The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Anisotropic galaxy clustering in Fourier-space

TL;DR

<p>We address how to extract cosmological information from wide-area galaxy clustering by analyzing anisotropic redshift-space distortions, BAO, and the Alcock-Paczynski effect in Fourier space using the final BOSS DR12 dataset. We implement a perturbation-theory–based model (TNS) with a comprehensive bias expansion, include the hexadecapole, and rigorously account for the survey window via a convolved multipole framework validated with realistic mocks. The analysis yields joint constraints on $f\sigma_8$, $\alpha_{\parallel}$, $\alpha_{\perp}$, and BAO-derived quantities, showing general consistency with Planck at low redshift and a mild tension at the highest redshift bin, while demonstrating that window effects and higher-order multipoles improve precision by about 20–30%. These results contribute to the robust, multi-probe BOSS cosmological constraints compiled in Alam et al. (2016).

Abstract

We investigate the anisotropic clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12 (DR12) sample, which consists of $1\,198\,006$ galaxies in the redshift range $0.2 < z < 0.75$ and a sky coverage of $10\,252\,$deg$^2$. We analyse this dataset in Fourier space, using the power spectrum multipoles to measure Redshift-Space Distortions (RSD) simultaneously with the Alcock-Paczynski (AP) effect and the Baryon Acoustic Oscillation (BAO) scale. We include the power spectrum monopole, quadrupole and hexadecapole in our analysis and compare our measurements with a perturbation theory based model, while properly accounting for the survey window function. To evaluate the reliability of our analysis pipeline we participate in a mock challenge, which resulted in systematic uncertainties significantly smaller than the statistical uncertainties. While the high-redshift constraint on $fσ_8$ at $z_{\rm eff}=0.61$ indicates a small ($\sim 1.4σ$) deviation from the prediction of the Planck $Λ$CDM model, the low-redshift constraint is in good agreement with Planck $Λ$CDM. This paper is part of a set that analyses the final galaxy clustering dataset from BOSS. The measurements and likelihoods presented here are combined with others in~\citet{Alam2016} to produce the final cosmological constraints from BOSS.

Figures (12)

• Figure 1: Galaxy density distribution for the North Galactic Cap (NGC, red), South Galactic Cap (SGC, black) as well as the early (E) region 2 and 3, consisting of chunks 2-6 (for details see section \ref{['sec:data']}).
• Figure 2: Window function multipoles for BOSS DR12 as given in eq. \ref{['eq:Well']} and used for the convolved correlation functions in eq. \ref{['eq:conv1']} - \ref{['eq:conv3']}. The top panels display the window functions for the North Galactic Cap (NGC) in the three redshift bins used in this analysis; the bottom panels show the window functions for the South Galactic Cap (SGC).
• Figure 3: The leakage of higher order multipoles to the observed monopole power spectrum due to the window function effect. The blue line shows the contribution from the monopole to the observed monopole; the red line indicates the contributions from the monopole and quadrupole and the black line represents the contributions from the monopole, quadrupole and hexadecapole. The total window function effect (black) is of the order of $2\%$ for $k \lesssim 0.04h{\rm\;Mpc^{-1}}$ and significantly increases for $k \lesssim 0.01h{\rm\;Mpc^{-1}}$. The quadrupole contribution (from the difference between the blue and red lines) becomes significant at $k \lesssim 0.015h{\rm\;Mpc^{-1}}$. The hexadecapole contribution (from the difference between the red and the black lines) is negligible on all scales.
• Figure 4: Illustration of the discreteness and the window function effects on the power spectrum multipoles for the low redshift bin in the South Galactic Cap (SGC). The monopole (top), the quadrupole (middle) and hexadecapole (bottom), are displayed in the range used in this analysis. The solid black lines show the input linear power spectrum multipoles using a linear bias of $b_1 = 2$ and a growth rate of $f = 0.7$, while the black dashed lines are the same power spectra convolved with the window function. The main effect of the window function is a damping at small $k$. The red line also includes the discreteness effect using eq. \ref{['eq:binning']}. The discreteness effect is caused by the finite k-space grid, used to estimate the power spectrum multipoles (see section \ref{['sec:binning']}).
• Figure 5: Here we show the difference between the mean power spectrum multipoles of a set of CMASS-like mock catalogues and the mean power spectrum multipoles of the corresponding periodic boxes convolved with the window function. A value of zero indicates that our window function convolution method does correctly model the effects introduced by the survey geometry. The colour bands indicate the uncertainties as given by the diagonal terms of the NGC covariance matrix for the second redshift bin.