arXiv subjects

Takashi Hamana

Publications and source records attributed to Takashi Hamana.

71 records · Page 4Linked to original sources

arXiv2002

Images for an Isothermal Ellipsoidal Gravitational Lens from a Single Real Algebraic Equation

We present explicit expressions for the lens equation for a cored isothermal ellipsoidal gravitational lens as a single real sixth-order algebraic equation in two approaches; 2-dimensional Cartesian coordinates and 3-dimensional polar ones. We find a condition for physical solutions which correspond to at most five images. For a singular isothermal ellipsoid, the sixth-order equation is reduced to fourth-order one for which analytic solutions are well-known. Furthermore, we derive analytic criteria for determining the number of images for the singular lens, which give us simple expressions for the caustics and critical curves. The present formulation offers a useful way for studying galaxy lenses frequently modeled as isothermal ellipsoids.

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arXiv2002

Non-Gaussian Tails of Cosmological Density Distribution Function from Dark Halo Approach

We present a simple model based on the dark halo approach which provides a useful way to understand key points determining the shape of the non-Gaussian tails of the dark matter one-point probability distribution function(PDF). In particular, using the scale-free models with power-law profile of dark halos, we derive a simple analytic expression for the one-point PDF. It is found that the shape of the PDF changes at the characteristic value of $δ_*$ which is defined by the smoothed density of a halo with the characteristic mass $M_*$ at the epoch. In cold dark matter models with top-hat smoothing filters, the characteristic smoothed density at present time typically takes the value $δ_*\gg 1$ for a small smoothing scale $\rth\sim 1$Mpc$/h$ and conversely $δ_*\ll 1$ for a large smoothing scale $\rth > 10$Mpc$/h$. On the range $δ/δ_*<1$, the shape of the PDF is almost solely determined by the outer slope of halos and scales as a power-law. The resultant non-Gaussian tails of PDF then resemble the log-normal PDFs in that range and show a good agreement with N-body simulations, which can be ascribed to the universality of the outer slope of the halo profile. In contrast, tails of one-point PDF in the range $δ/δ_*>1$ basically follow the steep exponential tails of the halo mass function, which exhibit a strong sensitivity to both the outer slope of the halo profile and the initial power spectrum. Based on these results, the discussion on the PDF of galaxy distribution and the application to the weak lensing statistics are also presented.

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arXiv2002

Measuring Omega_0 with higher-order Quasar-Galaxy Correlations induced by Weak Lensing

Via the magnification bias, gravitational lensing by large-scale structures causes angular cross-correlations between distant quasars and foreground galaxies on angular scales of arc minutes and above. We investigate the three-point cross-correlation between quasars and galaxy pairs measurable via the second moment of the galaxy counts around quasars and show that it reaches the level of a few per cent on angular scales near one arc minute. Combining two- and three-point correlations, a skewness parameter can be defined which is shown to be virtually independent on the shape and normalisation of the dark-matter power spectrum. If the galaxy bias is linear and deterministic, the skewness depends on the cosmic matter density parameter Omega_0 only; otherwise, it can be used to probe the linearity and stochasticity of the bias. We finally estimate the signal-to-noise ratio of a skewness determination and find that around twenty thousand distant quasars e.g. from the Sloan Digital Sky Survey should suffice for a direct measurement of Omega_0.

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arXiv2002

Reliability of the dark matter clustering in cosmological N-body simulation on scales below the mean separation length of particles

We critically examine the reliability of the dark matter clustering in high-resolution cosmological $N$-body simulations on scales below the mean separation length of particles. The particle discreteness effect imposes the two fundamental limitations on those scales; the lack of the initial fluctuation power and the finite mass resolution. We address this problem applying the dark halo approach and are able to discuss separately how those two limitations affect the dark matter clustering in $N$-body simulations at early epochs. We find that limitations of the dark matter clustering are primarily determined by the mass of particles. By a detailed comparison with three major cosmological simulations, we also find that in order to reproduce a proper amplitude of the dark matter clustering on small scales, halos with a characteristic nonlinear mass, $M_{\rm NL}(z)$ defined by $σ_R(M_{\rm NL}; z)=1$, must be resolved in the simulation. This leads to a critical redshift $z_{\rm crit}$ determined by $M_{\rm NL}(z_{\rm crit})=n_{\rm halo} m_{\rm part}$ where $n_{\rm halo}$ is the number of particles necessary to resolve the typical nonlinear mass halo ($\sim 10$). We conclude that, at least as far as the two-point correlation functions are concerned, the dark matter clustering in high-resolution $N$-body simulations on scales below the mean particle separation is reliable down to the gravitational force resolution length only for $z z_{\rm crit}$.

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arXiv2002

Subaru Spectroscopy of the Gravitational Lens HST 14176+5226: Implications for a Large Cosmological Constan

We present new optical spectroscopy of the lens elliptical galax in the ``Einstein Cross'' lens system HST 14176+5226, using the Faint Object Camera and Spectrograph (FOCAS) of the Subaru t Our spectroscopic observations are aimed at measuring the stella dispersion of the lens galaxy, located at high redshift of z_L= as an important component to lens models. We have measured this 230 +- 14 km s^{-1} (1 sigma) inside 0.35 effective radi based on the comparison between the observed galaxy spectrum and templates of three G-K giants by means of the Fourier cross-corr To extract the significance of this information on the geometry universe which also affects the lensing of the background image, to fit three different lens models to the available data of the Provided that the lens galaxy has the structural and dynamical p (i.e., its radial density profile, core radius, and velocity ani similar to those of local elliptical galaxies, we calculate the function for the simultaneous reproduction of both the observed and newly measured velocity dispersion of the lens. Although the interval depends rather sensitively on the adopted lens models o parameters, our experiments suggest the larger likelihood for a cosmological constant, Omega_Lambda: formal 1 sigma lower Omega_Lambda in the flat universe ranges 0.73 to 0.97, where lower limit is basically unavailable. This method for determinin model is thus dependent on lens models but is insensitive to oth ambiguities, such as the dust absorption or the evolutionary eff galaxies. Exploring spectroscopic observations of more lens gala redshift may minimize the model uncertainties and thus place a m constraint on Omega_Lambda.

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arXiv2001

Source-lens clustering effects on the skewness of the lensing convergence

The correlation between source galaxies and lensing potentials causes a systematic effect on measurements of cosmic shear statistics, known as the source-lens clustering (SLC) effect. The SLC effect on the skewness of lensing convergence, $S_3$, is examined using a nonlinear semi-analytic approach and is checked against numerical simulations. The semi-analytic calculations have been performed in a wide variety of generic models for the redshift distribution of source galaxies and power-law models for the bias parameter between the galaxy and dark matter distributions. The semi-analytic predictions are tested successfully against numerical simulations. We find the relative amplitude of the SLC effect on $S_3$ to be of the order of five to forty per cent. It depends significantly on the redshift distribution of sources and on the way the bias parameter evolves. We discuss possible measurement strategies to minimize the SLC effects.

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arXiv2001

Clustering of dark matter halos on the light-cone: scale-, time- and mass-dependence of the halo biasing in the Hubble volume simulations

We develop a phenomenological model to predict the clustering of dark matter halos on the light-cone by combining several existing theoretical models. Assuming that the velocity field of halos on large scales is approximated by linear theory, we propose an empirical prescription of a scale-, mass-, and time-dependence of halo biasing. We test our model against the Hubble Volume $N$-body simulation and examine its validity and limitations. We find a good agreement in two-point correlation functions of dark matter halos between the phenomenological model predictions and measurements from the simulation for $R>5h^{-1}$Mpc both in the real and redshift spaces. Although calibrated on the mass scale of groups and clusters and for redshifts up to $z\sim2$, the model is quite general and can be applied to a wider range of astrophysical objects, such as galaxies and quasars, if the relation between dark halos and visible objects is specified.

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arXiv2001

Lensing magnification effects on the cosmic shear statistics

Gravitational lensing causes a correlation between a population of foreground large-scale structures and the observed number density of the background distant galaxies as a consequence of the flux magnification and the lensing area distortion. This correlation has not been taken into account in calculations of the theoretical predictions of the cosmic shear statistics but may cause a systematic error in a cosmic shear measurement. We examine its impact on the cosmic shear statistics using the semi-analytic approach. We find that the lensing magnification has no practical influence on the cosmic shear variance. Exploring possible shapes of redshift distribution of source galaxies, we find that the relative amplitude of the effect on the convergence skewness is 3% at most

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arXiv2001

Numerical study of statistical properties of the lensing excursion angles

We present ray tracing simulations combined with sets of large N-body simulations. Experiments were performed to explore, for the first time, statistical properties of fluctuations in angular separations of nearby light ray pairs (the so-called lensing excursion angle) induced by weak lensing by large-scale structures. We found that the probability distribution function (PDF) of the lensing excursion angles is not simply Gaussian but has an exponential tail. It is, however, found that the tail, or more generally non-Gaussian nature in the PDF has no significant impact on the weak lensing of the CMB. Moreover, we found that the variance in the lensing excursion angles predicted by the power spectrum approach is in good agreement with our numerical results. These results demonstrate a validity of using the power spectrum approach to compute lensing effects on the CMB.

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arXiv2000

Two-point correlation functions on the light cone: testing theoretical predictions against N-body simulations

We examine the light-cone effect on the two-point correlation functions using numerical simulations for the first time. Specifically, we generate several sets of dark matter particle distributions on the light-cone up to z=0.4 and z=2 over the field-of-view of πdegree^2 from cosmological N-body simulations. Then we apply the selection function to the dark matter distribution according to the galaxy and QSO luminosity functions. Finally we compute the two-point correlation functions on the light-cone both in real and in redshift spaces using the pair-count estimator and compare with the theoretical predictions. We find that the previous theoretical modeling for nonlinear gravitational evolution, linear and nonlinear redshift-distortion, and the light-cone effect including the selection function is in good agreement with our numerical results, and thus is an accurate and reliable description of the clustering in the universe on the light-cone.

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arXiv2000

Numerical study of the cosmic shear

We study cosmic shear statistics using the ray-tracing simulation combined with a set of large $N$-body simulations. In this contribution, we first describe our method. Then we show some selected results especially focusing on effects of the deflection of light rays and the lens-lens coupling which are neglected in making the theoretical predictions of the cosmic shear statistics.

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arXiv1999

A new measure of $σ_8$ using the lensing dispersion in high-$z$ type Ia SNe

The gravitational lensing magnification or demagnification due to large-scale structures induces a scatter in peak magnitudes of high redshift type Ia supernovae (SNe Ia). The amplitude of the lensing dispersion strongly depends on that of density fluctuations characterized by the $σ_8$ parameter. Therefore the value of $σ_8$ is constrained by measuring the dispersion in the peak magnitudes. We examine how well SN Ia data will provide a constraint on the value of $σ_8$ using a likelihood analysis method. It is found that the number and quality of SN Ia data needed for placing a useful constraint on $σ_8$ is attainable with Next Generation Space Telescope.

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arXiv1999

Distances in Inhomogeneous Cosmological Models

Distances play important roles in cosmological observations, especially in gravitational lens systems, but there is a problem in determining distances because they are defined in terms of light propagation, which is influenced gravitationally by the inhomogeneities in the universe. In this paper we first give the basic optical relations and the definitions of different distances in inhomogeneous universes. Next we show how the observational relations depend quantitatively on the distances. Finally, we give results for the frequency distribution of different distances and the shear effect on distances obtained using various methods of numerical simulation.

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arXiv1999

Statistics of Weak Gravitational Lensing in Cold Dark Matter Models; Magnification Bias on Quasar Luminosity Functions

We compute statistical properties of weak gravitational lensing by large-scale structure in three Cold Dark Matter models. We use a P$^3$M $N$-body code to simulate the formation and evolution of large-scale structure in the universe. We perform $1.1\times10^7$ ray-tracing experiments for each model using the multiple lens-plane algorithm. From the results of these experiments, we calculate the probability distribution functions (PDF) of the convergences, shears, and magnifications, and their root-mean-square (rms) values. We find that the rms values of the convergence and shear agree with the predictions of a nonlinear analytical model. We also find that the PDFs of the magnifications $μ$ have a peak at values slightly smaller than $μ=1$, and are strongly skewed toward large magnifications. In particular, for the high-density model, a power-law tail appears in the magnification distribution at large magnifications for sources at redshifts $z_s>2$. The rms values of the magnifications essentially agree with the nonlinear analytical predictions for sources at low redshift, but exceed these predictions for high redshift sources, once the power-law tail appears. We study the effect of magnification bias on the luminosity functions of high-redshift quasars, using the calculated PDFs of the magnifications. We show that the magnification bias is moderate in the absence of the power-law tail in the magnification distribution, but depends strongly on the value of the density parameter. In presence of the power-law tail, the bias becomes considerable, especially at the bright end of the luminosity functions.

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arXiv1998

Weyl focusing effects on the image magnification due to randomly distributed isothermal objects

Weyl focusing effects on the image magnifications are investigated by using the multiple gravitational lens theory. We focus on the gravitational lensing effects due to the small scale virialized objects, such as galaxies and clusters of galaxies. We consider a simple model of an inhomogeneous universe. The matter distribution in the universe is modeled by randomly distributed isothermal objects. We found that, for the majority of the random lines of sight, the Weyl focusing has no significant effect and the image magnification of a point like source within redshift of 5 is dominated by the Ricci focusing.

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arXiv1998

Performance of the optimized Post-Zel'dovich approximation for CDM models in arbitrary FLRW cosmologies

We investigate the performance of the optimized Post-Zel'dovich approximation in three cold dark matter cosmologies. We consider two flat models with $Ω_0=1$ (SCDM) and with $Ω_0=0.3$ ($Λ$CDM) and an open model with $Ω_0=0.3$ (OCDM). We find that the optimization scheme proposed by Weiß, Gottlöber & Buchert (1996), in which the performance of the Lagrangian perturbation theory was optimized only for the Einstein-de Sitter cosmology, shows the excellent performances not only for SCDM model but also for both OCDM and $Λ$CDM models. This universality of the excellent performance of the optimized Post-Zel'dovich approximation is explained by the fact that a relation between the Post-Zel'dovich order's growth factor $E(a)$ and Zel'dovich order's one $D(a)$, $E(a)/D^2(a)$, is insensitive to the background cosmologies.

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arXiv1998

Comments on the gravitational lensing magnification

We rederive a relation between gravitational lensing magnification relative to the standard Friedmann distance and one relative to the Dyer-Roeder distance by investigating the null geodesic deviation equation. We show that the relation comes from a natural consequence of the definition of the lensing magnification matrices and is not based on the averaging of the magnifications, which has conventionally been used to derive it. We therefore conclude that the relation is true for each individual ray bundle.

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