The 3D power spectrum of galaxies from the SDSS

TL;DR

This work delivers a precise, large-scale measurement of the real-space matter power spectrum $P(k)$ from the SDSS DR1 galaxy sample by employing a matrix-based PKL estimator that yields uncorrelated, minimum-variance band-powers for three redshift-space spectra $P_{gg}(k)$, $P_{gv}(k)$, and $P_{vv}(k)$ across 22 $k$-bands. It robustly handles survey geometry, redshift-space distortions, and luminosity-dependent bias through finger-of-god compression, PKL pixelization, and bias corrections, with extensive Monte Carlo validation. The recovered $P_{gg}(k)$ is consistent with a flat, scale-invariant adiabatic LCDM model, and luminosity-dependent bias is shown to induce only a modest tilt that can be corrected to yield a bias-independent matter power spectrum on large scales. The methodology provides a framework for integrating SDSS measurements with CMB data to tighten cosmological constraints, and future SDSS data (notably LRGs) promise improved constraints on redshift distortions, baryon features, and neutrino masses.

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.

Figures (40)

• Figure 1: The upper panel shows the angular completeness map, the relative probabilities that galaxies in various directions get included, in Hammer-Aitoff projection in equatorial coordinates on a grayscale ranging from black (0) to white (1). It is this completeness map that we expand in spherical harmonics. The backdrop is the logarithm of the dust map from Schlegel, Finkbeiner, & Davis (1998), indicating which sky regions are most likely to be affected by extinction-related systematic errors. The lower panel illustrates the complex nature of the completeness map and the high average completeness with a zoom of a small sky region.
• Figure 2: The redshift distribution of the galaxies in sample safe13 is shown as a histogram and compared with the expected distribution in the absence of clustering, $\ln 10{\bar{n}}(r)r^3 d\Omega$ (solid curve) in comoving coordinates assuming a flat $\Omega_\Lambda=0.7$ cosmology. The bottom panel shows the ratio of observed and expected distributions. The vertical lines indicate the redshift limits ($50\,h^{-1}{\rm Mpc}<r<600\,h^{-1}{\rm Mpc}$) employed in the baseline analysis. This near cut removes only 22 galaxies, the far cut 3295.
• Figure 3: Same as Figure \ref{['zhistFig']} but plotted as comoving number density. The grey (background) histogram shows the full flux-limited sample and the others show the volume-limited subsamples, with lines indicating their predicted constant selection functions.
• Figure 4: The distribution of 67,676 galaxies within $5^\circ$ of the Equatorial plane, color coded by their absolute magnitudes. $M_r$ in the figure refers to the absolute $r$-magnitude $K$-corrected to $z=0.1$.
• Figure 5: The distribution of galaxies within $5^\circ$ of the equatorial plane is shown for the volume-limited subsamples L1, L3, L5 and L7 from Table 1.