arXiv subjects

Takahiko Matsubara

Publications and source records attributed to Takahiko Matsubara.

At least 73 records · Page 4Linked to original sources

arXiv2005

Topology Analysis of the Sloan Digital Sky Survey: I. Scale and Luminosity Dependences

We measure the topology of volume-limited galaxy samples selected from a parent sample of 314,050 galaxies in the Sloan Digital Sky Survey(SDSS), which is now complete enough to describe the fully three-dimensional topology and its dependence on galaxy properties. We compare the observed genus statistic Gν_f) to predictions for a Gaussian random field and to the genus measured for mock surveys constructed from new large-volume simulations of the LambdaCDM cosmology. In this analysis we carefully examine the dependence of the observed genus statistic on the Gaussian smoothing scale R_G from 3.5 to 11 h^-1Mpc and on the luminosity of galaxies over the range -22.50<M_r<-18.5. The void multiplicity A_V is less than unity at all smoothing scales. Because A_V cannot become less than 1 through gravitational evolution, this result provides strong evidence for biased galaxy formation in low density environments. We also find clear evidence of luminosity bias of topology within the volume-limited sub-samples. The shift parameter Delta nu indicates that the genus of brighter galaxies shows a negative shift toward a ``meatball'' (i.e. cluster-dominated) topology, while faint galaxies show a positive shift toward a ``bubble'' (i.e. void-dominated) topology. The transition from negative to positive shift occurs approximately at the characteristic absolute magnitude M_{r*}=-20.4. Even in this analysis of the largest galaxy sample to date, we detect the influence of individual large-scale structures, as the shift parameter Delta nu and cluster multiplicity A_C reflect (at ~3 sigma) the presence of the Sloan Great Wall and a X-shaped structure which runs for several hundred Mpc across the survey volume.

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arXiv2005

The Distribution Function of the Phase Sum as a Signature of Phase Correlations Induced by Nonlinear Gravitational Clustering

We explore a signature of phase correlations in Fourier modes of dark matter density fields induced by nonlinear gravitational clustering. We compute the distribution function of the phase sum of the Fourier modes, theta_k1+theta_k2+theta_k3, for triangle wavevectors satisfying k1+k2+k3=0, and compare with the analytic prediction in perturbation theory recently derived by one of us. Using a series of cosmological N-body simulations, we extensively examine the time evolution and the dependence on the configuration of triangles and the sampling volume. Overall we find that the numerical results are remarkably consistent with the analytic formula from the perturbation theory. Interestingly the validity of the perturbation theory at a scale k is determined by P(k)/V_samp, the ratio of the power spectrum P(k) and the sampling volume V_samp, not by k^3P(k) as in the case of the conventional cosmological perturbation theory. Consequently this statistics of phase correlations is sensitive to the size of the sampling volume itself. This feature does not show up in more conventional cosmological statistics including the one-point density distribution function and the two-point correlation functions except as a sample-to-sample variation. Similarly if the sampling volume size V_samp is fixed, the stronger phase correlation emerges first at the wavevector where P(k) becomes largest, i.e., in linear regimes according to the standard cosmological perturbation theory, while the distribution of the phase sum stays fairly uniform in nonlinear regimes. The above feature can be naturally understood from the corresponding density structures in real space as we discuss in detail.

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arXiv2005

Large Scale Clustering of Sloan Digital Sky Survey Quasars: Impact of the Baryon Density and the Cosmological Constant

We report the first result of the clustering analysis of Sloan Digital Sky Survey (SDSS) quasars. We compute the two-point correlation function (2PCF) of SDSS quasars in redshift space at $8h^{-1}{\rm Mpc} < s < 500h^{-1}{\rm Mpc}$, with particular attention to its baryonic signature. Our sample consists of 19986 quasars extracted from the SDSS Data Release 4 (DR4). The redshift range of the sample is $0.72 \le z \le 2.24$ (the mean redshift is $\bar z = 1.46$) and the reddening-corrected $i$-band apparent magnitude range is $15.0 \le m_{i,{\rm rc}} \le 19.1$. Due to the relatively low number density of the quasar sample, the bump in the power spectrum due to the baryon density, $Ω_{\rm b}$, is not clearly visible. The effect of the baryon density is, however, to distort the overall shape of the 2PCF.The degree of distortion makes it an interesting alternate measure of the baryonic signature. Assuming a scale-independent linear bias and the spatially flat universe, i.e., $Ω_{\rm b} + Ω_{\rm d} + Ω_Λ=1$, where $Ω_{\rm d}$ and $Ω_Λ$ denote the density parameters of dark matter and the cosmological constant, we combine the observed quasar 2PCF and the predicted matter 2PCF to put constraints on $Ω_{\rm b}$ and $Ω_Λ$. Our result is fitted as $0.80- 2.8Ω_{\rm b} < Ω_Λ< 0.90 - 1.4Ω_{\rm b}$ at the 2$σ$ confidence level, which is consistent with results from other cosmological observations such as WMAP. (abridged)

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arXiv2004

An Analysis of the Large Scale N-body Simulation using the Minkowski Functionals

We analyze the Minkowski functionals with a large $N$-body simulation of a standard $Λ$CDM model, focusing on transition scales between linear and non-linear gravitational evolution. We numerically calculate the Minkowski functionals with sufficient accuracies to investigate the transition scales, 10--$50\himpc$. The results are compared with analytic formulae of linear and second-order perturbation theories. We first show that the skewness parameters of the density fluctuations, which are important in second-order analytic formulae of the Minkowski functionals, are in good agreement with the perturbation theory. Considering relative differences between the Minkowski functionals of the analytic formulae and that of the simulation data, we evaluate accuracy levels of the predictions of the perturbation theory. When the straightforward threshold $ν$ by density value is used in Minkowski functionals, the accuracy of the second-order perturbation theory is within 10% for smoothing length $R > 15\himpc$, and within a several % for $R > 20\himpc$. The accuracies of the linear theory are 2--5 times worse than that. When the rescaled threshold by volume fraction, $ν_{\rm f}$ is used, accuracies of both linear and second-order theories are within a few % on all scales of $10\himpc < R < 50\himpc$.

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arXiv2004

Correlation Function in Deep Redshift Space as a Cosmological Probe

Recent development of galaxy surveys enables us to investigate the deep universe of high redshift. We quantitatively present the physical information extractable from the observable correlation function in deep redshift space in a framework of the linear theory. The correlation function depends on the underlying power spectrum, velocity distortions, and the Alcock-Paczyński (AP) effect. The underlying power spectrum is sensitive to the constituents of matters in the universe, the velocity distortions are sensitive to the galaxy bias as well as the amount of total matter, and the Alcock-Paczyński effect is sensitive to the dark energy components. Measuring the dark energy by means of the baryonic feature in the correlation function is one of the most interesting applications. We show that the ``baryon ridge'' in the correlation function serves as a statistically circular object in the AP effect. In order to sufficiently constrain the dark energy components, the redshift range of the galaxy survey should be as broad as possible. The survey area on the sky should be smaller at deep redshifts than at shallow redshifts to keep the number density as dense as possible. We illustrate an optimal survey design that are useful in cosmology. Assuming future redshift surveys of $z\simlt 3$ which are within reach of the present-day technology, achievable error bounds on cosmological parameters are estimated by calculating the Fisher matrix. According to an illustrated design, the equation of state of dark energy can be constrained within $\pm 5%$ error assuming that the bias is unknown and marginalized over. Even when all the other cosmological parameters should be simultaneously determined, the error bound for the equation of state is up to $\pm 10%$.

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arXiv2004

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

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 ($14.5<r<17.5$), and further divided the samples into two morphological types (early and late) or two color populations (red and blue). The three-point correlation function of SDSS galaxies follow the hierarchical relation well and the reduced three-point amplitudes in redshift--space are almost scale-independent ($Q_z=0.5\sim1.0$). In addition, their dependence on the morphology, color and luminosity is not statistically significant. Given the robust morphological, color and luminosity dependences of the two-point correlation function, this implies that galaxy biasing is complex on weakly non-linear to non-linear scales. We show that simple deterministic linear relation with the underlying mass could not explain our measurements on these scales.

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arXiv2004

Galaxy Structures and External Perturbations in Gravitational Lenses

In modeling strong gravitational lens systems, one often adopts simple models, such as singular isothermal elliptical density plus lowest-order external perturbation. However, such simple models may mislead us if the real mass distribution is more complicated than that in the assumed models. In particular, assumptions on mass models are crucial in studying flux ratio anomalies that have been suggested as evidence for a cold dark-matter substructure. We reinvestigated four quadruple lens systems using power-law Fourier models, which have advantages of clear physical meanings and the applicability of a linear method, as well as a simple singular isothermal elliptical density model. We also investigated the effect of external perturbations, including a singular isothermal sphere, lowest-order expansion, and next-order expansion. We have found that the $\cos3θ$ terms of the primary galaxy and/or of external perturbation significantly reduce the χ^2 in PG 1115+080 and B1422+231. In particular, we could reproduce the flux ratios of B1422+231 with next-order external perturbation assuming 5% flux uncertainties, suggesting that external perturbation cannot be described by a simple singular isothermal sphere approximation. On the other hand, we could not fit B0712+472 and B2045+265 very well even with our models, although the χ^2 were reduced compared with the case of using simple models. Our results clearly demonstrate that both the primary lens galaxy and the external perturbation are often more complicated than we usually assume.

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arXiv2004

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 3D power spectrum of density fluctuations using Sloan Digital Sky Survey galaxy redshifts. We use Omega_m*h and f_b = Omega_b/Omega_m to describe the shape of the power spectrum, sigma8 for the (linearly extrapolated) normalization, and beta to parametrize linear theory redshift space distortions. On scales k < 0.16 h/Mpc, our maximum likelihood values are Omega_m*h = 0.264 +/-0.043, f_b = 0.286 +/- 0.065, sigma8 = 0.966 +/- 0.048, and beta = 0.45 +/- 0.12. When we take a prior on Omega_b from WMAP, we find Omega_m*h = 0.207 +/- 0.030, which is in excellent agreement with WMAP and 2dF. This indicates that we have reasonably measured the gross shape of the power spectrum but we have difficulty breaking the degeneracy between Omega_m*h and f_b because the baryon oscillations are not resolved in the current spectroscopic survey window function.

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arXiv2004

Eigenmode Analysis of Galaxy Distributions in Redshift Space

Eigenmode analysis is one of the most promising methods of analyzing large data sets in ongoing and near-future galaxy surveys. In such analyses, a fast evaluation of the correlation matrix in arbitrary cosmological models is crucial. The observational effects, including peculiar velocity distortions in redshift space, light-cone effects, selection effects, and effects of the complex shape of the survey geometry, should be taken into account in the analysis. In the framework of the linear theory of gravitational instability, we provide the methodology to quickly compute the correlation matrix. Our methods are not restricted to shallow redshift surveys, arbitrarily deep samples can be dealt with as well. Therefore, our methods are useful in constraining the geometry of the universe and the dark energy component, as well as the power spectrum of galaxies, since ongoing and near-future galaxy surveys probe the universe at intermediate to deep redshifts, z ~ 0.2--5. In addition to the detailed methods to compute the correlation matrix in 3-dimensional redshift surveys, methods to calculate the matrix in 2-dimensional projected samples are also provided. Prospects of applying our methods to likelihood estimation of the cosmological parameters are discussed.

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arXiv2003

Phase Correlations in Non-Gaussian Fields

We present the general relationship between phase correlations and the hierarchy of polyspectra in the Fourier space, and the new theoretical understanding of the phase information is provided. Phase correlations are related to the polyspectra only through the non-uniform distributions of the phase sum $θ_{\sbfm{k}_1} + ... + θ_{\sbfm{k}_N}$ with closed wave vectors, $\bfm{k}_1 + ... + \bfm{k}_N = 0$. The exact relationship is given by the infinite series, which one can truncate in a consistent manner. The method to calculate the series to arbitrary order is explained, and the explicit expression of the first-order approximation is given. A numerical demonstration proves that the distribution of the phase sum is a robust estimator and provides an alternative statistic to search for the non-Gaussianity.

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arXiv2002

Apparent Clustering of Intermediate-redshift Galaxies as a Probe of Dark Energy

We show the apparent redshift-space clustering of galaxies in redshift range of 0.2--0.4 provides surprisingly useful constraints on dark energy component in the universe, because of the right balance between the density of objects and the survey depth. We apply Fisher matrix analysis to the the Luminous Red Galaxies (LRGs) in the Sloan Digital Sky Survey (SDSS), as a concrete example. Possible degeneracies in the evolution of the equation of state (EOS) and the other cosmological parameters are clarified.

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arXiv2002

Statistics of smoothed cosmic fields in perturbation theory I: Formulation and useful formulas in second-order perturbation theory

We formulate a general method for perturbative evaluations of statistics of smoothed cosmic fields, and provide useful formulas in application of the perturbation theory to various statistics. This formalism is an extensive generalization of the method used by Matsubara (1994) who derived a weakly nonlinear formula of the genus statistic in a 3D density field. After describing the general method, we apply the formalism to a series of statistics, including genus statistics, level-crossing statistics, Minkowski functionals, and a density extrema statistic, regardless of the dimensions in which each statistic is defined. The relation between the Minkowski functionals and other geometrical statistics is clarified. These statistics can be applied to several cosmic fields, including 3D density field, 3D velocity field, 2D projected density field, and so forth. The results are detailed for second order theory of the formalism. The effect of the bias is discussed. The statistics of smoothed cosmic fields as functions of rescaled threshold by volume-fraction are discussed in the framework of second-order perturbation theory. In CDM-like models, their functional deviations from linear predictions plotted against the rescaled threshold are generally much smaller than that plotted against the direct threshold. There is still slight meat-ball shift against rescaled threshold, which is characterized by asymmetry in depths of troughs in the genus curve. A theory-motivated asymmetry factor in genus curve is proposed.

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arXiv2002

Three-Dimensional Genus Statistics of Galaxies in the SDSS Early Data Release

We present the first analysis of three-dimensional genus statistics for the SDSS EDR galaxy sample. Due to the complicated survey volume and the selection function, analytic predictions of the genus statistics for this sample are not feasible, therefore we construct extensive mock catalogs from N-body simulations in order to compare the observed data with model predictions. This comparison allows us to evaluate the effects of a variety of observational systematics on the estimated genus for the SDSS sample, including the shape of the survey volume, the redshift distortion effect, and the radial selection function due to the magnitude limit. The observed genus for the SDSS EDR galaxy sample is consistent with that predicted by simulations of a $Λ$-dominated spatially-flat cold dark matter model. Standard ($Ω_0=1$) cold dark matter model predictions do not match the observations. We discuss how future SDSS galaxy samples will yield improved estimates of the genus.

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arXiv2002

Spatial Clustering of Galaxies in Large Datasets

Datasets with tens of millions of galaxies present new challenges for the analysis of spatial clustering. We have built a framework that integrates a database of object catalogs, tools for creating masks of bad regions, and a fast (NlogN) correlation code. This system has enabled unprecedented efficiency in carrying out the analysis of galaxy clustering in the SDSS catalog. A similar approach is used to compute the three-dimensional spatial clustering of galaxies on very large scales. We describe our strategy to estimate the effect of photometric errors using a database. We discuss our efforts as an early example of data-intensive science. While it would have been possible to get these results without the framework we describe, it will be infeasible to perform these computations on the future huge datasets without using this framework.

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arXiv2002

Cosmological Parameters from Redshift-Space Correlations

We estimate how clustering in large-scale redshift surveys can constrain various cosmological parameters. Depth and sky coverage of modern redshift surveys are greater than ever, opening new possibilities for statistical analysis. We have constructed a novel maximum likelihood technique applicable to deep redshift surveys of wide sky coverage by taking into account the effects of both curvature and linear velocity distortions. The Fisher information matrix is evaluated numerically to show the bounds derived from a given redshift sample. We find that intermediate-redshift galaxies, such as the Luminous Red Galaxies (LRGs) in the Sloan Digital Sky Survey, can constrain cosmological parameters, including the cosmological constant, unexpectedly well. The importance of the dense as well as deep sampling in designing redshift surveys is emphasized.

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arXiv2001

KL Estimation of the Power Spectrum Parameters from the Angular Distribution of Galaxies in Early SDSS Data

We present measurements of parameters of the 3-dimensional power spectrum of galaxy clustering from 222 square degrees of early imaging data in the Sloan Digital Sky Survey. The projected galaxy distribution on the sky is expanded over a set of Karhunen-Loeve eigenfunctions, which optimize the signal-to-noise ratio in our analysis. A maximum likelihood analysis is used to estimate parameters that set the shape and amplitude of the 3-dimensional power spectrum. Our best estimates are Gamma=0.188 +/- 0.04 and sigma_8L = 0.915 +/- 0.06 (statistical errors only), for a flat Universe with a cosmological constant. We demonstrate that our measurements contain signal from scales at or beyond the peak of the 3D power spectrum. We discuss how the results scale with systematic uncertainties, like the radial selection function. We find that the central values satisfy the analytically estimated scaling relation. We have also explored the effects of evolutionary corrections, various truncations of the KL basis, seeing, sample size and limiting magnitude. We find that the impact of most of these uncertainties stay within the 2-sigma uncertainties of our fiducial result.

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arXiv2001

Constraining the Cosmological Constant from Large-Scale Redshift-Space Clustering

We show how the cosmological constant can be estimated from redshift surveys at different redshifts, using maximum-likelihood techniques. The apparent redshift-space clustering on large scales (\simgt 20 \himpc) are affected in the radial direction by infall, and curvature influences the apparent correlations in the transverse direction. The relative strengths of the two effects will strongly vary with redshift. Using a simple idealized survey geometry, we compute the smoothed correlation matrix of the redshift-space correlation function, and the Fisher matrix for $\omm$ and $\oml$. These represent the best possible measurement of these parameters given the geometry. We find that the likelihood contours are turning, according to the behavior of the angular-diameter distance relation. The clustering measures from redshift surveys at intermediate-to-high redshifts can provide a surprisingly tight constraint on $\oml$. We also estimate confidence contours for real survey geometries, using the SDSS LRG and QSO surveys as specific examples. We believe that this method will become a practical tool to constrain the nature of the dark energy.

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arXiv2001

The Topology of Weak Lensing Fields

The topology of weak lensing fields is studied using the 2-dimensional genus statistic. Simulated fields of the weak lensing convergence are used to focus on the effect of nonlinear gravitional evolution and to model the statistical errors expected in observational surveys. For large smoothing angles, the topology is in agreement with the predictions from linear theory. On smoothing angles smaller than 10', the genus curve shows the non-Gaussian signatures of gravitational clustering and differs for open and flat cold dark matter models. Forthcoming surveys with areas larger than 10 square degrees should have adequate signal-to-noise to measure the non-Gaussian shape and the $Ω$-dependence of the genus statistic.

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