Gravitational Lensing by Ring-Like Structures

TL;DR

This paper investigates gravitational lensing by inclined ring structures, revealing the existence of pseudo-caustics where magnification changes abruptly without infinite magnification, affecting image formation and caustic structures.

Contribution

It introduces the concept of pseudo-caustics in ring-like lens systems and explains their origin from non-differentiability in the lens equation solutions.

Findings

Pseudo-caustics cause finite magnification jumps.

Pseudo-caustics can alter image multiplicity and size.

Caustic structures can be truncated or open.

Abstract

We study a class of gravitational lensing systems consisting of an inclined ring/belt, with and without an added point mass at the centre. We show that a common feature of such systems are so-called "pseudo-caustics", across which the magnification of a point source changes discontinuously and yet remains finite. Such a magnification change can be associated with either a change in image multiplicity or a sudden change in the size of a lensed image. The existence of pseudo-caustics and the complex interplay between them and the formal caustics (which correspond to points of infinite magnification) can lead to interesting consequences, such as truncated or open caustics and a non-conservation of total image parity. The origin of the pseudo-caustics is found to be the non-differentiability of the solutions to the lens equation across the ring/belt boundaries, with the pseudo-caustics corresponding to ring/belt boundaries mapped into the source plane. We provide a few illustrative examples to understand the pseudo-caustic features, and in a separate paper consider a specific astronomical application of our results to study microlensing by extrasolar asteroid belts.