Three Einstein rings: explicit solution and numerical simulation

TL;DR

This paper derives explicit solutions and performs numerical simulations of gravitational lensing in a system with a point mass and a homogeneous disc with a hole, revealing conditions for multiple Einstein rings and their properties.

Contribution

It provides the first explicit solution for such a lensing system and analyzes the formation of up to three Einstein rings through numerical modeling.

Findings

Existence conditions for multiple Einstein rings are identified.

Numerical simulations show how image formation depends on system parameters.

Magnification factors vary with source position in the system.

Abstract

We investigated the effects of gravitational lensing for a system in which a lens is a point mass and a homogeneous disc with a central hole. In such system there is a variety of cases resulting in formation of one, two and three Einstein rings. We found an explicit solution and considered conditions for existence of the second Einstein ring arising on the disc. Numerical modelling of the images was made for various ratios of the central mass to the disc one and for various values of the disc surface density. We also analysed dependence of the magnification factor on a source position for such system. The result of our work can be used in search of astrophysical objects with a toroidal (ring) structure.