A 2 per cent distance to z = 0.35 by reconstructing baryon acoustic oscillations - I. Methods and application to the Sloan Digital Sky Survey

We present the first application to density field reconstruction to a galaxy survey to undo the smoothing of the baryon acoustic oscillation (BAO) feature due to non-linear gravitational evolution and thereby improve the precision of the distance measurements possible. We apply the reconstruction technique to the clustering of galaxies from the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) luminous red galaxy (LRG) sample, sharpening the BAO feature and achieving a 1.9 per cent measurement of the distance to z = 0.35. We update the reconstruction algorithm of Eisenstein et al. to account for the effects of survey geometry as well as redshift-space distortions and validate it on 160 LasDamas simulations. We demonstrate that reconstruction sharpens the BAO feature in the angle averaged galaxy correlation function, reducing the non-linear smoothing scale Σ_nl from 8.1 to 4.4Mpch^-1. Reconstruction also significantly reduces the effects of redshift-space distortions at the BAO scale, isotropizing the correlation function. This sharpened BAO feature yields an unbiased distance estimate (<0.2 per cent) and reduces the scatter from 3.3 to 2.1 per cent. We demonstrate the robustness of these results to the various reconstruction parameters, including the smoothing scale, the galaxy bias and the linear growth rate. Applying this reconstruction algorithm to the SDSS LRG DR7 sample improves the significance of the BAO feature in these data from 3.3σ for the unreconstructed correlation function to 4.2σ after reconstruction. We estimate a relative distance scale D_V/r_s to z = 0.35 of 8.88 ± 0.17, where r_s is the sound horizon and DV≡(DA2H-1)1/3 is a combination of the angular diameter distance D_A and Hubble parameter H. Assuming a sound horizon of 154.25Mpc, this translates into a distance measurement D_V(z = 0.35) = 1.356 ± 0.025Gpc. We find that reconstruction reduces the distance error in the DR7 sample from 3.5 to 1.9 per cent, equivalent to a survey with three times the volume of SDSS.