## Eelco van Kampen

'Testing cluster mass reconstruction methods using a sample of galaxy cluster models'

For a statistical sample of numerical galaxy cluster models we have obtained surface mass density maps, from which we have calculated the cluster lens properties. We use these to test several mass reconstruction methods that apply either weak or strong lensing of background galaxies by clusters. As we have a fair sample of cluster lenses, we are able to do test these methods for many likely lens configurations and investigate how the estimated mass depends on lens characteristics like substructure, asphericity, and others. We focus on cluster mass reconstructions from recent HST observations.

## Matthias Bartelmann

Cluster Potential Reconstruction from Gravitational Lensing

Gravitational lensing provides a unique way to determine the mass distribution of galaxy clusters. In contrast to mass determinations based on galaxy kinematics or X-ray emission, gravitational lensing does not rely on any assumptions about the physical state and the nature of the matter in clusters. I first discuss what kind of information can be obtained from weak and strong lensing by galaxy clusters. I shall then proceed to compare mass estimates from gravitational lensing and X-ray emission. Finally, I shall discuss cosmological implications of the statistics of lensing phenomena, and applications of cluster lensing to a variety of cosmological questions.

## Gordon Squires

The Dynamical State of Clusters

Weak gravitational lensing provides a model independent method for determining the mass distribution on a variety of scales. Coupled with mass estimates from other methods (applications of the virial theorem and/or analyzes of the cluster X-ray emission), this also yields insight into the dynamical state of individual clusters. I present new results from wide field imaging of several intermediate redshift clusters, determining the 2D mass distribution and total mass from the weak gravitational lensing of background galaxies. I present comparisons with X-ray and/or virial analyses and discuss the implications of the agreements/disagreements among the methods. I also discuss the results of a previous analysis of A2218 and highlight the discrepancy between the lensing/X-ray mass estimates. The S-Z effect has been observed in this cluster and, coupled with X-ray data, the value of $H_0$ inferred ranges from $H_O = 24$ to 55~km~s$^{-1}$~Mpc$^{-1}$. I discuss the utility of the weak lensing mass map for quantifying the systematic uncertainties in the assumptions underlying the $H_0$ determinations.

## Andy Taylor

Clustering Confusion in Lens Magnification

Recent observations suggest that the lens magnification effect by a foreground cluster has been measured. These analyses use Poissonian statistics to estimate the significance of the estimate, neglecting the contributions from galaxy clustering. Here I will discuss the clustering contribution to the noise in the linear and nonlinear regimes and find it to be non-negligible. I also investigate the effects of induced clustering on the background galaxy distribution due to the presence of a massive foreground cluster and find that this is a bias in lens mass estimates. I derive the absolute cluster masses estimated from the magnification effect.

## Ioav Waga

Lensing by Voids

We investigate the gravitational lens effect due to underdensities in the matter distribution. We consider an ideal version of a void, constituted of a uniform spherical underdensity, surrounded by a uniform overdensity, embedded in an otherwise homogeneous medium. We show that inside the void the source image will be demagnified and that its shape is in general compressed in the radial direction (from the void center) less than it is in the orthogonal direction. We pay special attention to statistical demagnification of a large sample of galaxies whose line of sight intersects a void. We consider the magnification-bias effect of faint red galaxies (flat count-slope) and show that under reasonable assumptions a void lensing signal can be observed.

## Bhuvnesh Jain

Weak Lensing by Large Scale Structure

Weak lensing by large scale structure induces correlated ellipticities in the images of distant galaxies. We use the fully nonlinear evolution of the power spectrum of matter to compute the predicted ellipticity correlation for different values of the cosmological parameters $\Omega$ and $\Lambda$. The amplitude is sensitive primarily to the normalization $\sigma_8$ of the power spectrum and to $\Omega$. We present results for different statistics and for the range of angular scales from $1'-1^o$ in order to explore the best observational strategy for constraining the cosmological paramters. Nonlinear effects in the evolution of the power spectrum significantly enhance the signal on scales $< 10'$.

## Frank Tipler

Why Gravitational Lenses Are Absolutely Essential For Measuring the True Values of the Cosmological Parameters

The redshift $z_{h}$ of $\partial J^-(\gamma)\cap \partial J^+(\gamma)$ in matter-filled Friedmann universes is shown to be $z_{h} = 1 + 2/\sqrt\Omega_0$, where $\Omega_0$ is the density parameter and $\gamma$ is the past-endless worldline of Earth's location up to the present. Earth's particle horizon is $\partial J^+(\gamma)$ and $\partial J^-(\gamma)$ is its event horizon. The redshift $z_{h}$ marks the boundary between the spacetime region that could have been affected by events at Earth's location ($J^+(\gamma)\,)$ and events which can be observed on Earth today ($J^-(\gamma)\,)$. Thus only by going to redshifts larger than $z_{h}=3$ (in the flat universe case) can we be assured that we are measuring features which are truly universal, unaffected by events in the Earth's location. Measurements of the cosmological parameters by gravitational lensing is the only known method of achieving this.

## Priya Natarajan

Galaxy-galaxy lensing in clusters from HST clusters

There is ample evidence from lensing for the clumping of dark matter on different scales within clusters, although the spatial extent of dark halos of cluster galaxies are yet to be constrained. The issue is of crucial importance as it addresses the key question of whether the mass to light ratio of galaxies is a function of the environment, and if it is indeed significantly different in the high density regions like cluster cores as opposed to the field. Weak shear maps of the outer regions of clusters have been successfully used to map the distribution of mass at large radii. However the typical smoothing lengths generally employed preclude the systematic study of the effects of galactic-scale substructure on the measured weak lensing signal. We present two new methods to study the effect of bright cluster galaxies on the cluster weak shear field - aperture averaging of the local shear and a maximum likelihood method to obtain limits on parameters that characterize galaxy halos. The composite lensing effect of a cluster is modeled by the superposition of mass clumps with different scales: a large-scale clump to describe the cluster and smaller scale ones for individual cluster galaxies. Working in the local frame of each perturber, the shear induced by the larger scale component can be efficiently subtracted, yielding the averaged shear field induced by the smaller-scale mass component. Cluster galaxy halos are modeled using simple scaling relations and the background high redshift population is modeled in consonance with observations from redshift surveys and lensing constraints. We demonstrate using simulations that these observed local weak-shear effects on galaxy scales within the cluster can be used to statistically constrain reliably the mean M/L of cluster members, and fiducial parameters like the halo size, velocity dispersion and hence mass of cluster galaxies. The results of the members, and fiducial parameters like the halo size and the velocity dispersion. The results of the application of these techniques to the mosaic-ed HST data of the cluster AC114, and the stacked HST-archive clusters are presented.

## Liliya L.R. Williams

Undistorted Lensed Images in Galaxy Clusters

To date, the study of the gravitational lensing effects of clusters of galaxies has focused upon the study of the grossly distorted, luminous arc-like features, formed in massive, centrally condensed clusters. Here we study the occurrence of magnified {\it undistorted} images of background galaxies. The frequency of such images depends on the mass profile of the lensing clusters. If clusters have cores, $r_c\sim 40-90$ kpc, then the frequency of such images would be comparable to that of luminous arcs. If, on the other hand, cluster mass profiles are better represented by Navarro, Frenk, \& White (1995) type profile, then highly magnified undistorted images should be rare. This study was motivated by the recent discovery of cB58, a luminous, $z=2.72$ proto-galaxy, that appears to be much less distorted than the usual' thin arcs, dispite its proximity to the center of a foreground galaxy cluster.

## Steve Zepf, Moustakas, and Davis

Keck Spectroscopy of Candidate Gravitational Lenses in the HDF: Constraints on Lambda Models.

We have obtained spectra with the Keck telescope of three sets of objects in the HDF which have been identified as possible multiply lensed objects in this field. We show that one of these has at least two distinct components of z = 3.209 and z=3.220 which are separated by 0.5" spatially. In a second set of objects, we find a probable emission feature in the proposed "counterimage", and no corresponding line in the proposed "arc" feature. Only in the third case do our spectra not argue against a lensing model. We conclude that the frequency of strong gravitational lensing of galaxies in the HDF is very low. This result appears to be difficult to reconcile with the introduction of a significant cosmological constant to account for the large number of faint blue galaxies via a large volume element at high redshift.

## Andrew de Laix

GRAVITATIONAL LENSING SIGNATURE OF LONG COSMIC STRINGS

The gravitational lensing by long, wiggly cosmic strings is shown to produce a large number of lensed images of background galaxies that lie along the string and provide a highly distinctive signature of cosmic strings.

## Steven T. Myers

The CLASS Survey: 7723 sources, 5 lenses, and counting ...

The purpose of the Cosmic Lens All-Sky Survey, or CLASS, is to image more than 10000 flat--spectrum radio sources selected from the 87GB/GB6 catalogs with the aim of discovering new multiply-imaged gravitational lens systems. Observations with the VLA in A-configuration at 8.4~GHz are used to find new lenses that are well-suited for measurements of cosmological parameters such as the distance scale of the Universe. In the first phases of CLASS, observed in February--May 1994 (CLASS-1) and July--September 1995 (CLASS-2), 7723 radio sources were mapped. In CLASS-1, for which the follow-up of candidates is nearing completion, we have so far confirmed 4 new lensed systems. From CLASS-2, even though the follow-up has only just started, we already have one confirmed system and one which is highly probable. The quadruple lens 1608+656 is our most promising system thus far, and a number of follow-up observations have been carried out. The current status of the CLASS survey, and the properties of the lens systems discovered therein, will be discussed.

## Geraint Lewis

Optical Einstein Rings and the Dynamics of Galaxies

The recent discovery of an optically selected Einstein ring has provided a new and useful probe of the physical properties in high redshift galaxies. In this poster we present bi-dimen- sional spectra, taken with the ARGUS instrument on the 3.6m CFHT. From these we can draw conclusions on the dynamical nature of the high redshift, star-forming source galaxy. This poster also examines future prospects of this technique in light of forth- coming spectroscopic campaigns to search for a population of optical Einstein ring systems.

Is the rapid radio variability seen in PKS 0537-441 due to microlensing ? (Lewis and Williams)

BL Lacertae (BL Lac) Objects are a population of active galaxies that possess featureless spectra, rapid variability from the X-ray to the radio, and strongly varying polarization. One explanation of these extreme properties invokes the action of gravitational microlensing due to stars in an intervening galaxy, amplifying the continuum of a background active galaxy to swamp the line emission. The BL Lac object PKS 0537-441 exhibits rapid variability at radio frequencies and it has been suggested that microlensing by sub-solar mass stars is a possible source of these fluctuations. In this poster we argue, when considering the physical scale of the optical through radio emission region in BL Lac object systems, that microlensing can not have a dominant influence on the properties of this system, and therefore suggest that the observed variability is due to some other process.

## Brenda Frye

Measuring cluster magnification

We are conducting a program of faint galaxy spectroscopy with LRIS to measure the redshifts of galaxies behind massive clusters. The flux brightening of these galaxies by gravitational lensing allows one to sample objects at higher redshift compared with the far field to a fixed magnitude. By combining the magnification measurements with the lensed distortions we can measure the mass of clusters unambiguously.

## Kim Griest

MACHO Collaboration results and interpretations

Interpretation of the MACHO collaboration year (1+2) LMC events will be discussed. Limits on the Milky Way dark matter halo and estimates of mass of Machos will be given with discussion of uncertainties arising from small number statistics and halo modeling. More information can be obtained from rare events which show evidence of microlensing fine-structure such as parallax, or finite source size effects. Such fine-structure effects also allow the possibility of searching for extra-solar planets.

## Robert Schmidt

The effect of the bar in the gravitational lens system 2237+0305

In the gravitational lens 2237+0305 the four lensed images of a single background quasar are seen in a cross formation superimposed on the barred spiral lensing galaxy, so that theoretical lens models and the observed structure and dynamics of the galaxy can be compared. Nevertheless, the position angle of the inclination axis of this galaxy on the sky that is predicted by the available lensing models is still in contradiction with the observed position angle. We present a new galaxy model with an additional bar component that explains the lensing in this system with the effect of the bar.

The Study of Light Propagation in Inhomogeneous Universes \\ Using The Gravitational Lensing Method

We divide the universe, along the line of sight, into boxes of comoving size 128 Mpc. We then locate the galaxies in high density regions at present, and use the results of the N-body simulations to trace the trajectories of these galaxies back to $z=5$. The mass distribution for each box is projected onto a plane which is located approximately halfway between the walls perpendicular to our line of sight. The morphological type of each galaxy is determined by using the observed morphological type - density relation. For instance, ellipticals tend to be located in regions of higher density. We used the Schechter luminosity function to determine the mass, core radius, and luminosity of each galaxy at present. Next, we apply the properties of multi-plane gravitational lensing to follow a circular bundle of light rays back in time up to $z=5$ through the series of lens planes. We calculate the deflection angle, shear, and magnification caused by the galaxy distribution on each plane. The process is repeated many times with the initial beam located randomly. The results enabled us to build statistics of the shear and magnification with respect to redshifts. In addition to the circular beams, we propagate square shape beams with initial side size of a few hundred kpc consisted of $31^{2}$ cells each with a beam point in the middle. As the beam reaches the source plane, we check if there is any beam point that moves out of its original cell and enters other cell. If such a case occurs, we zoom that particular area and refine the mesh in it until an optimum is reached. If more than one beam point reside in that smallest cell, we decide that they originate from a single source. We then return to the image plane and construct the image of that source. Since our galaxy distribution also provides the luminosity of each galaxy, we can infer the amplification bias from this experiment.

## Avi Loeb

Gravitational Lensing of Quasars by Spiral Galaxies

Gravitational lensing by a spiral galaxy occurs when the line-of-sight to a background quasar passes within a few kpc from the center of the galactic disk. Since galactic disks are rich in neutral hydrogen, the quasar spectrum will likely be marked by a damped Lyman-alpha absorption trough at the lens redshift. We demonstrate that the efficiency of searches for gravitational lensing with sub-arcsecond splitting can be enhanced by 1-2 orders of magnitude by focusing on a subset of all bright quasars which show low-redshift (z<1) strong Lyman-alpha absorption (N>10^{21} cm^{-2}}) (Bartelmann & Loeb 1996). Moreover, the magnification bias due to lensing changes the statistics of damped Lyman-alpha absorbers by bringing into view quasars that are otherwise below the detection threshold. The double-image signature of lensing could, in principle, be identified spectroscopically and without the need for high-resolution imaging; the absorption spectrum of the lens might show a generic double-step profile due to the superposition of the two absorption troughs of the different images. The different images pass the absorbing disk at different impact parameters and therefore have different spectral widths. Lensing of optical sources by spiral galaxies is expected to be counteracted by dust obscuration. We calculate the impact of dust on lensing by disk galaxies using measurements of the dust-to-gas ratio in damped Lyman-alpha absorbers (Perna, Loeb, & Bartelmann 1996). We also examine the effect of microlensing by stars in disk lenses (Perna & Loeb 1996). The spiral galaxy lens B0218+357 constitutes a generic example for the above discussion. The high HI column density implied by 21 cm absorption in this lens (Carrili, Rupen, & Yanni 1993) will be calibrated spectroscopically by forthcoming HST observations (Falco, Loeb, & Bartelmann 1996).

## Sangeeta Malhotra

Evidence for Dusty Gravitational Lenses

Foreground galaxies that amplify the light from background quasars may also dim that light if the galaxies contain enough dust. We look for one signature of dust, namely reddening, by looking at optical-infrared colors of gravitationally lensed images of quasars. We find that the images identified in radio and infrared searches have redder optical-IR colors than optically selected ones. This could be due to the bias against selecting reddened (hence extincted) lenses in the optical surveys, or due to the differences in the intrinsic colors of optical and radio quasars. Comparing the radio-selected lensed quasars to unlensed radio-selected quasars shows that the lensed ones again have redder colors. We therefore conclude that at least part of the color difference between the two lens samples is due to dust. Extinction by dust in lenses can hide the large number of lensed systems predicted for a flat universe with a large value of cosmological constant $\Lambda$.

## Sergei Kopeikin

Propagation of Light in Gravitational Field of Multipolar Gravitational Lens

## Alexander F. Zakharov

Caustic singularities of the cusp type in the theory of gravitational lenses

The common solution of the gravitational lens equation near cusps was presented. We used the gravitational lens equation by Schneider \& Weiss. Using the symmetrical polynomials oh the roots of polynomial of third degree we obtained the weak generalization of Schneider \& Weiss statement on the magnification near different solutions of the gravitational lens equation. The analytical expressions for magnifications of different images near cusp were presented. It is well known when we consider mapping s of two dimensional surface into plane that there are only two types of stable singularities: folds and cusps (pleats). There are also similar singularities of caustics in gravitational lens optics. Schneider \& Weiss 1986; Schneider \& Weiss 1992 studied gravitational lens mapping near cusps. Some properties of the mappings are very important for solving of different problems of gravitational lensing, for example, in consideration of the mutual coherence of images near the cusps (Mandzhos 19 93). The analitical expressions are very useful for these purposes. Therefore, we will obtain the analytical expressions for solution of gravitational lens equation and magnifications of different images near the cusp.

The distortion of microlensing by mass distribution of our Galaxy

We consider the distortion of standard gravitational microlens model by gravitational field of our Galaxy. We use the Chang - Refsdal lens for our analysis. The detailed discussions of the clear model is presented. We show that the influence of gravitational field of our Galaxy during microlensing may yield large variations of the stellar light curve although a probability of the phenomena is small. We consider also microlensing by neutralino stars using very clear model. The neutralino stars were analyzed recently by Gurevich and Zybin, and besides the stars are considerable component of dark matter. We consider the optics of the microlens, namely lens equation, the magnification, critical and caustic curves.

## Takashi Nakamura

The Minimum Total Mass of MACHOs and Halo Models of the Galaxy

If the density distribution of MACHOs ($\rho (r)$) is spherically symmetric with respect to the Galactic center, it is shown that the minimum total mass of the MACHOs($M_{min}^{{\rm MACHO}}$) is $1.7\times 10^{10}\sol \tau_{-6.7}^{{\rm LMC}}$ where $\tau_{-6.7}^{{\rm LMC}}$ is the optical depth ($\tau^{{\rm LMC}}$) toward the Large Magellanic Cloud (LMC) in the unit of $2\times 10^{-7}$. If $\rho (r)$ is a decreasing function of $r$, it is proved that $M_{min}^{{\rm MACHO}}$ is $5.6\times 10^{10}\sol \tau_{-6.7}^{{\rm LMC}}$. Several spherical and axially symmetric halo models of the Galaxy with a few free parameters are also considered. It is found that $M_{min}^{{\rm MACHO}}$ ranges from $5.6\times 10^{10}\sol \tau_{-6.7}^{{\rm LMC}}$ to $\sim 3 \times 10^{11}\sol \tau_{-6.7}^{{\rm LMC}}$. For general case, the minimum column density of MACHOs ($\Sigma_{min}^{{\rm MACHO}}$) is obtained as $\Sigma_{min}^{{\rm MACHO}} =25 \sol {\rm pc}^{-2}\tau_{-6.7}^{{\rm LMC}}.$ If the clump of MACHOs exist only in the halfway between LMC and the sun, $M_{min}^{{\rm MACHO}}$ is $1.5\times 10^9\sol$. This shows that the total mass of MACHOs is smaller than $5 \times 10^{10}\sol$ ( i. e. $\sim$ 10\% of the mass of the halo inside LMC) either if the density distribution of MACHOs is unusual or $\tau^{{\rm LMC}}\ll 2\times 10^{-7}$.

Gravomagnetic Lensing by NUT Space

The usual gravitational lens effect is based on the bending of light rays passing a point mass $M$ (Schwarzschild lens) in Schwarzschild spacetime . The static nature of the Schwatzschild metric shows that it can only produce gravoelectric fields , but in the case of\ NUT metric ( sometimes called the generalized Schwarzschild metric ), the existence of the cross term `$d\phi dt$'' , shows that this space has the gravomagnetic field of a monopole . \par Using the fact that the null geodesics in NUT space lie on 3-dim. spatial cones ( in the Landau and Lifshitz approach to stationary spacetimes) , we consider the gravomagnetic lens effect on light rays passing a NUT deflector. We show that this effect changes the shape , size and the orientation of a source , as seen by an observer . Compared to the Schwarzschild lens, there is an extra shear due to the effect of the gravomagnetic field of the lens , which is basically a twist in the shape of the source. Gravomagnetic monopoles can thus be recognized by the spirality that they produce in the lensing pattern. \par All the results obtained in this case ( magnification factor , orientation of images , multiplicity of images and etc. ) depend on $Q$, the strength of the gravomagnetic monopole represented by NUT metric .One recovers the results of the usual Schwarzschild lens effect by putting this factor equal to zero .

## Alexandre Refregier & Abraham Loeb

Effect of gravitational lensing on measurements of the Sunyaev-Zel'dovich Effect

The Sunyaev-Zel'dovich (SZ) effect of a cluster of galaxies is usually measured after background radio sources are removed from the cluster field. Gravitational lensing by the cluster potential leads to a systematic deficit in the residual intensity of unresolved sources behind the cluster core relative to a control field far from the cluster center. As a result, the measured decrement in the Rayleigh-Jeans temperature of the cosmic microwave background is overestimated. We calculate the associated systematic bias which is inevitably introduced into measurements of the Hubble constant using the SZ effect. For the cluster A2218, we find that observations at 15 GHz with a beam radius of 0'.4 and a source removal threshold of 100 microjansky underestimate the Hubble constant by 6-10%. If the profile of the gas pressure declines more steeply with radius than that of the dark matter density, then the ratio of lensing to SZ decrements increases towards the outer part of the cluster.

## Chris Fluke and Rachel Webster

Investigating the Geometry of Quasars with Microlensing

When a source crosses the caustics of a gravitational microlens at cosmological distances, a high magnification event occurs. This is seen as a change in the total flux of the image of the source. In this work, we study the magnification characteristics of an extended source either crossing a fold caustic or passing near a cusp. One important application of this work will be the determination of the geometric structure of quasars. By observing the flux changes of a quasar image during a microlensing event, it is possible to determine features of quasar structure which would otherwise be below the resolution limit available with existing methods. We present an analytic result for the magnification of a point source near a parabolic fold caustic. This is a higher order approximation to the existing solution for a straight fold caustic. We show from a study of fold-crossing events that we can distinguish between disk and annular source geometries. From microlensing of extended sources which pass outside cusps, we show that a definite signature for asymmetric sources (for example accretion disks inclined to the line of sight) exists and should be observable.

## Yun Wang and Edwin L. Turner

Astrophysical Effects of Extreme Gravitational Lensing Events

Every astrophysical object (dark or not) is a gravitational lens, as well as a receiver/observer of the light from sources lensed by other objects in its neighborhood. For a given pair of source and lens, there is a thin on-axis tubelike volumn behind the lens in which the radiation flux from the source is greatly increased due to gravitational lensing. Any objects which pass through such a thin tube will experience strong bursts of radiation, i.e., Extreme Gravitational Lensing Events (EGLEs). We have studied the physics and statistics of EGLEs. EGLEs may have interesting astrophysical effects, such as the destruction of dust grains, ignition of masers, etc. Here we illustrate the possible astrophysical effects of EGLEs with one specific example,the destruction of dust grains in globular clusters.