The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: theoretical systematics and Baryon Acoustic Oscillations in the galaxy correlation function

TL;DR

This work rigorously characterizes theoretical systematics affecting anisotropic BAO distance measurements from the final BOSS DR12 clustering data, using a comprehensive suite of mocks and methodological variations. It dissects how choices in estimators, random catalogs, covariance modeling, reconstruction, fiducial cosmology, and nonlinear modeling influence the extracted dilation parameters α and ε and the inferred distance scales. The study finds small but non-negligible systematic uncertainties, with dominant contributions arising from reconstruction and estimator/covariance choices, culminating in total systematic shifts of about Δα ≈ 0.002 and Δε ≈ 0.003. Incorporating these systematics yields precise DR12 BAO distances: D_A(z) and H(z) constrained to a few percent across z_eff = 0.38, 0.51, 0.61, consistent with Planck ΛCDM, and reinforcing the robustness of BAO as a distance probe for current and future surveys. These results provide a rigorous framework for systematic budgeting in ongoing and upcoming large-scale structure experiments, including DESI and Euclid.

Abstract

We investigate the potential sources of theoretical systematics in the anisotropic Baryon Acoustic Oscillation (BAO) distance scale measurements from the clustering of galaxies in configuration space using the final Data Release (DR12) of the Baryon Oscillation Spectroscopic Survey (BOSS). We perform a detailed study of the impact on BAO measurements from choices in the methodology such as fiducial cosmology, clustering estimators, random catalogues, fitting templates, and covariance matrices. The theoretical systematic uncertainties in BAO parameters are found to be 0.002 in the isotropic dilation $α$ and 0.003 in the quadrupolar dilation $ε$. The leading source of systematic uncertainty is related to the reconstruction techniques. Theoretical uncertainties are sub-dominant compared with the statistical uncertainties for BOSS survey, accounting $0.2σ_{stat}$ for $α$ and $0.25σ_{stat}$ for $ε$ ($σ_{α,stat} \sim$0.010 and $σ_{ε,stat}\sim$ 0.012 respectively). We also present BAO-only distance scale constraints from the anisotropic analysis of the correlation function. Our constraints on the angular diameter distance $D_A(z)$ and the Hubble parameter $H(z)$, including both statistical and theoretical systematic uncertainties, are 1.5\% and 2.8\% at $z_{\rm eff}=0.38$, 1.4\% and 2.4\% at $z_{\rm eff}=0.51$, and 1.7\% and 2.6\% at $z_{\rm eff}=0.61$. This paper is part of a set that analyzes the final galaxy clustering dataset from BOSS. The measurements and likelihoods presented here are cross-checked with other BAO analysis in \citet{Acacia16}. The systematic error budget concerning the methodology on post-reconstruction BAO analysis presented here is used in \citet{Acacia16} to produce the final cosmological constraints from BOSS.

Figures (23)

• Figure 1: [Top panels Multipoles]. Mean monopole, quadrupole, and hexadecapole from 1000 MD-PATCHY mocks of BOSS Combined Samples pre- (left) and post-reconstruction (right). [Intermediate Panels] Wedges clustering estimator: Mean of 1000 MD-PATCHY pre-reconstruction (left) and post-reconstruction (right) mocks for the 3 redshift bins. [Bottom Panels] $\omega_\ell$ clustering estimator: Mean of 1000 MD-PATCHY mocks pre-reconstruction (left) and post-reconstruction (right) for the 3 redshift bins. "Bin 1" refers to the lower redshift bin ($z= 0.2 - 0.5$); "Bin 2" considers the intermediate redshift range ($z= 0.4 - 0.6$), and "Bin 3" refers to higher redshift range ($z= 0.5 - 0.75$).
• Figure 2: Error Histograms from different clustering estimators $\xi_{0, 2},\xi_{\parallel, \perp}, \omega_l$ for 1000 MD-PATCHY post-reconstruction mocks for the lowest redshift bin. Left panel shows distribution for $\sigma_\alpha$ and right panel for $\sigma_\epsilon$. Similar plots are obtained for the intermediate and higher redshift bins.
• Figure 3: Precision matrix for the post-reconstruction MD-PATCHY mocks (for the intermediate redshift bin, $z= 0.4 - 0.6$) with different scalings. On the left, the precision matrix with no rescaling applied. It illustrates that the bulk of the structure in the precision matrix is on the diagonal and first off-diagonal. In the middle, we divide out the naive scaling with $r$ and plot $\Psi_{ab}/r_{a}r_{b}$.This illustrates that the naive scaling largely captures the $r$-dependence of the precision matrix. On the right, we apply the radial scaling and scale up the quadrupole by a factor chosen to put the monopole and quadrupole on equal footing, which helps assess the amplitude of the main monopole-quadrupole entries.
• Figure 4: Precision matrix for 1000 MD-PATCHY mocks. In the first row, the pre-reconstruction precision matrix obtained for the 3 redshift bins: low, intermediate, and high redshift bin (from left to right). In the second row, the post-reconstruction precision matrices for the corresponding redshift bins. In the third row, the difference between post- and pre-reconstruction precision matrices.
• Figure 5: Diagonal [left] and first off-diagonal [right] terms of precision matrices of MD-PATCHY for 1000 mocks for the 3 redshift bins, pre-(dashed lines) /post-reconstruction (solid lines). "Bin 1" refers to the lower redshift bin ($z= 0.2 - 0.5$); "Bin 2" considers the intermediate redshift range ($z= 0.4 - 0.6$ ), and "Bin 3" refers to higher redshift range ($z= 0.5 - 0.75$). Top panels are monopole terms, bottom panels are quadrupole terms.