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&

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

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

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

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.Comment: 14 pages, 14 figures, accepted for publication in MNRA

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

Effects of tape covering and vine vigor on development of surface callus in girdle of grapevine

The effects of vine vigor (shoot growth) and covering the girdle surface with plastic tape on the development of a surface callus (SC) in the girdle of grapevine were studied by histological observation. The SC was formed in a tape-covering treatment but was not formed unless the girdle surface was covered with plastic tape (exposing treatment). Histological observation revealed that in the tape-covering treatment, callus cells developed mainly from the ray parenchyma cells on the girdle surface 2 days after girdling (DAG), leading to the formation of the SC, which grew and filled the girdle portion by 7 DAG. When 16 vines were divided into three categories based on scaffold branch length, vines with 7.5 m scaffold branches developed shorter shoots with smaller internode diameters than did vines with 4.5 and 6.0 m scaffold branches. In vines with 7.5 m scaffold branches, the SC covered a smaller area of the girdle surface than in vines with 4.5 and 6.0 m scaffold branches. The length and diameter of the shoot were significantly correlated (r2 = 0.75** and 0.70**, respectively) with the ratio of the girdle area covered by the SC to the whole girdle area (SC covering ratio). These results show that the SC originates mainly from the ray parenchyma cells and that SC development is strongly affected by vine vigor. Consequently, to ensure SC development, girdling should be done by tape covering in vines with shoot diameters larger than 8 mm.