The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: RSD measurement from the LOS-dependent power spectrum of DR12 BOSS galaxies

TL;DR

This work delivers LOS-relative galaxy clustering measurements from the BOSS DR12 sample, extracting redshift-space distortion and geometric information to constrain the growth rate via fσ_8 and distance scales via H(z) r_s(z_d) and D_A(z)/r_s(z_d). It combines resumed perturbation theory-based RSD modelling with a non-local Eulerian bias framework, incorporates Alcock-Paczynski distortions, and accounts for survey geometry through a window convolution. The authors validate their approach with MD-Patchy and qpm mocks, achieving tight DR12 constraints (e.g., fσ_8 ≈ 0.44 at z ≈ 0.57 and fσ_8 ≈ 0.40 at z ≈ 0.32) that are consistent with Planck ΛCDM+GR and previous DR11 analyses. The results advance precision tests of gravity and cosmology by providing robust, jointly constrained measurements of growth and geometry that are suitable for combination with other data sets.

Abstract

We measure and analyse the clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) relative to the line-of-sight (LOS), for LOWZ and CMASS galaxy samples drawn from the final Data Release 12 (DR12). The LOWZ sample contains 361\,762 galaxies with an effective redshift of $z_{\rm lowz}=0.32$, and the CMASS sample 777\,202 galaxies with an effective redshift of $z_{\rm cmass}=0.57$. From the power spectrum monopole and quadrupole moments around the LOS, we measure the growth of structure parameter $f$ times the amplitude of dark matter density fluctuations $σ_8$ by modeling the Redshift-Space Distortion signal. When the geometrical Alcock-Paczynski effect is also constrained from the same data, we find joint constraints on $fσ_8$, the product of the Hubble constant and the comoving sound horizon at the baryon drag epoch $H(z)r_s(z_d)$, and the angular distance parameter divided by the sound horizon $D_A(z)/r_s(z_d)$. We find $f(z_{\rm lowz})σ_8(z_{\rm lowz})=0.394\pm0.062$, $D_A(z_{\rm lowz})/r_s(z_d)=6.35\pm0.19$, $H(z_{\rm lowz})r_s(z_d)=(11.41\pm 0.56)\,{10^3\rm km}s^{-1}$ for the LOWZ sample, and $f(z_{\rm cmass})σ_8(z_{\rm cmass})=0.444\pm0.038$, $D_A(z_{\rm cmass})/r_s(z_d)=9.42\pm0.15$, $H(z_{\rm cmass})r_s(z_d)=(13.92 \pm 0.44)\, {10^3\rm km}s^{-1}$ for the CMASS sample. We find general agreement with previous BOSS DR11 measurements. Assuming the Hubble parameter and angular distance parameter are fixed at fiducial $Λ$CDM values, we find $f(z_{\rm lowz})σ_8(z_{\rm lowz})=0.485\pm0.044$ and $f(z_{\rm cmass})σ_8(z_{\rm cmass})=0.436\pm0.022$ for the LOWZ and CMASS samples, respectively.

Figures (15)

• Figure 1: The top sub-panels display the measured LOWZ- (top panel) and CMASS-DR12 (bottom panel), monopole (blue squares) and quadrupole (red circles) power spectra. For both cases, the measurements correspond to a combination of the northern and southern galaxy caps according to their effective areas as presented in Eq.\ref{['eq:areas_combination']}. The error-bars are the average values of the dispersion among realizations of the qpm and MD-Patchy mocks. The red and blue solid lines correspond to the best-fit model using the parameters listed in Table \ref{['table_results1']}, for $k_{\rm max}=0.24\,h{\rm Mpc}^{-1}$. For simplicity, we plot the average between models corresponding to the parameters obtained using qpm and MD-Patchy covariance matrices. The bottom sub-panels show the ratio between the power spectrum multipoles measurements and the best-fit model presented in the top sub-panel. The quadrupole symbols have been displaced horizontally for clarity. The dotted black lines represent a $3\%$ deviation.
• Figure 2: Top sub-panels: Effect of the window function on the monopole (blue lines) and on the quadrupole (red lines) for the LOWZ-DR12 sample (left panel) and for the CMASS-DR12 sample (right panel). The solid lines correspond to a toy-model for ${P^{\rm theo.}}^{(0)}$ and ${P^{\rm theo.}}^{(2)}$ in Eq. \ref{['eq:Ptheo']}. The dashed lines correspond to ${P^{(0)}}^{\rm win.}$ and ${P^{(2)}}^{\rm win.}$ in Eq. \ref{['eq:Wijll']}. Lower sub-panels: Relative deviation between ${P^{(\ell)}}^{\rm win.}$ and its convolution with the window mask.
• Figure 3: Correlation coefficients of the monopole-quadrupole covariance matrix from LOWZ-DR12 sample (left panels) and from the CMASS-DR12 sample (right panels), extracted from 1000 realizations of the qpm mocks and from 2048 realizations of the MD-Patchy mocks. The top panels show the results for qpm mocks, the middle panels for the MD-Patchy mocks, and the bottom panels their ratio.
• Figure 4: Percentile diagonal errors corresponding to the $k$-bins used in §\ref{['sec:results']} in which the monopole and quadrupole have been measured for the mocks. Solid lines display the CMASS-DR12 statistics and dashed lines the LOWZ-DR12 ones. Red lines are the predictions inferred from the MD-Patchy mocks, whereas the blue lines are according to qpm mocks.
• Figure 5: Performance of the qpm (black dashed lines) and MD-Patchy (black dotted lines) mocks compared to the data, blue squares for the monopole and red circles for the quadrupole. The left and right panels display the results for the LOWZ and CMASS samples, respectively. For clarity, the amplitude of the power spectrum multipoles have been normalised by a smoothed linear power spectrum, $P_{\rm smooth}$.