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We study the clustering of luminous red galaxies in the latest spectroscopic Sloan Digital Sky Survey data releases (DR), DR6 and DR7, which sample over  1 Gpc 3   h  −3   to   z = 0.47 . The two‐point correlation function  ξ(σ, π)  is estimated as a function of perpendicular σ and line‐of‐sight π (radial) directions. We find significant detection of a peak at   r ≃ 110 Mpc  h  −1  , which shows as a circular ring in the  σ–π  plane. There is also significant evidence of a peak along the radial direction whose shape is consistent with its origination from the recombination‐epoch baryon acoustic oscillations (BAO). A  ξ(σ, π)  model with no radial BAO peak is disfavoured at 3.2σ, whereas a model with no magnification bias is disfavoured 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 of 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 ± 2.32 (±1.29) km s −1  Mpc −1   for   z = 0.15–0.30  and   H ( z = 0.43) = 86.45 ± 3.27 (±1.69) km s −1  Mpc −1   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 ± 2.96 (±1.59) km s −1  Mpc −1  .

Clustering of luminous red galaxies – IV. Baryon acoustic peak in the line‐of‐sight direction and a direct measurement of H ( z )