The different regimes of gravitational lensing constitutes an interesting tool in order to map the mass distribution in galaxy clusters on different scales. In this proceedings article, I review some work I have performed on this topic. More precisely, I will focus on : (i) galaxy scale substructures, using weak galaxy-galaxy lensing in order to study how does the environment shape their properties; (ii) the mass profile of Abell~1689 as probed combining strong and weak lensing; (iii) the slope of the inner dark matter distribution in Abell~1703 as measured by strong lensing. The lensing results will be compared to the expectations from numerical simulations, when available.
We review theory and applications of weak gravitational lensing. After summarising Friedmann-Lemaitre cosmological models, we present the formalism of gravitational lensing and light propagation in arbitrary space-times. We discuss how weak-lensing effects can be measured. The formalism is then applied to reconstructions of galaxy-cluster mass distributions, gravitational lensing by large-scale matter distributions, QSO-galaxy correlations induced by weak lensing, lensing of galaxies by galaxies, and weak lensing of the cosmic microwave background. Contents: Introduction - Cosmological Backgro…
Gravitational lensing in a modified gravity (MOG) is derived and shown to describe lensing without postulating dark matter. The recent data for merging clusters identified with the interacting cluster 1E0657-56 is shown to be consistent with a weak lensing construction based on MOG without exotic dark matter.
A possible wave effect in the gravitational lensing phenomenon is discussed. We consider the interference of two coherent gravitational waves of slightly different frequencies from a compact binary, due to the gravitational lensing by a galaxy halo. This system shows the modulation of the wave amplitude. The lensing probability of such the phenomenon is of order 10^{-5} for a high-z source, but it may be advantageous to the observation due to the magnification of the amplitude.
These lectures give an introduction to Gravitational Lensing. We discuss lensing by point masses, lensing by galaxies, and lensing by clusters and larger-scale structures in the Universe. The relevant theory is developed and applications to astrophysical problems are discussed.
This review forms the Weak Lensing part of the Saas-Fee Advanced Course on Gravitational Lensing. It describes the basicsm applications and results of weak lensing. Contents: (1) Introduction (2) The principles of weak gravitational lensing (3) Observational issues and challenges (4) Clusters of galaxies: Introduction, and strong lensing (5) Mass reconstructions from weak lensing (6) Cosmic shear -- lensing by the LSS (7) Large-scale structure lensing: results (8) The mass of, and associated with galaxies (9) Additional issues in cosmic shear (10) Concluding remarks.
We study the general theorem about gravitational lensing which states the relationship between the numbers of images with different parities. Our formulation allows an extension to the nontransparent and singular model.
Gravitational lensing in clusters of galaxies is an efficient tool to probe the mass distribution of galaxies and clusters, high redshift objects thanks to the gravitational amplification, and the geometry of the universe. We review some important aspects of cluster lensing and related issues in observational cosmology.
Gravitational lensing has established itself as a valuable tool in many astrophysical fields in the roughly 20 years of its existence as an observational science. In this brief review, first the basics of lensing are introduced. Then it is shown that the two propagation effects, gravitational lensing and interstellar scintillation, have a number of properties in common. Finally, various lensing phenomena are discussed with emphasis on recent observations.
This work reviews the basic theoretical aspects, the main observational evidences and the recent applications of gravitational lensing in the Universe. The article is aimed particularly at providing the readers who don't work on gravitational lensing a relatively easy introduction to this active research field in today's astrophysics.
Gravitational Lensing is an efficient tool to probe: the mass distribution of collapsed systems: galaxies and clusters; high redshift objects thanks to the gravitational amplification; and the geometry of the Universe. I will review here some important aspects of lensing and related issues in observational cosmology.
I show how weak gravitational lensing can be used to image the 3-D mass distribution in the Universe. An inverse relation to the lensing equation, relating the lensing potential evaluated at each source to the full 3-D Newtonian potential, is derived. I consider the normal modes of the lensing problem and clarify the equations using a small-angle approximation. Finally I consider the prospects of using this method to estimate the 3-D matter distribution from a realistic galaxy lensing survey.
Underlying cosmologies with deceleration parameter, $q_0=-0.51^{+0.03}_{-0.24},$ may be interpreted as having $q_0=-0.55,$ on the basis of weak gravitational lensing effects.
We have conducted a new deep SCUBA survey, which has targetted 12 lensing galaxy clusters and one blank field. In this survey we have detected several sub-mJy sources after correcting for the gravitational lensing by the intervening clusters. We here present the preliminary results and point out two highlights.
The last decade has seen an enormous increase of activity in the field of gravitational lensing, mainly driven by improvements of observational capabilities. I will review the basics of gravitational lens theory, just enough to understand the rest of this contribution, and will then concentrate on several of the main applications in cosmology. Cluster lensing, and weak lensing, will constitute the main part of this review.
The wave effect in the gravitational lensing phenomenon by a straight cosmic string is investigated. The interference pattern is expressed in terms of a simple formula. We demonstrate that modulations of the interfered wave amplitude can be a unique signature of the wave effect. We briefly mention a possible chance of detecting the wave effect in future gravitational wave observatories.
Gravitational lenses are a unique new constraint on the structure of galaxies. We review the evidence that most lenses are early-type galaxies, the optical properties of the lens galaxies, the evidence against constant M/L models, recent work on the axis ratios of the mass distribution, and the role stellar dynamics plays in gravitational lensing.
The traditional perturbative method is applied to the case of gravitational lensing of planetary systems. A complete and detailed description of the structure of caustics for a system with an arbitrary number of planets can be obtained. I have also found precise analytical expressions for microlensing light curves perturbed by the presence of planets.
Cosmological simulation of gravitational weak lensing in open models is treated using the direct integration method, which is independent of the mult-lens-plane method. Statistical averages of optical quantuties (the convergencen shear and amplification) are derived for ray bundles passing through the clumpy universe, in which the initial state has the CDM spectrum with the power n = 1.
We introduce a new complex formalism to describe arclet fields in clusters of galaxies and derive the appropriate inversion techniques to find the related mass distribution of the lensing cluster. Applying the complex formalism to the statistics of lensed background sources shows that the mean of the axial ratios of locally lensed isotropically distributed elliptical sources is {\em not} influenced by the intrinsic ellipticity distribution, if the cluster is subcritical in that region.
Gravitational lensing by a spinning deflector in translational motion relative to the observer is discussed in the weak field, slow motion approximation. The effect of rotation, which generates an intrinsic gravito-magnetic field, separates from that due to radial motion. Corrections to the lens equation, deflection angle and time delay are derived.
We consider the prospects for detecting weak gravitational lensing by underdensities (voids) in the large-scale matter distribution. We derive the basic expressions for magnification and distortion by spherical voids. Clustering of the background sources and cosmic variance are the main factors which limit in principle the detection of lensing by voids. We conclude that only voids with radii larger than $\sim 100$ \hm have lensing signal to noise larger than unity.
We examine the gravitational lensing effect of a foreground galaxy cluster on the number count statistics of background X-ray sources. The lensing produces a deficit in the number of resolved sources in a ring close to the critical radius of the cluster. This deficit could be detected at the $\sim 3σ$ level with the AXAF-ACIS camera.
Many different families of mass models are used in modern applications of strong gravitational lensing. I review a wide range of popular models, with two points of emphasis: (1) a discussion of strategies for building models suited to a particular lensing problem; and (2) a summary of technical results for a canonical set of models. All of the models reviewed here are included in publicly-available lensing software called gravlens.
The gravitational lensing, as well as the velocity field and the cosmological light-cone warp, changes the observed correlation function of high-redshift objects. We present an analytical expression of 3D correlation function, simultaneously including those three effects. When two objects are separated over several hundreds Mpc along a line of sight, the observed correlation function is dominated by the effect of gravitational lensing rather than the intrinsic clustering. For a canonical lambda-CDM model, the lensing signals in the galaxy-galaxy and galaxy-QSO correlations are beyond noise lev…
We describe a new 1.3 m Warsaw telescope located at Las Campanas Observatory and new instruments of the second phase of the Optical Gravitational Lensing Experiment - OGLE-2. Results of first observations are also presented.
In this review I will describe progress that has been made in determining masses of galaxy clusters using `weak lensing' and how this technique my be applied in the future to determine the dark matter distribution both on supercluster scales and on the scale of galaxy haloes.
In this brief review I consider the advances made in weak gravitational lensing over the last 8 years, concentrating on the large scales - cosmic shear. I outline the theoretical developments, observational status, and the challenges which cosmic shear must overcome to realise its full potential. Finally I consider the prospects for probing Dark Energy and extra-dimensional gravity theories with future experiments.
We give a non-exhaustive review of the use of strong gravitational lensing in placing constraints on the quantity of dark and visible mass in galaxies. We discuss development of the methodology and summarise some recent results.
Gravitational lensing by spinning stars, approximated as homogeneous spheres, is discussed in the weak field limit. Dragging of inertial frames, induced by angular momentum of the deflector, breaks spherical symmetry. I examine how the gravito-magnetic field affects image positions, caustics and critical curves. Distortion in microlensing-induced light curves is also considered.
Gravitational lensing has become one of the most interesting tools to study the mass distribution in the Universe. Since gravitational light deflection is independent of the nature and state of the matter, it is ideally suited to investigate the distribution of all (and thus also of dark) matter in the Universe. Lensing results have now become available over a wide range of scales, from the search for MACHOs in the Galactic halo, to the mass distribution in galaxies and clusters of galaxies, and the statistical properties of the large-scale matter distribution in the Universe. Here, after intr…
We present a list of clusters that have had their dark matter content measured using weak gravitational lensing. The list consists of 139 clusters, with weak lensing measurements reported in 64 different publications. Details are provided about the selection criteria and some basic properties of the sample, such as the redshift distribution. An electronic, sortable version of this list with links to public database information on the clusters and publications is provided at http://folk.uio.no/hdahle/WLclusters.html
We investigate the possibility to use higher order moments of gravitational lensed images in the weak lensing analysis. For this purpose we employ spin-2 component of HOLICs(Higher Order Lensing Characteristics) developed by us. We test the weak lensing analysis with spin-2 HOLICs using actual, ground based Subaru observations of the massive galaxy cluster A1689(z=0.183). It turns out that spin-2 HOLICs of order up to 8 are sufficiently applicable for weak lensing analysis after correcting PSF anisotropy as well as isotropic PSF smearing.
The effect of currents of mass on bending of light rays is considered in the weak field regime. Following Fermat's principle and the standard theory of gravitational lensing, we derive the gravitomagnetic correction to time delay function and deflection angle caused by a geometrically-thin lens. The cases of both rotating and shifting deflectors are discussed.
By using the comoving distance, we derive an analytic expression for the optical depth of gravitational lensing, which depends on the redshift to the source and the cosmological model characterized by the cosmic mass density parameter $Ω_m$, the dark energy density parameter $Ω_x$ and its equation of state $ω_x = p_x/ρ_x$. It is shown that, the larger the dark energy density is and the more negative its pressure is, the higher the gravitational lensing probability is. This fact can provide an independent constraint for dark energy.
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.
This course presents some applications of gravitational lensing to the measurement of masses of galaxies (galaxy-galaxy lensing, Eintein rings, perturbations of giant arcs) and cluster of galaxies (strong and weak lensing). This complements the F. Bernardeau's course dedicated to some theoretical aspects and weak lensing by large scale structures. In the first section, I describe the most important lensing quantities and lensing properties useful for astrophycal applications. Then I briefly present some academic exemples. Section three is devoted to exemples of mass reconstruction and the stud…
We investigate the potential of weak gravitational lensing maps to differentiate between distinct cosmological models, considering cosmic variance due to a limited map extension and the presence of noise. We introduce a measure of the differentiation between two models under a chosen lensing statistics. That enables one to determine in which circumstances (map size and noise level), and for which lensing measures two models can be differentiated at a desired confidence level. As an application, we simulate convergence maps for three cosmological models (SCDM, OCDM, and $Λ$CDM), calculate sever…
Gravitational lensing, caused by matter perturbations along the line-of-sight to the last scattering surface, can modify the shape of the cosmic microwave background (CMB) anisotropy power spectrum. We discuss the detectability of lensing distortions to the temperature, polarisation and temperature-polarisation cross-correlation power spectra and we analyse how lensing might affect the estimation of cosmological parameters. For cold dark matter-like models with present-day matter power spectra normalised to match the abundances of rich clusters of galaxies, gravitational lensing causes detecta…
Recently, Y. Sobouti (2007) has provided a metric theory f(R) that can account for certain dynamical anomalies observed in spiral galaxies. Mendoza & Rosas-Guevara (2007) have shown that in this theory there is an extra-bending as compared to standard general relativity. In the present work we have developed in more specific detail this additional lensing effect and we have made evaluations of the alpha parameter used in the model adjusting the theory to observations in X-rays of 13 clusters of galaxies with gravitational lensing (Hoekstra (2007)).
Gravitational lensing is most often used as a tool to investigate the distribution of (dark) matter in the universe, but, if the mass distribution is known a priori, it becomes, at least in principle, a powerful probe of gravity itself. Lensing observations are a more powerful tool than dynamical measurements because they allow measurements of the gravitational field far away from visible matter. For example, modified Newtonian dynamics (MOND) has no relativistic extension, and so makes no firm lensing predictions, but galaxy-galaxy lensing data can be used to empirically the deflection law of…
We discuss the gravitational lensing of gravitational waves from merging neutron star binaries, in the context of advanced LIGO type gravitational wave detectors. We consider properties of the expected observational data with cut on the signal-to-noise ratio $ρ$, i.e., $ρ>ρ_0$. An advanced LIGO should see unlensed inspiral events with a redshift distribution with cut-off at a redshift $z_{\rm max} < 1$ for $h \leq 0.8$. Any inspiral events detected at $z>z_{\rm max}$ should be lensed. We compute the expected total number of events which are present due to gravitational lensing and their redshi…
We describe the simulation data produced by a pilot programme to compute mock weak gravitational lensing maps for a range of currently popular cosmological models by ray tracing through high-resolution N-body simulations. The programme required only a modest investment in computer time to produce maps accurate to arcminute scales covering hundreds of square degrees of sky for 4 cosmological models.
We describe a new approach for the determination of cosmological parameters using gravitational lensing systems with multiple arcs, exploiting the fact that a given cluster can produce multiple arcs from sources over a broad range in redshift. The coupling between the critical radius of a single arc and the projected mass density of the lensing cluster can be avoided by considering the relative positions of two or more arcs. Cosmological sensitivity appears through the angular size-redshift relation. We consider simulated data constructed using a more general form for the potential, realistic …
We investigate the effect of gravitational lensing on the farthest known supernova, SN1997ff. The SN was found at z~1.7 in the Hubble Deep Field North and is most likely of Type Ia. Due to our poor knowledge of the properties of the lensing foreground galaxies, we conclude that large magnification effects are possible for reasonable lens parameter values implying that this single SN does not put any strong constraints on the cosmological parameters, grey dust obscuration or luminosity evolution of SNIa until we can model the lensing with high accuracy.
Deflection of light by gravity was predicted by General Relativity and observationaly confirmed in 1919. In the following decades various aspects of the gravitational lens effect were explored theoretically, among them the possibility of multiple or ring-like images of background sources, the use of lensing as a gravitational telescope on very faint and distant objects, and the possibility to determine Hubble's constant with lensing. Only relatively recently gravitational lensing became an observational science after the discovery of the first doubly imaged quasar in 1979. Today lensing is a b…
The four observables associated with gravitational lensing of distant quasars by intervening galaxies: image splittings, relative amplifications, time delays, and optical depths, provide separate measures of the strength of the gravitational constant $G$ at cosmological distances. These allow one, in principle, to factor out unknown lensing parameters to directly to probe the variation of $G$ over cosmological time. We estimate constraints on $\dot{G}$ which may be derivable by this method both now and in the future. The limits one may obtain can compete or exceed other direct limits on $\dot{…
Inflationary cosmologies predict Gaussian primordial fluctuations, but subsequent gravitational lensing of the CMB disturbs its Gaussianity. Knowledge of the specific signature of lensing is necessary to distinguish a lensed Gaussian sky from an intrinsically non-Gaussian one. In this paper we investigate the pattern of non-Gaussian features in the CMB resulting from gravitational lensing, both analytically and numerically. We describe the lensed CMB temperature distribution using the formalism of generating functionals and obtain the complete picture of emerging non-Gaussian effects. To test …
We assess the feasibility of probing dark energy with strong gravitational lensing systems. The capability of the method, which depends on the accuracy with which the lensing systems are modeled, is quantitatively investigated using the Fisher-matrix formalism. We show that this method might place useful constraints on the density parameter and the redshift evolution of the dark energy by combining it with a constraint from supernova measurements. For this purpose, the lens potential needs to be precisely reconstructed. We determine the required quality of data. We also briefly discuss the opt…
Most problems in gravitational lensing require numerical solutions. The most frequent types of problems are (1) finding multiple images of a single source and classifying the images according to their properties like magnification or distortion; (2) propagating light rays through large cosmological simulations; and (3) reconstructing mass distributions from their tidal field. This lecture describes methods for solving such problems. Emphasis is put on using adaptive-grid methods for finding images, issues of spatial resolution and reliability of statistics for weak lensing by large-scale struc…
We review all the cosmic shear results obtained so far, with a critical discussion of the present strengths and weaknesses. We discuss the future prospects and the role cosmic shear could play in a precision cosmology era.
I review simultaneous constraints on the cosmological parameters lambda_0 and Omega_0 from gravitational lensing. The emphasis is on systematic extragalactic surveys for strong gravitational lenses, mainly the largest and best-defined such survey, JVAS/CLASS.
Gravitational weak lensing by large scale structures is view as a tool to probe the bias relation between the mass and the light distributions. It is explained how a particular statistic can be used to deproject the 2D mass distribution observed by weak lensing, in order to probe the bias at a given redshift and a given scale. Dependence with the cosmology is written, and observational issues are pointed out, like the importance of the redshift distribution of the galaxies. A signal to noise analysis shows that the scale dependence of the bias can be measured with a rather modest lensing surve…
We use a series of ray-tracing experiments to determine the magnification distribution of high-redshift sources by gravitational lensing. We determine empirically the relation between magnification and redshift, for various cosmological models. We then use this relation to estimate the effect of lensing on the determination of the cosmological parameters from observations of high-z supernovae. We found that, for supernovae at redshifts z<1.8, the effect of lensing is negligible compared to the intrinsic uncertainty in the measurements. Using mock data in the range 1.8<z<8, we show that the eff…
We have studied the mass distribution in the lensing galaxy 2237+0305 using constraints from both gravitational lensing and photometric and spectroscopic observations. We find that with sufficient dynamical information we can constrain the mass-to-light ratio of the luminous components and determine the dynamical contribution of the disk. In addition, future observations should allow us to place constraints on the shape of the dark matter halo and its inner slope.
Gravitational lensing is now widely and successfully used to study a range of astronomical phenomena, from individual objects, like galaxies and clusters, to the mass distribution on various scales, to the overall geometry of the Universe. Here we describe and assess the use of gravitational lensing as ``gold standards'' in addressing one of the fundamental problems in astronomy, the determination of the absolute distance scale to extragalactic objects. This is commonly parameterized by the Hubble constant, $H_0$, the current expansion rate of the Universe. The elegance of the underlying geome…
The nature of Galactic Center could be probed by lensing experiments capable of testing the spatial and velocity distributions of stars nearby and beyond it. Several hypotheses are possible (e.g. massive neutrino condensation, boson star) which avoid the shortcomings of the supermassive black hole model.
Weak gravitational lensing is a unique probe of the dark side of the universe: it provides a direct way to map the distribution of dark matter around galaxies, clusters of galaxies and on cosmological scales. Furthermore, the measurement of lensing induced distortions of the shapes of distant galaxies is a powerful probe of dark energy. In this review we describe how lensing measurements are made and interpreted. We discuss various systematic effects that can hamper progress and how they may be overcome. We review some of the recent results in weak lensing by galaxies, galaxy clusters and cosm…
We investigate the effect of gravitational lensing, produced by linear density perturbations, for anisotropies of the Cosmic Background Radiation (CBR) on scales of arcminutes. In calculations, a flat universe ($Ω=1$) and the Harrison-Zel'dovich spectrum ($n=1$) are assumed. The numerical results show that on scales of a few arcminutes, gravitational lensing produces only negligible anisotropies in the temperature of the CBR. Our conclusion disagrees with that of Cayón {\it et al.} who argue that the amplification of $ΔT/T$ on scales $\le 3'$ may even be larger than 100\%.
