A 2% Distance to z=0.35 by Reconstructing Baryon Acoustic Oscillations - I : Methods and Application to the Sloan Digital Sky Survey

Abstract

We apply the reconstruction technique to the clustering of galaxies from the SDSS DR7 LRG sample, sharpening the baryon acoustic oscillation (BAO) feature and achieving a 1.9% measurement of the distance to z=0.35. This is the first application of reconstruction of the BAO feature in a galaxy redshift survey. We update the reconstruction algorithm of Eisenstein et al, 2007 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 nonlinear smoothing scale Σ_nl from 8.1 Mpc/h to 4.4 Mpc/h. 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%) and reduces the scatter from 3.3% to 2.1%. 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 3.3 sigma for the unreconstructed correlation function, to 4.2 sigma 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 D_V = (D_A^2/H)^{1/3} is a combination of the angular diameter distance D_A and Hubble parameter H. Assuming a sound horizon of 154.25 Mpc, this translates into a distance measurement D_V (z=0.35) = 1.356+/-0.025 Gpc. We find that reconstruction reduces the distance error in the DR7 sample from 3.5% to 1.9%, equivalent to a survey with three times the volume of SDSS.

Figures (15)

• Figure 1: A pictoral explanation of how density-field reconstruction can improve the acoustic scale measurement. In each panel, we show a thin slice of a simulated cosmological density field. ( top left) In the early universe, the initial densities are very smooth. We mark the acoustic feature with a ring of 150 Mpc radius from the central points. A Gaussian with the same rms width as the radial distribution of the black points from the centroid of the blue points is shown in the inset. ( top right) We evolve the particles to the present day, here by the Zel'dovich approximation 1970AA.....5...84Z. The red circle shows the initial radius of the ring, centered on the current centroid of the blue points. The large-scale velocity field has caused the black points to spread out; this causes the acoustic feature to be broader. The inset shows the current rms radius of the black points relative to the centroid of the blue points (solid line) compared to the initial rms (dashed line). ( bottom left) As before, but overplotted with the Lagrangian displacement field, smoothed by a 10$h^{-1}$ Mpc Gaussian filter. The concept of reconstruction is to estimate this displacement field from the final density field and then move the particles back to their initial positions. ( bottom right) We displace the present-day position of the particles by the opposite of the displacement field in the previous panel. Because of the smoothing of the displacement field, the result is not uniform. However, the acoustic ring has been moved substantially closer to the red circle. The inset shows that the new rms radius of the black points (solid), compared to the initial width (long-dashed) and the uncorrected present-day width (short-dashed). The narrower peak will make it easier to measure the acoustic scale. Note that the algorithm applied to the data is more complex than was just described, but this figure illustrates the basic opportunity of reconstruction.
• Figure 2: The footprint of the DR7 LRG sample used in this paper, plotted in equatorial coordinates and an Albers equal area projection. The area covered is 7189 deg$^2$.
• Figure 3: The redshift distribution of the DR7 LRG sample used in this paper. The dashed [red] line is a smooth fit to the redshift distribution used in the determination of the weights used in the correlation function.
• Figure 4: The LasDamas galaxy correlation function, averaged over the 160 simulations, as a function of the separation perpendicular ($\perp$) and parallel ($||$) to the line of sight. The correlation functions have been scaled by $r^2$ to highlight the BAO feature. The top panels show the unreconstructed correlation functions, while the bottom panels show the reconstructed correlation functions; the left and right panels are real and redshift space respectively. The BAO feature is visible as a ring at $\sim\! 110 {\rm Mpc}/h$ in the top left panel. Redshift space distortions destroy the isotropy of the correlation function (top right). Reconstruction both sharpens the BAO feature (highlighted in the bottom left panel) and restores the isotropy (bottom right) of the correlation function on the BAO scale.
• Figure 5: [left]The angle averaged correlation function in real space, before [red circles] and after [blue squares] reconstruction and averaging over the 160 LasDamas simulations. The reconstruction algorithm assumes the default parameters described in the text. The acoustic feature is clearly sharpened after reconstruction. [right] Same as the left panel, except in redshift space. Also shown for comparison is the average reconstructed real-space correlation [dashed line]. In addition to sharpening the acoustic feature, the reconstruction algorithm also reduces the effects of redshift-space distortions on the correlation function.