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 agalaxy survey to undo the smoothing of the baryon acoustic oscillation(BAO) feature due to non-linear gravitational evolution and therebyimprove the precision of the distance measurements possible. We applythe reconstruction technique to the clustering of galaxies from theSloan Digital Sky Survey (SDSS) Data Release 7 (DR7) luminous red galaxy(LRG) sample, sharpening the BAO feature and achieving a 1.9 per centmeasurement of the distance to z = 0.35. We update the reconstructionalgorithm of Eisenstein et al. to account for the effects of surveygeometry as well as redshift-space distortions and validate it on 160LasDamas simulations. We demonstrate that reconstruction sharpens theBAO feature in the angle averaged galaxy correlation function, reducingthe non-linear smoothing scale Σ_nl from 8.1 to 4.4 Mpch^-1. Reconstruction also significantly reduces the effects ofredshift-space distortions at the BAO scale, isotropizing thecorrelation function. This sharpened BAO feature yields an unbiaseddistance estimate (0.2 per cent) and reduces the scatter from 3.3 to2.1 per cent. We demonstrate the robustness of these results to thevarious reconstruction parameters, including the smoothing scale, thegalaxy bias and the linear growth rate. Applying this reconstructionalgorithm to the SDSS LRG DR7 sample improves the significance of theBAO feature in these data from 3.3σ for the unreconstructedcorrelation function to 4.2σ after reconstruction. We estimate arelative distance scale D_V/r_s to z = 0.35 of 8.88± 0.17, where r_s is the sound horizon andDV≡(DA2H-1)1/3 is a combination of the angular diameter distanceD_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 ± 0.025 Gpc. We find that reconstruction reduces thedistance error in the DR7 sample from 3.5 to 1.9 per cent, equivalent toa survey with three times the volume of SDSS.