On Multiple Einstein Rings

TL;DR

This paper analytically investigates the occurrence of multiple Einstein rings, proving that multiple rings can only occur in multi-plane lensing and demonstrating conditions under which a single source can produce more than one Einstein ring.

Contribution

It provides a rigorous proof that multiple Einstein rings originate only from multi-plane lensing and explores configurations producing multiple rings from a single source.

Findings

At most one Einstein ring from a single-plane lensing system.

Up to three Einstein rings can be produced by two aligned point masses in different planes.

First instances of magnification invariants in two-plane lensing systems.

Abstract

A number of recent surveys for gravitational lenses have found examples of double Einstein rings. Here, we investigate analytically the occurrence of multiple Einstein rings. We prove, under very general assumptions, that at most one Einstein ring can arise from a mass distribution in a single plane lensing a single background source. Two or more Einstein rings can therefore only occur in multi-plane lensing. Surprisingly, we show that it is possible for a single source to produce more than one Einstein ring. If two point masses (or two isothermal spheres) in different planes are aligned with observer and source on the optical axis, we show that there are up to three Einstein rings. We also discuss the image morphologies for these two models if axisymmetry is broken, and give the first instances of magnification invariants in the case of two lens planes.