The Three‐Dimensional Power Spectrum of Galaxies from the Sloan Digital Sky Survey

We measure the large-scale real-space power spectrum P(k) using a sample of205,443 galaxies from the Sloan Digital Sky Survey, covering 2417 squaredegrees with mean redshift z~0.1. We employ a matrix-based method usingpseudo-Karhunen-Loeve eigenmodes, producing uncorrelated minimum-variancemeasurements in 22 k-bands of both the clustering power and its anisotropy dueto redshift-space distortions, with narrow and well-behaved window functions inthe range 0.02 h/Mpc < k < 0.3h/Mpc. We pay particular attention to modeling,quantifying and correcting for potential systematic errors, nonlinear redshiftdistortions and the artificial red-tilt caused by luminosity-dependent bias.Our final result is a measurement of the real-space matter power spectrum P(k)up to an unknown overall multiplicative bias factor. Our calculations suggestthat this bias factor is independent of scale to better than a few percent fork<0.1h/Mpc, thereby making our results useful for precision measurements ofcosmological parameters in conjunction with data from other experiments such asthe WMAP satellite. As a simple characterization of the data, our measurementsare well fit by a flat scale-invariant adiabatic cosmological model with hOmega_m =0.201+/- 0.017 and L* galaxy sigma_8=0.89 +/- 0.02 when fixing thebaryon fraction Omega_b/Omega_m=0.17 and the Hubble parameter h=0.72;cosmological interpretation is given in a companion paper.