Abstract
We measure the large-scale real-space power spectrum P(k) using a sample of 205,443 galaxies from the Sloan Digital Sky Survey, covering 2417 square degrees with mean redshift z~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 < k < 0.3h/Mpc. 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 final result is a measurement of the real-space matter power spectrum P(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<0.1h/Mpc, thereby making our results useful for precision measurements of cosmological parameters in conjunction with data from other experiments such as the WMAP satellite. As a simple characterization of the data, our measurements are well fit by a flat scale-invariant adiabatic cosmological model with h Omega_m =0.201+/- 0.017 and L* galaxy sigma_8=0.89 +/- 0.02 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.
Highlights
Since we have used only 4000 PKL modes, most of the information from scales k 3 0:1 h MpcÀ1 is excluded from our analysis
Nonlinear clustering per se would not bias quadratic estimators of the power spectrum, but how much do nonlinearities in the redshift-space distortions affect the results? Figure 25 shows that the sensitivity of the PggðkÞ measurement to FOG nonlinearities is around 1% at k $ 0:1 h MpcÀ1, i.e., negligible compared with our statistical measurement errors
We have argued that any scale-dependent statistical bias in our PggðkÞ results due to nonlinear redshift distortions is smaller than a few percent for k < 0:1 h MpcÀ1, i.e., that the systematic errors associated with this are negligible compared with the statistical errors
Summary
3 Princeton University Observatory, Princeton, NJ 08544. 4 Department of Physics, Drexel University, Philadelphia, PA 19104. 5 Department of Astronomy, Ohio State University, Columbus, OH 43210. 6 Center for Cosmological Physics and Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL 60637. 7 Department of Physics and Astronomy, Johns Hopkins University, 3701. 8 University of Pittsburgh, Department of Physics and Astronomy, 3941. 9 Department of Astronomy, University of Arizona, 933 North Cherry. 12 Department of Physics, 5000 Forbes Avenue, Carnegie Mellon University, Pittsburgh, PA 15213. 13 Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822. 14 Apache Point Observatory, 2001 Apache Point Road, Sunspot, NM. 15 Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139. 22 Department of Astronomy and Astrophysics, Pennsylvania State. 23 Enrico Fermi Institute, University of Chicago, Chicago, IL 60637
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