (i.e., in the left-hand panels) after mutual addition. Dotted lines show the Gaussian damping model with $\Sigma_{\rm nl}(k=0.3h{\rm\;Mpc^{-1}})$: the red dotted line shows the modified Gaussian damping model while the blue dotted line shows the original Gaussian damping model.
• Figure 2: Left-hand panels: propagators of the mock CMASS galaxy density field before (black) and after reconstruction as a function of smoothing length $\Sigma_{\rm sm}$: red, magenta, and blue correspond to $\Sigma_{\rm sm} = 10, 14, 20h^{-1}{\rm\;Mpc}$. The right-hand panels show the corresponding individual density fields, i.e., the displaced random field ($-\delta_s$, the set of three thinner curves peaking at low $k$) and displaced galaxy density field ($\delta_d$, the set of three thicker curves peaking at high $k$) that forms the reconstructed density field (i.e., in the left-hand panels) after mutual addition. Top panels show the propagators for the modes across the line-of-sight direction (cosine the line-of-sight angle $\mu=0.05-1$) and the bottom panels show the propagators for the modes almost along the line of sight ($\mu = 0.95-1$). Black dotted lines show the Gaussian damping model with $\Sigma_{\rm nl}(k=0.3h{\rm\;Mpc^{-1}})$ before reconstruction. Red, magenta, and blue dotted lines show the modified Gaussian damping model with $\Sigma_{\rm nl}(k=0.3h{\rm\;Mpc^{-1}})$. Gray reference lines are located at unity and $(1+\beta\mu^2)$.
• Figure 3: The same as the left panels of Figure \ref{['fig:figSm']} except that cyan and green lines correspond to $\Sigma=5$ and $7~h^{-1}{\rm\;Mpc}$. Red, magenta, and blue correspond to $\Sigma_{\rm sm} = 10, 14$, and $20h^{-1}{\rm\;Mpc}$ as before.
• Figure 4: Left: Mode-coupling components (solid lines, $P_{\rm MC}=P_{\rm nl}-C(k,\mu)^2P_{\rm lin}$) relative the BAO signal estimated by $C_G(k,\mu)^2P_{\rm lin}$ (dashed lines) for the two anisotropy conventions while fixing smoothing length $\Sigma_{\rm sm} = 20h^{-1}{\rm\;Mpc}$. Black line: pre-reconstructed density field. Red: post-reconstructed field with the isotropic reconstruction. Blue: using the anisotropic reconstruction. In the upper left and right panels for $\mu=0.05$, the blue line and the red line are almost over-imposed. The dotted black lines show $P_{\rm MC}$ when using the corresponding Gaussian models for the propagators, i.e., $P_{\rm MC}=P_{\rm nl}-C_G(k,\mu)^2P_{\rm lin}$ for the pre-reconstructed field and $P_{\rm nl}-C_{\rm MG}(k,\mu)^2P_{\rm lin}$ for the post-reconstructed field. Right: the BAO signal to noise ratio for each $k$ mode, i.e., $C^2P_{\rm lin}/P_{\rm nl}$. Note that, with $P_{\rm nl}$ in the denominator, the 'noise' is now the total noise that includes the sample variance from the signal $C(k,\mu)^2P_{\rm lin}$ in additional to $P_{\rm MC}$.
• Figure 5: Left: Mode-coupling components (solid lines, $P_{\rm MC}=P_{\rm nl}-C(k,\mu)^2P_{\rm lin}$) relative the BAO signal estimated by $C_G(k,\mu)^2P_{\rm lin}$ (dashed lines). Cyan, green, red, magenta, and blue correspond to the reconstructed density field using $\Sigma_{\rm sm} = 5, 7, 10, 14$, and $20h^{-1}{\rm\;Mpc}$ and the black corresponds to the pre-reconstructed density field. The dotted black lines show $P_{\rm MC}$ when using the corresponding Gaussian models for the propagators, i.e., $P_{\rm MC}=P_{\rm nl}-C_G(k,\mu)^2P_{\rm lin}$ for the pre-reconstructed field and $P_{\rm nl}-C_{\rm MG}(k,\mu)^2P_{\rm lin}$ for the post-reconstructed field. Right: the BAO signal to noise ratio for each $k$ mode, i.e., $C^2P_{\rm lin}/P_{\rm nl}$. Note that, with $P_{\rm nl}$ in the denominator, the 'noise' is now the total noise that includes the sample variance from the signal $C(k,\mu)^2P_{\rm lin}$ in additional to $P_{\rm MC}$. In the top right panel, the green ($\Sigma_{\rm sm}=7h^{-1}{\rm\;Mpc}$) and the red ($10h^{-1}{\rm\;Mpc}$) lines are almost super-imposed while the cyan ($5h^{-1}{\rm\;Mpc}$) and magenta ($14h^{-1}{\rm\;Mpc}$) are almost super-imposed in the bottom panel.