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

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 effective square degrees with mean redshift z ≈ 0.1. We employ a matrix-based method using pseudo-Karhunen-Loève eigenmodes, producing uncorrelated minimumvariance 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 < 0.3 h/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 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 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 < 0.1 h/Mpc, thereby making our results useful for precision measurements of cosmological parameters in conjunction with data from other experiments such as the WMAP 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 fit by a flat scaleinvariant adiabatic cosmological model with hΩ m = 0.213 ± 0.023 and σ 8 = 0.89 ± 0.02 for L * galaxies, when fixing the baryon fraction Ω b /Ω m = 0.17 and the Hubble parameter h = 0.72; cosmological interpretation is given in a companion paper.

Observational probes of cosmic acceleration

“…In the galaxy correlation function, one can remove the effects of redshift-space distortion straightforwardly by projection, counting galaxy pairs as a function of projected separation rather than 3-d redshift-space separation. For the power spectrum, one can correct for redshift-space distortion, but the analysis is more model-dependent (see, e.g., Tegmark et al 2004). However, redshift-space distortion can be an asset as well as a nuisance, since it provides a route to measuring d ln G/d ln a.…”

Clustering of intermediate redshift quasars using the final SDSS III-BOSS sample

“…Quasar spectra in BOSS were obtained using a set of spectroscopic tiles that can be modeled as polygons using the MANGLE software (Blanton et al 2003;Tegmark et al 2004;Swanson et al 2008). The fraction of targets (quasars) in an area of the sky that has been covered by a unique set of these tiles (called a sector) is used to define the completeness of the sample.…”

“…The elongation of virialized overdensities such as clusters of galaxies along the line of sight, caused by small peculiar velocities that are not associated with the Hubble flow, should be visible in 2-D redshift-space maps as long, narrow filaments aligned with the line of sight (Tegmark et al 2004). To check whether this "Fingers of God" effect is apparent in our sample, we measure ξ(rp, π) for our NGC-CORE quasars out to scales of ±20 h −1 Mpc, and display the results in Fig.…”

Re-examining the too-big-to-fail problem for dark matter haloes with central density cores

“…The current standard paradigm, the Λ cold dark matter (ΛCDM) model, reproduces the large-scale properties of the universe successfully (e.g., Tegmark et al 2004;Eisenstein et al 2005;Hinshaw et al 2007). However, some serious discrepancies between the ΛCDM prediction and observations have been identified in the local universe and are known as still remaining small-scale problems of ΛCDM cosmology.…”