Max Tegmark

DETECTION OF THE BARYON ACOUSTIC PEAK IN THE LARGE-SCALE CORRELATION FUNCTION OF SDSS LUMINOUS RED GALAXIES

We present the large-scale correlation function measured from a spectroscopic sample of 46,748 luminous red galaxies from the Sloan Digital Sky Survey. The survey region covers 0.72h −3 Gpc 3 over 3816 square degrees and 0.16 < z < 0.47, making it the best sample yet for the study of large-scale structure. We find a well-detected peak in the correlation function at 100h −1 Mpc separation that is an excellent match to the predicted shape and location of the imprint of the recombination-epoch acoustic oscillations on the low-redshift clustering of matter. This detection demonstrates the linear growth of structure by gravitational instability between z ≈ 1000 and the present and confirms a firm prediction of the standard cosmological theory. The acoustic peak provides a standard ruler by which we can measure the ratio of the distances to z = 0.35 and z = 1089 to 4% fractional accuracy and the absolute distance to z = 0.35 to 5% accuracy. From the overall shape of the correlation function, we measure the matter density mh 2 to 8% and find agreement with the value from cosmic microwave background (CMB) anisotropies. Independent of the constraints provided by the CMB acoustic scale, we find m = 0.273 ±0.025+0.123(1+ w0)+0.137K. Including the CMB acoustic scale, we find that the spatial curvature is K = −0.010 ± 0.009 if the dark energy is a cosmological constant. More generally, our results provide a measurement of cosmological distance, and hence an argument for dark energy, based on a geometric method with the same simple physics as the microwave background anisotropies. The standard cosmological model convincingly passes these new and robust tests of its fundamental properties. Subject headings: cosmology: observations — large-scale structure of the universe — distance scale — cosmological parameters — cosmic microwave background — galaxies: elliptical and lenticular, cD

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.

Baryon Acoustic Oscillations in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample

The spectroscopic Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) galaxy sample represents the final set of galaxies observed using the original SDSS target selection criteria. We analyse the clustering of galaxies within this sample, including both the luminous red galaxy and main samples, and also include the 2-degree Field Galaxy Redshift Survey data. In total, this sample comprises 893 319 galaxies over 9100 deg(2). Baryon acoustic oscillations (BAO) are observed in power spectra measured for different slices in redshift; this allows us to constrain the distance-redshift relation at multiple epochs. We achieve a distance measure at redshift z = 0.275, of r(s)(z(d))/D-V(0.275) = 0.1390 +/- 0.0037 (2.7 per cent accuracy), where r(s)(z(d)) is the comoving sound horizon at the baryon-drag epoch, D-V(z) equivalent to [(1 + z)(2)D(A)(2)cz/H(z)](1/3), D-A(z) is the angular diameter distance and H(z) is the Hubble parameter. We find an almost independent constraint on the ratio of distances D-V(0.35)/D-V(0.2) = 1.736 +/- 0.065, which is consistent at the 1.1 sigma level with the best-fitting Lambda cold dark matter model obtained when combining our z = 0.275 distance constraint with the Wilkinson Microwave Anisotropy Probe 5-year (WMAP5) data. The offset is similar to that found in previous analyses of the SDSS DR5 sample, but the discrepancy is now of lower significance, a change caused by a revised error analysis and a change in the methodology adopted, as well as the addition of more data. Using WMAP5 constraints on Omega(b)h(2) and Omega(c) h(2), and combining our BAO distance measurements with those from the Union supernova sample, places a tight constraint on Omega(m) = 0.286 +/- 0.018 and H-0 = 68.2 +/- 2.2 km s(-1) Mpc(-1) that is robust to allowing Omega(k) not equal 0 and omega not equal -1. This result is independent of the behaviour of dark energy at redshifts greater than those probed by the BAO and supernova measurements. Combining these data sets with the full WMAP5 likelihood constraints provides tight constraints on both Omega(k) = -0.006 +/- 0.008 and omega = -0.97 +/- 0.10 for a constant dark energy equation of state.

Cosmological constraints from the SDSS luminous red galaxies

We measure the large-scale real-space power spectrum P(k) using luminous red galaxies (LRGs) in the Sloan Digital Sky Survey (SDSS) and use this measurement to sharpen constraints on cosmological parameters from the Wilkinson Microwave Anisotropy Probe (WMAP). We employ a matrix-based power spectrum estimation method using Pseudo-Karhunen-Loeve eigenmodes, producing uncorrelated minimum-variance measurements in 20 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 0.01h/Mpc 0.1h/Mpc and associated nonlinear complications, yet agree well with more aggressive published analyses where nonlinear modeling is crucial.

The Galaxy Luminosity Function and Luminosity Density at Redshift z = 0.1

Using a catalog of 147,986 galaxy redshifts and fluxes from the Sloan Digital Sky Survey (SDSS), we measure the galaxy luminosity density at z = 0.1 in five optical bandpasses corresponding to the SDSS bandpasses shifted to match their rest-frame shape at z = 0.1. We denote the bands 0.1u, 0.1g, 0.1r, 0.1i, 0.1z with λeff = (3216, 4240, 5595, 6792, 8111 A), respectively. To estimate the luminosity function, we use a maximum likelihood method that allows for a general form for the shape of the luminosity function, fits for simple luminosity and number evolution, incorporates the flux uncertainties, and accounts for the flux limits of the survey. We find luminosity densities at z = 0.1 expressed in absolute AB magnitudes in a Mpc3 to be (-14.10 ± 0.15, -15.18 ± 0.03, -15.90 ± 0.03, -16.24 ± 0.03, -16.56 ± 0.02) in (0.1u, 0.1g, 0.1r, 0.1i, 0.1z), respectively, for a cosmological model with Ω0 = 0.3, ΩΛ = 0.7, and h = 1 and using SDSS Petrosian magnitudes. Similar results are obtained using Sersic model magnitudes, suggesting that flux from outside the Petrosian apertures is not a major correction. In the 0.1r band, the best-fit Schechter function to our results has * = (1.49 ± 0.04) × 10-2 h3 Mpc-3, M* - 5 log10 h = -20.44 ± 0.01, and α = -1.05 ± 0.01. In solar luminosities, the luminosity density in 0.1r is (1.84 ± 0.04) × 108 h L0.1r,☉ Mpc-3. Our results in the 0.1g band are consistent with other estimates of the luminosity density, from the Two-Degree Field Galaxy Redshift Survey and the Millennium Galaxy Catalog. They represent a substantial change (~0.5 mag) from earlier SDSS luminosity density results based on commissioning data, almost entirely because of the inclusion of evolution in the luminosity function model.

New York University Value-Added Galaxy Catalog: A Galaxy Catalog Based on New Public Surveys*

Here we present the New York University Value-Added Galaxy Catalog (NYU-VAGC), a catalog of local galaxies (mostly below z ≈ 0.3) based on a set of publicly released surveys matched to the Sloan Digital Sky Survey (SDSS) Data Release 2. The photometric catalog consists of 693,319 galaxies, QSOs, and stars; 343,568 of these have redshift determinations, mostly from the SDSS. Excluding areas masked by bright stars, the photometric sample covers 3514 deg2, and the spectroscopic sample covers 2627 deg2 (with about 85% completeness). Earlier, proprietary versions of this catalog have formed the basis of many SDSS investigations of the power spectrum, correlation function, and luminosity function of galaxies. Future releases will follow future public releases of the SDSS. The catalog includes matches to the Two Micron All Sky Survey Point Source Catalog and Extended Source Catalog, the IRAS Point Source Catalog Redshift Survey, the Two-Degree Field Galaxy Redshift Survey, the Third Reference Catalogue of Bright Galaxies, and the Faint Images of the Radio Sky at Twenty cm survey. We calculate and compile derived quantities from the images and spectra of the galaxies in the catalogs (for example, K-corrections and structural parameters for the galaxies). The SDSS catalog presented here is photometrically calibrated in a more consistent way than that distributed by the SDSS Data Release 2 Archive Servers and is thus more appropriate for large-scale structure statistics, reducing systematic calibration errors across the sky from ~2% to ~1%. We include an explicit description of the geometry of the catalog, including all imaging and targeting information as a function of sky position. Finally, we have performed eyeball quality checks on a large number of objects in the catalog in order to flag errors (such as errors in deblending). This catalog is complementary to the SDSS Archive Servers in that NYU-VAGCs calibration, geometric description, and conveniently small size are specifically designed for studying galaxy properties and large-scale structure statistics using the SDSS spectroscopic catalog.Here we present the New York University Value-Added Galaxy Catalog (NYU-VAGC), a catalog of local galaxies (mostly below a redshift of about 0.3) based on a set of publicly-released surveys (including the 2dFGRS, 2MASS, PSCz, FIRST, and RC3) matched to the Sloan Digital Sky Survey (SDSS) Data Release 2. Excluding areas masked by bright stars, the photometric sample covers 3514 square degrees and the spectroscopic sample covers 2627 square degrees (with about 85% completeness). Earlier, proprietary versions of this catalog have formed the basis of many SDSS investigations of the power spectrum, correlation function, and luminosity function of galaxies. We calculate and compile derived quantities (for example, K-corrections and structural parameters for galaxies). The SDSS catalog presented here is photometrically recalibrated, reducing systematic calibration errors across the sky from about 2% to about 1%. We include an explicit description of the geometry of the catalog, including all imaging and targeting information as a function of sky position. Finally, we have performed eyeball quality checks on a large number of objects in the catalog in order to flag deblending and other errors. This catalog is complementary to the SDSS Archive Servers, in that NYU-VAGCs calibration, geometrical description, and conveniently small size are specifically designed for studying galaxy properties and large-scale structure statistics using the SDSS spectroscopic catalog.

Cosmological parameter analysis including SDSS lyα forest and galaxy bias : Constraints on the primordial spectrum of fluctuations, neutrino mass, and dark energy

We combine the constraints from the recent Lyα forest analysis of the Sloan Digital Sky Survey (SDSS) and the SDSS galaxy bias analysis with previous constraints from SDSS galaxy clustering, the latest supernovae, and 1st year WMAP cosmic microwave background anisotropies. We find significant improvements on all of the cosmological parameters compared to previous constraints, which highlights the importance of combining Lyα forest constraints with other probes. combining WMAP and the Lyα forest we find for the primordial slope ns = 0:98±0:02. We see no evidence of running, dn/=d lnk 0:003±0:010, a factor of 3 improvement over previous constraints. We also find no evidence of tensors, r < 0:36 (95% c.l.). Inflationary models predict the absence of running and many among them satisfy these constraints, particularly negative curvature models such as those based on spontaneous symmetry breaking. A positive correlation between tensors and primordial slope disfavors chaotic inflation-type models with steep slopes: while the V αo 2 model is within the 2-sigma contour, V αo4 is outside the 3- sigma contour. For the amplitude we find σ8 = 0:90 ± 0:03 from the Lyα forest and WMAP alone. We find no evidence of neutrino mass: for the case of 3 massive neutrino families with an inflationary prior, Σmv < 0:42 eV and the mass of lightest neutrino is m1 < 0:13 eV at 95% c.l. For the 3 massless +1 massive neutrino case we find mv < 0:79 eV for the massive neutrino, excluding at 95% c.l. all neutrino mass solutions compatible with the LSND results. We explore dark energy constraints in models with a fairly general time dependence of dark energy equation of state, finding Ωλ =0:72± 0:02, w(z = 0:3) = 0:98+0.10 -0.12,the latter changing to w(z = 0:3) = -0.92+0.09-0.10 if tensors are allowed. We find no evidence for variation of the equation of state with redshift, w(z = 1) = -1.03+0.21-0.28. These results rely on the current understanding of the Lyα forest and other probes, which need to be explored further both observationally and theoretically, but extensive tests reveal no evidence of inconsistency among different data sets used here.

THE LUMINOSITY AND COLOR DEPENDENCE OF THE GALAXY CORRELATION FUNCTION

Westudytheluminosityandcolordependenceofthegalaxytwo-pointcorrelationfunctionintheSloanDigitalSky Survey, starting from a sample of � 200,000 galaxies over 2500 deg 2 . We concentrate our analysis on volume-limited subsamples of specified luminosity ranges, for which we measure the projected correlation function wp(rp), which is directly related to the real-space correlation function � (r). The amplitude of wp(rp) rises continuously with luminosity from Mr �� 17: 5t oMr �� 22:5, with the most rapid increase occurring above the characteristic luminosity L� (Mr �� 20:5). Over the scales 0:1 h � 1 Mpc � 22 can be approximated, imperfectly, by power-law three-dimensional correlation functions � (r) ¼ (r/r0) � � with � � 1:8 and r0(L� ) � 5:0 h � 1 Mpc. The brightest subsample, � 23 < Mr < � 22, has a significantly steeper � (r). When we divide samples by color, redder galaxies exhibit a higher amplitude and steeper correlation function at all luminosities. The correlation amplitude of blue galaxies increases continuously with luminosity, but the luminosity dependence for red galaxies is less regular, with bright red galaxies exhibiting the strongest clustering at large scales and faint red galaxies exhibiting the strongest clustering at small scales. We interpret these results using halo occupation distribution (HOD) models assuming concordance cosmological parameters. For most samples, an HOD model with two adjustable parameters fits the wp(rp) data better than a power law, explaining inflections at rp � 1 3 h � 1 Mpc as the transition between the one-halo and two-halo regimes of � (r). The implied minimum mass for a halo hosting a central galaxy more luminous than L grows steadily, with Mmin / L at low luminosities and a steeper dependence above L� . The mass at which a halo has, on average, one satellite galaxy brighter than L is M1 � 23Mmin(L), at all luminosities. These results imply a conditional luminosity function (at fixed halo mass) in which central galaxies lie far above a Schechter function extrapolation of the satellite population. The HOD model fits nicely explain the color dependence of wp(rp) and the cross correlation between red and blue galaxies. For galaxies with Mr < � 21, halos slightly above Mmin have blue central galaxies, while more massive halos have red central galaxies and predominantly red satellite populations. The fraction of blue central galaxies increases steadily with decreasing luminosity and host halo mass. The strong clustering offaint red galaxies follows from the fact that nearly all of them are satellite systems in high-mass halos. The HOD fitting results are in good qualitative agreement with the predictions of numerical and semianalytic models of galaxy formation. Subject headingg cosmology: observations — cosmology: theory — galaxies: distances and redshifts — galaxies: halos — galaxies: statistics — large-scale structure of universe

How small were the first cosmological objects

The minimum mass that a virialized gas cloud must have in order to be able to cool in a Hubble time is computed, using a detailed treatment of the chemistry of molecular hydrogen. With a simple model for halo profiles, we reduce the problem to that of numerically integrating a system of chemical equations. The results agree well with numerically expensive three-dimensional simulations, and our approach has the advantage of being able to explore large regions of parameter space rapidly. The minimum baryonic mass Mb is found to be strongly redshift dependent, dropping from 106 M☉ at z ~ 15 to 5 × 103 M☉ at z ~ 100 as molecular cooling becomes effective. For z 100, Mb rises again, as cosmic microwave background photons inhibit H2 formation through the H- channel. Finally, for z 200, the H -->+2 channel for H2 formation becomes effective, driving Mb down toward Mb ~ 103 M☉. With a standard cold dark matter power spectrum with σ8 = 0.7, this implies that a fraction 10-3 of all baryons may have formed luminous objects by z = 30, which could be sufficient to reheat the 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 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.