The three-dimensional power spectrum of galaxies from the Sloan Digital Sky Survey

We measure the large-scale real-space power spectrum Pd(k) by using a sample of 205,443 galaxies from the Sloan Digital Sky Survey, covering 2417 effective square degrees with mean redshift z approximate to 0.1. We employ a matrix-based method using pseudo-Karhunen-Loeve eigenmodes, producing uncorrelated minimum-variance measurements in 22 k-bands of both the clustering power and its anisotropy due to redshift-space distortions, with narrow and well-behaved window functions in the range 0.02 h Mpc(-1) < k < 0.3 h Mpc(-1). We pay particular attention to modeling, quantifying, and correcting for potential systematic errors, nonlinear redshift distortions, and the artificial red-tilt caused by luminosity-dependent bias. Our results are robust to omitting angular and radial density fluctuations and are consistent between different parts of the sky. Our final result is a measurement of the real-space matter power spectrum Pd(k) up to an unknown overall multiplicative bias factor. Our calculations suggest that this bias factor is independent of scale to better than a few percent for k < 0.1 h Mpc(-1), thereby making our results useful for precision measurements of cosmological parameters in conjunction with data from other experiments such as the Wilkinson Microwave Anisotropy Probe satellite. The power spectrum is not well-characterized by a single power law but unambiguously shows curvature. As a simple characterization of the data, our measurements are well fitted by a flat scale-invariant adiabatic cosmological model with h Omega(m) = 0.213 +/- 0.023 and sigma(8) = 0.89 +/- 0.02 for L-* galaxies, when fixing the baryon fraction Omega(b).Omega(m) = 0.17 and the Hubble parameter h = 0.72; cosmological interpretation is given in a companion paper.