Measuring D_A and H at z=0.35 from the SDSS DR7 LRGs using baryon acoustic oscillations

TL;DR

This work demonstrates that the anisotropic BAO signal, when measured in the DR7 SDSS LRG sample and enhanced by density-field reconstruction, yields direct constraints on the angular diameter distance $D_A(z)$ and the Hubble parameter $H(z)$ at $z=0.35$, via the isotropic dilation $\alpha$ and anisotropic warping $\\epsilon$ parameters. The authors develop a robust theoretical and statistical framework for modeling the BAO signal, including non-linear damping, redshift-space distortions, and a tailored covariance treatment calibrated on 160 LasDamas mocks. They validate the method with mocks and apply it to DR7, obtaining $D_A(z=0.35)=1050\pm38$ Mpc and $H(z=0.35)=84.4\pm7.0$ km s$^{-1}$ Mpc$^{-1}$ (with $r_s=152.76$ Mpc), noting a correlation $\\rho_{D_AH}=0.57$ between the two. The anisotropic results align with previous monopole analyses but offer additional, complementary cosmological constraints, demonstrating the value of anisotropic BAO measurements for probing the expansion history and dark-energy properties, especially as future higher-redshift data become available.

Abstract

We present measurements of the angular diameter distance D_A(z) and the Hubble parameter H(z) at z=0.35 using the anisotropy of the baryon acoustic oscillation (BAO) signal measured in the galaxy clustering distribution of the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) Luminous Red Galaxies (LRG) sample. Our work is the first to apply density-field reconstruction to an anisotropic analysis of the acoustic peak. Reconstruction partially removes the effects of non-linear evolution and redshift-space distortions in order to sharpen the acoustic signal. We present the theoretical framework behind the anisotropic BAO signal and give a detailed account of the fitting model we use to extract this signal from the data. Our method focuses only on the acoustic peak anisotropy, rather than the more model-dependent anisotropic information from the broadband power. We test the robustness of our analysis methods on 160 LasDamas DR7 mock catalogues and find that our models are unbiased at the ~0.2% level in measuring the BAO anisotropy. After reconstruction we measure D_A(z=0.35)=1050+/-38 Mpc and H(z=0.35)=84.4+/-7.0 km/s/Mpc assuming a sound horizon of r_s=152.76 Mpc. Note that these measurements are correlated with a correlation coefficient of 0.58. This represents a factor of 1.4 improvement in the error on D_A relative to the pre-reconstruction case; a factor of 1.2 improvement is seen for H.

Figures (21)

• Figure 1: Variation of our models with $\epsilon$ for a linear theory based model including the Kaiser redshift-space distortion (a) and a full non-linear model including FoG and Kaiser redshift-space distortions as well as anisotropic $\Sigma_{\rm nl}$ (b). In these and the following two figures, we have assumed a cosmology of $\Omega_b = 0.04$, $\Omega_m = 0.25$, $h=0.7$, $n_s=1.0$ and $\sigma_8=0.8$. $\epsilon$ parameterizes the amount of Alcock-Paczynski anisotropy, which, if there was none, would be equal to 0. The left panel shows the monopole (black), the transverse correlation function (red) and the radial correlation function (blue), where the difference between these latter two yields a measurement of the quadrupole. Solid, dashed and dotted lines are defined as in the plot legend of the right panel which shows the quadrupole. Note that the quadrupole BAO feature is much weaker in the more realistic non-linear model.
• Figure 2: Variation of the non-linear monopole and quadrupole models with different model parameters: $\Sigma_{\rm nl}$ (a), $\Sigma_s$ (b) and $\beta$ (c). Comparing the behaviour of these parameters to $\epsilon$ (Figure \ref{['fig:epfig']}) indicates that the various model parameters have mostly different effects on the quadrupole. While all of these parameters can affect the shape of the quadrupole, only $\epsilon$ can change the quadrupole BAO position separately from the monopole BAO ($\alpha$ changes both in lock-step). Hence we expect that the effects of $\epsilon$ should be detectable.
• Figure 3: Derivatives of the model quadrupole with respect to $\Sigma_\perp$ (top left), $\Sigma_\parallel$ (top right), $\Sigma_s$ (middle left), $\beta$ (middle right), $\alpha$ (bottom left) and $\epsilon$ (bottom right). The plotted derivatives illustrate how the model changes with these various parameters and is especially interesting near the BAO scale marked by the dashed line. Note that near the acoustic scale, the $\Sigma_\perp$, $\Sigma_\parallel$ and $\Sigma_s$ cases look like derivatives of a Gaussian with respect to its width. The $\beta$ case looks like the derivative of a Gaussian with respect to its height. The $\epsilon$ case looks like the derivative of a Gaussian with respect to its center. These behaviours are all different. We see that the $\Sigma_\perp$ and $\Sigma_\parallel$ derivatives are similar in nature at the acoustic scale but opposite in sign. The $\Sigma_\parallel$ and $\Sigma_s$ derivatives, however, are of the same sign and show the same up-down-up structure near the BAO scale, but differ at small scales. The $\beta$ derivative only shows a single peak near the acoustic scale. We also see that the $\Sigma_\perp$, $\Sigma_\parallel$, $\Sigma_s$ and $\beta$ derivatives are symmetric about the acoustic scale while the $\alpha$ and $\epsilon$ derivatives are anti-symmetric. The $\alpha$ derivative has the most structure near the acoustic scale. The $\epsilon$ derivative shows a simple up-down structure. Despite their opposite symmetries near the acoustic scale, the various crests and troughs of the $\alpha$ and $\epsilon$ derivatives will be partially degenerate with the other parameters. However, given reasonable priors on the other parameters, the model will not be allowed to explore these degeneracies and we will recover robust measurements of $\epsilon$.
• Figure 4: Average monopole (left) and quadrupole (right) of the 160 mock catalogues before reconstruction. The monopole and the quadrupole at large scales are similar to the fiducial templates (grey dotted lines, identical to the solid lines plotted in Figures \ref{['fig:epfig']} & \ref{['fig:varyfig']}). The quadrupole on small scales ($r\lesssim50h^{-1}\rm{Mpc}$), however, shows substantially different structure to the fiducial template. The fit to the average of the monopole and quadrupole from the mocks is overplotted in red. The solid line corresponds to a fit using the fiducial $A_{0,2}(r)$ (Equation (\ref{['eqn:fida']})) and the dashed line corresponds to a fit using $A_{0,2}(r)=0$. We allow $\Sigma_\perp$ and $\Sigma_\parallel$ to vary in these fits and obtain best-fit values of $6.3h^{-1}\rm{Mpc}$ and $10.4h^{-1}\rm{Mpc}$ respectively using the fiducial $A_{0,2}(r)$. In the monopole case, the fit using the fiducial $A_{0,2}(r)$ is very similar to the $A_{0,2}(r)=0$ fit. In the quadrupole, the $A_{0,2}(r)=0$ fit is much worse around the acoustic scale. Overall, $\chi^2$ decreased by $\sim33$ going from $A_{0,2}(r)=0$ to the fiducial $A_{0,2}(r)$.
• Figure 5: The average monopole (left) and quadrupole (right) of the 160 mocks before (gray crosses) and after (black crosses) reconstruction. One can see that after reconstruction, the acoustic peak in the monopole has sharpened up, indicating that reconstruction is effective at removing the degradation of the BAO caused by non-linear structure growth. In the quadrupole, the power at large-scales goes close to 0 which implies that reconstruction was effective at removing the Kaiser effect. It is not exactly zero due to some small anisotropy introduced by the reconstruction technique itself (see Figure \ref{['fig:realfig']}). We note that the quadrupole is multiplied by $r^2$ in this figure and hence the magnitude of this anisotropy is exaggerated.