Large-Scale Anisotropic Correlation Function of SDSS Luminous Red Galaxies

TL;DR

This study analyzes the anisotropic two-point correlation function of SDSS LRGs to exploit baryon acoustic features in two dimensions, enabling separation of dynamical and geometric redshift distortions. Using 2LPT-based mocks for covariance, it constrains key cosmological parameters within a flat ΛCDM framework and derives meaningful constraints on dark energy w from the baryon ridge and overall anisotropy. The results are consistent with CMB measurements and demonstrate the potential of anisotropic BAO analyses in large-scale structure surveys, while highlighting the need for nonlinear modeling and improved covariance for tighter future constraints.

Abstract

We study the large-scale anisotropic two-point correlation function using 46,760 luminous red galaxies at redshifts 0.16 -- 0.47 from the Sloan Digital Sky Survey. We measure the correlation function as a function of separations parallel and perpendicular to the line-of-sight in order to take account of anisotropy of the large-scale structure in redshift space. We find a slight signal of baryonic features in the anisotropic correlation function, i.e., a ``baryon ridge'' which corresponds to a baryon acoustic peak in the spherically averaged correlation function which has already been reported using the same sample. The baryon ridge has primarily a spherical structure with a known radius in comoving coordinates. It enables us to divide the redshift distortion effects into dynamical and geometrical components and provides further constraints on cosmological parameters, including the dark energy equation-of-state. With an assumption of a flat $Λ$ cosmology, we find the best-fit values of $Ω_{\rm m} = 0.218^{+0.047}_{-0.037}$ and $Ω_{\rm b} = 0.047^{+0.016}_{-0.016}$ (68% C.L.) when we use the overall shape of the anisotropic correlation function of $40<s<200\himpc$ including a scale of baryon acoustic oscillations. When an additional assumption $Ω_{\rm b}h^2=0.024$ is adopted, we obtain $Ω_{\rm DE}=0.770^{+0.051}_{-0.040}$ and $w=-0.93^{+0.45}_{-0.35}$. These constraints are estimated only from our data of the anisotropic correlation function, and they agree quite well with values both from the cosmic microwave background (CMB) anisotropies and from other complementary statistics using the LRG sample. With the CMB prior from the 3 year WMAP results, we give stronger constraints on those parameters.

Figures (9)

• Figure 1: Illustration of geometrical quantities used in this paper.
• Figure 2: Contour plots of the redshift-space 2PCF measured from the SDSS LRG sample ( right) and the corresponding analytical formula derived by M2004 using a linear perturbation theory ( left). The dashed black lines show $\xi < -0.01$ increasing logarithmically with $0.25$ and $-0.01 \leq \xi < 0$ linearly with $0.0025$. The solid thin lines colored red show $0 \leq \xi <0.01$ increasing linearly with $0.0025$ and the solid thick ones colored red $\xi \geq 0.01$ logarithmically with $0.25$. The baryonic feature slightly appears as ridge structures around the scale $s =(s_{\perp}^2+s_{\parallel}^2)^{1/2} \simeq 100{\hbox{$~h^{-1}$}{\rm ~Mpc}}$, and the dashed circle traces the peaks of the baryon ridges . For the theoretical predictions, we adopt the best-fit values assuming a flat cosmology, $\Omega_{\rm m}=0.218$, $\Omega_b=0.0473$, $h=0.702$, $\sigma_8=0.660$, $b=1.55$, while the fiducial values, $n_s=1$ and $w=-1$ are fixed. We also set the redshift at the origin to be $0.34$, which is typical in our LRG sample.
• Figure 3: Comparison of the 2PCFs times $s^2$ between the observed LRGs and the mock catalogs. The horizontal axis is logarithmic while the vertical axis is linear. The red points show the angle-averaged 2PCF of the LRGs and the error bars are from the mock catalogs. The dashed line shows the 2PCF averaged over the mock catalogs. The baryon peak detected in these plots is obtained from the integration of baryon ridges in Fig. \ref{['fig:xi_lrg_2d']} over angular orientation.
• Figure 4: Anisotropic 2PCFs as functions of two variables, separations perpendicular and parallel to the line of sight. The right side shows the LRG 2PCF, which is the same as the right one of Fig. \ref{['fig:xi_lrg_2d']}. The left side shows the corresponding averaged 2PCF of our mock catalogs. The difference between 2PCFs in each mock and their average is used for construction of the covariance matrix. The 2PCF from our mock catalogs does not have large deviation from that of the observed 2PCFs, even for the quadrupole components.
• Figure 5: Display of the reliability of the recovery of $\Omega_{\rm m}$ and $h$ from 15 realizations. The horizontal axis shows the realization number, while the vertical axis shows the value of $\Omega_m$ and $h$ and the horizontal dashed lines show their input parameters. Solid and dashed error bars shows the $68\%$ and $95\%$ confidence levels, respectively. Among these 15 realizations, there are 10 and 11 realizations including input values of $\Omega_m$ and $h$, respectively, at $68\%$ confidence intervals , and 14 and 15 at $95\%$ intervals.