arXiv subjects

Masahiro Takada

Publications and source records attributed to Masahiro Takada.

197 records · Page 11Linked to original sources

arXiv2003

Halo model prediction of the cosmic magnification statistics: the full non-linear contribution

The lensing magnification effect due to large-scale structure is statistically measurable by correlation of size fluctuations in distant galaxy images as well as by the QSO-galaxy cross-correlation. We use the halo model formulation of Takada & Jain (2003) to compute these magnification-induced correlations without employing the weak lensing approximation, mu=1+2kappa. Our predictions thus include the full contribution from non-linear magnification that is due to lensing halos. We compare the model prediction with ray-tracing simulations and find excellent agreement over a range of angular scales (0.'5<theta<30'). The non-linear magnification contribution enhances the amplitude of the magnification correlation relative to the weak lensing approximation, and the non-linear correction is more significant on smaller angular scales and for sources at higher redshifts. The enhancement amounts to 10-25% on arcminite scales for the QSO-galaxy cross-correlation, even after inclusion of a realistic model of galaxy clustering within the host halo. Therefore, it is necessary to account for the non-linear contribution in theoretical models in order to make an unbiased, cosmological interpretation of the precise measurements expected from forthcoming massive surveys.

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arXiv2003

Three-Point Correlations in Weak Lensing Surveys: Model Predictions and Applications

We use the halo model of clustering to compute two- and three-point correlation functions for weak lensing, and apply them in a new statistical technique to measure properties of massive halos. We present analytical results on the eight shear three-point correlation functions constructed using combination of the two shear components at each vertex of a triangle. We compare the amplitude and configuration dependence of the functions with ray-tracing simulations and find excellent agreement for different scales and models. These results are promising, since shear statistics are easier to measure than the convergence. In addition, the symmetry properties of the shear three-point functions provide a new and precise way of disentangling the lensing E-mode from the B-mode due to possible systematic errors. We develop an approach based on correlation functions to measure the properties of galaxy-group and cluster halos from lensing surveys. Shear correlations on small scales arise from the lensing matter within halos of mass M > 10^13 solar masses. Thus the measurement of two- and three-point correlations can be used to extract information on halo density profiles, primarily the inner slope and halo concentration. We demonstrate the feasibility of such an analysis for forthcoming surveys. We include covariances in the correlation functions due to sample variance and intrinsic ellipticity noise to show that 10% accuracy on profile parameters is achievable with surveys like the CFHT Legacy survey, and significantly better with future surveys. Our statistical approach is complementary to the standard approach of identifying individual objects in survey data and measuring their properties.

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arXiv2003

The Three-Point Correlation Function in Cosmology

With the advent of high-quality surveys in cosmology the full three-point correlation function will be a valuable statistic for describing structure formation models. It contains information on cosmological parameters and detailed halo properties that cannot be extracted from the two-point correlation function. We use the halo clustering model to analytically calculate the three-point correlation function (3PCF) for general cosmological fields. We present detailed results for the configuration dependence of the 3-dimensional mass and galaxy distributions and the 2-dimensional cosmic shear field. We work in real space, where higher order correlation functions on small scales are easier to measure and interpret, but halo model calculations get rapidly intractable. Hence we develop techniques for accurate evaluations of the 1, 2 and 3-halo contributions to the 3PCF. The 3PCF violates the hierarchical ansatz in both its scale and configuration dependence. We study the behavior of the coefficient Q in the hierarchical expansion from large, quasilinear scales down to about 20 kpc. We find that the nonlinear 3PCF is sensitive to the halo profile of massive halos, especially its inner slope. We model the distribution of galaxies in halos and show that the 3PCF of red galaxies has a weaker configuration and scale dependence than the mass, while for blue galaxies it is very sensitive to the parameters of the galaxy formation model. The 3PCF from weak lensing on the other hand shows different scalings due to projection effects and a sensitivity to cosmological parameters.

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arXiv2002

The Three-Point Correlation Function for Spin-2 Fields

The three-point correlation function (3PCF) of the spin-2 fields, the cosmic shear and cosmic microwave background polarization fields, is a statistical measure of non-Gaussian signals. At each vertex of a triangle, the shear field has two independent components. The resulting eight possible 3PCFs were recently investigated by Schneider & Lombardi (2002) and Zaldarriaga & Scoccimarro (2002). Using rotation and parity transformations they addressed the question: how many non-zero components for the shear 3PCF exist? We address this question using an analytical model and measurements from ray-tracing simulations. We show that all the eight 3PCFs are generally non-zero and have comparable amplitude. These eight 3PCFs can be used to improve the signal-to-noise from survey data and their configuration dependence can be used to separate the contribution from E and B-modes. We estimate the signal-to-noise for measuring the shear 3PCF from weak lensing surveys using simulated maps that include the noise due to intrinsic ellipticities. A deep lensing survey with area exceeding 10 square degrees would allow for the detection of the shear 3PCFs, but a survey area of order 100 square degrees is needed for accurate measurements.

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arXiv2002

Probing Intracluster Magnetic Fields with Cosmic Microwave Background Polarization

Intracluster magnetic fields with $ \sim μG $ strength induce Faraday rotation on the cosmic microwave background (CMB) polarization. Measurements of this effect can potentially probe the detailed structure of intracluster magnetic fields across clusters, since the CMB polarization is a continuously varying field on the sky, in contrast to the conventional method restricted by the limited number of radio sources behind or inside a cluster. We here construct a method for extracting information on magnetic fields from measurements of the effect, combined with possible observations of the Sunyaev-Zel'dovich effect and X-ray emission for the same cluster which are needed to reconstruct the electron density fields. Employing the high-resolution magneto-hydrodynamic simulations performed by Dolag, Bartelmann & Lesch (1999) as a realistic model of magnetized intracluster gas distribution, we demonstrate how our reconstruction technique can well reproduce the magnetic fields, i.e., the spherically average radial profiles of the field strength and the coherence length.

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arXiv2002

The Kurtosis of the Cosmic Shear Field

We study the fourth-order moment of the cosmic shear field using the dark matter halo approach to describe the nonlinear gravitational evolution of structure in the universe. Since the third-order moment of the shear field vanishes because of symmetry, non-Gaussian signatures in its one-point statistics emerge at the fourth-order level. We argue that the shear kurtosis parameter S_4 = / ^3 may be more directly applicable to realistic data than the well-studied higher-order statistics of the convergence field, since obtaining the convergence requires a non-local reconstruction from the measured shear field. We compare our halo model predictions for the variance, skewness and kurtosis of lensing fields with ray-tracing simulations of cold dark matter models and find good agreement. The shear kurtosis calculation is made tractable by developing approximations for fast and accurate evaluations of the 8-dimensional integrals needed to obtain the kurtosis. We show that on small scales it is dominated by correlations within halos more massive than 10^14 solar masses. The shear kurtosis is sensitive to the mass density parameter of the universe, Omega, and has relatively weak dependences on other parameters. The approximations we develop for the third- and fourth-order moments allow for accurate halo model predictions for the 3-dimensional mass distribution as well. We demonstrate their accuracy in the small scale regime, below 2 Mpc, where analytical approaches used in the literature so far cease to be accurate.

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arXiv2001

Faraday Rotation Effect of Intracluster Magnetic Field on Cosmic Microwave Background Polarization

The observed magnetic field of microgauss strength in clusters of galaxies should induce the Faraday rotation effect on the linearly polarized cosmic microwave background (CMB) radiation when the CMB radiation propagates through a cluster at low redshift. Employing the Press-Schechter prescription for the cluster abundance under the cold dark matter (CDM) scenario and a plausible isothermal $β$-model for the gas distribution, we compute angular power spectra of the CMB polarization fields including the Faraday rotation mixing effect under the simple assumption of uniform magnetic field configuration across a cluster. As a result, we find that a parity-odd B-type polarization pattern is statistically generated on the observed sky, even when the primary polarization only contains the parity-even E-mode component, such as in the case of pure scalar perturbations. The generated B-type polarization has a peak with amplitude of $\sim0.1 μ{\rm K}(B_0/0.1 μ{\rm G})(ν_0/10 {\rm GHz})^{-2}$ at angular scales of $l\approx 1000$ for the currently favored adiabatic $Λ$CDM model. This result also implies that, if the magnetic field has a $0.5 μ{\rm G}$ strength and we observe at lower frequencies such as $ν_0\simlt 5 {\rm GHz}$, the secondary signal due to the Faraday rotation effect could be comparable to the magnitude of the primary polarization. The frequency dependence of the Faraday rotation can be then used to discriminate the effect from primary and other secondary signals on the CMB polarizations. Our results therefore offer a new empirical opportunity to measure or constrain the intracluster magnetic field in the average sense.

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arXiv2001

On the Cross-Correlation between Dark Matter Distribution and Secondary CMB Anisotropies by Ionized Intergalactic Medium

We investigate a cross-correlation between the weak gravitational lensing field of the large-scale structure, $κ$, and the secondary temperature fluctuation field, $Δ$, of cosmic microwave background (CMB) induced by Thomson scattering of CMB photons off the ionized medium in the mildly nonlinear structure. The cross-correlation is expected to observationally unveil the biasing relation between the dark matter and ionized medium distributions in the large-scale structure. We develop a formalism for calculating the cross-correlation function and its angular power spectrum based on the small angle approximation. As a result, we find that leading contribution to the cross-correlation comes from the secondary CMB fluctuation field induced by the quadratic Doppler effects of the bulk velocity field $v$ of ionized medium. The magnitude of the cross-correlation can be estimated as $\kaco{κΔ}\sim 10^{-10}$ on small angular scales ($l\simgt 1000$) under the currently favored cold CDM model of the structure formation and the simplest scenario of homogeneous reionization after a given redshift of $z_{\rm ion}\simgt 5$. Interestingly, we find that the density-modulated quadratic Doppler effect of $O(δ_e v^2)$ produces the cross-correlation with the weak lensing field that has {\em linear} dependence on the electron density fluctuation field $δ_e$ or equivalently on the biasing relation between the dark matter and electron distributions. In other words, the angular power spectrum could be both positive or negative, depending on the positive biasing or antibiasing, respectively. Detection of the cross-correlation thus offers a new opportunity to observationally understand the reionization history of intergalactic medium connected to the dark matter clustering.

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arXiv2001

Lensing-induced Non-Gaussian Signatures in the Cosmic Microwave Background

We propose a new method for extracting the non-Gaussian signatures on the isotemperature statistics in the cosmic microwave background (CMB) sky, which is induced by the gravitational lensing due to the intervening large-scale structure of the universe. To develop the method, we focus on a specific statistical property of the intrinsic Gaussian CMB field; a field point in the map that has a larger absolute value of the temperature threshold tends to have a larger absolute value of the curvature parameter defined by a trace of second derivative matrix of the temperature field, while the ellipticity parameter similarly defined is uniformly distributed independently of the threshold because of the isotropic nature of the Gaussian field. The weak lensing then causes a stronger distortion effect on the isotemperature contours with higher threshold and especially induces a coherent distribution of the ellipticity parameter correlated with the threshold as a result of the coupling between the CMB curvature parameter and the gravitational tidal shear in the observed map. These characteristic patterns can be statistically picked up by considering three independent characteristic functions, which are obtained from the averages of quadratic combinations of the second derivative fields of CMB over isotemperature contours with each threshold. Consequently, we find that the lensing effect generates non-Gaussian signatures on those functions that have a distinct functional dependence of the threshold. We test the method using numerical simulations of CMB maps and show that the lensing signals can be measured definitely, provided that we use CMB data with sufficiently low noise and high angular resolution.

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arXiv2001

Implication of Omega_m through the Morphological Analysis of Weak Lensing Fields

We apply the morphological descriptions of two-dimensional contour map, the so-called Minkowski functionals (the area fraction, circumference, and Euler characteristics), to the convergence field $κ(\bmθ)$ of the large-scale structure reconstructed from the shear map produced by the ray-tracing simulations. The perturbation theory of structure formation has suggested that the non-Gaussian features on the Minkowski functionals with respect to the threshold in the weakly nonlinear regime are induced by the three skewness parameters of $κ$ that are sensitive to the density parameter of matter, $Ω_{\rm m}$. We show that, in the absence of noise due to the intrinsic ellipticities of source galaxies with which the perturbation theory results can be recovered, the accuracy of $Ω_{\rm m}$ determination is improved by $\sim 20%$ using the Minkowski functionals compared to the conventional method of using the direct measure of skewness.

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arXiv2000

Effects of weak lensing on the topology of CMB maps

We investigate the non-Gaussian signatures in Cosmic Microwave Background (CMB) maps induced by the intervening large-scale structure through weak lensing. In order to measure the deviation from the Gaussian behavior of the intrinsic temperature anisotropies, we use a family of three morphological descriptors, the so-called Minkowski functionals. We show analytically how these quantities depend on the temperature threshold, and compare the results to numerical experiments including the instrumental effects of Planck. Minkowski functionals can directly measure the statistical properties of the displacement field and hence provide useful constraints on large-scale structure formation in the past.

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arXiv2000

Number Count of Peaks in the CMB Map

We investigate the dependence of cosmological parameters on the number count of peaks (local maxima and minima) in the cosmic microwave background (CMB) sky. The peak statistics contains the whole information of acoustic oscillations in the angular power spectrum $C_l$ over $l$-space and thus it can place complementary constraints on the cosmological parameters to those obtained from measurements of $C_l$. Based on the instrumental specifications of Planck, we find that the number count of peaks can provide new constraints on the combination of the matter density $Ω_{\rm m}$ and the Hubble parameter $h$ approximately scaled as $Ω_{\rm m} h^{-4.9}$ for a flat $Λ$CDM model with $Ω_{m}=0.3$ and $h=0.7$. Therefore, we suggest that combining it with the constraints from $C_l$ scaled as $Ω_{m}h^{3.8}$ (or commonly $Ω_{\rm m}h^2$) can potentially determine $Ω_{\rm m}$ or equivalently solve the cosmic degeneracy by the CMB data alone.

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arXiv2000

Detectability of Gravitational Lensing Effect on the Two-point Correlation Function of Hotspots in the CMB maps

We present quantitative investigations of the weak lensing effect on the two-point correlation functions of local maxima (hotspots), $\xipk(θ)$, in the cosmic microwave background (CMB) maps. The lensing effect depends on the projected mass fluctuations between today and the redshift $z_{\rm rec}\approx1100$. If adopting the Gaussian assumption for the primordial temperature fluctuations field, the peak statistics can provide an additional information about the intrinsic distribution of hotspots that those pairs have some characteristic separation angles. The weak lensing then redistributes hotspots in the observed CMB maps from the intrinsic distribution and consequently imprints non-Gaussian signatures onto $\xipk(θ)$. Especially, since the intrinsic $\xipk(θ)$ has a pronounced depression feature around the angular scale of $θ\approx 70'$ for a flat universe, the weak lensing induces a large smoothing at the scale. We show that the lensing signature therefore has an advantage to effectively probe mass fluctuations with large wavelength modes around $λ\approx 50 h^{-1}{\rm Mpc}$. To reveal the detectability, we performed numerical experiments with specifications of {\em MAP} and {\em Planck Surveyor} including the instrumental effects of beam smoothing and detector noise. It is then found that our method can successfully provide constraints on amplitude of the mass fluctuations and cosmological parameters in a flat universe with and without cosmological constant, provided that we use maps with 65% sky coverage expected from Planck.

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arXiv2000

Gravitational Lensing Effect on the Two-point Correlation of Hotspots in the Cosmic Microwave Background

We investigate the weak gravitational lensing effect due to the large-scale structure of the universe on two-point correlations of local maxima ({\em hotspots}) in the 2D sky map of the cosmic microwave background (CMB) anisotropy. According to the Gaussian random statistics as most inflationary scenarios predict, the hotspots are discretely distributed with some {\em characteristic} angular separations on the last scattering surface owing to oscillations of the CMB angular power spectrum. The weak lensing then causes pairs of hotspots which are separated with the characteristic scale to be observed with various separations. We found that the lensing fairly smoothes the oscillatory features of the two-point correlation function of hotspots. This indicates that the hotspots correlations can be a new statistical tool for measuring shape and normalization of the power spectrum of matter fluctuations from the lensing signatures.

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arXiv1999

Post-Newtonian Lagrangian Perturbation Approach to the Large-Scale Structure Formation

We formulate the Lagrangian perturbation theory to solve the non-linear dynamics of self-gravitating fluid within the framework of the post-Newtonian approximation in general relativity, using the (3+1) formalism. Our formulation coincides with Newtonian Lagrangian perturbation theory developed by Buchert for the scale much smaller than the horizon scale, and with the gauge invariant linearized theory in the longitudinal gauge conditions for the linear regime. These are achieved by using the gauge invariant quantities at the initial time when the linearized theory is valid enough. The post-Newtonian corrections in the solution of the trajectory field of fluid elements are calculated in the explicit forms. Thus our formulation allows us to investigate the evolution of the large-scale fluctuations involving relativistic corrections from the early regime such as the decoupling time of matter and radiation until today. As a result, we are able to show that naive Newtonian cosmology to the structure formation will be a good approximation even for the perturbations with scales not only inside but also beyond the present horizon scale in the longitudinal coordinates. Although the post-Newtonian corrections are small, it is shown that they have a growing transverse mode which is not present in Newtonian theory as well as in the gauge invariant linearized theory. Such post-Newtonian order effects might produce characteristic appearances of the large-scale structure formation, for example, through the observation of anisotropies of the cosmic microwave background radiation (CMB). Furthermore since our approach has a straightforward Newtonian limit, it will be also convenient for numerical implementation based on the presently available Newtonian simulation. ......

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arXiv1999

How is the local-scale gravitational instability influenced by the surrounding large-scale structure formation?

We develop the formalism to investigate the relation between the evolution of the large-scale (quasi) linear structure and that of the small-scale nonlinear structure in Newtonian cosmology within the Lagrangian framework. In doing so, we first derive the standard Friedmann expansion law using the averaging procedure over the present horizon scale. Then the large-scale (quasi) linear flow is defined by averaging the full trajectory field over a large-scale domain, but much smaller than the horizon scale. The rest of the full trajectory field is supposed to describe small-scale nonlinear dynamics. We obtain the evolution equations for the large-scale and small-scale parts of the trajectory field. These are coupled to each other in most general situations. It is shown that if the shear deformation of fluid elements is ignored in the averaged large-scale dynamics, the small-scale dynamics is described by Newtonian dynamics in an effective Friedmann-Robertson-Walker (FRW) background with a local scale factor. The local scale factor is defined by the sum of the global scale factor and the expansion deformation of the averaged large-scale displacement field. This means that the evolution of small-scale fluctuations is influenced by the surrounding large-scale structure through the modification of FRW scale factor. The effect might play an important role in the structure formation scenario. Furthermore, it is argued that the so-called {\it optimized} or {\it truncated} Lagrangian perturbation theory is a good approximation in investigating the large-scale structure formation up to the quasi nonlinear regime, even when the small-scale fluctuations are in the non-linear regime.

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arXiv1998

On a Growing Transverse Mode as a Post-Newtonian Effect in the Large-Scale Structure Formation

We point out the existence of a new type of growing transverse mode in the gravitational instability. This appears as a post-Newtonian effect to Newtonian dynamics. We demonstrate this existence by formulating the Lagrangian perturbation theory in the framework of the cosmological post-Newtonian approximation in general relativity. Such post-Newtonian order effects might produce characteristic appearances of large-scale structure formation, for example, through the observation of anisotropy of the cosmic microwave background radiation (CMB).

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