Observable properties of strong gravitational lenses

TL;DR

This paper demonstrates how multiple extended images in strong gravitational lensing can reveal properties of the lens without prior assumptions, using the image mapping derivatives to recover convergence ratios and shear.

Contribution

It establishes a method to extract lens properties directly from observations of multiple images without assumptions about the lens or sources.

Findings

For two images, convergence ratio and shear cannot be simultaneously reconstructed.

For three images, convergence ratios and reduced shears can be fully recovered.

With four or more images, the properties can be theoretically determined despite overdetermined constraints.

Abstract

It is shown which properties of a strong gravitational lens can in principle be recovered from observations of multiple extended images when no assumptions are made about the deflector or sources. The mapping between individual multiple images is identified as the carrier of information about the gravitational lens and it is shown how this information can be extracted from a hypothetical observation. The derivatives of the image map contain information about convergence ratios and reduced shears over the regions of the multiple images. For two observed images, it is not possible to reconstruct the convergence ratio and shear at the same time. For three observed images, it is possible to recover the convergence ratios and reduced shears identically. For four or more observed images, the system of constraints is overdetermined, but the same quantities can theoretically be recovered.