Idit Zehavi

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

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.We measure the large-scale real-space power spectrum P(k) by 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-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 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-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 Ωm = 0.213 ± 0.023 and σ8 = 0.89 ± 0.02 for L* galaxies, when fixing the baryon fraction Ωb/Ωm = 0.17 and the Hubble parameter h = 0.72; cosmological interpretation is given in a companion paper.

Spectroscopic Target Selection in the Sloan Digital Sky Survey: The Main Galaxy Sample

We describe the algorithm that selects the main sample of galaxies for spectroscopy in the Sloan Digital Sky Survey (SDSS) from the photometric data obtained by the imaging survey. Galaxy photometric properties are measured using the Petrosian magnitude system, which measures flux in apertures determined by the shape of the surface brightness profile. The metric aperture used is essentially independent of cosmological surface brightness dimming, foreground extinction, sky brightness, and the galaxy central surface brightness. The main galaxy sample consists of galaxies with r-band Petrosian magnitudes r ≤ 17.77 and r-band Petrosian half-light surface brightnesses μ50 ≤ 24.5 mag arcsec-2. These cuts select about 90 galaxy targets per square degree, with a median redshift of 0.104. We carry out a number of tests to show that (1) our star-galaxy separation criterion is effective at eliminating nearly all stellar contamination while removing almost no genuine galaxies, (2) the fraction of galaxies eliminated by our surface brightness cut is very small (~0.1%), (3) the completeness of the sample is high, exceeding 99%, and (4) the reproducibility of target selection based on repeated imaging scans is consistent with the expected random photometric errors. The main cause of incompleteness is blending with saturated stars, which becomes more significant for brighter, larger galaxies. The SDSS spectra are of high enough signal-to-noise ratio (S/N > 4 per pixel) that essentially all targeted galaxies (99.9%) yield a reliable redshift (i.e., with statistical error less than 30 km s-1). About 6% of galaxies that satisfy the selection criteria are not observed because they have a companion closer than the 55 minimum separation of spectroscopic fibers, but these galaxies can be accounted for in statistical analyses of clustering or galaxy properties. The uniformity and completeness of the galaxy sample make it ideal for studies of large-scale structure and the characteristics of the galaxy population in the local universe.

Galaxy Clustering in Early Sloan Digital Sky Survey Redshift Data

We present the first measurements of clustering in the Sloan Digital Sky Survey (SDSS) galaxy redshift survey. Our sample consists of 29,300 galaxies with redshifts 5,700 km/s < cz < 39,000 km/s, distributed in several long but narrow (2.5-5 degree) segments, covering 690 square degrees. For the full, flux-limited sample, the redshift-space correlation length is approximately 8 Mpc/h. The two-dimensional correlation function xi(r_p,pi) shows clear signatures of both the small-scale, ``fingers-of-God distortion caused by velocity dispersions in collapsed objects and the large-scale compression caused by coherent flows, though the latter cannot be measured with high precision in the present sample. The inferred real-space correlation function is well described by a power law, xi(r)=(r/6.1+/-0.2 Mpc/h)^{-1.75+/-0.03}, for 0.1 Mpc/h < r < 16 Mpc/h. The galaxy pairwise velocity dispersion is sigma_{12} ~ 600+/-100 km/s for projected separations 0.15 Mpc/h < r_p < 5 Mpc/h. When we divide the sample by color, the red galaxies exhibit a stronger and steeper real-space correlation function and a higher pairwise velocity dispersion than do the blue galaxies. The relative behavior of subsamples defined by high/low profile concentration or high/low surface brightness is qualitatively similar to that of the red/blue subsamples. Our most striking result is a clear measurement of scale-independent luminosity bias at r < 10 Mpc/h: subsamples with absolute magnitude ranges centered on M_*-1.5, M_*, and M_*+1.5 have real-space correlation functions that are parallel power laws of slope ~ -1.8 with correlation lengths of approximately 7.4 Mpc/h, 6.3 Mpc/h, and 4.7 Mpc/h, respectively.We present the first measurements of clustering in the Sloan Digital Sky Survey (SDSS) galaxy redshift survey. Our sample consists of 29,300 galaxies with redshifts 5700 km s-1 ≤ cz ≤ 39,000 km s-1, distributed in several long but narrow (25-5°) segments, covering 690 deg2. For the full, flux-limited sample, the redshift-space correlation length is approximately 8 h-1 Mpc. The two-dimensional correlation function ξ(rp,π) shows clear signatures of both the small-scale, fingers-of-God distortion caused by velocity dispersions in collapsed objects and the large-scale compression caused by coherent flows, though the latter cannot be measured with high precision in the present sample. The inferred real-space correlation function is well described by a power law, ξ(r) = (r/6.1 ± 0.2 h-1 Mpc)-1.75±0.03, for 0.1 h-1 Mpc ≤ r ≤ 16 h-1 Mpc. The galaxy pairwise velocity dispersion is σ12 ≈ 600 ± 100 km s-1 for projected separations 0.15 h-1 Mpc ≤ rp ≤ 5 h-1 Mpc. When we divide the sample by color, the red galaxies exhibit a stronger and steeper real-space correlation function and a higher pairwise velocity dispersion than do the blue galaxies. The relative behavior of subsamples defined by high/low profile concentration or high/low surface brightness is qualitatively similar to that of the red/blue subsamples. Our most striking result is a clear measurement of scale-independent luminosity bias at r 10 h-1 Mpc: subsamples with absolute magnitude ranges centered on M* - 1.5, M*, and M* + 1.5 have real-space correlation functions that are parallel power laws of slope ≈-1.8 with correlation lengths of approximately 7.4, 6.3, and 4.7 h-1 Mpc, respectively.

An Efficient Targeting Strategy for Multiobject Spectrograph Surveys: the Sloan Digital Sky Survey "Tiling" Algorithm

Large surveys using multiobject spectrographs require automated methods for deciding how to efficiently point observations and how to assign targets to each pointing. The Sloan Digital Sky Survey (SDSS) will observe around 10 6 spectra from targets distributed over an area of about 10,000 deg 2 , using a multiobject fiber spectrograph that can simultaneously observe 640 objects in a circular field of view (referred to as a ‘‘ tile ’’) 1=49 in radius. No two fibers can be placed closer than 55 00 during the same observation; multiple targets closer than this distance are said to ‘‘ collide.’’ We present here a method of allocating fibers to desired targets given a set of tile centers that includes the effects of collisions and that is nearly optimally efficient and uniform. Because of large-scale structure in the galaxy distribution (which form the bulk of the SDSS targets), a naive covering of the sky with equally spaced tiles does not yield uniform sampling. Thus, we present a heuristic for perturbing the centers of the tiles from the equally spaced distribution that provides more uniform completeness. For the SDSS sample, we can attain a sampling rate of greater than 92% for all targets, and greater than 99% for the set of targets that do not collide with each other, with an efficiency greater than 90% (defined as the fraction of available fibers assigned to targets). The methods used here may prove useful to those planning other large surveys.The Sloan Digital Sky Survey (SDSS) will observe around 10^6 spectra from targets distributed over an area of about 10,000 square degrees, using a multi-object fiber spectrograph which can simultaneously observe 640 objects in a circular field-of-view (referred to as a ``tile) 1.49 degrees in radius. No two fibers can be placed closer than 55 during the same observation; multiple targets closer than this distance are said to ``collide. We present here a method of allocating fibers to desired targets given a set of tile centers which includes the effects of collisions and which is nearly optimally efficient and uniform. Because of large-scale structure in the galaxy distribution (which form the bulk of the SDSS targets), a naive covering the sky with equally-spaced tiles does not yield uniform sampling. Thus, we present a heuristic for perturbing the centers of the tiles from the equally-spaced distribution which provides more uniform completeness. For the SDSS sample, we can attain a sampling rate greater than 92% for all targets, and greater than 99% for the set of targets which do not collide with each other, with an efficiency greater than 90% (defined as the fraction of available fibers assigned to targets).

The overdensities of galaxy environments as a function of luminosity and color

We study the mean environments of galaxies in the Sloan Digital Sky Survey (SDSS) as a function of rest-frame luminosity and color. Overdensities in galaxy number are estimated in 8 and 1 h-1 Mpc spheres centered on 115,000 galaxies taken from the SDSS spectroscopic sample. We find that, at constant color, overdensity is independent of luminosity for galaxies with the blue colors of spirals. This suggests that at fixed star formation history, spiral-galaxy mass is a very weak function of environment. Overdensity does depend on luminosity for galaxies with the red colors of early types; both low-luminosity and high-luminosity red galaxies are found to be in highly overdense regions.

Cosmological Parameters from Eigenmode Analysis of Sloan Digital Sky Survey Galaxy Redshifts

We present estimates of cosmological parameters from the application of the Karhunen-Loeve transform to the analysis of the three-dimensional power spectrum of density fluctuations using Sloan Digital Sky Survey galaxy redshifts. We use Ωmh and fb = Ωb/Ωm to describe the shape of the power spectrum, σ for the (linearly extrapolated) normalization, and β to parameterize linear theory redshift-space distortions. On scales k 0.16 h Mpc-1, our maximum likelihood values are Ωmh = 0.264 ± 0.043, fb = 0.286 ± 0.065, σ = 0.966 ± 0.048, and β = 0.45 ± 0.12. When we take a prior on Ωb from the Wilkinson Microwave Anisotropy Probe (WMAP), we find Ωmh = 0.207 ± 0.030, which is in excellent agreement with WMAP and the Two-Degree Field. This indicates that we have reasonably measured the gross shape of the power spectrum, but we have difficulty breaking the degeneracy between Ωmh and fb, because the baryon oscillations are not resolved in the current spectroscopic survey window function.

Angular Clustering with Photometric Redshifts in the Sloan Digital Sky Survey: Bimodality in the Clustering Properties of Galaxies

Understanding the clustering of galaxies has long been a goal of modern observational cosmology. Redshift surveys have been used to measure the correlation length as a function of luminosity and color. However, when subdividing the catalogs into multiple subsets, the errors increase rapidly. Angular clustering in magnitude-limited photometric surveys has the advantage of much larger catalogs but suffers from a dilution of the clustering signal because of the broad radial distribution of the sample. Also, up to now it has not been possible to select uniform subsamples based on physical parameters, such as luminosity and rest-frame color. Utilizing our photometric redshift technique, a volume-limited sample (0:1 < z < 0:3) containing more than 2 million galaxies is constructed from the Sloan Digital Sky Survey galaxy catalog. In the largest such analysis to date, we study the angular clustering as a function of luminosity and spectral type. Using Limber’s equation, we calculate the clustering length for the full data set as r0 ¼ 5:77 � 0:10 h � 1 Mpc. We find that r0 increases with luminosity by a factor of 1.6 over the sampled luminosity range, in agreement with previous redshift surveys. We also find that both the clustering length and the slope of the correlation function depend on the galaxy type. In particular, by splitting the galaxies in four groups by their rest-frame type, we find a bimodal behavior in their clustering properties. Galaxies with spectral types similar to elliptical galaxies have a correlation length of 6:59 � 0:17 h � 1 Mpc and a slope of the angular correlation function of 0:96 � 0:05, while blue galaxies have a clustering length of 4:51 � 0:19 h � 1 Mpc and a slope of 0:68 � 0:09. The two intermediate color groups behave like their more extreme ‘‘ siblings ’’ rather than showing a gradual transition in slope. We discuss these correlations in the context of current cosmological models for structure formation. Subject headings: cosmology: observations — galaxies: clusters: general — galaxies: distances and redshifts — galaxies: evolution — galaxies: photometry — large-scale structure of universe

The Scale-dependence of relative galaxy bias: Encouragement for the halo model description

We investigate the relationship between the colors, luminosities, and environments of galaxies in the Sloan Digital Sky Survey spectroscopic sample, using environmental measurements on scales ranging from 0.2 to 6 h-1 Mpc. We find that (1) the relationship between color and environment persists even to the lowest luminosities we probe (Mr - 5 h ~ -14); (2) at luminosities and colors for which the galaxy correlation function has a large amplitude, it also has a steep slope; and (3) in regions of a given overdensity on small scales (1 h-1 Mpc), the overdensity on large scales (6 h-1 Mpc) does not appear to relate to the recent star formation history of the galaxies. Of these results, the last has the most immediate application to galaxy formation theory. In particular, it lends support to the notion that a galaxys properties are related only to the mass of its host dark matter halo, and not to the larger scale environment.

The angular correlation function of galaxies from early sloan digital sky survey data

The Sloan Digital Sky Survey is one of the first multicolor photometric and spectroscopic surveys designed to measure the statistical properties of galaxies within the local universe. In this paper we present some of the initial results on the angular two-point correlation function measured from the early SDSS galaxy data. The form of the correlation function, over the magnitude interval 18 < r* < 22, is shown to be consistent with results from existing wide-field, photographic-based surveys and narrower CCD galaxy surveys. On scales between 1 and 1° the correlation function is well described by a power law with an exponent of ≈-0.7. The amplitude of the correlation function, within this angular interval, decreases with fainter magnitudes in good agreement with analysis from existing galaxy surveys. There is a characteristic break in the correlation function on scales of approximately 1°-2°. On small scales, θ < 1, the SDSS correlation function does not appear to be consistent with the power-law form fitted to the 1 < θ < 05 data. With a data set that is less than 2% of the full SDSS survey area, we have obtained high-precision measurements of the power-law angular correlation function on angular scales 1 < θ < 1°, which are robust to systematic uncertainties. Because of the limited area and the highly correlated nature of the error covariance matrix, these initial results do not yet provide a definitive characterization of departures from the power-law form at smaller and larger angles. In the near future, however, the area of the SDSS imaging survey will be sufficient to allow detailed analysis of the small- and large-scale regimes, measurements of higher order correlations, and studies of angular clustering as a function of redshift and galaxy type.

The angular power spectrum of galaxies from early Sloan Digital Sky Survey data

We compute the angular power spectrum Cl from 1.5 million galaxies in early Sloan Digital Sky Survey (SDSS) data on large angular scales, l 600. The data set covers about 160 deg2, with a characteristic depth on the order of 1 h-1 Gpc in the faintest (21 < r* < 22) of our four magnitude bins. Cosmological interpretations of these results are presented in a companion paper by Dodelson and coworkers. The data in all four magnitude bins are consistent with a simple flat concordance model with nonlinear evolution and linear bias factors on the order of unity. Nonlinear evolution is particularly evident for the brightest galaxies. A series of tests suggests that systematic errors related to seeing, reddening, etc. are negligible, which bodes well for the 60-fold larger sample that the SDSS is currently collecting. Uncorrelated error bars and well-behaved window functions make our measurements a convenient starting point for cosmological model fitting.