Daniel J. Eisenstein

THE 3D POWER SPECTRUM FROM ANGULAR CLUSTERING OF GALAXIES IN EARLY SDSS DATA 1

Early photometric data from the Sloan Digital Sky Survey (SDSS) contain angular positions for 1.5 million galaxies. In companion papers, the angular correlation function w(θ) and two-dimensional power spectrum Cl of these galaxies are presented. Here we invert Limbers equation to extract the three-dimensional power spectrum from the angular results. We accomplish this using an estimate of dn/dz, the redshift distribution of galaxies in four different magnitude slices in the SDSS photometric catalog. The resulting three-dimensional power spectrum estimates from w(θ) and Cl agree with each other and with previous estimates over a range in wavenumbers 0.03 < k/(h Mpc-1) < 1. The galaxies in the faintest magnitude bin (21 < r* < 22, which have median redshift zm = 0.43) are less clustered than the galaxies in the brightest magnitude bin (18 < r* < 19 with zm = 0.17), especially on scales where nonlinearities are important. The derived power spectrum agrees with that of Szalay et al., who go directly from the raw data to a parametric estimate of the power spectrum. The strongest constraints on the shape parameter Γ come from the faintest galaxies (in the magnitude bin 21 < r* < 22), from which we infer Γ = 0.14 (95% CL).Early photometric data from the Sloan Digital Sky Survey (SDSS) contain angular positions for 1.5 million galaxies. In companion papers, the angular correlation function w(�) and 2D power spectrum Cl of these galaxies are presented. Here we invert Limber’s equation to extract the 3D power spectrum from the angular results. We accomplish this using an estimate of dn/dz, the redshift distribution of galaxies in four different magnitude slices in the SDSS photometric catalog. The resulting 3D power spectrum estimates from w(�) and Cl agree with each other and with previous estimates over a range in wavenumbers 0.03 < k/h Mpc −1 < 1. The galaxies in the faintest magnitude bin (21 < r ∗ < 22, which have median redshift zm = 0.43) are less clustered than the galaxies in the brightest magnitude bin (18 < r ∗ < 19 with zm = 0.17), especially on scales where nonlinearities are important. The derived power spectrum agrees with that of Szalay et al. (2001) who go directly from the raw data to a parametric estimate of the power spectrum. The strongest constraints on the shape parameter come from the faintest galaxies (in the magnitude bin 21 < r ∗ < 22), from which we infer = 0 .14 +0.11 −0.06 (95% C.L.).

Cosmological Parameters from Galaxy Clustering in the SDSS

We present estimates of cosmological parameters from the application of the Karhunen-Loève transform to the analysis of the 3D power spectrum of density fluctuations using Sloan Digital Sky Survey galaxy redshifts. We use Ωmh and fb Ωb Ωm to describe the shape of the power spectrum, σ8g for the (linearly extrapolated) normalization, and β to parametrize linear theory redshift space distortions. On scales k 0 16hMpc 1, our maximum likelihood values are Ωmh 0 264 0 043, fb 0 286 0 065, σ8g 0 966 0 048, and β 0 45 0 12. When we take a prior on Ωb from WMAP, we find Ωmh 0 207 0 030, which is in excellent agreement with WMAP and 2dF. This indicates that we have reasonably measured the gross shape of the power spectrum but we have difficulty breaking the degeneracy between Ωmh and fb because the baryon oscillations are not resolved in the current spectroscopic survey window function.