Weak gravitational lensing

I'm interested in weak lensing, where we want to recover the mass distribution of the lens(es) by measuring small distortions in the shape of lensed sources. The problem is: we know neighter the intrinsic shape of the sources nor the properties of the lens which give rise to a change of this shape. For a single galaxy it is impossible to distinguish whether the shape we see is its intrinsic shape or has been modified by the gravitational lensing effect.

The only way out is to look for trends in the shape of groups of closely adjacent galaxies. For instance, without the presence of a lens, there is no preferred direction in space. This means, when averaging over (sufficiently many) unlensed galaxies, the result will be circular. If this is not the case, gravitational lensing is responsible for the deviation from roundness. Furthermore, from the direction and the strength of this average distortion we can infer the strength of the lens at the position of the group of galaxies.

Thus, for building a map of the strength of a extended lens we need many source galaxies. But this time we are lucky: nature provides a huge number of distant faint blue galaxies, which are essentially isotropically distributed. On the area of the full moon you could find thousands of them if the telescope permits.

Normally we are interested in the matter distribution of the lens. Since matter causes the lensing effect, it must be possible to recover (at least parts) of the matter distribution from the map of the lensing strength. And indeed, after doing some algebra we are able to convert the map of the lensing strength into a map of the lens matter.

The great benefit of this complicated procedure is that it does not depend on any assumptions on the connection between the light emitted by the lens and the matter of the lens. This is particularly important as we believe that large objects like galaxies or clusters of galaxies are largely made up by dark matter, which does not emit light but acts gravitationally. Therefore, with matter maps from weak lensing we can actually look at the total distribution of matter, may it be luminous or not.