Mass Reconstruction from Lensing

Abstract

One of the most striking consequences of Einstein’s general relativity is the ability of a large concentrated mass to deflect photons as they pass near a massive object. An example of this is a galaxy or a galaxy cluster. Because of this quality, massive objects are usually referred as gravitational lenses. The level of deflection differs depending on the minimum distance the photon approaches the deflecting object and the total mass of the lens. The weak lensing regime occurs when the deflection angle is small, normally occurring when the photon is at a large distance from the gravitational lens. The deflection angle in this regime decreases approximately linearly as the distance to the lens increases. When the distance is small we are in the strong lensing regime (hereafter SL). The SL effect creates a more complex distortion of the background sources (normally galaxies or quasars). The deflection angle becomes less linear as the photons get closer to the lens. As a result, the effect can create multiple images of the source. The number and distribution of these multiple images will depend on the geometry of the problem (observer– lens–source) as well as on the internal distribution of matter in the source. A beautiful example is shown in Fig. 1 where large arcs can be seen around the centre of gravity of the cluster. While weak lensing distortions appear as a stretched version of the background sky, strong lensing distortions are rich in complexity, making evident the non-linear nature of the deflection angle. This complex structure of arcs appearing in the strong lensing regime can be used effectively to reveal the internal gravitational structure of the lens. Solving the problem of inverting this rich data to get the gravitational potential responsible for it is not a trivial task. The unknowns of the problem are the distribution of matter in the lens and the position and shape of the source (or sources). These two unknowns have to be modelled and adjusted in order to reproduce the observed arcs. Usually, degeneracies between the model (lens and sources) and the data (position and shape of the arcs) appear. The range of possible models explaining the data (arcs) reduces as the number of available arcs increases. Problems arise when the observed arcs are