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52-413: If a compact object (which may be dark or bright) is located very close to the line of sight to a background star, then gravitational lensing causes the star to appear to split into two images on opposite sides of the compact object (or a complete ring if the alignment is almost perfect). Microlensing refers to the special case of lensing where the two images are too close to be seen as separate objects in

104-428: A Solar Gravitational Lens Mission. The lens could reconstruct the exoplanet image with ~25 km-scale surface resolution, enough to see surface features and signs of habitability. Kaiser, Squires and Broadhurst (1995), Luppino & Kaiser (1997) 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

156-477: A point particle , that bends light from a distant source as it travels toward an observer. The amount of gravitational lensing is described by Albert Einstein 's general theory of relativity . If light is treated as corpuscles travelling at the speed of light , Newtonian physics also predicts the bending of light, but only half of that predicted by general relativity. Orest Khvolson (1924) and Frantisek Link (1936) are generally credited with being

208-427: A constant speed of light along the parallel direction, d r ∥ ≈ c d t {\displaystyle dr_{\parallel }\approx c\,dt} , and that the light is only being deflected a small amount. After plugging these assumptions into the above equation and further simplifying, one can solve for the velocity boost in the perpendicular direction. The angle of deflection between

260-448: A corpuscle of mass m {\displaystyle m} feels a force where r {\displaystyle r} is the lens-corpuscle separation. If we equate this force with Newton's second law , we can solve for the acceleration that the light undergoes: The light interacts with the lens from initial time t = 0 {\displaystyle t=0} to t {\displaystyle t} , and

312-525: A lens, for it has no focal length". 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 (provided the lens has circular symmetry). 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 Khvolson , and quantified by Albert Einstein in 1936. It

364-406: A massive object as had already been supposed by Isaac Newton in 1704 in his Queries No.1 in his book Opticks . The same value as Soldner's was calculated by Einstein in 1911 based on the equivalence principle alone. 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

416-419: 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 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

468-481: A number of notable discoveries documented in around 35 scientific papers published between 1993 and 2003: the most important results were firstly, upper limits on the contribution of MACHOs to the dark matter in the Milky Way: no more than xx percent can be composed of MACHOs between xx solar masses () and xx solar masses; secondly, confirmation that microlensing occurs as expected, based on large samples of events with

520-464: A professor in 1891. He authored works on electricity , magnetism , photometry , and actinometry . He proposed the designs of an actinometer and a pyrheliometer , which would be used by the Russian weather stations for many years. After 1896, Khvolson was mainly engaged in compiling the five-volume Physics Course (Курс физики), which would improve immensely the teaching of physics throughout

572-611: A search is done using well-calibrated and well-parameterized instruments and data, a result similar to the northern survey can be expected. The use of the Australia Telescope 20 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

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624-598: A short article discussing the "halo effect" of gravitation when the source, lens, and observer are in near-perfect alignment, 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 . In 1937, Fritz Zwicky first considered

676-406: A telescope, but the time-varying geometry (as the source and lens move) causes the apparent brightness (the sum of the two images) to vary with time; this variation has a characteristic shape which can be calculated theoretically. Microlensing is predicted and observed to be very rare, typically less than 1 star per million microlensed at any given moment in time, but it is a powerful technique because

728-461: 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. LSST ) may need much better accuracy than KSB can provide. Orest Khvolson Orest Danilovich Khvolson or Chwolson ( Russian : Орест Данилович Хвольсон ) (November 22 ( N.S. December 4), 1852 – May 11, 1934)

780-451: Is defined as v e = 2 G m / r = β e c {\textstyle v_{\text{e}}={\sqrt {2Gm/r}}=\beta _{\text{e}}c} , this can also be expressed in simple form as 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

832-399: 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

884-410: Is usually referred to in the literature as an Einstein ring , since Khvolson 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 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

936-436: The Einstein ring ), although he did not explicitly discuss the use of the ring as lens. The concept of gravitational lenses did not get much attention until 1936, when Albert Einstein wrote about the gravitational lens effect. The "halo" effect of a gravitational lens, where one source (sun or galaxy) produces a ring around another source is referred to as an Chwolson ring, or Einstein ring. He became an honorary member of

988-707: The Large Magellanic Cloud or 100 fields in the Galactic Bulge on a regular basis, with each field observed from twice per night to weekly, depending on field priority and season. From this image data, light curves (brightness vs time) were constructed for over 8 million stars in the LMC, and 15 million stars in the Bulge; large computer searches were then run to find brightening events characteristic of microlensing, and also variable stars. The project made

1040-483: The Milky Way galaxy hosted at least one orbiting planet within 0.5 to 10 AU. In 2009, weak gravitational lensing was used to extend the mass-X-ray-luminosity relation to older and smaller structures than was previously possible to improve measurements of distant galaxies. As of 2013 the most distant gravitational lens galaxy, J1000+0221 , had been found using NASA 's Hubble Space Telescope . While it remains

1092-512: 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. 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

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1144-483: The OGLE and MOA projects, with the main focus after 2000 changing towards microlensing as a method for detection of exoplanets . Microlensing planet searches are especially sensitive to low-mass exoplanets and those in fairly wide orbits (many astronomical units, beyond the snow-line), and are also the only way of detecting "orphan planets" ejected from their parent systems; so microlensing planet searches are complementary to

1196-480: The Sun's corona. A critique of the concept was given by Landis, 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. In 2020, NASA physicist Slava Turyshev presented his idea of Direct Multipixel Imaging and Spectroscopy of an Exoplanet with

1248-594: 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

1300-419: The better-known radial velocity and transit methods. As of 2017 the new Korean Microlensing Telescope Network ( KMTNet ) is a new-generation microlensing survey. The future NASA NGRST space mission (planned launch c.  2027 ) includes a substantial microlensing planet survey as one of its key projects. Gravitational lensing A gravitational lens is matter, such as a cluster of galaxies or

1352-491: 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 . Newton wondered whether light, in

1404-406: The case where the newly discovered 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. In 1963 Yu. G. Klimov, S. Liebes, and Sjur Refsdal recognized independently that quasars are an ideal light source for the gravitational lens effect. It was not until 1979 that

1456-470: The corpuscle’s initial and final trajectories is therefore (see, e.g., M. Meneghetti 2021) Although this result appears to be half the prediction from general relativity, classical physics predicts that the speed of light c {\displaystyle c} is observer-dependent (see, e.g., L. Susskind and A. Friedman 2018) which was superseded by a universal speed of light in special relativity . In general relativity, light follows

1508-592: The country and remain a principal textbook in universities for years to come. It was even translated into the German , French , and Spanish languages. His most noted accomplishment was in 1924, when he published about gravitational lenses in Astronomische Nachrichten , a scientific journal on astronomy. In the article he mentioned the "halo effect" of gravitation when the source, lens, and observer are in near-perfect alignment (now referred to as

1560-440: 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 path of light depends on the shape of space (i.e. the metric). The gravitational attraction can be viewed as the motion of undisturbed objects in a background curved geometry or alternatively as

1612-413: The dear Lord. The theory is correct anyway." 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

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1664-448: The early days of SETI that a probe could be sent to this distance. A multipurpose probe SETISAIL and later FOCAL was proposed to the ESA in 1993, but is expected to be a difficult task. 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

1716-428: The effect relies only on the gravity of the lensing object, rather than its light: therefore it is sensitive to completely dark or very faint objects including black holes, substellar brown dwarfs and remnants of dead stars (e.g. old white dwarfs and neutron stars). For these reasons, microlensing is very useful for testing whether dark matter is made of such objects. The 1.27-metre (50 in) telescope at Mt. Stromlo

1768-510: 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. KSB's primary advantages are its mathematical ease and relatively simple implementation. However, KSB

1820-582: 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 . In the 1980s, astronomers realized that the combination of CCD imagers and computers would allow

1872-399: The first to calculate the correct value for light bending. The first observation of light deflection was performed by noting the change in position of stars as they passed near the Sun on the celestial sphere . The observations were performed in 1919 by Arthur Eddington , Frank Watson Dyson , and their collaborators during the total solar eclipse on May 29 . The solar eclipse allowed

1924-482: The first to discuss the effect in print, but it is more commonly associated with Einstein, who made unpublished calculations on it in 1912 and published an article on the subject in 1936. In 1937, Fritz Zwicky posited that galaxy clusters could act as gravitational lenses, a claim confirmed in 1979 by observation of the Twin QSO SBS 0957+561. Unlike an optical lens , a point-like gravitational lens produces

1976-408: 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. Although Einstein made unpublished calculations on the subject, the first discussion of the gravitational lens in print was by Khvolson, in

2028-459: The form of corpuscles, would be bent due to gravity. The Newtonian prediction for light deflection refers to the amount of deflection a corpuscle would feel under the effect of gravity, and therefore one should read "Newtonian" in this context as the referring to the following calculations and not a belief that Newton held in the validity of these calculations. For a gravitational point-mass lens of mass M {\displaystyle M} ,

2080-550: 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. Research published Sep 30, 2013 in

2132-632: 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. Albert Einstein predicted in 1936 that rays of light from

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2184-640: The response of objects to a force in a flat geometry. The angle of deflection is 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 vacuum. Since the Schwarzschild radius r s {\displaystyle r_{\text{s}}} is defined as r s = 2 G m / c 2 {\displaystyle r_{\text{s}}=2Gm/c^{2}} , and escape velocity v e {\displaystyle v_{\text{e}}}

2236-458: The same direction that skirt the edges of the Sun would converge to a focal point approximately 542 AU from the Sun. 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. A probe's location could shift around as needed to select different targets relative to the Sun. This distance

2288-453: 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. There are three classes of gravitational lensing: Gravitational lenses act equally on all kinds of electromagnetic radiation , not just visible light, and also in non-electromagnetic radiation, like gravitational waves. Weak lensing effects are being studied for

2340-455: 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 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

2392-731: 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. The observations demonstrated that the light from stars passing close to the Sun was slightly bent, so that stars appeared slightly out of position. 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

2444-421: The systematic distortion of the PSF. This method (KSB+) is the most widely used method in weak lensing shear measurements. 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

2496-531: The theoretically predicted properties. The project also achieved several "firsts" in microlensing, including the following: The MACHO project completed observations in December 1999; after 2000 the telescope+camera system was then used for a supernova search, but this was cut short when the telescope was destroyed by the January 2003 Canberra bushfires . Several other microlensing surveys continued, including

2548-402: 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. 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

2600-541: The velocity boost the corpuscle receives is If one assumes that initially the light is far enough from the lens to neglect gravity, the perpendicular distance between the light's initial trajectory and the lens is b (the impact parameter ), and the parallel distance is r ∥ {\displaystyle r_{\parallel }} , such that r 2 = b 2 + r ∥ 2 {\displaystyle r^{2}=b^{2}+r_{\parallel }^{2}} . We additionally assume

2652-531: Was a Russian and later Soviet physicist and honorary member of the Soviet Academy of Sciences (1920). He is most noted for being one of the first to study the gravitational lens effect. Orest, son of the noted Orientalist Daniel Chwolson , was born in Saint Petersburg . He graduated from St. Petersburg University in 1873. Khvolson began teaching at his alma mater in 1876 and became

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2704-423: Was refurbished for the project, and equipped with a prime-focus wide-field corrector, a dichroic beamsplitter and a pair of 16 megapixel CCD cameras (between 1992 and 1995, this was the largest CCD system in astronomical use). The cameras imaged a 42 by 42 arcminute square field of sky in two colours (blue-green and red light) simultaneously. Every clear night, the system monitored dense star fields, up to 80 fields in

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