Clustering of luminous red galaxies I: large scale redshift space distortions

TL;DR

This paper analyzes SDSS DR6 LRGs to model large-scale redshift-space distortions using xi(σ,π) and a Kaiser-based framework, validating error estimates with extensive MICE mocks. By combining the quadrupole Q(s) to constrain β and fitting ξ(π,σ) on large scales to obtain Ω_m and Amp ≡ b σ_8, it breaks degeneracies between bias and σ_8 and derives a consistent growth history. The results imply Ω_m ≈ 0.23–0.27, σ_8 ≈ 0.85 ± 0.06, and f(Ω_m) ≈ 0.64 ± 0.09, with standard gravity remaining viable for 0.80 ≤ σ_8 ≤ 0.92; modified gravity scenarios are increasingly constrained. Cross-correlation with WMAP ISW measurements provides an independent check on growth history and bias, while BAO detections in the monopole across redshift slices validate the modeling on large scales. Overall, the study demonstrates robust error modeling and yields consistent cosmological constraints, setting the stage for deeper analyses of small-scale dynamics and higher-order statistics in future papers.

Abstract

This is the first paper of a series where we study the clustering of LRG galaxies in the latest spectroscopic SDSS data release, DR6, which has 75000 LRG galaxies covering over 1 $Gpc^3/h^3$ at $0.15<z<0.47$. Here we focus on modeling redshift space distortions in $\xips$, the 2-point correlation in separate line-of-sight and perpendicular directions, on large scales. % and away from the line-of-sight. We use large mock simulations to study the validity of models and errors. We show that errors in the data are dominated by a shot-noise term that is 40% larger than the Poisson error commonly used. We first use the normalized quadrupole for the whole sample (mean z=0.34) to estimate $β=f(Ω_m)/b=0.34 \pm 0.03$, where $f(Ω_m)$ is the linear velocity growth factor and $b$ is the linear bias parameter that relates galaxy to matter fluctuations on large scales. We next use the full $\xips$ plane to find $Ω_{0m}= 0.245 \pm 0.020$ (h=0.72) and the biased amplitude $b σ_8 = 1.56 \pm 0.09$. For standard gravity, we can combine these measurements to break degeneracies and find $σ_8=0.85 \pm 0.06$, $b=1.85 \pm 0.25$ and $f(Ω_m)=0.64 \pm 0.09$. We present constraints for modified theories of gravity and find that standard gravity is consistent with data as long as $0.80<σ_8<0.92$. We also calculate the cross-correlation with WMAP5 and show how both methods to measure the growth history are complementary to constrain non-standard models of gravity. Finally, we show results for different redshift slices, including a prominent BAO peak in the monopole at different redshifts. (Abridged)

Figures (45)

• Figure 1: Top: Solid line shows the projected perpendicular correlation function $\Xi(\sigma)$ calculated theoretically from $\xi(r)$ in Eq.(\ref{['e:proj']}), for a model with $\beta=0.35$ and $\sigma_v=400km/s$. This is compared to integral of $\xi(\pi,\sigma)$ in Eq.(\ref{['e:Xi']}) with $\pi_{max}$=60.(red dashed), 80.(blue dashed), 100.(red dash-dot), 200.(blue dash-dot). Bottom: Estimation of the real space correlation function by deprojecting the color lines of $\Xi(r)$ in the top panel using Eq.(\ref{['eq:xirr']}). We can see good agreement on scales smaller than 30Mpc/h.
• Figure 2: Comoving density vs redshift for our selected LRGs
• Figure 3: Slice in dec = 32-40 deg showing ra vs redshift, in order to see the structure of the data (left panel). We also plot the random distribution for this slice (right panel)
• Figure 4: 2-point anisotropic redshift correlation function $\xi(\sigma, \pi)$ for LRG galaxies in DR6 catalog (top panel) and mock MICE simulations (bottom panel, with a linear bias b=2, in order to be similar in amplitude to real LRG). Contours are -0.5 to -0.004 with logarithmic bin of 0.4, 0. (over-plotted as a line), 0.003 to 40. with log bin=0.4. We see how the real LRG have a less flattened shape around the center, since $\beta$ is smaller because of higher bias
• Figure 5: Q(s) (points with errors) and best fit asymptotic value of $\beta$ at large scales (Eq.(\ref{['eq:quadrub']})) translated to the quadrupole (red dotted)