Clustering of Luminous Red Galaxies IV: Baryon Acoustic Peak in the Line-of-Sight Direction and a Direct Measurement of H(z)

TL;DR

The paper analyzes the anisotropic clustering of luminous red galaxies (LRGs) in SDSS DR6/DR7 to detect the baryon acoustic oscillation (BAO) feature in the line-of-sight direction. By measuring $\xi(\sigma,\pi)$, including magnification bias and redshift-space distortions, the authors observe a radial BAO peak around $r_{BAO} \approx 110$ Mpc/$h$ and demonstrate a direct, model-independent determination of $H(z)$ from the radial BAO signal. They validate the BAO interpretation using the monopole, the BAO ring in the $\sigma$–$\pi$ plane, and extensive systematics checks, finding that a no-BAO model is ruled out at roughly $3\sigma$, while a no-magnification-bias model is disfavored at about $2\sigma$. They present two approaches to measure $H(z)$: a shape-based method that constrains $H(z)/H_0$ and a peak method that yields $H(z)$ in physical units, with results at multiple redshifts that are broadly consistent with a flat LCDM cosmology. The work demonstrates the viability of LOS BAO as a direct cosmological ruler and highlights the potential for more precise constraints from upcoming surveys (e.g., PAU).

Abstract

We study the clustering of LRG galaxies in the latest spectroscopic SDSS data releases, DR6 and DR7, which sample over 1 Gpc^3/h^3 to z=0.47. The 2-point correlation function $\xisp$ is estimated as a function of perpendicular $σ$ and line-of-sight $π$ (radial) directions. We find a significant detection of a peak at $r\simeq 110$Mpc/h, which shows as a circular ring in the $σ-π$ plane. There is also significant evidence for a peak along the radial direction whose shape is consistent with its originating from the recombination-epoch baryon acoustic oscillations (BAO). A $\xisp$ model with no radial BAO peak is disfavored at $3.2σ$, whereas a model with no magnification bias is disfavored at $2σ$. The radial data enable, for the first time, a direct measurement of the Hubble parameter $H(z)$ as a function of redshift. This is independent from earlier BAO measurements which used the spherically averaged (monopole) correlation to constrain an integral of $H(z)$. Using the BAO peak position as a standard ruler in the radial direction, we find: $H(z=0.24)= 79.69 \pm 2.32 (\pm 1.29)$ km/s/Mpc for z=0.15-0.30 and $H(z=0.43)= 86.45 \pm 3.27 (\pm 1.69)$ km/s/Mpc for $z=0.40-0.47$. The first error is a model independent statistical estimation and the second accounts for systematics both in the measurements and in the model. For the full sample, $z=0.15-0.47$, we find $H(z=0.34)= 83.80 \pm 2.96 (\pm 1.59)$ km/s/Mpc.

Figures (25)

• Figure 1: Top panel: Theoretical $\xi(\sigma, \pi)$ with linear redshift space distortions convolved with a dispersion model , assuming a cosmology and bias (linear and non-linear) as observed in LRG in paper I and II. Note the ring around $\simeq 100$ Mpc/h that becomes narrow and less prominent in the radial direction. Bottom panel: same with magnification bias added (slope = 2 to see clearly the effect). The main effect is the boosting of the BAO peak in the $\pi$ direction. In both cases we take into account the bin smoothing at 5Mpc/h.
• Figure 2: Same as Fig.\ref{['fig:baoteoric1']}, with different panels corresponding to different cosmological parameters as labeled in the figures: left panels show change with the baryon density $\Omega_b$, middle panels with the scalar spectral index $n_s$ and right panels with the matter density $\Omega_m$.
• Figure 3: LRG number count slope $s$ as a function of limiting apparent magnitude $m_r$ using all SDSS DR6 photometric catalog.
• Figure 4: This is the observed LRG clustering bias as a function of scale $r$, defined by $b(r) = \sqrt{\xi_{\rm obs} (r)/\xi_{\rm DM} (r)}$, where $\xi_{\rm obs}$ is the galaxy correlation function and $\xi_{\rm DM}$ is the theoretical nonlinear dark matter correlation, both in real space.
• Figure 5: In this figure we show different error estimates for the 2-point correlation in the line-of-sight direction $\pi$, averaged over $\sigma=0 - 5$ Mpc/h. The black solid line and red solid line shows the dispersion for dark matter and halos respectively computed from 216 mock catalogs (the dark matter mocks are at z=0.3, and the halo mocks are at z=0 chosen with a large scale bias of 1.9). We also calculate the Jack-knife (JK) error for each mock and we plot its dispersion as a shaded region (gray for dark matter and orange for halos). For comparison, we also show the JK error for the real sample of LRGs (blue dotted line). The dashed lines show the error estimates from our analytic model for dark matter (black), halos (red) and LRGs (blue) respectively (see text).