Caustics of $1/r^n$ binary gravitational lenses: from galactic haloes to exotic matter

TL;DR

This paper analyzes the caustic structures of binary gravitational lenses with potentials declining as 1/r^n, revealing new features for exotic matter scenarios and providing analytical insights into their lensing phenomenology.

Contribution

It introduces analytical formulas and numerical methods for understanding caustic topologies in binary lenses with various power-law potentials, including exotic matter cases.

Findings

Caustic topologies are similar to standard cases, with notable differences in secondary caustics at higher n.

Secondary caustics become significantly larger as n increases.

Analytical formulas help understand lensing signatures of exotic matter and galaxy clusters.

Abstract

We investigate the caustic topologies for binary gravitational lenses made up of two objects whose gravitational potential declines as $1/r^n$. With $n<1$ this corresponds to power-law dust distributions like the singular isothermal sphere. The $n>1$ regime can be obtained with some violations of the energy conditions, one famous example being the Ellis wormhole. Gravitational lensing provides a natural arena to distinguish and identify such exotic objects in our Universe. We find that there are still three topologies for caustics as in the standard Schwarzschild binary lens, with the main novelty coming from the secondary caustics of the close topology, which become huge at higher $n$. After drawing caustics by numerical methods, we derive a large amount of analytical formulae in all limits that are useful to provide deeper insight in the mathematics of the problem. Our study is useful to better understand the phenomenology of galaxy lensing in clusters as well as the distinct signatures of exotic matter in complex systems.