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.Comment: 5 pages; accepted for publication in A&

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 \pi degree^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

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.Comment: 11 pages, 6 figures, submitted to Astronomy and Astrophysic

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 $\sigma_R(M_{\rm NL}; z)=1$, 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 $zz_{\rm crit}$

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

Subaru Suprime-Cam Weak Lensing Survey over 33 deg^2

Under the currently popular CDM model, mass plays the major role in evolution of large scale structure of the universe. In order to examine the paradigm based on observations, it ould be ideal to use purely mass selected object catalog. Weak lensing surveys enable a blind search of cluster scale objects, and thus could provide such catalogs. We are working on a weak lensing survey using Subaru Prime Focus Camera (Suprime-Cam). In this note, we introduce our survey strategy, and the status as well as the performance of Suprime-Cam as a weak lensing surveyor

A new measure of σ8\sigma_8 using the lensing dispersion in high-zz 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 $\sigma_8$ parameter. Therefore the value of $\sigma_8$ 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 $\sigma_8$ using a likelihood analysis method. It is found that the number and quality of SN Ia data needed for placing a useful constraint on $\sigma_8$ is attainable with Next Generation Space Telescope.Comment: 9 pages, 3 figures. Accepted for publication in The Astrophysical Journa

Universal Profiles of the Intracluster Medium from Suzaku X-Ray and Subaru Weak Lensing Obesrvations

We conduct a joint X-ray and weak-lensing study of four relaxed galaxy clusters (Hydra A, A478, A1689 and A1835) observed by both Suzaku and Subaru out to virial radii, with an aim to understand recently-discovered unexpected feature of the ICM in cluster outskirts. We show that the average hydrostatic-to-lensing total mass ratio for the four clusters decreases from \sim 70% to \sim 40% as the overdensity contrast decreases from 500 to the virial value.The average gas mass fraction from lensing total mass estimates increases with cluster radius and agrees with the cosmic mean baryon fraction within the virial radius, whereas the X-ray-based gas fraction considerably exceeds the cosmic values due to underestimation of the hydrostatic mass. We also develop a new advanced method for determining normalized cluster radial profiles for multiple X-ray observables by simultaneously taking into account both their radial dependence and multivariate scaling relations with weak-lensing masses. Although the four clusters span a range of halo mass, concentration, X-ray luminosity and redshift, we find that the gas entropy, pressure, temperature and density profiles are all remarkably self-similar when scaled with the lensing M_200 mass and r_200 radius.The entropy monotonically increases out to \sim 0.5r_200 following the accretion shock heating model K(r)\propto r^1.1, and flattens at \simgt 0.5r_200.The universality of the scaled entropy profiles indicates that the thermalization mechanism over the entire cluster region (>0.1r_200) is controlled by gravitation in a common to all clusters, although the heating efficiency in the outskirts needs to be modified from the standard law.The bivariate scaling functions of the gas density and temperature reveal that the flattening of the outskirts entropy profile is caused by the steepening of the temperature, rather than the flattening of the gas density.Comment: accepted for publication in PASJ : 13 pages 6 figures and 4 table

Lensing Effects on the Protogalaxy Candidate cB58 and their Implications for the Cosmological Constant

The amplification of the protogalaxy candidate cB58 due to gravitational lensing by the foreground cluster of galaxies MS1512.4+3647 is quantified based on recent ROSAT and ASCA X-ray observations. It is found that the amplification is at most 25 for any reasonable cosmological model with or without cosmological constant. It is also argued that the system may be used to place new constraints on the value of the cosmological constant. The gas mass fraction for this cluster is found to be about 0.2.Comment: LaTex, 9 pages, 9 figures, uses aas2pp4.sty, Accepted for publication in Ap