We outline the noise-filtering finite-field inversion kernel and the regularized maximum likelihood methods for cluster reconstruction.

Arclets in clusters of galaxies can be used to determine the lens mapping and not only to constrain the mass density of the cluster. Multiply imaged arclets are therefore easily identified without further modeling.

Weak shear maps of the outer regions of clusters have been successfully used to map the distribution of mass at large radii. The effects of substructure in clusters on such reconstructions of the total mass have not been systematically studied. We propose a new method to study the effect of perturbers (bright cluster galaxies or sub-groups within the cluster) on the weak shear field. We present some analytic results below.

We combine the X-ray data and the Sunyaev-Zel'dovich effect with the constraints from gravitational lensing for an intermediate redshift cluster to check the consistency of various mass estimates and the validity of the assumption of hydrostatic equilibrium, and to deduce the properties of the intra-cluster gas, the profile of the cluster potential and Ho.

Abell 963 (z = 0.206) is still the best candidate for a true arc-counterarc lens configuration (Lavery & Henry 1988). A simple model explains the positions, lengths and patchy light distribution of the two arcs. Photometry indicates the arcs also have the same B-R color (Lavery & Henry 1988; Ellis et al. 1991). However, spectroscopic observations have not confirmed that these arcs originate from the same background galaxy. Ellis et al. (1991) detected a single emission line in the spectrum of the smaller northern arc, identifying it as [O II] λ3727 at a redshift of 0.77. Neither Lavery (1989) or Ellis et al. (1991) detected this emission line in the larger southern arc.

Gravitational lensing is one of a number of methods used to probe the distribution of dark mass in the Universe. On galactic scales, complementary techniques include the use of stellar kinematics, the kinematics and morphology of the neutral gas layer, kinematics of satellites, and the morphology and temperature profile of X-ray halos. These methods are compared, with emphasis on their relative strengths and weaknesses in constraining the distribution and extent of dark matter in the Milky Way and other galaxies. It is concluded that (1) the extent of dark halos remains ill-constrained, (2) halos need not be isothermal, and (3) the dark mass is probably quite flattened.

From their rotation curves, most spiral galaxies appear to have massive dark coronas. The inferred masses of these dark coronas are typically 5 to 10 times the mass of the underlying stellar component. I will review the evidence that our Galaxy also has a dark corona. Our position in the galactic disk makes it difficult to measure the galactic rotation curve beyond about 20 kpc from the galactic center. However it does allow several other indicators of the total galactic mass out to very large distances. It seems clear that the Galaxy does indeed have a massive dark corona. The data indicate that the enclosed mass within radius R increases like M(R) ≈ R(kpc) × 1010M⊙, out to a radius of more than 100 kpc. The total galactic mass is at least 12 × 1011M⊙.

Nearly singular isothermal mass distributions with small core radii are consistent with stellar dynamics, lens statistics, and lens models as a model for E/S0 galaxies. Models like the de Vaucouleurs model with a constant mass-to-light ratio are not. While the isothermal distributions are probably an oversimplification, E/S0 galaxies (at least in projection) must have significant amounts of dark matter on scales of an effective radius.

In this paper we report on an investigation of statistical weak gravitational lensing of cosmologically distant faint galaxies by foreground galaxies. The signal we seek is a distortion of the images of faint galaxies resulting in a weakly preferred tangential alignment of faint galaxies around brighter galaxies. That is, if the faint galaxies have been gravitationally lensed by the brighter systems, the major axes of their images will tend to lie perpendicular to the radius vectors joining the centroids of the faint and bright galaxies (Fig. 1). Modeling a lens galaxy as a singular isothermal sphere with circular velocity Vc, an ellipticity of ∼ 2πVc2 /c2θ is induced in the image of a source galaxy at an angular separation θ from the lens. This is of order a few percent for faint–bright galaxy pairs with separations θ ∼ 30″ where the lens is a typical bright spiral. Over 1000 pairs must be measured in order to detect such a signal in the presence of the noise associated with the intrinsic galaxy shapes. Given a sufficiently large number of pairs, it may be possible to use the variation of the induced ellipticity with θ to study the angular extent of the halos of the lens galaxies.

Baryonic Dark Matter (BDM) candidates are segregated into two main mass ranges: (i) sub-solar mass dwarf stars (MACHOS) and (ii) ∼ 104–106M⊙ Very Massive Objects (VMOs). The lower mass range has been the target of the various micro-lensing programs but the first, tentative conclusions (see Stubbs et al. these proceedings) seem to suggest that MACHOs are unlikely to provide the bulk of the dark matter in the galactic halo. Meanwhile the upper mass range (104–106M⊙) remains largely unexplored. However, Wambsganss & Paczynski 1992 (hereafter WP92), have shown that this mass range is perfectly tuned to a straightforward and direct test: gravitational milli-lensing of macro-lensed images (Fig 1).

In JVAS we find more 5-image systems than 3-image systems. On conventional assumptions, we predict the ratio to be ∼5:1.

MG2016+112, discovered by Lawrence et al. (1984) is one of the best–studied among multiply–imaged systems, but is still only partially understood. Ostensibly a three–image system consisting of images A, B and C of a quasar at z = 3.273, the observed lensing galaxy D (a giant elliptical at z = 1.01) at the centroid of the image system seems inadequate to provide the minimum mass of ∼ 2.5 × 1012 M⊙ within 10 kpc of its center (in projection along the l.o.s.) required to produce the observed 3.″9 image–splitting. C itself appears to consist of two components, radio emission that may be associated with the faint optical image counterpart of A and B (called C2, see Garrett et al. 1994) and flat-spectrum C1, which dominates radio observations of the system and apparently consists of at least three linearly stretched subcomponents, C11 to C13 (see Garrett et al. in these proceedings).

The smallest radio Einstein Ring, B2018+357, discovered by Patnaik et al. (1993), shows much promise as a tool to constrain the parameters of cosmological models (Refsdal 1964). Dominating this system is a pair of 0.″335–separation compact radio images, with image A between 2.7 to 3.9 times as strong as image B (λλ 18 to 2 cm). Observations have established the lens redshift (zl = 0.685, O'Dea et al. 1992, Browne et al. 1993), a possible source redshift (zs = 0.96, Lawrence, this conference), and a tentative value for the time–delay between the highly polarized images A and B (12 ± 3 days, Browne, this conference). Recent mas–resolution observations have made it possible to understand the imaging of A and B in sufficient detail as to provide constraints on an elliptical lens model for B0218+357; this work presents a model and provides an estimate of Hubble's Constant.

A high optical depth to gravitational microlensing towards the galactic bulge is consistent with current models of the galactic bar. The low optical depth towards the LMC can probably be accounted for by the ordinary stars in our galaxy and in the LMC itself. No conclusive evidence is available yet for the presence or absence of a large number of brown dwarfs or other non-stellar compact objects which might account for the dark matter. There is little doubt that the amount of mass in objects in the range 10–8 ≤ M/M⊙ ≤ 106 will be determined within the next few years with the continuing and expanding searches.

Billions of photometric measurements generated by the microlensing searches have lead to the discovery of ∼ 105 variable stars. In particular, a number of detached eclipsing binaries were discovered in the galactic bulge, in the LMC, and in the globular cluster Omega Centauri. The follow-up observations of these binaries will allow the determination of accurate distances to all these objects, as well as robust age determination of globular clusters.

Gravitational microlensing is the most straightforward interpretation of the stellar brightenings that have been observed by our team and other experiments. These data have provided some of the most stringent limits to date on the nature of the Galaxy's dark matter halo. The number of events seen towards the LMC indicate that our Galaxy is not surrounded by a “standard” halo of MACHOs in the mass range of 10–6 to 0.3 solar masses. The observed optical depth towards the Galactic Center is an important constraint on the distribution of mass in the plane of the Galaxy.

The DUO (Disk Unseen Objects) program is a project with the main goal of searching for galactic dark matter in a field towards the Galactic Bulge (Alard et al. 1995b). In this paper I present the results obtained from the analysis of half of the data collected during the 1994 season. I start with a brief description of the DUO project, and I will continue with an analysis of the microlensing candidates that I found. In all I found 13 microlensing events in the DUO data, including a double lens event. A model of the double lens light curve predicts a blending effect. The presence of the blended component was confirmed by a gravity center shift during the event. Taking into account the model prediction and the shift, we could predict the exact geometry of the blend. This prediction was recently confirmed by direct imaging of the blend under good seeing conditions. The durations of the single lens events are quite short, but the durations can be seriously affected by blending. I propose a simple experimental test to quantify this duration bias. In the conclusion I emphasize the great importance of a good knowledge of the inner Galactic structure to get a reliable quantitative description of microlensing towards the bulge. Finally I will show that the large number of variables stars found in the data could be a powerful tool to probe this structure.

Real-time detection of microlensing has moved from proof of concept in 1994 (Udalski et al. 1994a, Alcock et al. 1994) to a steady stream of events this year. Global dissemination of these events by the MACHO and OGLE collaborations has made possible intensive photometric and spectroscopic follow up from widely dispersed sites confirming the microlensing hypothesis (Benetti 1995). Improved photometry and increased temporal resolution from follow up observations greatly increases the possibility of detecting deviations from the standard point-source, point-lens, inertial motion microlensing model. These deviations are crucial in understanding individual lensing systems by breaking the degeneracy between lens mass, position and velocity. We report here on GMAN (Global Microlensing Alert Network), the coordinated follow up of MACHO alerts.

A newly-formed microlensing monitoring network, the PLANET collaboration, is briefly described.

Most of the detected galactic microlensing events are commonly explained as due to microlensing of a pointlike source by a pointlike lens. We have found statistical methods to determine the goodness-of-fit for a specific model of source and lens beyond the assumption that the errors are normal, which does not always hold. In particular, we argue that at least one weak binary lensing event has already been detected (MACHO LMC#1) and thereby confirm our former hypothesis (Dominik & Hirshfeld 1994). We also find that this fit is not unique. We emphasize that knowledge of the fraction of binaries among the observed microlensing events is crucial for estimating the mass distribution of the observed dark objects.

Of the large number of microlensing events detected towards the galactic bulge, there has been at least one clear case of a binary lens system, the OGLE 7 event. If this event had been observed simultaneously from three 1 m class ground-based telescopes during its second caustic crossing, an identification of the lens as a bulge or disk object and a determination of the orientation of the lens velocity on the sky could have been made.