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

Testing the reliability of weak lensing cluster detections

We study the reliability of dark-matter halo detections with three different linear filters applied to weak-lensing data. We use ray-tracing in the multiple lens-plane approximation through a large cosmological simulation to construct realizations of cosmic lensing by large-scale structures between redshifts zero and two. We apply the filters mentioned above to detect peaks in the weak-lensing signal and compare them with the true population of dark matter halos present in the simulation. We confirm the stability and performance of a filter optimized for suppressing the contamination by large-scale structure. It allows the reliable detection of dark-matter halos with masses above a few times 1e13 M_sun/h with a fraction of spurious detections below ~10%. For sources at redshift two, 50% of the halos more massive than ~7e13 M_sun/h are detected, and completeness is reached at ~2e14 M_sun/h.Comment: 14 pages, 13 figures, accepted on A&

Optimal filtering of optical and weak lensing data to search for galaxy clusters: application to the COSMOS field

Galaxy clusters are usually detected in blind optical surveys via suitable filtering methods. We present an optimal matched filter which maximizes their signal-to-noise ratio by taking advantage of the knowledge we have of their intrinsic physical properties and of the data noise properties. In this paper we restrict our application to galaxy magnitudes, positions and photometric redshifts if available, and we also apply the filter separately to weak lensing data. The method is suitable to be naturally extended to a multi-band approach which could include not only additional optical bands but also observables with different nature such as X-rays. For each detection, the filter provides its significance, an estimate for the richness and for the redshift even if photo-z are not given. The provided analytical error estimate is tested against numerical simulations. We finally apply our method to the COSMOS field and compare the results with previous cluster detections obtained with different methods. Our catalogue contains 27 galaxy clusters with minimal threshold at 3-sigma level including both optical and weak-lensing information.Comment: 15 pages, 15 figures, accepted for publication in MNRA

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

Fitting formulae of the reduced-shear power spectrum for weak lensing

Context. Weak gravitational lensing is a powerful probe of large-scale structure and cosmology. Most commonly, second-order correlations of observed galaxy ellipticities are expressed as a projection of the matter power spectrum, corresponding to the lowest-order approximation between the projected and 3d power spectrum. Aims. The dominant lensing-only contribution beyond the zero-order approximation is the reduced shear, which takes into account not only lensing-induced distortions but also isotropic magnification of galaxy images. This involves an integral over the matter bispectrum. We provide a fast and general way to calculate this correction term. Methods. Using a model for the matter bispectrum, we fit elementary functions to the reduced-shear contribution and its derivatives with respect to cosmological parameters. The dependence on cosmology is encompassed in a Taylor-expansion around a fiducial model. Results. Within a region in parameter space comprising the WMAP7 68% error ellipsoid, the total reduced-shear power spectrum (shear plus fitted reduced-shear correction) is accurate to 1% (2%) for l<10^4 (l<2x10^5). This corresponds to a factor of four reduction of the bias compared to the case where no correction is used. This precision is necessary to match the accuracy of current non-linear power spectrum predictions from numerical simulations.Comment: 7 pages, 3 figures. A&A in press. Revised version with minor change

Polymorphic Abstract Syntax via Grothendieck Construction

Abstract. Abstract syntax with variable binding is known to be characterised as an initial algebra in a presheaf category. This paper extends it to the case of poly-morphic typed abstract syntax with binding. We consider two variations, second-order and higher-order polymorphic syntax. The central idea is to apply Fiore’s initial algebra characterisation of typed abstract syntax with binding repeatedly, i.e. first to the type structure and secondly to the term structure of polymorphic system. In this process, we use the Grothendieck construction to combine differ-ently staged categories of polymorphic contexts.

A Subaru Weak Lensing Survey I: Cluster Candidates and Spectroscopic Verification

We present the results of an ongoing weak lensing survey conducted with the Subaru telescope whose initial goal is to locate and study the distribution of shear-selected structures or halos. Using a Suprime-cam imaging survey spanning 21.82 square degree, we present a catalog of 100 candidate halos located from lensing convergence maps. Our sample is reliably drawn from that subset of our survey area, (totaling 16.72 square degree) uncontaminated by bright stars and edge effects and limited at a convergence signal to noise ratio of 3.69. To validate the sample detailed spectroscopic measures have been made for 26 candidates using the Subaru multi-object spectrograph, FOCAS. All are confirmed as clusters of galaxies but two arise as the superposition of multiple clusters viewed along the line of sight. Including data available in the literature and an ongoing Keck spectroscopic campaign, a total of 41 halos now have reliable redshifts. For one of our survey fields, the XMM LSS (Pierre et al. 2004) field, we compare our lensing-selected halo catalog with its X-ray equivalent. Of 15 halos detected in the XMM-LSS field, 10 match with published X-ray selected clusters and a further 2 are newly-detected and spectroscopically confirmed in this work. Although three halos have not yet been confirmed, the high success rate within the XMM-LSS field (12/15) confirms that weak lensing provides a reliable method for constructing cluster catalogs, irrespective of the nature of the constituent galaxies or the intracluster medium.Comment: To appear in ApJ, High resolution preprint available at http://anela.mtk.nao.ac.jp/suprime33/papers/p1.ps.g

An Upper Limit on Omega_matter Using Lensed Arcs

We use current observations on the number statistics of gravitationally lensed optical arcs towards galaxy clusters to derive an upper limit on the cosmological mass density of the Universe. The gravitational lensing statistics due to foreground clusters combine properties of both cluster evolution, which is sensitive to the matter density, and volume change, which is sensitive to the cosmological constant. The uncertainties associated with the predicted number of lensing events, however, currently do not allow one to distinguish between flat and open cosmological models with and without a cosmological constant. Still, after accounting for known errors, and assuming that clusters in general have dark matter core radii of the order ~ 35 h^-1 kpc, we find that the cosmological mass density, Omega_m, is less than 0.56 at the 95% confidence. Such a dark matter core radius is consistent with cluster potentials determined recently by detailed numerical inversions of strong and weak lensing imaging data. If no core radius is present, the upper limit on Omega_m increases to 0.62 (95% confidence level). The estimated upper limit on Omega_m is consistent with various cosmological probes that suggest a low matter density for the Universe.Comment: 6 pages, 3 figures. Accepted version (ApJ in press

Arc Statistics in Clusters: Galaxy Contribution

The frequency with which background galaxies appear as long arcs as a result of gravitational lensing by foreground clusters of galaxies has recently been found to be a very sensitive probe of cosmological models by Bartelmann et al. (1998). They have found that such arcs would be expected far less frequently than observed (by an order of magnitude) in the currently favored model for the universe, with a large cosmological constant $\Omega_\Lambda \sim 0.7$. Here we analyze whether including the effect of cluster galaxies on the likelihood of clusters to generate long-arc images of background galaxies can change the statistics. Taking into account a variety of constraints on the properties of cluster galaxies, we find that there are not enough sufficiently massive galaxies in a cluster for them to significantly enhance the cross section of clusters to generate long arcs. We find that cluster galaxies typically enhance the cross section by only $\lesssim 15$.Comment: 19 pages, 1 figure, uses aasms4.sty, submitted to Ap