Showing papers by "Ravi K. Sheth published in 2004"

Cosmological parameters from SDSS and WMAP

Abstract: We measure cosmological parameters using the three-dimensional power spectrum P(k) from over 200,000 galaxies in the Sloan Digital Sky Survey (SDSS) in combination with WMAP and other data. Our results are consistent with a "vanilla" flat adiabaticCDM model without tilt (ns = 1), running tilt, tensor modes or massive neutrinos. Adding SDSS information more than halves the WMAP-only error bars on some parameters, tightening 1� constraints on the Hubble parameter from h � 0.74 +0.18 −0.07 to h � 0.70 +0.04 −0.03, on the matter density from m � 0.25 ± 0.10 to m � 0.30 ± 0.04 (1�) and on neutrino masses from < 11 eV to < 0.6 eV (95%). SDSS helps even more when dropping prior assumptions about curvature, neutrinos, tensor modes and the equation of state. Our results are in substantial agreement with the joint analysis of WMAP and the 2dF Galaxy Redshift Survey, which is an impressive consistency check with independent redshift survey data and analysis techniques. In this paper, we place particular emphasis on clarifying the physical origin of the constraints, i.e., what we do and do not know when using different data sets and prior assumptions. For instance, dropping the assumption that space is perfectly flat, the WMAP-only constraint on the measured age of the Universe tightens from t0 � 16.3 +2.3

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) 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.

The Luminosity and Color Dependence of the Galaxy Correlation Function

Abstract: We study the luminosity and color dependence of the galaxy 2-point correlation function in the Sloan Digital Sky Survey, starting from a sample of 200,000 galaxies over 2500 deg^2. We concentrate on the projected correlation function w(r_p), which is directly related to the real space \xi(r). The amplitude of w(r_p) grows continuously with luminosity, rising more steeply above the characteristic luminosity L_*. 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 more strongly clustered at large scales and faint red galaxies more strongly clustered 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 w(r_p) data better than a power-law, explaining inflections at r_p ~ 1-3 Mpc/h as the transition between the 1-halo and 2-halo regimes of \xi(r). The implied minimum mass for a halo hosting a central galaxy above a luminosity threshold L grows as M_min ~ L at low luminosities and more steeply above L_*. The mass at which an average halo has one satellite galaxy brighter than L is M_1 ~ 23 M_min(L). 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. HOD models nicely explain the joint luminosity-color dependence of w(r_p) in terms of the color fractions of central and satellite populations as a function of halo mass. The inferred HOD properties are in good qualitative agreement with theoretical predictions.

A hierarchy of voids: much ado about nothing

Abstract: We present a model for the distribution of void sizes and its evolution in the context of hierarchical scenarios of gravitational structure formation. We find that at any cosmic epoch the voids have a size distribution that is well-peaked about a characteristic void size that evolves self-similarly in time. This is in distinct contrast to the distribution of virialized halo masses, which does not have a small-scale cut-off. In our model, the fate of voids is ruled by two processes. The first process affects those voids which are embedded in larger underdense regions: the evolution is effectively one in which a larger void is made up by the mergers of smaller voids, and is analogous to how massive clusters form from the mergers of less massive progenitors. The second process is unique to voids, and occurs to voids that happen to be embedded within a larger-scale overdensity: these voids get squeezed out of existence as the overdensity collapses around them. It is this second process which produces the cut-off at small scales. In the excursion set formulation of cluster abundance and evolution, the solution of the cloud-in-cloud problem, i.e. counting as clusters only those objects which are not embedded in larger clusters, requires the study of random walks crossing one barrier. We show that a similar formulation of void evolution requires the study of a two-barrier problem: one barrier is required to account for voids-in-voids, and the other for voids-in-clouds. Thus, in our model, the void size distribution is a function of two parameters, one of which reflects the dynamics of void formation, and the other the formation of collapsed objects.

On Departures from a Power Law in the Galaxy Correlation Function

Abstract: We measure the projected correlation function wp from the Sloan Digital Sky Survey for a flux-limited sample of 118,000 galaxies and a volume-limited subset of 22,000 galaxies with absolute magnitude Mr M1 = 4.74 × 1013 h-1 M☉ is M = 0.89, with 75% of the galaxies residing in less massive, single-galaxy halos and simple auxiliary assumptions about the spatial distribution of galaxies within halos and the fluctuations about the mean occupation. This physically motivated model has the same number of free parameters as a power law, and it fits the wp data better, with a χ2/dof = 0.93, compared to 6.12 (for 10 degrees of freedom, incorporating the covariance of the correlation function errors). Departures from a power-law correlation function encode information about the relation between galaxies and dark matter halos. Higher precision measurements of these departures for multiple classes of galaxies will constrain galaxy bias and provide new tests of the theory of galaxy formation.

On the environmental dependence of halo formation

Abstract: A generic prediction of hierarchical gravitationalclustering models is that the distribu-tion of halo formation times should depend relatively strongly on halo mass, massivehaloes forming more recently, and depend only weakly, if at all, on the large scaleenvironment of the haloes. We present a novel test of this assumption which uses thestatistics of weighted or ‘marked’ correlations, which prove to be particularly well-suited to detecting and quantifying weak correlations with environment. We find thatclose pairs of haloes form at slightly higher redshifts than do more widely separatedhalo pairs, suggesting that haloes in dense regions form at slightly earlier times thando haloes of the same mass in less dense regions. The environmental trends we findare useful for models which relate the properties of galaxies to the formation historiesof the haloes which surround them.Key words: galaxies: clustering – cosmology: theory – dark matter. 1 INTRODUCTIONThe excursion set model of hierarchical clustering (Epstein1983; Bond et al. 1991) has been remarkably successful. Itprovides useful analytic approximations for the abundanceof haloes of mass m at time t (Bond et al. 1991; Sheth,Mo & Tormen 2001), for the conditional mass function ofm haloes at t which are later (at T > t) in more massivehaloes M > m (Bond et al. 1991; Lacey & Cole 1993; Sheth& Tormen 2002), for the abundance of haloes as a functionof the larger scale environment (Mo & White 1996; Lemson& Kauffmann 1999; Sheth & Tormen 2002) for the distribu-tion of halo formation times (Lacey & Cole 1993) and masses(Nusser & Sheth 1999; Sheth & Tormen 2004). Here, forma-tion is typically defined as that time when the most massiveprogenitor contains at least half the final mass.In the simplest and most used approximation, this ap-proach ignores most correlations between different spatialscales. In this approximation, the approach predicts thatthere should be no correlation between halo formation andthe large scale environment in which the halo sits (White1996). This is because, in the model, formation refers toa smaller mass than the final virial mass, and hence toa smaller spatial scale than that associated with the La-grangian radius of an object, whereas the larger scale envi-ronment, by definition, refers to scales which are larger thanthat of the halo.Lemson & Kauffmann (1999) presented evidence frommeasurements in numerical simulations of clustering thathalo formation times were indeed independent of environ-ment. They interpreted this as evidence that the excursionset neglect of correlations was justified. (Lemson & Kauff-mann also presented evidence that a number of other physi-cal properties of haloes were also independent of environ-ment, and this evidence has been used to justify an as-sumption which enormously simplifies semi-analytic mod-els of galaxy formation: that the properties of galaxies aredetermined by the haloes in which they form, and not bythe surrounding larger-scale environment.) Their conclusionis somewhat surprising for the following reason. It is quitewell established that the ratio of massive to low mass haloesis larger in dense regions, and that the excursion set modelis able to quantify this dependence quite well (see the refer-ences given earlier). It is also well established that, on aver-age, low mass haloes form at higher redshifts (see referencesgiven earlier). Together, these suggest that if one averagesover the entire range of halo masses in any given region,then the mean formation time in dense regions should beshifted to lower redshifts, simply because these regions con-tain more massive haloes which, on average, form later. InFigure 4 of their paper, Lemson & Kauffmann averaged overthe entire range of halo masses accessible to them in theirsimulations, and found no dependence of formation time onenvironement; at face value, this is inconsistent with thesimplest excursion set prediction!The main goal of this paper is to repeat the test for envi-ronmental effects on halo formation. Section 2 shows that asimple plot of formation time versus local density does notshow strong trends, suggesting that the excursion set ap-proximation is rather accurate. But then, Section 3 presents

Voids in a $\Lambda$CDM Universe

Abstract: We study the formation and evolution of voids in the dark matter distribution using various simulations of the popular $\Lambda$ Cold Dark Matter cosmogony. We identify voids by requiring them to be regions of space with a mean overdensity of -0.8 or less. Each of the simulations contains thousands of voids. The distribution of void sizes in the different simulations shows good agreement. Voids very clearly correspond to minima in the smoothed initial density field. We find a universal void mass profile of the form $\rho(

Three-Point Correlation Functions of SDSS Galaxies in Redshift Space: Morphology, Color, and Luminosity Dependence

Abstract: We present measurements of the redshift-space three-point correlation function of galaxies in the Sloan Digital Sky Survey (SDSS). For the first time, we analyze the dependence of this statistic on galaxy morphology, color, and luminosity. In order to control systematics due to selection effects, we used r-band, volume-limited samples of galaxies, constructed from magnitude-limited SDSS data (14.5

Formation times and masses of dark matter haloes

Abstract: The most commonly used definition of halo formation is the time when the most massive progenitor of a halo first contains at least half the final mass of its parent. Reasonably accurate formulae for the distribution of formation times of haloes of fixed mass have been available for some time. We use numerical simulations of hierarchical gravitational clustering to test the accuracy of formulae for the mass at formation. We also derive and test a formula for the joint distribution of formation masses and times. The structure of a halo is expected to be related to its accretion history. Our tests show that our formulae for formation masses and times are reasonably accurate, so we expect that they will aid future analytical studies of halo structure.

Robust Cosmological Constraints from Gravitational Lens Statistics

Abstract: We combine the Cosmic Lens All-Sky Survey (CLASS) with new Sloan Digital Sky Survey (SDSS) data on the local velocity dispersion distribution function of E/S0 galaxies, φ(σ), to derive lens statistics constraints on ΩΛ and Ωm. Previous studies of this kind relied on a combination of the E/S0 galaxy luminosity function and the Faber-Jackson relation to characterize the lens galaxy population. However, ignoring dispersion in the Faber-Jackson relation leads to a biased estimate of φ(σ) and therefore biased and overconfident constraints on the cosmological parameters. The measured velocity dispersion function from a large sample of E/S0 galaxies provides a more reliable method for probing cosmology with strong lens statistics. Our new constraints are in good agreement with recent results from the redshift-magnitude relation of Type Ia supernovae. Adopting the traditional assumption that the E/S0 velocity function is constant in comoving units, we find a maximum likelihood estimate of ΩΛ = 0.74–0.78 for a spatially flat universe (where the range reflects uncertainty in the number of E/S0 lenses in the CLASS sample), and a 95% confidence upper bound of ΩΛ < 0.86. If φ(σ) instead evolves in accord with extended Press-Schechter theory, then the maximum likelihood estimate for ΩΛ becomes 0.72–0.78, with the 95% confidence upper bound ΩΛ < 0.89. Even without assuming flatness, lensing provides independent confirmation of the evidence from Type Ia supernovae for a nonzero dark energy component in the universe. Subject headings: cosmological parameters — cosmology: observations — cosmology: theory — gravitational lensing

A hierarchy of voids

Abstract: We present a model for the distribution of void sizes and its evolution within the context of hierarchical scenarios of gravitational structure formation. For a proper description of the hierarchical buildup of the system of voids in the matter distribution, not only the voidin-void problem should be taken into account, but also that of the void-in-cloud issue. Within the context of the excursion set formulation of an evolving void hierarchy is one involving a two-barrier excursion problem, unlike the one-barrier problem for the dark halo evolution. This leads to voids having a peaked size distribution at any cosmic epoch, centered on a characteristic void size that evolves self-similarly in time, in distinct contrast to the distribution of virialized halo masses in not having a small-scale cut-off.

Three-point Correlation Functions of SDSS Galaxies in Redshift Space: Morphology, Color, and Luminosity Dependence

Abstract: We present measurements of the redshift--space three-point correlation function of galaxies in the Sloan Digital Sky Survey (SDSS). For the first time, we analyze the dependence of this statistic on galaxy morphology, color and luminosity. In order to control systematics due to selection effects, we used $r$--band, volume-limited samples of galaxies, constructed from the magnitude-limited SDSS data ($14.5

A Hierarchy of Voids

Abstract: We present a model for the distribution of void sizes and its evolution within the context of hierarchical scenarios of gravitational structure formation. For a proper description of the hierarchical buildup of the system of voids in the matter distribution, not only the "void-in-void" problem should be taken into account, but also that of the "void-in-cloud" issue. Within the context of the excursion set formulation of an evolving void hierarchy is one involving a "two-barrier" excursion problem, unlike the "one-barrier" problem for the dark halo evolution. This leads to voids having a peaked size distribution at any cosmic epoch, centered on a characteristic void size that evolves self-similarly in time, this in distinct contrast to the distribution of virialized halo masses which do not have a small-scale cut-off.

Void Hierarchy and Cosmic Structure

Abstract: Within the context of hierarchical scenarios of gravitational structure formation we describe how an evolving hierarchy of voids evolves on the basis of two processes, the void-in-void process and the void-in-cloud process. The related analytical formulation in terms of a two-barrier excursion problem leads to a self-similarly evolving peaked void size distribution.