What is Gravitational Lensing and its Cosmological Applications

Einstein Ring due to gravitational lensing
Ring shaped image due to gravitational lensing. Source: NASA

The size of the observable universe is unimaginably large. The galaxies are separated from each other by such a large distance that even light takes millions and billions of year to travel from one galaxy to other. The galaxies present at these distant positions appear as point size and their brightness is so dim that they are invisible to naked eyes. We need various astronomical instruments to observe these distant galaxies.

One of these instruments is telescope. What telescope does is, it magnifies and brings the image closer to us. The telescope has lenses and mirrors which bend the light and lead to the magnified image. Do you know that the nature has already blessed us with natural lenses? Yes! I am talking about Gravitational Lens.

The astronomical objects lying between source and observer magnify and distort the image. You must be thinking that if the gravitational lensing distorts the image then how can it be helpful? These distorted images contain the information about the source and the intermediate objects. Let’s discuss the gravitational lensing in detail and we will try to understand phenomena caused by gravitational lensing.

What is Gravitational Lensing?

Gravitational lensing was the prediction of The General Theory of Relativity (GTR) proposed by Einstein. According to GTR, the gravity curves the space time, this curvature of space time affects the path of light. The light travels in straight line in four dimensional space time but in three dimensional space light appears to travel along curved path. As a result, the light bends around the gravitational body.

This phenomenon of bending of light around gravitational body was confirmed by Arthur Eddington and his group during solar eclipse in 1919. They measured the position of star present near the sun during the solar eclipse in day, the position of star was found to be shifted by the exact amount as predicted by Einstein. This experiment confirmed that the light bends when it passes close to a gravitational body and the amount of bending depends on the strength of gravitational field created by the body.

In 1924, Chwolson mentioned the idea of a fictitious “double star” and the mirror reversed nature of the secondary image. He also mentioned the symmetric case in which a star behind a star results a circular image. In 1936, Einstein published an article which mentioned the appearance of a “luminous circle” for perfect alignment between source and lens and of two magnified images for slightly displaced positions. Today, such a lens configuration is called “Einstein Ring”.

Gravitational lensing due to bending of light
The gravitational lensing due to bending of light by galaxy cluster. Source: ESA/NASA

Einstein was never sure whether we will be able to detect these images because the gravitational lensing produced by a star is very small. In 1937, Fritz Zwicky pointed out that galaxies are much more likely to be gravitationally lensed then stars and that one can use the gravitational lens effect as a “natural telescope”.

Difference between gravitational lensing and optical lensing

The gravitational lensing is different from optical lensing. One difference is that the gravitational lensing is same for all wavelengths. The light of all wavelength bend by same amount under the influence of gravity. On the other hand, the bending of light is different for various wavelengths in the case of optical lens.

The other difference is the non-uniform lensing in the case of gravitational lens. The light passing closure to gravitational lens is deviated more as compared to the light passing further away from the gravitational lens. Thus the gravitational lens does not have a single focal point instead it has a focal line.

Detection of gravitational lensing

The gravitational lensing was confirmed in 1979 by the detection of the double quasar Q0957+561. This was the first example of a lensed object. This gravitational lens was discovered by Dennis Walsh, Bob Carswell, and Ray Weymann using 2.1 meter telescope at the Kitt Peak National Observatory.

Gravitational lensing due to bending of light
The Twin Quasar QSP 0987+561, which lies 7.8 billion light years from Earth, is seen right in the center of this picture. Source: ESA/Hubble & NASA

In the beginning it was not clear whether the two quasars were two images produced by gravitational lensing or the two actual quasars. But intensive observations confirmed that these quasars had same redshift and identical spectra. The intervening lensing galaxy and the galaxy cluster were also found with lesser red shift (smaller distance from Earth then that of source quasar). Later very similar light curves of the two images confirmed that this system was a gravitational lens.

Various Lensing Phenomena

Let’s discuss different groups of gravitational lens observations:

Multiply-imaged quasars

The quasar appears as multiple images when a galaxy or galaxy cluster comes between the quasar and the observer. The two or more images are formed when the source, lens and observer are not aligned properly. Gravitationally lensed quasars come in a variety of classes: double, triple and quadruple systems; symmetric and asymmetric image configurations are known.

The main problem related to double quasars is the question whether the two quasars are gravitational lensed images or actually two physical bodies. There are few criteria which are used to confirm whether the two quasars are gravitational images:

• The optical color of two or more point-like images is very similar.
• Redshifts (or distance) of both quasar images are identical or very similar.
• Spectra of the various images are identical or very similar to each other.
• There is a lens found between the images with redshift much smaller than the quasar redshift.
• The images follow very similar light curve with certain time delay.

The study of gravitationally lensed quasar systems helps us to get a better understanding of both lens and source. The measurement of time delay can be used to determine the Hubble constant. The statistical analysis of lens systems helps us to get the information about the population of lenses in the universe and their distribution in distance and mass.

Quasar microlensing

Light bundles from “lensed” quasars are split by intervening galaxies. When the separation between the center of galaxy and quasar is of the order of one arcsecond then the quasar light passes through the galaxy and/or the galaxy halo. Galaxies consist at least partly of stars, and galaxy haloes consist possible of compact objects as well.

Each of these stars acts as a “compact lens” or “microlens” and produces at least one new image of the source. In fact, the “macro-image” consists of many “micro-images”. Since the image splitting is proportional to the mass of the micro lens, these micro-images are only of the order of microarcsecond apart and cannot be resolved.

Quasar Micro-Image
”Micro-Images”: The top left panel shows an assumed “unlensed” source profile of a quasar. The other three panels illustrate the micro-image configuration as it would be produced by stellar objects in the foreground. The surface mass density of the lenses is 20% (top right), 50% (bottom left) and 80% (bottom right) of the critical density.

Due to the relative motion between observer, lens and source, the quasar changes its relative position and the brightness of quasar changes with time. Thus, this change in lens configuration produces fluctuations in the brightness. The microlens-induced fluctuations in the observed brightness of quasars contain information about both the light-emitting source and the lensing objects. Hence, one can draw conclusions about the density and mass scale of the microlenses by comparing the observed and simulated quasar microlensing.

Einstein Ring

When a point source is present exactly behind a point lens then a ring like image occurs which is called Einstein Ring. There are two necessary requirements for their occurrence: the mass distribution of the lens should be axially symmetric, as seen from the observer, and the source must lie exactly on top of the resulting degenerate point-like caustic.

In 1998, the first example of an “Einstein Ring” was discovered. The extended radio source MG1131+0456 turned out to be a ring with a diameter of about 1.75 arcseconds with high resolution radio observation.  The source was identified as a radio lobe at a redshift of 1.13, whereas the lens is a galaxy at redshift of 0.85.

The diameter of Einstein rings ranges from 0.33 to 2 arcseconds. All of them are found in the radio regime, some have optical or infrared counterparts as well. Some of the Einstein Rings are not complete rings instead they are broken rings with one or two interruptions along the circle. Sometimes the compact sources are variable which gives opportunity to measure the time delay and the Hubble constant in these systems.

Einstein Rings
Some observed Einstein rings by SLACS. Source: NASA

The Einstein ring systems provide advantage over multiply-imaged quasars systems in determining the lens structure and the Hubble constant. Since the diameter of observed rings are of the order of one or two arcseconds, the expected time delay  must be much shorter than the one in the double quasars. So, one does not have to wait so long to establish a time delay. Since the radio lightcurves of the different images are not affected by microlensing, hence the lightcurve of different images should agree well with each other.

Giant Luminous arcs and arclets

The galaxies are extended objects and hence they get heavily deformed after the strong lensing. In 1986 quite surprisingly, Lynds & Petrosian and Soucail et al. independently discovered this new gravitational lensing phenomenon: magnified, distorted and strongly elongated images of the background galaxies which happen to lie behind foreground clusters of galaxies.

Since most of the clusters do not have spherically symmetric mass distribution and since the alignment between the lens and source is usually not perfect, no complete Einstein rings have been found around clusters of galaxies. But there are examples of many spectacularly long arcs which are curved around the cluster center, with the length up to about 20 arcseconds.

galaxy cluster abell 2218
Galaxy Cluster Abell 2218 with Giant Luminous Arcs and many arclets, imaged with the Hubble Space Telescope. Source: NASA

The giant arcs can be used in two ways. Firstly they provide us with strongly magnified galaxies at high redshifts (far away). These galaxies would be too faint to be detected and analysed in their unlensed state. Hence with the lensing boost we can study these galaxies in their early evolutionary stages, possibly as infant or proto-galaxies, relatively shortly after the big bang.

The second application of the arcs is in the study of the potential and mass distribution of the lensing galaxy cluster. Considering the spherical mass distribution for the cluster, giant arcs can be approximated to the Einstein ring. So it is possible to estimate the mass of lensing galaxy cluster after knowing the redshift of cluster and the radius of curvature of the arc by interpreting it as Einstein ring.

The analysis of giant arcs in the galaxy clusters shows that the clusters are dominated by dark matter. The distribution of dark matter follows roughly the distribution of the light in the galaxies, in particular in the central part of the cluster.

Statistical or Weak Gravitational Lensing

Weak Gravitational lensing involves the effect of light deflection that cannot be measured for individual lens but can be studied in statistical way. The strong lensing which involves multiple images, high magnification and caustics in the source plane is a rare phenomenon. On the other hand, weak lensing is more common phenomena because each photon is affected by the matter inhomogeneities along or near its path.

A weak lensing effect can be a small deformation of the shape of a cosmic object, or a small modification in its brightness, or a small change in its position. The change in position cannot be detection because we do not know the unaffected position. The shape deformation cannot be measured for individual images instead shape deformation can be measured when averaged over the ensemble of images.

The change in brightness can be problematic for astronomers, for example the change in apparent brightness of “standard candles” like type Ia supernovae affects the accuracy in the determination of cosmological parameters.

The first real detection of a coherent weak lensing signal of distorted background galaxies was measured in 1990 around the galaxy cluster Abell 1689 and CL1409+52. It was shown that the orientation of background galaxies- the angle of the semi-major axes of the elliptical isophotes relative to the center of cluster- was more likely to be tangentially oriented relative to the cluster than radially. For an unaffected population of background galaxies one would expect no preferential direction.


The gravitational lensing is a powerful tool for astronomy which helps in exploring a particular lens system in great detail and in determining all possible observational parameters like image position, brightness, and shape, mass and light distribution of lens. In this way, gravitational lensing helps in determining the amount of dark matter in the lens. And more importantly, the value of Hubble constant can be found using gravitational lensing.

In the future, microlensing will help in determination of frequency of binary stars. The increase in sensitivity of the binary lenses to smaller companions will lead to the application of microlensing for the determination of planets around the other stars.

Now, I hope you must have enjoyed learning about gravitational lensing and must be excited to know more. You can go through the following references and please comment if you have any query or idea. If you like this article, please share with your friend using following social media share buttons. You may also subscribe us for email notification if you want to know more about astronomy.


http://relativity.livingreviews.org/Articles/lrr-1998-12/download/lrr-1998-12BW.pdfTilman Sauer, ” A brief history of gravitational lensing ” in: Einstein Online Vol. 04 (2010), 1005http://spiff.rit.edu/classes/phys240/lectures/grav_lens/grav_lens.html

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