# Gravitational lens

Template:General relativity Template:Gravitational Lensing A gravitational lens is formed when the light from a very distant, bright source (such as a quasar) is "bent" around a massive object (such as a cluster of galaxies) between the source object and the observer. The process is known as gravitational lensing, and is one of the predictions of Albert Einstein's general theory of relativity.

Although Orest Chwolson is credited as being the first to discuss the effect in print (in 1924), the effect is more usually associated with Einstein, who published a more famous article on the subject in 1936.

Fritz Zwicky posited in 1937 that the effect could allow galaxy clusters to act as gravitational lenses. It was not until 1979 that this effect was confirmed by observation of the so-called "Twin Quasar" Q0957+561.

## Description

Bending light around a massive object from a distant source. The orange arrows show the apparent position of the background source. The white arrows show the path of the light from the true position of the source.

The gravity from a massive object (such as a galaxy cluster or black hole) can warp space-time, bending everything in it - including the paths followed by light rays from a bright background source. This alters the time taken for the light to reach an observer, and can both magnify and distort the apparent image of the background source.

Unlike an optical lens, maximum 'bending' occurs closest to, and minimum 'bending' furthest from, the center of a gravitational lens. Consequently, a gravitational lens has no single focal point, but a focal line instead. If the source, massive lensing object, and observer lie in a straight line, the source will appear as a ring behind the massive object. This phenomenon was first mentioned in 1924 by the St. Petersburg physicist Orest Chwolson [1], and quantified by Albert Einstein in 1936. It is usually referred to in the literature as an Einstein ring, since Chwolson did not concern himself with the flux or radius of the ring image. More commonly, if the lens is slightly misaligned, the source will resemble partial arcs around the lens. The observer may see multiple images of the same source; the number and shape of these depends upon the relative positions of the source, lens, and observer, and the shape of the gravitational well of the lens object.

File:Einstein ring.jpg
In the formation known as Einstein's Cross four images of the same distant quasar appears around a foreground galaxy due to strong gravitational lensing

There are three classes of gravitational lensing:

1. Strong lensing: where there are easily visible distortions such as the formation of Einstein rings, arcs, and multiple images.
2. Weak lensing: where the distortions of background sources are much smaller and can only be detected by analyzing large numbers of sources to find coherent distortions of only a few percent. The lensing shows up statistically as a preferred stretching of the background objects perpendicular to the direction to the center of the lens.
3. Microlensing: where no distortion in shape can be seen but the amount of light received from a background object changes in time. The background source and the lens may be stars in the Milky Way in one typical case, and stars in a remote galaxy and an even more distant quasar in another case.

The effect is small, such that (in the case of strong lensing) even a galaxy with a mass more than 100 billion times that of the sun will produce multiple images separated by only a few arcseconds. Galaxy clusters can produce separations of several arcminutes. In both cases the galaxies and sources are quite distant, many hundreds of megaparsecs away from our Galaxy.

Gravitational lenses act equally on all kinds of electromagnetic radiation, not just visible light. Weak lensing effects are being studied for the cosmic microwave background as well as galaxy surveys. Strong lenses have been observed in radio and x-ray regimes as well. If a strong lens produces multiple images, there will be a relative time delay between two paths: that is, in one image the lensed object will be observed before the other image.

### Simulation

File:Black hole lensing web.gif
Simulated gravitational lensing (black hole going past a background galaxy).

To the right is a simulation of gravitational lensing caused by a Schwartzschild black hole passing in front of a background galaxy. A secondary image of the galaxy can be seen within the black hole's Einstein radius on the side opposite the galaxy. The secondary image grows (remaining within the Einstein ring) as the primary image approaches the black hole. The surface brightness of the two images remains constant, but their angular sizes vary, hence producing an amplification of the galaxy luminosity as seen by a distant observer. Maximum amplification occurs when the galaxy (or in this case a bright part of it) is exactly behind the black hole.

## History

According to general relativity, mass "warps" space-time to create gravitational fields and therefore bend light as a result. This theory was confirmed in 1919 during a solar eclipse, when Arthur Eddington observed the light from stars passing close to the sun was slightly bent, so that stars appeared slightly out of position.

Einstein realized that it was also possible for astronomical objects to bend light, and that under the correct conditions, one would observe multiple images of a single source, called a gravitational lens or sometimes a gravitational mirage. However, as he only considered gravitational lensing by single stars, he concluded that the phenomenon would most likely remain unobserved for the foreseeable future. In 1937, Fritz Zwicky first considered the case where a galaxy could act as a source, something that according to his calculations should be well within the reach of observations.

It was not until 1979 that the first gravitational lens would be discovered. It became known as the "Twin Quasar" since it initially looked like two identical quasars; it is officially named Q0957+561. This gravitational lens was discovered accidentally by Dennis Walsh, Bob Carswell, and Ray Weymann using the Kitt Peak National Observatory 2.1 meter telescope.

In the 1980s, astronomers realized that the combination of CCD imagers and computers would allow the brightness of millions of stars to be measured each night. In a dense field, such as the galactic center or the Magellanic clouds, many microlensing events per year could potentially be found. This lead to efforts such as Optical Gravitational Lensing Experiment, or OGLE, that have characterized hundreds of such events.

## Explanation in terms of space-time curvature

In general relativity, gravity is not construed as a force; hence, if the net force of non-gravitational interactions is negligible, the law that describes motion is Newton's First Law rather than Newton's Second Law. Newton's First Law models position as a function of time in non-relativistic mechanics, but in general relativity the law is rewritten to demand motion along a space-time geodesic. This curvature of space-time causes the path of even a massless particle like a photon to deviate from the straight lines expected from Euclidean intuition; and, in particular, the path is observed to curve in exactly the same way as the geodesics predicted by general relativity.

Since the speed of electromagnetic radiation in a vacuum is invariant in both theories of relativity, lensing changes the direction of the velocity vector but not its magnitude. Weak lensing and micro-lensing in particular cause deflection through an angle

${\displaystyle \theta ={\frac {GM}{rc^{2}}}}$

toward the mass M at a distance r from the affected radiation, where G is the universal constant of gravitation and c is the speed of light in a vacuum. Some care needs to be taken in defining this distance because gravity is not instantaneous: like light, it propagates at speed c. The path of the gravitational wave and the electromagnetic radiation intersect at specific space-time coordinates, and the lensing is determined by the component of the incident gravitational wave perpendicular to the direction of the electromagnetic radiation's motion.

## Applications

File:Abell.lensing.arp.750pix.jpg
Actual gravitational lensing effects as observed by the Hubble Space Telescope in Abell 1689 - Enlarge the image to see the lensing arcs

### Studying the background sources

Gravitational lenses can be used as gravitational telescopes, because they concentrate the light from objects seen behind them, making very faint objects appear brighter, larger and therefore more easily studied. Researchers at Caltech have used the strong gravitational lensing afforded by the Abell 2218 cluster of galaxies to detect the most distant galaxy known (February 15, 2004) through imaging with the Hubble Space Telescope. Objects at such distances would not normally be visible, providing information from further back in time than otherwise possible.

Similarly, microlensing events can be used to obtain additional information about the source star. In addition to the greater brightness, limb darkening can be measured during high magnification events[1]. If the source star is part of a binary system, the orbital motion of the source can sometimes be measured (called the xallarap effect, by analogy to parallax which is caused by the orbital motion of the Earth).

### Studying the foreground lenses

Observations of gravitational lensing can also be inverted to examine the lens itself. Direct measurements of the mass in any astronomical object are rare, and always welcome. While most other astronomical observations are sensitive only to emitted light, theories are generally concerned with the distribution of mass. Comparing mass and light typically involves assumptions about complicated astrophysical processes. Gravitational lensing is particularly useful if the lens is for some reason difficult to see.

Gravitational microlensing can provide information on comparatively small astronomical objects, such as MACHOs within our own galaxy, or extrasolar planets (planets beyond the solar system). Three extrasolar planets have been found in this way, and this technique has the promise of finding Earth-mass planets around sunlike stars within the 21st century. The MOA and PLANET collaborations focus on this research.

File:COSMOS 3D dark matter map.jpg
3D map of the large-scale distribution of dark matter, reconstructed from measurements of weak gravitational lensing with the Hubble Space Telescope.

Strong and weak gravitational lensing of distant galaxies by foreground clusters can probe the amount and distribution of mass, which is dominated by invisible dark matter. Aside from determining how much dark matter they contain, its distribution in these systems depends upon properties including the mass of its (unknown) constituent particles and their collisional cross-section. The number of strong gravitational lenses throughout the sky can also be used to measure values of cosmological parameters such as the mean density of matter in the universe. Presently, the statistics do not place very strong limits on cosmological parameters, partly because the number of strong lenses found is relatively small (fewer than a hundred). Weak gravitational lensing can extend the analysis away from these most massive clusters and, for example, reconstruct the large-scale distribution of mass. This is sensitive to cosmological parameters including the mean density of matter, its clustering properties and the cosmological constant.

### Geometry of the Universe

A purely geometric effect, gravitational lensing can be used to measure the expansion history of the universe (its size as a function of time since the big bang), which is encoded in Hubble's law. If the mass distribution in a foreground lens is well understood (typically from multiple strong lensing arcs, and possibly weak lensing in the outskirts), two other free parameters can be used to constrain the Hubble constant, or deviations from Hubble's law caused by dark energy. In principle, and in both cases, only one gravitational lens for the best possible measurement. The search continues for that perfect lens, with many multiply-imaged arcs.

There will be a time delay (around days or weeks) between multiple images of the same source because of

1. the delay due to the difference in optical path length between the two rays.
2. the general relativistic Shapiro effect, which describes light rays as taking longer to traverse a region of stronger gravitation, (see: gravity well, gravitational time dilation). Because the two rays travel through different parts of the potential well created by the deflector, the clocks carrying the source's signal will differ by a small amount.

If either the amount or the spectrum of light emitted by the background source varies over time, characteristic variations can be seen to occur first in one image and then others.

A gravitational lens magnifies and distorts very distant sources more than those only just behind the lens (and it does not distort those in front of the lens). Indeed, simple geometry can be used to calculate the efficiency of a gravitational lens as a function of the angular diameter distance to the source. If the distortion can be measured at multiple distances, this distance can be compared to the redshift of those sources: a direct Hubble diagram. Furthermore, this technique effectively requires only the ratio of the distortion at two distances. The total mass of the foreground lens therefore cancels out and does not need to be constrained (although its radial profile does). Using a more massive lens simply increases the signal to noise of the measurement.

## Search for Gravitational lenses

Most of the gravitational lenses in the past have been discovered accidentally. A search for gravitational lenses in the northern hemisphere (Cosmic Lens All Sky Survey, CLASS), done in radio frequencies using the Very Large Array (VLA) in New Mexico, led to the discovery of 22 new lensing systems, a major milestone in the gravitational lenses history. This has opened a whole new avenue for research ranging from finding very distant objects to finding values for cosmological parameters so we can understand the universe better.

A similar search in the southern hemisphere would be a very good step towards complimenting the northern hemisphere search as well as obtaining other objectives for study. As can be expected, if such a search is done using well calibrated and well parametrized instrument and data, we can expect to have a very good outcome. The use of the Australia Telescope 20GHz (AT20G) Survey data collected using the Australia Telesope Compact Array (ATCA) stands to be such a collection of data. As the data was collected using the same instrument maintaining a very stringent quality of data we should expect to obtain good results from the search. The AT20G survey is a blind survey at 20 GHz frequency in the radio domain of the electromagnetic spectrum. Due to the high frequency used, the chances finding gravitational lenses increases as the relative number of compact core objects (eg. Quasars) are higher ( Sadler et al. 2006). This is important as the lensing is easier to detect and identify in simple objects compared to objects with complexity in them. This search involves the use of interferometric methods to identify candidates and follow them up at higher resolution to identify them. Full detail of the project is currently under works for publication.

## Historical papers and references

• Chwolson, O (1924). "Über eine mögliche Form fiktiver Doppelsterne". Astronomische Nachrichten. 221: 329. doi:10.1002/asna.19242212003.
• Einstein, Albert (1936). "Lens-like Action of a Star by the Deviation of Light in the Gravitational Field". Science. 84: 506–507. doi:10.1126/science.84.2188.506. PMID 17769014.
• Renn, Jürgen (1997). "The Origin of Gravitational Lensing: A Postscript to Einstein's 1936 Science paper". Science. 275: 184–186. doi:10.1126/science.275.5297.184. PMID 8985006. Unknown parameter |coauthors= ignored (help)

## Citations

1. "Stellar Atmospheres". MOA collaboration.