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| {{Gravitational Lensing}}
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| [[Image:Einstein Rings.jpg|thumb||Some observed Einstein rings]]
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| In observational [[astronomy]] an '''Einstein ring''' is the deformation of the light from a source (such as a [[galaxy]] or [[star]]) into a ring through [[gravitational lens]]ing of the source's light by an object with an extremely large mass (such as another galaxy, or a [[black hole]]). This occurs when the source, lens and observer are all aligned. The first complete Einstein ring, designated B1938+666, was discovered by collaboration between astronomers at the [[University of Manchester]] and [[Nasa|NASA's]] [[Hubble Space Telescope]] in 1998.<ref>{{cite web | url=http://www.merlin.ac.uk/press/PR9801/press.html | title=A Bull's Eye for MERLIN and the Hubble | publisher=University of Manchester | date=27 March 1998}}</ref>
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| == Introduction ==
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| Gravitational lensing is predicted by [[Albert Einstein]]'s theory of [[general relativity]]. Instead of light from a source traveling in a straight line (in three dimensions), it is bent by the presence of a massive body, which distorts [[spacetime]]. An Einstein Ring is a special case of gravitational lensing, caused by the exact alignment of the source, lens and observer. This results in a symmetry around the lens, causing a ring-like structure.
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| [[Image:Gravitational lens geometry.svg|thumb|The geometry of a gravitational lens]]
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| The size of an Einstein ring is given by the [[Einstein radius]]. In [[radians]], it is
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| :<math>\theta_E = \sqrt{\frac{4GM}{c^2}\;\frac{d_{LS}}{d_L d_S}},</math> | | '''MathML''' |
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| where
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| : <math>G</math> is the [[gravitational constant]],
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| : <math>M</math> is the mass of the lens,
| | :<math forcemathmode="source">E=mc^2</math> --> |
| : <math>c</math> is the [[speed of light]], | |
| : <math>d_L</math> is the [[angular diameter distance]] to the lens,
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| : <math>d_S</math> is the [[angular diameter distance]] to the source, and
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| : <math>d_{LS}</math> is the [[angular diameter distance]] between the lens and the source.
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| Note that, over cosmological distances <math>d_{LS}\ne d_S-d_L</math> in general.
| | <span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples]. |
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| == History == | | ==Demos== |
| The bending of light by a gravitational body was predicted by Einstein in 1912, a few years before the publication of General Relativity in 1916 (see Renn et al. 1997). The ring effect was first mentioned in [[academic journal|academic literature]] by [[Orest Chwolson]] in 1924. [[Albert Einstein]] remarked upon this effect in 1936 in a paper prompted by a letter by a Czech engineer, R W Mandl [http://www.slac.stanford.edu/pubs/beamline/31/1/31-1-maurer.pdf], but stated
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| {{quote|Of course, there is no hope of observing this phenomenon directly. First, we shall scarcely ever approach closely enough to such a central line. Second, the angle β will defy the resolving power of our instruments.|''Science'' vol 84 p 506 1936}}
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| In this statement, β is the Einstein Radius currently denoted by <math>\theta_E</math> (see above). However, Einstein was only considering the chance of observing Einstein rings produced by stars, which is low; however, the chance of observing those produced by larger lenses such as galaxies or black holes is higher since the angular size of an Einstein ring increases with the mass of the lens.
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| === Known Einstein rings ===
| | Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]: |
| Hundreds of gravitational lenses are currently known. About half a dozen of them are partial Einstein rings with diameters up to an [[arcsecond]], although as either the mass distribution of the lenses is not perfectly axially symmetrical, or the source, lens and observer are not perfectly aligned, we have yet to see a perfect Einstein ring. Most rings have been discovered in the radio range.
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| The first Einstein ring was discovered by Hewett et al. (1988), who observed the radio source MG1131+0456 using the [[Very Large Array]].<ref>{{cite web | url=http://www.nrao.edu/pr/2000/vla20/background/ering/ | title=Discovery of the First "Einstein Ring" Gravitational Lens | publisher=[[NRAO]] | date=2000 | accessdate=2012-02-08}}</ref> The first complete Einstein ring to be discovered was B1938+666, which was found by King et al. (1998) via optical follow-up with the Hubble Space Telescope of a gravitational lens imaged with [[MERLIN]].<ref>{{cite web | url=http://www.merlin.ac.uk/press/PR9801/press.html | title=A Bull's Eye for MERLIN and the Hubble | publisher=University of Manchester | date=27 March 1998}}</ref><ref>{{cite news| url=http://query.nytimes.com/gst/fullpage.html?res=9906EFDF103BF932A05750C0A96E958260 | work=The New York Times | title='Einstein Ring' Caused by Space Warping Is Found | first=Malcolm W. | last=Browne | date=1998-03-31 | accessdate=2010-05-01}}</ref>
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| | ** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]] |
| ! Location ([[Right ascension|RA]], [[Declination|dec]])
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)] |
| ! Radius
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)] |
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| ! [[Optical]]/[[radio frequency|radio]]
| | ** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]]. |
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| |- | | ** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode. |
| | [[FOR J0332-3557]] | |
| | 03<sup>h</sup>:32<sup>m</sup>:59<sup>s</sup>:94, -35°57'51".7, [[J2000]]
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| | 1".48 | |
| | Partial, 260° | |
| | Radio | |
| | Cabanac (2005)
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| | [[SDSSJ0946+1006]]
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| | 09<sup>h</sup> 46<sup>m</sup> 56.<sup>s</sup>68, +10° 06' 52."6 [[J2000]]
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| | Optical | |
| | Gavazzi (2008) | |
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| | [[MG1131 + 0456]] | |
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| {{Expand section|date=June 2008}}
| | ==Test pages == |
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| == Extra rings ==
| | To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages: |
| [[Image:SDSSJ0946+1006.jpg|thumb|left|SDSSJ0946+1006 is a Double Einstein Ring. Credit: [[Hubble Space Telescope|HST]]/[[NASA]]/[[ESA]]]] | | *[[Displaystyle]] |
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| Using the [[Hubble Space Telescope]], a double ring has been found by [[Raphael Gavazzi]] of the [[STScI]] and [[Tommaso Treu]] of the [[University of California, Santa Barbara]]. This arises from the light from three galaxies at distances of 3, 6 and 11 billion light years. Such rings help in understanding the distribution of [[dark matter]], [[dark energy]], the nature of distant [[galaxies]], and the [[curvature of the universe]]. The odds of finding such a double ring are 1 in 10,000. Sampling 50 suitable double rings would provide astronomers with a more accurate measurement of the dark matter content of the universe and the equation of state of the dark energy to within 10 percent precision.<ref>{{cite web |url=http://hubblesite.org/newscenter/archive/releases/2008/04/full/ |title=Hubble Finds Double Einstein Ring |accessdate=2008-01-26 |work=http://hubblesite.org |publisher=Space Telescope Science Institute }}</ref>
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| === A simulation ===
| | ==Bug reporting== |
| [[Image:EnsteinRingZoomOptimised.gif|thumb|Einstein rings near a black hole]]
| | If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de . |
| To the right is a simulation depicting a zoom on a [[Schwarzschild metric|Schwarzschild black hole]] in front of the [[Milky Way]]. The first Einstein ring corresponds to the most distorted region of the picture and is clearly depicted by the [[Disc (galaxy)|galactic disc]]. The zoom then reveals a series of 4 extra rings, increasingly thinner and closer to the black hole shadow. They are easily seen through the multiple images of the galactic disk. The odd-numbered rings correspond to points which are behind the black hole (from the observer's position) and correspond here to the bright yellow region of the galactic disc (close to the galactic center), whereas the even-numbered rings correspond to images of objects which are behind the observer, which appear bluer since the corresponding part of the galactic disc is thinner and hence dimmer here.
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| {{clearleft}}
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| == See also == | |
| * [[Einstein cross]]
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| * [[Einstein radius]]
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| * [[Gravitational lens]]
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| == References ==
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| {{reflist}}
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| === Journals ===
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| <div class="references-small">
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| * {{cite journal | first = R. A. | last = Cabanac | coauthors = et al. | title = Discovery of a high-redshift Einstein ring | year = 2005 | journal = Astronomy and Astrophysics. | volume = 436 | issue = 2 | pages = L21–L25 | url = http://www.arxiv.org/astro-ph/0504585 | doi = 10.1051/0004-6361:200500115 | bibcode=2005A&A...436L..21C|arxiv = astro-ph/0504585 }} (refers to FOR J0332-3357)
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| * {{cite journal | first = O | last = Chwolson | title = Über eine mögliche Form fiktiver Doppelsterne | journal = Astronomische Nachrichten | volume = 221 | issue = 20 | pages = 329 | year = 1924 | bibcode = 1924AN....221..329C | doi = 10.1002/asna.19242212003}} (The first paper to propose rings)
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| * {{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 = 506–507 | year = 1936 | url = http://www.to.infn.it/~zaninett/projects/storia/einstein1936.pdf | doi = 10.1126/science.84.2188.506 | pmid = 17769014 | issue = 2188|bibcode = 1936Sci....84..506E }} (The famous Einstein Ring paper)
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| * {{cite journal | first=J | last=Hewitt | title=Unusual radio source MG1131+0456 - A possible Einstein ring | journal=Nature | volume=333 | pages=537 | year=1988 | bibcode=1988Natur.333..537H|doi = 10.1038/333537a0 }}
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| * {{cite journal | first = Jurgen | last = Renn | coauthors = Tilman Sauer and John Stachel | title =The Origin of Gravitational Lensing: A Postscript to Einstein's 1936 Science paper | journal = Science | volume = 275 | pages = 184–186 | year = 1997 | doi = 10.1126/science.275.5297.184 | pmid =8985006 | issue = 5297|bibcode = 1997Sci...275..184R }}
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| * {{cite journal | first=L | last=King | title=A complete infrared Einstein ring in the gravitational lens system B1938 + 666 | journal=MNRAS | volume = 295 | pages=41 | year=1998 | bibcode=1998MNRAS.295L..41K|arxiv = astro-ph/9710171 |doi = 10.1046/j.1365-8711.1998.295241.x }}
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| </div>
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| === News ===
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| * {{cite news | url = http://www.universetoday.com/am/publish/perfect_einstein_ring.html | title = Nearly perfect Einstein ring discovered | publisher = Universe Today | first = Jeff | last = Barbour | date = 2005-04-29 | accessdate = 2006-06-15}} (refers to FOR J0332-3357)
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| * {{cite news | url = http://www.sciencedaily.com/releases/2008/01/080110102319.htm | title = Hubble Finds Double Einstein Ring | publisher = Science Daily | date = 2008-01-12 | accessdate = 2008-01-14}}
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| </div>
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| == Further reading ==
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| * {{cite journal | first = C.S. | last = Kochanek | coauthors = C.R. Keeton and B.A. McLeod | title = The Importance of Einstein Rings | journal = The Astrophysical Journal | year = 2001 | volume = 547 | issue = 1 | pages = 50–59 | arxiv = astro-ph/0006116 | doi = 10.1086/318350 | bibcode=2001ApJ...547...50K}}
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| {{Commons category|Einstein Rings}}
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| {{DEFAULTSORT:Einstein Ring}}
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| [[Category:Effects of gravitation]]
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| [[Category:Albert Einstein|Ring]]
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| [[Category:Optical phenomena]]
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| [[Category:Gravitational lensing]]
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| [[ar:حلقة آينشتاين]]
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