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{{Gravitational lensing}}
{{General relativity sidebar |phenomena}}
[[File:Imageedit 6 2578820362.gif|thumb|231x231px|A light source passes behind a gravitational lens (point mass placed in the center of the image). The aqua circle is the light source as it would be seen if there was no lens, white spots are the multiple images (or Einstein ring) of the source.]]

A '''gravitational lens''' is a distribution of matter (such as a [[galaxy cluster|cluster of galaxies]]) between a distant light source and an observer, that is capable of bending the light from the source as the light travels towards the observer. This effect is known as '''gravitational lensing''', and the amount of bending is one of the predictions of [[Albert Einstein]]'s [[General relativity|general theory of relativity]].<ref name="NYT-20150305-video">{{cite news |last1=Drakeford |first1=Jason |last2=Corum |first2=Jonathan |last3=Overbye |first3=Dennis |title=Einstein’s Telescope - video (02:32) |url=https://www.nytimes.com/video/science/100000003552687/out-there-einsteins-telescope.html |date=March 5, 2015 |work=[[New York Times]] |accessdate=December 27, 2015 }}</ref><ref name="NYT-20150305">{{cite news |last=Overbye |first=Dennis |authorlink=Dennis Overbye |title=Astronomers Observe Supernova and Find They’re Watching Reruns |url=https://www.nytimes.com/2015/03/06/science/astronomers-observe-supernova-and-find-theyre-watching-reruns.html |date=March 5, 2015 |work=[[New York Times]] |accessdate=March 5, 2015 }}</ref>  ([[Classical physics]] also predicts the bending of light, but only half of that predicted by general relativity.)<ref>Cf. {{Harvnb|Kennefick|2005}} for the classic early measurements by the [[Arthur Eddington|Eddington]] expeditions; for an overview of more recent measurements, see {{Harvnb|Ohanian|Ruffini|1994|loc=ch. 4.3}}. For the most precise direct modern observations using quasars, cf. {{Harvnb|Shapiro|Davis|Lebach|Gregory|2004}}</ref>

Although Einstein made unpublished calculations on the subject in 1912,<ref name="origin of the idea">{{Cite journal | arxiv=0704.0963 | author1=Tilman Sauer | title=Nova Geminorum 1912 and the Origin of the Idea of Gravitational Lensing | year=2008 | doi=10.1007/s00407-007-0008-4 | volume=62 | issue=1 | journal=Archive for History of Exact Sciences | pages=1–22}}</ref> [[Orest Khvolson]] (1924)<ref name="Early History of Gravitational Lensing">{{cite web|url=http://www.nd.edu/~hps/turner.pdf|title=The Early History of Gravitational Lensing|first=Christina|last=Turner|date=February 14, 2006|url-status=dead|archiveurl=https://web.archive.org/web/20080725085534/http://www.nd.edu/%7Ehps/turner.pdf|archivedate=July 25, 2008}}</ref> and Frantisek Link (1936)<ref>{{cite book |title=General Relativity, Cosmology and Astrophysics: Perspectives 100 years after Einstein's stay in Prague |edition=illustrated |first1=Jiří |last1=Bičák |first2=Tomáš |last2=Ledvinka |publisher=Springer |year=2014 |isbn=9783319063492 |pages=49–50 |url=https://books.google.com/books?id=Ax0qBAAAQBAJ&pg=PA49}}</ref> are generally credited with being the first to discuss the effect in print. However, this effect is more commonly associated with Einstein, who published an article on the subject in 1936.<ref name=":0" />

[[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 QSO]] SBS 0957+561.

==Description==
[[File:Artist's impression of gravitational lensing of a distant merger.ogv|thumb|left|Gravitational lensing – intervening galaxy modifies appearance of a galaxy far behind it (video; artist's concept).]]
[[File:Gravitational lensing of distant star-forming galaxies (schematic) -vid-.webm|thumb|left|This schematic image shows how light from a distant galaxy is distorted by the gravitational effects of a foreground galaxy, which acts like a lens and makes the distant source appear distorted, but magnified, forming characteristic rings of light, known as Einstein rings.]]
[[File:Gravitational lensing of distant star-forming galaxies (schematic) 2.webm|thumb|An analysis of the distortion of SDP.81 caused by this effect has revealed star-forming clumps of matter.]]

Unlike an [[lens (optics)|optical lens]], a gravitational lens produces a maximum deflection of light that passes closest to its center, and a minimum deflection of light that travels furthest from its center. Consequently, a gravitational lens has no single [[focus (optics)|focal point]], but a focal line.  The term "lens" in the context of gravitational light deflection was first used by O.J. Lodge, who remarked that it is "not permissible to say that the solar gravitational field acts like a lens, for it has no focal length".<ref name="Schneider, Peter; Ehlers, Jürgen; Falco, Emilio E. 1992">{{cite book | title = Gravitational Lenses |author1=Schneider, Peter |author2=Ehlers, Jürgen |author3=Falco, Emilio E. | publisher = Springer-Verlag Berlin Heidelberg New York Press | date = 1992 | isbn =  978-3-540-97070-5}}</ref> If the (light) source, the massive lensing object, and the observer lie in a straight line, the original light source will appear as a ring around the massive lensing object. If there is any misalignment, the observer will see an arc segment instead. This phenomenon was first mentioned in 1924 by the [[St. Petersburg]] physicist [[Orest Chwolson]],<ref>[http://www.abc.net.au/science/k2/moments/gmis9737.htm Gravity Lens – Part 2 (Great Moments in Science, ABS Science)]</ref> 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, where the lensing mass is complex (such as a [[galaxy group]] or [[galaxy cluster|cluster]]) and does not cause a spherical distortion of spacetime, the source will resemble partial arcs scattered around the lens. The observer may then see multiple distorted images of the same source; the number and shape of these depending upon the relative positions of the source, lens, and observer, and the shape of the gravitational well of the lensing object.<ref>[http://astroreview.com/issue/2012/article/black-hole-horizons-and-how-they-begin Dieter Brill, "Black Hole Horizons and How They Begin", Astronomical Review (2012); Online Article, cited Sept.2012.]</ref>

There are three classes of gravitational lensing:<ref name="Schneider, Peter; Ehlers, Jürgen; Falco, Emilio E. 1992"/><ref>{{cite book | title = The Galactic Supermassive Black Hole | author = Melia, Fulvio | authorlink = Fulvio Melia | publisher = Princeton University Press | date = 2007 | isbn = 978-0-691-13129-0 | pages = 255–256}}</ref>

1. [[Strong gravitational lensing|Strong lensing]]: where there are easily visible distortions such as the formation of [[Einstein ring]]s, arcs, and multiple images.

2. [[Weak gravitational lensing|Weak lensing]]: where the distortions of background sources are much smaller and can only be detected by analyzing large numbers of sources in a statistical way 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 centre of the lens.
By measuring the shapes and orientations of large numbers of distant galaxies, their orientations can be averaged to measure the [[Shear matrix|shear]] of the lensing field in any region. This, in turn, can be used to reconstruct the mass distribution in the area: in particular, the background distribution of [[dark matter]] can be reconstructed. Since galaxies are intrinsically elliptical and the weak gravitational lensing signal is small, a very large number of galaxies must be used in these surveys. These weak lensing surveys must carefully avoid a number of important sources of [[systematic error]]: the intrinsic shape of galaxies, the tendency of a camera's [[point spread function]] to distort the shape of a galaxy and the tendency of [[atmospheric seeing]] to distort images must be understood and carefully accounted for. The results of these surveys are important for cosmological parameter estimation, to better understand and improve upon the [[Lambda-CDM model]], and to provide a consistency check on other cosmological observations. They may also provide an important future constraint on [[dark energy]].

3. [[Gravitational microlensing|Microlensing]]: where no distortion in shape can be seen but the amount of light received from a background object changes in time. The lensing object may be stars in the [[Milky Way Galaxy|Milky Way]] in one typical case, with the background source being stars in a remote galaxy, or, in another case, an even more distant [[quasar]]. The effect is small, such that (in the case of strong lensing) even a galaxy with a mass more than 100 billion times [[solar mass|that of the Sun]] will produce multiple images separated by only a few [[arcsecond]]s. [[Galaxy cluster]]s can produce separations of several arcminutes. In both cases the galaxies and sources are quite distant, many hundreds of [[megaparsec]]s 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 survey]]s. 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.

==History==
[[File:1919 eclipse negative.jpg|right|thumb|150px|One of [[Sir Arthur Eddington|Eddington]]'s photographs of the 1919 [[solar eclipse]] experiment, presented in his 1920 paper announcing its success]]

[[Henry Cavendish]] in 1784 (in an unpublished manuscript) and [[Johann Georg von Soldner]] in 1801 (published in 1804) had pointed out that Newtonian gravity predicts that starlight will bend around a massive object<ref>{{Cite journal |author=Soldner, J. G. V. |date=1804 |title=On the deflection of a light ray from its rectilinear motion, by the attraction of a celestial body at which it nearly passes by |journal=Berliner Astronomisches Jahrbuch |pages =161–172|title-link=s:Translation:On the Deflection of a Light Ray from its Rectilinear Motion }}</ref> as had  already been supposed by [[Isaac Newton]] in 1704 in his [[The Queries|Queries]] No.1 in his book [[Opticks]].<ref name=Opticks>{{cite book|last=Newton|first=Isaac|author-link=Isaac Newton |title=Opticks: or, a treatise of the reflexions, refractions, inflexions and colours of light. Also two treatises of the species and magnitude of curvilinear figures.|date=1998|publisher=Octavo|location=Palo Alto, Calif.|isbn=978-1-891788-04-8|edition=Octavo |others=Commentary by Nicholas Humez}} (''Opticks'' was originally published in 1704).</ref> The same value as Soldner's was calculated by Einstein in 1911 based on the [[equivalence principle]] alone.<ref name="Schneider, Peter; Ehlers, Jürgen; Falco, Emilio E. 1992"/> However, Einstein noted in 1915, in the process of completing general relativity, that his (and thus Soldner's) 1911-result is only half of the correct value. Einstein became the first to calculate the correct value for light bending.<ref>{{Cite journal |author=Will, C.M.|date=2006 |title=The Confrontation between General Relativity and Experiment |journal=Living Reviews in Relativity |volume =9 |issue=1 |page=39 |doi=10.12942/lrr-2006-3|arxiv = gr-qc/0510072 |bibcode = 2006LRR.....9....3W }}</ref>

The first observation of light deflection was performed by noting the change in position of [[star]]s as they passed near the Sun on the [[celestial sphere]]. The observations were performed in 1919 by [[Sir Arthur Eddington|Arthur Eddington]], [[Frank Watson Dyson]], and their collaborators during the total [[solar eclipse]] on [[Solar eclipse of May 29, 1919|May 29]].<ref>{{cite journal| last = Dyson| first = F. W.| title = A determination of the deflection of light by the Sun's gravitational field, from observations made at the total eclipse of 29 May 1919| journal = Philosophical Transactions of the Royal Society | volume = 220A | issue = 571–581| pages = 291–333| date = 1920| author2 = Eddington, A. S. | author3 = Davidson C. | doi=10.1098/rsta.1920.0009 | bibcode=1920RSPTA.220..291D| url = https://zenodo.org/record/1432106}}</ref> The solar eclipse allowed the stars near the Sun to be observed. Observations were made simultaneously in the cities of [[Sobral, Ceará]], Brazil and in [[São Tomé and Príncipe]] on the west coast of Africa.<ref>{{cite journal| last = Stanley| first = Matthew| title = 'An Expedition to Heal the Wounds of War': The 1919 Eclipse and Eddington as Quaker Adventurer| journal = Isis | volume = 94| issue = 1| pages = 57–89| date = 2003| doi = 10.1086/376099| pmid = 12725104}}</ref> The observations demonstrated that the light from [[star]]s passing close to the [[Sun]] was slightly bent, so that stars appeared slightly out of position.<ref>{{cite journal|last=Dyson|first=F. W.|date=1 January 1920|title=A Determination of the Deflection of Light by the Sun's Gravitational Field, from Observations Made at the Total Eclipse of May 29, 1919|journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences|volume=220|issue=571–581|pages=291–333|bibcode=1920RSPTA.220..291D|doi=10.1098/rsta.1920.0009|author2=Eddington, A. S.|author3=Davidson, C.|url=https://zenodo.org/record/1432106}}</ref>

[[Image:Gravitational lens-full.jpg|thumb|left|Bending light|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.]]
[[Image:Einstein cross.jpg|thumb|In the formation known as [[Einstein's Cross]], four images of the same distant quasar appear around a foreground galaxy due to strong gravitational lensing.]]
The result was considered spectacular news and made the front page of most major newspapers. It made Einstein and his theory of general relativity world-famous. When asked by his assistant what his reaction would have been if general relativity had not been confirmed by Eddington and Dyson in 1919, Einstein said "Then I would feel sorry for the dear Lord. The theory is correct anyway."<ref>Rosenthal-Schneider, Ilse: Reality and Scientific Truth. Detroit: Wayne State University Press, 1980. p 74. (See also Calaprice, Alice: ''The New Quotable Einstein''. Princeton: Princeton University Press, 2005. p 227.)</ref> In 1912, Einstein had speculated that an observer could see multiple images of a single light source, if the light were deflected around a mass.  This effect would make the mass act as a kind of gravitational lens. However, as he only considered the effect of deflection around a single star, he seemed to conclude that the phenomenon was unlikely to be observed for the foreseeable future since the necessary alignments between stars and observer would be highly improbable. Several other physicists speculated about gravitational lensing as well, but all reached the same conclusion that it would be nearly impossible to observe.<ref name=":0">{{Cite web|url=http://www.einstein-online.info/spotlights/grav_lensing_history|title=A brief history of gravitational lensing — Einstein Online|website=www.einstein-online.info|access-date=2016-06-29|archive-url=https://web.archive.org/web/20160701154224/http://www.einstein-online.info/spotlights/grav_lensing_history|archive-date=2016-07-01|url-status=dead}}</ref>

Although Einstein made unpublished calculations on the subject,<ref name="origin of the idea"/> the first discussion of the gravitational lens in print was by Khvolson, in a short article discussing the “halo effect” of gravitation when the source, lens, and observer are in near-perfect alignment,<ref name="Early History of Gravitational Lensing" /> now referred to as the [[Einstein ring]].

In 1936, after some urging by Rudi W. Mandl, Einstein reluctantly published the short article "Lens-Like Action of a Star By the Deviation of Light In the Gravitational Field" in the journal ''Science''.<ref name=":0" />

In 1937, [[Fritz Zwicky]] first considered the case where the newly discovered [[galaxy|galaxies]] (which were called 'nebulae' at the time) could act as both source and lens, and that, because of the mass and sizes involved, the effect was much more likely to be observed.<ref>{{cite journal|title=Nebulae as Gravitational lenses|author=F. Zwicky|journal=[[Physical Review]]|year=1937|issue=4|volume=51|page=290|doi=10.1103/PhysRev.51.290|url=http://authors.library.caltech.edu/5611/1/ZWIpr37a.pdf|bibcode = 1937PhRv...51..290Z }}</ref>

In 1963 Yu. G. Klimov, S. Liebes, and [[Sjur Refsdal]] recognized independently that quasars are an ideal light source for the gravitational lens effect.<ref name="Schneider, Peter; Kochanek, Christopher; Wambsganss, Joachim">{{cite book|title=Gravitational Lensing: Strong, Weak and Micro|pages=4|author1=Schneider Peter|author2=Kochanek, Christopher|author3=Wambsganss, Joachim|publisher=Springer Verlag Berlin Heidelberg New York Press|date=2006|isbn=978-3-540-30309-1}}</ref>

It was not until 1979 that the first gravitational lens would be discovered. It became known as the "[[Twin QSO]]" since it initially looked like two identical quasistellar objects. (It is officially named [[SBS 0957+561]].) This gravitational lens was discovered by [[Dennis Walsh]], Bob Carswell, and [[Ray Weymann]] using the [[Kitt Peak National Observatory]] 2.1 meter [[telescope]].<ref>{{cite journal|last=Walsh|first=D.|author2=Carswell, R. F. |author3=Weymann, R. J. |title=0957 + 561 A, B: twin quasistellar objects or gravitational lens?|journal=Nature|date=31 May 1979|volume=279|issue=5712|pages=381–384|doi=10.1038/279381a0|bibcode = 1979Natur.279..381W|pmid=16068158}}</ref>

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 led to efforts such as [[Optical Gravitational Lensing Experiment]], or OGLE, that have characterized hundreds of such events, including those of [[OGLE-2016-BLG-1190Lb]] and [[OGLE-2016-BLG-1195Lb]].

==Explanation in terms of spacetime curvature==
{{See also|Kepler problem in general relativity}}
[[Image:Black hole lensing web.gif|thumb|left|Simulated gravitational lensing (black hole passing in front of a background galaxy).]]
In general relativity, light follows the curvature of spacetime, hence when light passes around a massive object, it is bent. This means that the light from an object on the other side will be bent towards an observer's eye, just like an ordinary lens. In General Relativity the speed of light depends on the gravitational potential (aka the metric) and this bending can be viewed as a consequence of the light traveling along a gradient in light speed.
Light rays are the boundary between the future, the spacelike, and the past regions. The gravitational attraction can be viewed as the motion of undisturbed objects in a background curved ''[[geometry]]'' or alternatively as the response of objects to a ''force'' in a flat [[geometry]]. The angle of deflection is:

:<math>\theta = \frac{4GM}{rc^2}</math>

toward the mass ''M'' at a distance ''r'' from the affected radiation, where ''G'' is the [[Gravitational constant|universal constant of gravitation]] and ''c'' is the speed of light in a vacuum. This formula is identical to the formula for weak gravitational lensing derived using [[relativistic Newtonian dynamics]] <ref name="Lens">{{Cite journal |last=Friedman |first=Y. |last2=Steiner |first2=J. M.|date=2017 |title= Gravitational Deflection in Relativistic Newtonian Dynamics |journal=Europhysics Letters |volume=117|issue=5 |pages=59001 |arxiv=1705.06967|bibcode=2017EL....11759001F |doi=10.1209/0295-5075/117/59001 }}</ref> without curving spacetime.

Since the [[Schwarzschild radius]] <math>r_\mathrm{s}</math> is defined as <math>r_\mathrm{s} = {2Gm}/{c^2}</math>, this can also be expressed in simple form as

:<math>\theta = 2 \frac{r_\mathrm{s}}{r}</math>

==Search for gravitational lenses==
<!---[[File:Heic1401a-Abell2744-20140107.jpg|thumb|[[Abell 2744]] [[galaxy cluster]] - [[Hubble Space Telescope#Frontier Fields program|Hubble Frontier Fields view]] (7 January 2014).<ref name="NASA-20140107">{{cite news |last1=Clavin |first1=Whitney |last2=Jenkins |first2=Ann |last3=Villard |first3=Ray |title=NASA's Hubble and Spitzer Team up to Probe Faraway Galaxies |url=http://www.jpl.nasa.gov/news/news.php?release=2014-007 |date=7 January 2014 |work=[[NASA]] |accessdate=8 January 2014 }}</ref>]]--->
[[File:MACS J1206.jpg|thumb|This image from the NASA/ESA Hubble Space Telescope shows the galaxy cluster [[MACS J1206]].]]

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. 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 complementing the northern hemisphere search as well as obtaining other objectives for study. If such a search is done using well-calibrated and well-parameterized instrument and data, a result similar to the northern survey can be expected. The use of the Australia Telescope 20&nbsp;GHz (AT20G) Survey data collected using the Australia Telescope Compact Array (ATCA) stands to be such a collection of data. As the data were 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&nbsp;GHz frequency in the radio domain of the electromagnetic spectrum. Due to the high frequency used, the chances of finding gravitational lenses increases as the relative number of compact core objects (e.g. 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.

[[File:Helping Hubble SDSS J0915+3826.tif|thumb|left|Galaxy cluster SDSS J0915+3826 helps astronomers to study star formation in galaxies.<ref>{{cite web |title=Helping Hubble |url=https://www.spacetelescope.org/images/potw1844a/ |website=www.spacetelescope.org |accessdate=29 October 2018}}</ref>]]

Microlensing techniques have been used to search for planets outside our solar system.  A statistical analysis of specific cases of observed microlensing over the time period of 2002 to 2007 found that most stars in the [[Milky Way]] galaxy hosted at least one orbiting planet within .5 to 10 AUs.<ref>{{Cite journal|last=Cassan|first=A.|last2=Kubas|first2=D.|last3=Beaulieu|first3=J.-P.|last4=Dominik|first4=M.|last5=Horne|first5=K.|last6=Greenhill|first6=J.|last7=Wambsganss|first7=J.|last8=Menzies|first8=J.|last9=Williams|first9=A.|title=One or more bound planets per Milky Way star from microlensing observations|journal=Nature|volume=481|issue=7380|pages=167–169|doi=10.1038/nature10684|arxiv = 1202.0903 |bibcode = 2012Natur.481..167C |year=2012}}</ref>

In a 2009 article on Science Daily a team of scientists led by a cosmologist from the U.S. Department of Energy's Lawrence Berkeley National Laboratory has made major progress in extending the use of gravitational lensing to the study of much older and smaller structures than was previously possible by stating that weak gravitational lensing improves measurements of distant galaxies.<ref>[https://www.sciencedaily.com/releases/2010/01/100119172846.htm Cosmology: Weak gravitational lensing improves measurements of distant galaxies<!-- Bot generated title -->]</ref>

Astronomers from the [[Max Planck Institute]] for Astronomy in [[Heidelberg]], [[Germany]], the results of which are accepted for publication on Oct 21, 2013 in the ''[[Astrophysical Journal Letters]]'' (arXiv.org), discovered what at the time was the most distant gravitational lens galaxy termed as [[J1000+0221]] using [[NASA]]’s [[Hubble Space Telescope]].<ref>{{cite web|last=Sci-News.com|title=Most Distant Gravitational Lens Discovered|url=http://www.sci-news.com/astronomy/science-gravitational-lens-01478.html|website=Sci-News.com|accessdate=22 October 2013|date=21 Oct 2013}}</ref><ref>{{cite journal|last=van der Wel|first=A.|display-authors=etal|title=Discovery of a Quadruple Lens in CANDELS with a Record Lens Redshift|journal=Astrophysical Journal Letters|date=2013|arxiv=1309.2826|bibcode = 2013ApJ...777L..17V |doi = 10.1088/2041-8205/777/1/L17|volume=777|issue=1|pages=L17}}</ref>  While it remains the most distant quad-image lensing galaxy known, an even more distant two-image lensing galaxy was subsequently discovered by an international team of astronomers using a combination of [[Hubble Space Telescope]] and [[Keck telescope]] imaging and spectroscopy.  The discovery and analysis of the [[IRC 0218 lens]] was published in the ''[[Astrophysical Journal Letters]]'' on June 23, 2014.<ref>{{cite journal|last=Wong|first=K.|display-authors=etal|title=Discovery of a Strong Lensing Galaxy Embedded in a Cluster at z = 1.62|journal=Astrophysical Journal Letters|date=2014|volume=789|issue=2|pages=L31|doi=10.1088/2041-8205/789/2/L31|bibcode=2014ApJ...789L..31W|arxiv = 1405.3661 }}</ref>

Research published Sep 30, 2013 in the online edition of ''[[Physical Review Letters]]'', led by [[McGill University]] in [[Montreal]], [[Québec]], Canada, has discovered the [[B-modes]], that are formed due to gravitational lensing effect, using [[National Science Foundation]]'s [[South Pole Telescope]] and with help from the Herschel space observatory. This discovery would open the possibilities of testing the theories of how our universe originated.<ref>{{cite journal|last=NASA/Jet Propulsion Laboratory|date=October 22, 2013|title=Long-sought pattern of ancient light detected|journal=ScienceDaily|accessdate=October 23, 2013|url=https://www.sciencedaily.com/releases/2013/10/131022101009.htm}}</ref><ref>{{cite journal|author=Hanson, D. <!---|authors=D. Hanson, S. Hoover, A. Crites, P. A. R. Ade, K. A. Aird, J. E. Austermann, J. A. Beall, A. N. Bender, B. A. Benson, L. E. Bleem, J. J. Bock, J. E. Carlstrom, C. L. Chang, H. C. Chiang, H-M. Cho, A. Conley, T. M. Crawford, T. de Haan, M. A. Dobbs, W. Everett, J. Gallicchio, J. Gao, E. M. George, N. W. Halverson, N. Harrington, J. W. Henning, G. C. Hilton, G. P. Holder, W. L. Holzapfel, J. D. Hrubes, N. Huang, J. Hubmayr, K. D. Irwin, R. Keisler, L. Knox, A. T. Lee, E. Leitch, D. Li, C. Liang, D. Luong-Van, G. Marsden, J. J. McMahon, J. Mehl, S. S. Meyer, L. Mocanu, T. E. Montroy, T. Natoli, J. P. Nibarger, V. Novosad, S. Padin, C. Pryke, C. L. Reichardt, J. E. Ruhl, B. R. Saliwanchik, J. T. Sayre, K. K. Schaffer, B. Schulz, G. Smecher, A. A. Stark, K. T. Story, C. Tucker, K. Vanderlinde, J. D. Vieira, M. P. Viero, G. Wang, V. Yefremenko, O. Zahn, M. Zemcov--->
|title=Detection of B-Mode Polarization in the Cosmic Microwave Background with Data from the South Pole Telescope|journal=Physical Review Letters|date=Sep 30, 2013|volume=111|issue=14|pages=141301|series=14|doi=10.1103/PhysRevLett.111.141301|arxiv = 1307.5830 |bibcode = 2013PhRvL.111n1301H |display-authors=etal}}</ref>
{{wide image|14-283-Abell2744-DistantGalaxies-20141016.jpg|800px|align-cap=center|[[Abell 2744]] [[galaxy cluster]] - extremely distant [[galaxies]] revealed by [[gravitational lensing]] (16 October 2014).<ref name="NASA-20140107">{{cite news |last1=Clavin |first1=Whitney |last2=Jenkins |first2=Ann |last3=Villard |first3=Ray |title=NASA's Hubble and Spitzer Team up to Probe Faraway Galaxies |url=http://www.jpl.nasa.gov/news/news.php?release=2014-007 |date=7 January 2014 |work=[[NASA]] |accessdate=8 January 2014 }}</ref><ref name="NASA-20141016">{{cite web |last=Chou |first=Felecia |last2=Weaver |first2=Donna |title=RELEASE 14-283 - NASA's Hubble Finds Extremely Distant Galaxy through Cosmic Magnifying Glass |url=http://www.nasa.gov/press/2014/october/nasa-s-hubble-finds-extremely-distant-galaxy-through-cosmic-magnifying-glass/ |date=16 October 2014 |work=[[NASA]] |accessdate=17 October 2014 }}</ref>}}

==Solar gravitational lens==
Albert Einstein predicted in 1936 that rays of light from the same direction that skirt the edges of the [[Sun]] would converge to a focal point approximately 542 [[astronomical unit|AUs]] from the Sun.<ref>{{cite journal|author= Einstein, Albert|title=Lens-Like Action of a Star by the Deviation of Light in the Gravitational Field|journal=Science|volume=84|date=1936|pages=506–507|bibcode = 1936Sci....84..506E |doi = 10.1126/science.84.2188.506|pmid=17769014|issue=2188}}</ref> Thus, a probe positioned at this distance (or greater) from the Sun could use the Sun as a gravitational lens for magnifying distant objects on the opposite side of the Sun.<ref>Eshleman, Von R. (1979). "Gravitational lens of the sun: its potential for observations and communications over interstellar distances," ''Science'',  '''205''' (4411): 1133–1135.</ref> A probe's location could shift around as needed to select different targets relative to the Sun.

This distance is far beyond the progress and equipment capabilities of space probes such as ''[[Voyager 1]]'', and beyond the known planets and dwarf planets, though over thousands of years [[90377 Sedna]] will move farther away on its highly elliptical orbit.  The high gain for potentially detecting signals through this lens, such as microwaves at the 21-cm [[hydrogen line]], led to the suggestion by [[Frank Drake]] in the early days of [[SETI]] that a probe could be sent to this distance.  A multipurpose probe SETISAIL and later [[FOCAL (spacecraft)|FOCAL]] was proposed to the ESA in 1993, but is expected to be a difficult task.<ref name="Landis">Geoffrey A. Landis, [https://arxiv.org/abs/1604.06351 "Mission to the Gravitational Focus of the Sun: A Critical Analysis,"] ArXiv, paper 1604.06351, Cornell University, 21 Apr 2016 (downloaded 30 April 2016)</ref>  If a probe does pass 542 AU, magnification capabilities of the lens will continue to act at farther distances, as the rays that come to a focus at larger distances pass further away from the distortions of the Sun's corona.<ref>{{cite book|url=https://books.google.com/books?id=nGBhKDE1SFEC&pg=PA6|title=Deep Space Flight and Communications: Exploiting the Sun as a Gravitational Lens|author=Claudio Maccone|date=2009|publisher=Springer|isbn=9783540729433}}</ref> A critique of the concept was given by Landis,<ref>Landis, Geoffrey A., “Mission to the Gravitational Focus of the Sun: A Critical Analysis,” paper AIAA-2017-1679, AIAA Science and Technology Forum and Exposition 2017, Grapevine TX, January 9–13, 2017. [https://arxiv.org/abs/1604.06351 Preprint] at arXiv.org (accessed 24 December 2016).</ref> who discussed issues including interference of the solar corona, the high magnification of the target, which will make the design of the mission focal plane difficult, and an analysis of the inherent [[spherical aberration]] of the lens.

==Measuring weak lensing==
[[File:Galaxy cluster MACS J2129-0741 and lensed galaxy MACS2129-1.jpg|thumb|Galaxy cluster MACS J2129-0741 and lensed galaxy MACS2129-1.<ref>{{cite web|title=Galaxy cluster MACS J2129-0741 and lensed galaxy MACS2129-1|url=https://www.spacetelescope.org/images/opo1726a/|website=www.spacetelescope.org|accessdate=23 June 2017}}</ref>]]
Kaiser, Squires and Broadhurst (1995),<ref name=KSB-1995>{{cite journal|last1=Kaiser|first1=Nick|last2=Squires|first2=Gordon|last3=Broadhurst|first3=Tom|title=A Method for Weak Lensing Observations|journal=The Astrophysical Journal|date=August 1995|volume=449|pages=460–475|doi=10.1086/176071|arxiv = astro-ph/9411005 |bibcode = 1995ApJ...449..460K }}</ref> Luppino & Kaiser (1997)<ref name=LK-1997>{{cite journal|last1=Luppino|first1=G. A.|last2=Kaiser|first2=Nick|title=Detection of Weak Lensing by a Cluster of Galaxies at z = 0.83|journal=The Astrophysical Journal|date=20 January 1997|volume=475|issue=1|pages=20–28|doi=10.1086/303508|arxiv = astro-ph/9601194 |bibcode = 1997ApJ...475...20L }}</ref> and Hoekstra et al. (1998) prescribed a method to invert the effects of the Point Spread Function (PSF) smearing and shearing, recovering a shear estimator uncontaminated by the systematic distortion of the PSF. This method (KSB+) is the most widely used method in weak lensing shear measurements.<ref>{{cite book |title=Statistical Challenges in Modern Astronomy IV: Proceedings of a Conference Held at Pennsylvania State University, University Park, Pennsylvania, USA, 12–15 June 2006, Volume 371 |edition=illustrated |first1=Gutti Jogesh |last1=Babu |first2=Eric D. |last2=Feigelson |publisher=Astronomical Society of the Pacific |year=2007 |isbn=978-1-58381-240-2 |page=66 |url=https://books.google.com/books?id=dHPvAAAAMAAJ}}</ref><ref>{{cite book |title=A Pan-Chromatic View of Clusters of Galaxies and the Large-Scale Structure |edition=illustrated |first1=Manolis |last1=Plionis |first2=O. |last2=López-Cruz |first3=D. |last3=Hughes |publisher=Springer Science & Business Media |year=2008 |isbn=978-1-4020-6940-6 |page=233 |url=https://books.google.com/books?id=TnovKp-nJuMC&pg=PA233}}</ref>
 
Galaxies have random rotations and inclinations. As a result, the shear effects in weak lensing need to be determined by statistically preferred orientations. The primary source of error in lensing measurement is due to the convolution of the PSF with the lensed image. The KSB method measures the ellipticity of a galaxy image. The shear is proportional to the ellipticity. The objects in lensed images are parameterized according to their weighted quadrupole moments. For a perfect ellipse, the weighted quadrupole moments are related to the weighted ellipticity. KSB calculate how a weighted ellipticity measure is related to the shear and use the same formalism to remove the effects of the PSF.<ref>{{cite book |title=Gravitational Lensing: An Astrophysical Tool |edition=illustrated |first1=Frederic Courbin, Dante Minniti |last1=Frederic Courbin, Dante Minniti |publisher=Springer |year=2008 |isbn=978-3-540-45857-9 |page=69 |url=https://books.google.com/books?id=TsxrCQAAQBAJ&pg=PA69}}</ref>

KSB's primary advantages are its mathematical ease and relatively simple implementation. However, KSB is based on a key assumption that the PSF is circular with an anisotropic distortion. This is a reasonable assumption for cosmic shear surveys, but the next generation of surveys (e.g. [[Large Synoptic Survey Telescope|LSST]]) may need much better accuracy than KSB can provide.

==Gallery==
{{Commons category|Gravitational lensing}}
<gallery>
Image:The Sunburst Arc PSZ1 G311.65-18.48.jpg|Sunburst Arc galaxy.<ref>{{cite web |title=Hubble Captures a Dozen Sunburst Arc Doppelgangers |url=https://spacetelescope.org/news/heic1920/ |website=www.spacetelescope.org |accessdate=11 November 2019 |language=en}}</ref>
Image:Hubble’s view on distant quasar J043947.08+163415.7.tif|Gravitationally lensed Quasar.<ref>{{cite web |title=Hubble sees the brightest quasar in the early Universe |url=https://www.spacetelescope.org/news/heic1902/ |website=www.spacetelescope.org |accessdate=10 January 2019 |language=en}}</ref>
Image:On the hunt for newborn stars.tif|In SDSS J0952+3434, the lower arc-shaped galaxy has the characteristic shape of a galaxy that has been gravitationally lensed.<ref>{{cite web |title=On the hunt for newborn stars |url=https://www.spacetelescope.org/images/potw1842a/ |website=www.spacetelescope.org |accessdate=15 October 2018}}</ref>
Image:Warped and distorted SDSS J1050+0017.jpg|Warped and distorted around SDSS J1050+0017.<ref>{{cite web |title=Warped and distorted |url=https://www.spacetelescope.org/images/potw1839a/ |website=www.spacetelescope.org |accessdate=24 September 2018}}</ref>
Image:Stretched out image of distant galaxy.jpg|Galaxy [[SPT0615-JD]] existed when the Universe was just 500 million years old.<ref>{{cite web|title=Stretched out image of distant galaxy|url=https://www.spacetelescope.org/images/opo1802a/|website=www.spacetelescope.org|accessdate=16 January 2018}}</ref>
Image:Cosmic snake pregnant with stars.tif|Regions of intense star formation that appear warped by the effect of gravitational lensing.<ref>{{cite web|title=Cosmic snake pregnant with stars|url=http://www.spacetelescope.org/images/potw1747a/|website=www.spacetelescope.org|accessdate=20 November 2017}}</ref>
Image:Hubble captures gallery of ultra-bright galaxies.jpg|The lensing phenomenon allows for features as small as about 100 light-years or less.<ref>{{cite web|title=Hubble captures gallery of ultra-bright galaxies|url=https://www.spacetelescope.org/images/opo1724a/|website=www.spacetelescope.org|accessdate=8 June 2017}}</ref>
Image:Detailed look at a gravitationally lensed supernova.jpg|Detailed look at a gravitationally lensed [[type Ia supernova]] [[iPTF16geu]].<ref>{{cite web|title=Detailed look at a gravitationally lensed supernova|url=https://www.spacetelescope.org/images/heic1710a/|website=www.spacetelescope.org|accessdate=21 April 2017}}</ref>
Image:HST-Smiling-GalaxyClusterSDSS-J1038+4849-20150210.jpg|"Smiley" image of [[galaxy cluster]] (SDSS J1038+4849) & gravitational lensing (an [[Einstein ring]]) ([[Hubble Space Telescope|HST]]).<ref name="NASA-20150210">{{cite web |last1=Loff |first1=Sarah |last2=Dunbar |first2=Brian |title=Hubble Sees A Smiling Lens |url=http://www.nasa.gov/content/hubble-sees-a-smiling-lens/ |date=February 10, 2015 |work=[[NASA]] |accessdate=February 10, 2015 }}</ref>
Image:Gravitationell-lins-4.jpg|[[Abell 1689]] - actual gravitational lensing effects ([[Hubble Space Telescope]]).
Image:COSMOS 3D dark matter map.jpg|[[Dark matter]] distribution - weak gravitational lensing ([[Hubble Space Telescope]]).
Image:The most distant gravitational lens yet discovered.jpg|Gravitational lens discovered at [[redshift]] z = 1.53.<ref>{{cite news|title=Most distant gravitational lens helps weigh galaxies|url=http://www.spacetelescope.org/news/heic1319/|accessdate=18 October 2013|newspaper=ESA/Hubble Press Release}}</ref>
File:EinsteinLeiden4.jpg|Gravitational lens with the Einstein equations, [[Museum Boerhaave]], Leiden
</gallery>
{{wide image|Gravitationally-lensed distant star-forming galaxy.jpg|800px|align-cap=center|Gravitationally-lensed distant star-forming galaxies.<ref>{{cite news|title=ALMA Rewrites History of Universe's Stellar Baby Boom|url=http://www.eso.org/public/news/eso1313/|accessdate=2 April 2013|newspaper=ESO}}</ref>}}

==See also==
* [[Gravitational lensing formalism]]
* [[Strong gravitational lensing]]
* [[Weak gravitational lensing]]
* [[Gravitational microlensing]]
* [[Einstein cross]]
* [[Einstein ring]]
* [[SN Refsdal]]

==Historical papers and references==
* {{cite journal | first = O | last = Chwolson | title = Über eine mögliche Form fiktiver Doppelsterne | journal = Astronomische Nachrichten | volume = 221 | issue = 20 | pages = 329–330 | date = 1924 | bibcode = 1924AN....221..329C | doi = 10.1002/asna.19242212003}}
* {{cite journal | first = Albert | last = Einstein | authorlink = Albert Einstein | title = Lens-like Action of a Star by the Deviation of Light in the Gravitational Field | journal = Science | volume = 84 | pages = 506–7 | date = 1936 | doi = 10.1126/science.84.2188.506 | pmid = 17769014 | issue = 2188 | jstor=1663250|bibcode = 1936Sci....84..506E }}
* {{cite journal | first = Jürgen | last = Renn | author2 = Tilman Sauer | author3 = John Stachel | title = The Origin of Gravitational Lensing: A Postscript to Einstein's 1936 Science paper | journal = Science | volume = 275 | pages = 184–6 | date = 1997 | doi = 10.1126/science.275.5297.184 | pmid =8985006 | issue = 5297|bibcode = 1997Sci...275..184R }}

==References==
;Notes
{{Reflist|30em}}

;Bibliography
* "''[http://www.sciencenews.org/view/generic/id/33082/title/Math_Trek__Accidental_astrophysicists Accidental Astrophysicists]''". Science News, June 13, 2008.
* "''[https://web.archive.org/web/20101210135526/http://www.cinespa.ucr.ac.cr/software/xfgl/index.html XFGLenses]''". A Computer Program to visualize Gravitational Lenses, Francisco Frutos-Alfaro
* "''[https://web.archive.org/web/20070929124804/http://www.btinternet.com/~Boughen/G-LenS G-LenS]''". A Point Mass Gravitational Lens Simulation, Mark Boughen.
* Newbury, Pete, "''[http://www.iam.ubc.ca/old_pages/newbury/lenses/lenses.html Gravitational Lensing]{{dead link|date=January 2018 |bot=InternetArchiveBot |fix-attempted=yes }}''". Institute of Applied Mathematics, The University of British Columbia.
* Cohen, N., "Gravity's Lens: Views of the New Cosmology", Wiley and Sons, 1988.
* "''[http://cfa-www.harvard.edu/~rschild/qgl.html Q0957+561 Gravitational Lens]''". Harvard.edu.
* Bridges, Andrew, "''[http://www.signonsandiego.com/news/science/20040215-1033-ca-farthestgalaxy.html Most distant known object in universe discovered]''". [[Associated Press]]. February 15, 2004. (Farthest galaxy found by gravitational lensing, using Abell 2218 and Hubble Space Telescope.)
* [https://web.archive.org/web/20070310222247/http://sciencecareers.sciencemag.org/career_development/previous_issues/articles/2006_05_12/analysing_corporations_and_the_cosmos/(parent)/12100 Analyzing Corporations ... and the Cosmos] An unusual career path in gravitational lensing.
* "''[http://cfa-www.harvard.edu/castles HST images of strong gravitational lenses]''". Harvard-Smithsonian Center for Astrophysics.
* "''[https://arxiv.org/abs/astro-ph/0404309 A planetary microlensing event]''" and "''[https://arxiv.org/abs/astro-ph/0505451 A Jovian-mass Planet in Microlensing Event OGLE-2005-BLG-071]''", the first [[Extrasolar planet|extra-solar planet]] detections using microlensing.
* [http://xstructure.inr.ac.ru/x-bin/theme3.py?level=2&index1=-188353 Gravitational lensing on arxiv.org]
* [http://www.aoc.nrao.edu/~smyers/class.html NRAO CLASS home page]
* [http://www.atnf.csiro.au/research/AT20G AT20G survey]
* [http://cdsads.u-strasbg.fr/full/1981Ap%26SS..78..199B ''A diffraction limit on the gravitational lens effect'' (Bontz, R. J. and Haugan, M. P. "Astrophysics and Space Science" vol. 78, no. 1, p. 199-210. August 1981)]

;Further reading
* {{cite journal
 | author = Blandford & Narayan
 | date = 1992
 | title = Cosmological applications of gravitational lensing
 | journal = Annual Review of Astronomy and Astrophysics
 | pages = 311–358
 | issue = 1
 | volume = 30
 | bibcode = 1992ARA&A..30..311B
 | doi = 10.1146/annurev.aa.30.090192.001523
 | last2 = Narayan
 | first2 = R
}}
* {{cite journal|title=Weak Gravitational Lensing|author1=Matthias Bartelmann|author2=Peter Schneider|date=2000-08-17|url=http://www.mpa-garching.mpg.de/Lenses/WLRevEls.pdf|url-status=dead|archiveurl=https://web.archive.org/web/20070226035150/http://www.mpa-garching.mpg.de/Lenses/WLRevEls.pdf|archivedate=2007-02-26}}
* {{Cite journal | first1=Dmitry | last1=Khavinson | first2=Genevra | last2=Neumann | url=http://www.ams.org/notices/200806/tx080600666p.pdf | title=From Fundamental Theorem of Algebra to Astrophysics: A "Harmonious" Path | journal=Notices of the AMS |date=June–July 2008 | volume=55 | issue=6 | pages=666–675 }}.
* {{cite book | first1=Arlie O. | last1=Petters | authorlink = Arlie Petters | first2=Harold | last2=Levine | first3=Joachim | last3=Wambsganss | url=https://www.springer.com/birkhauser/physics/book/978-0-8176-3668-5 | title=Singularity Theory and Gravitational Lensing | series=Progress in Mathematical Physics | volume=21 | publisher=Birkhäuser | date=2001 }}
* [http://www.matnat.uio.no/proveforelesninger/g-i/haugan-stein-vidar-hagfors.xml ''Tools for the evaluation of the possibilities of using parallax measurements of gravitationally lensed sources'' (Stein Vidar Hagfors Haugan. June 2008)]

==External links==
{{Commons category|Gravitational lensing}}
* [http://www.pdxjustice.org/node/54 Video: Evalyn Gates – ''Einstein's Telescope: The Search for Dark Matter and Dark Energy in the Universe''], presentation in Portland, Oregon, on April 19, 2009, from the author's recent book tour.
* [http://www.astronomycast.com/stars/episode-37-gravitational-lensing/ Audio: Fraser Cain and Dr. Pamela Gay – Astronomy Cast: Gravitational Lensing, May 2007]

==Featured in science-fiction works==
* [http://www.davidbrin.com/existence.html ''Existence'', by David Brin, 2012]

{{Relativity}}

{{Authority control}}

{{DEFAULTSORT:Gravitational Lens}}
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