Lam Hui

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.

Equation of state of the photoionized intergalactic medium

We develop an efficient method to study the effects of reionization history on the temperature-density relation of the intergalactic medium in the low density limit (overdensity less than 5). It is applied to the study of photo-reionization models in which the amplitude, spectrum and onset epoch of the ionizing flux, as well as the cosmology, are systematically varied. We find that the mean temperature-density relation at z=2-4 is well approximated by a power-law equation of state for uniform reionization models. We derive analytical expressions for its evolution and exhibit its asymptotic behavior: it is found that for sufficiently early reionization, imprints of reionization history prior to z=10 on the temperature-density relation are washed out. In this limit the temperature at cosmic mean density is proportional to (\Omega_b h/\sqrt\Omega_0)^{1/1.7}. While the amplitude of the radiation flux at the ionizing frequency of HI is found to have a negligible effect on the temperature-density relation as long as the universe reionizes before z=5, the spectrum can change the overall temperature by about 20%, through variations in the abundances of helium species. However the slope of the mean equation of state is found to lie within a narrow range for all reionization models we study, where reionization takes place before z=5. We discuss the implications of these findings for the observational properties of the Lyman-alpha forest. In particular, uncertainties in the temperature of the intergalactic medium, due to the uncertain reionization history of our universe, introduces a 30% scaling in the amplitude of the column density distribution while the the slope of the distribution is only affected by about 5%. Finally, we discuss how a fluctuating ionizing field affects the above results. We argue that under

How Many Galaxies Fit in a Halo? Constraints on Galaxy Formation Efficiency from Spatial Clustering

We study galaxy clustering in the framework of halo models, where gravitational clustering is described in terms of dark matter halos. At small scales, dark matter clustering statistics are dominated by halo density profiles, whereas at large scales, correlations are the result of combining nonlinear perturbation theory with halo biasing. Galaxies are assumed to follow the dark matter profiles of the halo they inhabit, and galaxy formation efficiency is characterized by the number of galaxies that populate a halo of given mass. This approach leads to generic predictions: the galaxy power spectrum shows a power-law behavior even though the dark matter does not, and the galaxy higher order correlations show smaller amplitudes at small scales than their dark matter counterparts. Both are in qualitatively agreement with measurements in galaxy catalogs. We find that requiring the model to fit both the second- and third-order moments of the Automatic Plate Measuring Facility (APM) galaxies provides a strong constraint on galaxy formation models. The data at large scales require that galaxy formation be relatively efficient at small masses, m ≈ 1010 M☉ h-1, whereas data at smaller scales require that the number of galaxies in a halo scale approximately as the mass to the 0.8th power in the high-mass limit. These constraints are independent of those derived from the luminosity function or Tully-Fisher relation. We also predict the power spectrum, bispectrum, and higher order moments of the mass density field in this framework. Although halo models agree well with measurements of the mass power spectrum and the higher order Sp parameters in N-body simulations, the model assumption that halos are spherical leads to disagreement in the configuration dependence of the bispectrum at small scales. We stress the importance of finite-volume effects in higher order statistics and show how they can be estimated in this approach.

Clustering of luminous red galaxies – IV. Baryon acoustic peak in the line-of-sight direction and a direct measurement of H(z)

We study the clustering of luminous red galaxies in the latest spectroscopic Sloan Digital Sky Survey data releases (DR), DR6 and DR7, which sample over 1 Gpc 3 h ―3 to z = 0.47. The two-point correlation function ξ(σ, π) is estimated as a function of perpendicular σ and line-of-sight π (radial) directions. We find significant detection of a peak at r ≃ 110 Mpc h ―1 , which shows as a circular ring in the σ―π plane. There is also significant evidence of a peak along the radial direction whose shape is consistent with its origination from the recombination-epoch baryon acoustic oscillations (BAO). A ξ (σ, π) model with no radial BAO peak is disfavoured at 3.2σ, whereas a model with no magnification bias is disfavoured at 2σ. The radial data enable, for the first time, a direct measurement of the Hubble parameter H(z) as a function of redshift. This is independent of earlier BAO measurements which used the spherically averaged (monopole) correlation to constrain an integral of H(z). Using the BAO peak position as a standard ruler in the radial direction, we find H(z = 0.24) = 79.69 ± 2.32 (±1.29) km s ―1 Mpc ―1 for z = 0.15-0.30 and H(z = 0.43) = 86.45 ± 3.27 (±1.69) km s ―1 Mac ―1 for z = 0.40-0.47. The first error is a model-independent statistical estimation and the second accounts for systematics both in the measurements and in the model. For the full sample, z = 0.15-0.47, we find H(z = 0.34) = 83.80 ± 2.96 (±1.59) km s ―1 Mpc ―1 .

Probing the Universe with the Lyα forest — I. Hydrodynamics of the low-density intergalactic medium

We introduce an efficient and accurate alternative to full hydrodynamic simulations, Hydro-PM (HPM), for the study of the low column density Lyman-alpha forest (NHI <∼ 10 14 cm−2). It consists of a Particle-Mesh (PM) solver, modified to compute, in addition to the gravitational potential, an effective potential due to the gas pressure. Such an effective potential can be computed from the density field because of a tight correlation between density and pressure in the low density limit (δ <∼ 10), which can be calculated for any photo-reionization history by a method outlined in Hui & Gnedin (1997). Such a correlation exists, in part, because of minimal shock-heating in the low density limit. We compare carefully the density and velocity fields as well as absorption spectra, computed using HPM versus hydrodynamic simulations, and find good agreement. We show that HPM is capable of reproducing measurable quantities, such as the column density distribution, computed from full hydrodynamic simulations, to a precision comparable to that of observations. We discuss how, by virtue of its speed and accuracy, HPM can enable us to use the Lyman-alpha forest as a cosmological probe. We also discuss in detail the smoothing of the gas (or baryon) fluctuation relative to that of the dark matter on small scales due to finite gas pressure: (1) It is shown the conventional wisdom that the linear gas fluctuation is smoothed on the Jeans scale is incorrect for general reionization (or reheating) history; the correct linear filtering scale is in general smaller than the Jeans scale after reheating, but larger prior to it. (2) It is demonstrated further that in the mildly nonlinear regime, a PM solver, combined with suitable pre-filtering of the initial conditions, can be used to model the low density IGM. But such an approximation is shown to be less accurate than HPM, unless a non-uniform pre-filtering scheme is implemented.

Analysis of systematic effects and statistical uncertainties in angular clustering of galaxies from early sloan digital sky survey data

The angular distribution of galaxies encodes a wealth of information about large-scale structure. Ultimately, the Sloan Digital Sky Survey (SDSS) will record the angular positions of order of 108 galaxies in five bands, adding significantly to the cosmological constraints. This is the first in a series of papers analyzing a rectangular stripe of 25 × 90° from early SDSS data. We present the angular correlation function for galaxies in four separate magnitude bins on angular scales ranging from 0003 to 15°. Much of the focus of this paper is on potential systematic effects. We show that the final galaxy catalog—with the mask accounting for regions of poor seeing, reddening, bright stars, etc.—is free from external and internal systematic effects for galaxies brighter than r* = 22. Our estimator of the angular correlation function includes the effects of the integral constraint and the mask. The full covariance matrix of errors in these estimates is derived using mock catalogs with further estimates using a number of other methods.

Analysis of Systematic Effects and Statistical Uncertainties in Angular Clustering of Galaxies from Early SDSS Data

The angular distribution of galaxies encodes a wealth of information about large-scale structure. Ultimately, the Sloan Digital Sky Survey (SDSS) will record the angular positions of order of 108 galaxies in five bands, adding significantly to the cosmological constraints. This is the first in a series of papers analyzing a rectangular stripe of 25 × 90° from early SDSS data. We present the angular correlation function for galaxies in four separate magnitude bins on angular scales ranging from 0003 to 15°. Much of the focus of this paper is on potential systematic effects. We show that the final galaxy catalog—with the mask accounting for regions of poor seeing, reddening, bright stars, etc.—is free from external and internal systematic effects for galaxies brighter than r* = 22. Our estimator of the angular correlation function includes the effects of the integral constraint and the mask. The full covariance matrix of errors in these estimates is derived using mock catalogs with further estimates using a number of other methods.

Constraining the Lifetime of Quasars from Their Spatial Clustering

The lifetime of the luminous phase of quasars is constrained by current observations to be 106 tQ 108 yr but is otherwise unknown. We model the quasar luminosity function in detail in the optical and X-ray bands using the Press-Schechter formalism and show that the expected clustering of quasars depends strongly on their assumed lifetime tQ. We quantify this dependence and find that existing measurements of the correlation length of quasars are consistent with the range 106 tQ 108 yr. We then show that future measurements of the power spectrum of quasars out to z ~ 3, from the Anglo-Australian Telescope Two-Degree Field or Sloan Digital Sky Survey, can significantly improve this constraint and in principle allow a precise determination of tQ. We estimate the systematic errors introduced by uncertainties in the modeling of the quasar-halo relationship, as well as by the possible existence of obscured quasars.

Power Spectrum Correlations Induced by Nonlinear Clustering

Gravitational clustering is an intrinsically nonlinear process that generates significant non-Gaussian signatures in the density field. We consider how these affect power spectrum determinations from galaxy and weak-lensing surveys. Non-Gaussian effects not only increase the individual error bars compared to the Gaussian case but, most importantly, lead to nontrivial cross-correlations between different band powers, correlating small-scale band powers both among themselves and with those at large scales. We calculate the power-spectrum covariance matrix in nonlinear perturbation theory (weakly nonlinear regime), in the hierarchical model (strongly nonlinear regime), and from numerical simulations in real and redshift space. In particular, we show that the hierarchical Ansatz cannot be strictly valid for the configurations of the trispectrum involved in the calculation of the power-spectrum covariance matrix. We discuss the impact of these results on parameter estimation from power-spectrum measurements and their dependence on the size of the survey and the choice of band powers. We show that the non-Gaussian terms in the covariance matrix become dominant for scales smaller than the nonlinear scale knl ~ 0.2 h-1 Mpc-1, depending somewhat on power normalization. Furthermore, we find that cross-correlations mostly deteriorate the determination of the amplitude of a rescaled power spectrum, whereas its shape is less affected. In weak lensing surveys the projection tends to reduce the importance of non-Gaussian effects. Even so, for background galaxies at redshift z ~ 1, the non-Gaussian contribution rises significantly around l ~ 1000 and could become comparable to the Gaussian terms depending upon the power spectrum normalization and cosmology. The projection has another interesting effect: the ratio between non-Gaussian and Gaussian contributions saturates and can even decrease at small enough angular scales if the power spectrum of the three-dimensional field falls faster than k-2.

Constraints from the Lyα Forest Power Spectrum

We use published measurements of the transmission power spectrum of the Ly? forest to constrain several parameters that describe cosmology and thermal properties of the intergalactic medium (IGM). A six-parameter grid is constructed using particle-mesh dark matter simulations together with scaling relations to make predictions for the gas properties. We fit for all parameters simultaneously and identify several degeneracies. We find that the temperature of the IGM can be well determined from the falloff of the power spectrum at small scales. We find a temperature of around 2 ? 104 K, dependent on the slope of the gas equation of state. We see no evidence for evolution in the IGM temperature. We place constraints on the amplitude of the dark matter fluctuations. However, contrary to previous results, the slope of the dark matter power spectrum is poorly constrained. This is because of uncertainty in the effective Jeans smoothing scale, which depends on the temperature as well as the thermal history of the gas.