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

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.