Compound lensing: Einstein Zig-Zags and high multiplicity lensed images

TL;DR

This paper analytically and numerically studies compound gravitational lensing, revealing the potential for high image multiplicity and extreme magnifications, and emphasizing the need for specialized detection methods in future surveys.

Contribution

It provides an analytical understanding of image multiplicity in compound lensing and models the optical depth and magnification possibilities in the universe.

Findings

Up to six images can form in compound lensing systems.

Extreme magnifications of 100+ are possible for high-redshift sources.

Distinct image configurations require dedicated detection strategies.

Abstract

Compound strong gravitational lensing is a rare phenomenon, but a handful of such lensed systems are likely to be discovered in forthcoming surveys. In this work, we use a double SIS lens model to analytically understand how the properties of the system impact image multiplicity for the final source. We find that up to six images of a background source can form, but only if the second lens is multiply imaged by the first and the Einstein radius of the second lens is comparable to, but does not exceed that of the first. We then build a model of compound lensing masses in the Universe, using SIE lenses, and assess how the optical depth for multiple imaging by a galaxy-galaxy compound lens varies with source redshift. For a source redshift of 4, we find optical depths of $6 \times 10^{-6}$ for multiple imaging and $5 \times 10^{-8}$ for multiplicity of 6 or greater. We find that extreme magnifications are possible, with magnifications of 100 or more for $6 \times 10^{-9}$ of $z=10$ sources with 0.1 kpc radii. We show some of the image configurations that can be generated by compound lenses, and demonstrate that they are qualitatively different to those generated by single-plane lenses; dedicated compound lens finders will be necessary if these systems are to be discovered in forthcoming surveys.