Karhunen-Loève estimation of the power spectrum parameters from the angular distribution of galaxies in early Sloan digital sky survey data

Alexander S. Szalay, Bhuvnesh Jain, Takahiko Matsubara, Ryan Scranton, Michael S. Vogeley, Andrew Connolly, Scott Dodelson, Daniel Eisenstein, Joshua A. Frieman, James E. Gunn, Lam Hui, David Johnston, Stephen Kent, Martin Kerscher, Jon Loveday, Avery Meiksin, Vijay Narayanan, Robert C. Nichol, Liam O'Connell, Adrian PopeRoman Scoccimarro, Ravi K. Sheth, Albert Stebbins, Michael A. Strauss, István Szapudi, Max Tegmark, Idit Zehavi, James Annis, Neta Bahcall, Jon Brinkmann, István Csabai, Masataka Fukugita, Greg Hennessy, Zeljko Ivezic, Gillian R. Knapp, Peter Z. Kunszt, Don Q. Lamb, Brian C. Lee, Robert H. Lupton, Jeffrey R. Munn, John Peoples, Jeffrey R. Pier, Constance Rockosi, David Schlegel, Christopher Stoughton, Douglas L. Tucker, Brian Yanny, Donald G. York

    Research output: Contribution to journalReview articlepeer-review


    We present measurements of parameters of the three-dimensional power spectrum of galaxy clustering from 222 square degrees of early imaging data in the Sloan Digital Sky Survey (SDSS). The projected galaxy distribution on the sky is expanded over a set of Karhunen-Loève (KL) eigenfunctions, which optimize the signal-to-noise ratio in our analysis. A maximum likelihood analysis is used to estimate parameters that set the shape and amplitude of the three-dimensional power spectrum of galaxies in the SDSS magnitude-limited sample with r* < 21. Our best estimates are γ = 0.188 ± 0.04 and σ8L = 0.915 ± 0.06 (statistical errors only), for a flat universe with a cosmological constant. We demonstrate that our measurements contain signal from scales at or beyond the peak of the three-dimensional power spectrum. We discuss how the results scale with systematic uncertainties, like the radial selection function. We find that the central values satisfy the analytically estimated scaling relation. We have also explored the effects of evolutionary corrections, various truncations of the KL basis, seeing, sample size, and limiting magnitude. We find that the impact of most of these uncertainties stay within the 2 σ uncertainties of our fiducial result.

    Original languageEnglish (US)
    Pages (from-to)1-11
    Number of pages11
    JournalAstrophysical Journal
    Issue number1 I
    StatePublished - Jul 1 2003


    • Cosmology: theory
    • Galaxies: clusters: general
    • Galaxies: formation
    • Large-scale structure of universe
    • Methods: data analysis
    • Methods: statistical

    ASJC Scopus subject areas

    • Astronomy and Astrophysics
    • Space and Planetary Science


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