*This article is a discussion piece, focusing on the paper “Essentials of Strong Gravitational Lensing” by P. Saha, D. Sluse, J. Wagner, and L. L. R. Williams. It reviews and explains the key points, mechanisms, and significance of strong gravitational lensing as presented in the original publication.*

Source article

Title: Essentials of strong gravitational lensing

Authors: P. Saha, D. Sluse, J. Wagner, L. L. R. Williams

First Author’s Institution: Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8

057 Zurich, Switzerland

Status: Published in the Space Science Reviews, February 2024.

## Introduction

Light from distant astronomical objects travels through the vast expanse of the universe encountering in its way massive objects like galaxies or clusters and other large scale structures which deflect its path. This bending of light leads to distortion in the image of the source. This phenomenon is known as gravitational lensing. There are three types of gravitational lensing, and they are strong lensing, weak lensing and micro lensing. In this article we talk about the paper “Essentials of strong gravitational lensing” by Prasenjit Saha, Dominique Sluse, Jenny Wagner, and Liliya L. R. Williams which provides an introduction to the mechanisms, applications, and significance of strong gravitational lensing. Here’s an overview of its key points and broader implications.

## Gravitational – Lensing: A Cosmic Telescope

Strong gravitational lensing occurs when a foreground object (massive), such as a galaxy or galaxy cluster, deflects a light emanating from the background source, leading to distortions, even multiple images of a source or distorted arcs of the background objects. This effect is an direct consequence of Einstein’s theory of general relativity, which says that mass leads to curvature in spacetime, which then leads to bending of light when it traverses through the curved spacetime.

## Key Concepts

### Lens Equation and Fermat Potential

Gravitational lensing relies on Fermat’s principle, which states that light follows paths that minimise travel time. The lens equation relates the observed image positions to the true position of position of the source accounting for the gravitational deflection introduced by the lens. The Fermat potential or arrival-time surface gives us the total travel time of light classifying images into three categories: maxima, minima, or saddle points. A thorough study of lens potential leads to critical curves which are regions on the lens place that are associated with extreme magnification, and caustics which are boundaries (curves with infinite magnification) on the source plane that separates regions with different number of images. Now, when a source crosses a caustic, it changes the number of images that can be observed and provide essential information about the lens structure.

### Cosmological Context

The phenomenon of strong lensing occurs frequently at cosmological scales, where it is crucial that we understand different forms of distances such as comoving distance and angular diameter. Redshifts on the other hand demonstrates the universe’s expansion to determine the relative positions of source and lens. Multi-plane lensing, considers the collective effect of several massive objects along the line of sight (LOS) leading to complex image patterns. So, recognising the various relationships between measures of distances helps us explain the scales of lensing effects. For example, the interplay between angular diameters determines how the gravitational lens leads to light from distant sources to bend.

## Findings and Methods

### Lens Formalism

The Einstein radius serves as a measure of angular distances around a lens. If the source aligns with the lens and the observer perfectly then this leads to the formation of an Einstein ring, and the magnification matrix tells us how the images compresses or stretches in the curvature formed under the effect of the Fermat potential.

As we talked earlier, the properties of the lens potential and its derivatives define the three types of images formed – maxima, minima, and saddle points. So when, we map the lens potential allows us to predict number of images and their structures.

### Common Image Configurations

The phenomenon of strong lensing leads to different image configurations – doubles (two images), quads (four images) and Einstein rings, and these patterns depend on the mass and geometry of the lens and position of the source.

• Doubles – It is formed when the source lies inside the outer caustic but outside the inner one, and this results in the formation of two images.

• Quads – Source is within the inner caustic leading to four images around the lens.

• Einstein Rings – formed when there is a perfect alignment resulting in a continuous circular light ring around the lens.

Now all of these arrangements provide various details regarding lens’ geometry and its mass distribution, and the location of source.

## Lens Modelling

The authors of the paper reconstruct the mass distribution and the intrinsic brightness of the sources derived from the observed images. They employ modelling techniques such as fitting analytical mass distributions to numerically solve inverse problems that help us map the mass distribution. However, these models face challenges in degeneracies, where identical image patterns are revealed from different mass distributions.

## Conclusion and Outlook

We can think of gravitational lensing as a cosmic magnifying lens, which proves to be a powerful tool for studying dark matter, galaxy evolution, and cosmology in general. Even though there are challenges such as degeneracies, the increase in the observational data for lensing systems and the advancement of modelling techniques offer many valuable insights. Future surveys and better computational techniques and tools presents with an opportunity to learn more about dark matter and it role in the evolution of galaxies, brightness of distant sources, offering detailed insights giving information about star formation, galaxy evolution, and even placement of super massive black holes.