The Search for Matter with Gravitational Lensing

Gravitational lensing is a powerful tool to detect compact matter on very different mass scales. Of particular importance is the fact that lensing is sensitive to both luminous and dark matter alike. Depending on the mass scale, all lensing effects are used in the search for matter: offset in position, image distortion, magnification, and multiple images. Gravitational lens detections cover three main mass ranges: roughly stellar mass, galaxy mass and galaxy cluster mass scales, i.e. well known classes of objects. Various searches based on different techniques explored the frequency of compact objects over more than 15 orders of magnitude, so far mostly providing null results in mass ranges different from the ones just mentioned. In particular, no population of " compact dark objects " could be detected so far. Combined, the lensing results offer some interesting limits on the cosmological frequency of compact objects in the mass interval 10 −3 ≤ M/M ⊙ ≤ 10 15 , unfortunately still with some gaps in between. In the near future, further studies along these lines promise to fill the gaps and to push the limits further down, or they might even detect new object classes. The basic setup for a gravitational lens scenario is displayed in Figure 1. The three ingredients in such a lensing situation are the source S, the lens L, and the observer O. Light rays emitted from the source are deflected by the lens. For a point-like lens, there will always be (at least) two images S 1 and S 2 of the source. With external shear – due to the tidal field of objects outside but near the light bundles – there can be more images. The observer sees the images in directions corresponding to the tangents of the incoming light paths. In Figure 1 the corresponding angles and angular diameter distances D L , D S , D LS are indicated. In the thin-lens approximation, the hyperbolic paths are approximated by their asymptotes. In the circular-symmetric case, the deflection angle is given as ˜ α(ξ) = 4GM (ξ) c 2 1 ξ. (1) where M (ξ) is the mass inside a radius ξ. In this depiction the origin is chosen at the observer. From the diagram it can be seen that the following relation holds: θD S = βD S + ˜ αD LS (2) (for θ, β, ˜ α ≪ 1; this condition is fulfilled …