The gravitational lens effect isEinsteinOfGeneral relativityA phenomenon predicted.Because space-timeMassive celestial bodyDistortion will occur nearby, which will bend the light when passing near a massive object.If there is a massive celestial body on the line from the observer to the light source, the observer will see one or more images formed due to the bending of light, which is called gravitational lens phenomenon.
So is gravitational lensAstrophysicsOne of the most important research tools and means incosmologydark substance、Dark energy、large scaleGravitation on and exoplanet exploration play a huge role.
Chinese name
Gravitational lensing effect
Foreign name
Gravitational lens effect
Status
The best measurement in cosmologydark substanceMethod of
Gravitational lens is a special optical effect in strong gravitational field.Suppose that there is just a strong gravitational field celestial body between the earth and a distant celestial body, and the three are almost in a straight line. The curvature of space-time near the strong gravitational field celestial body makes the light of the distant celestial body cannot reach the earth along a straight line, and makes the image observed on the earth deviate from its original direction. Its effect is similar to the refraction of light by a lens, which is called gravitational lens effect.As early as 1911, Einstein proposed that the light of distant stars would deflect slightly when passing over the sun's surface. On May 25, 1919, an observation team led by British astronomer Eddington verified this result by observing a total solar eclipse on the African island of Principe.This is the original concept of gravitational lens effect.The intermediate objects that produce gravitational lensing effect are called prepositive objects.This effect may produce double or multiple images, which have the same spectral structure and spectral line displacement.Under special circumstances, the image of a distant celestial body will form a ring (Einstein ring).[1]
Physical principles
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Figure 1
Physical principle (as shown in Figure 1)
The simplest model is the deflection of light when it passes through a mass particle, as shown in Figure 1.In this case, assuming that the aiming distance of the photon is b and the mass of the particle is M, the photon'sLateral accelerationIs: (see Figure 2)
Figure 2
The speed in the transverse direction is: (see Figure 3)
Figure 3
Therefore, the deflection angle of light is: (see Figure 4)
Figure 4
This is the deflection angle of light obtained by Newtonian mechanics, and under the correction of general relativity, the deflection angle should be twice the above equation, namely: (see Figure 5)
Figure 5
Although the result of light deflection based on particle is simple, its discussion is too rough.The more general case is the deflection of light under the condition of non particle.For the mass distribution ρ (ξoneξtwoξthree）As the distance from the lens to the observer and the source is far greater than the thickness of the lens itself, the lens can be regarded as a two-dimensional plane when calculating.Therefore, the total deflection angle is equal to the vector sum of the deflection angles of each element: (see Figure 6)
Figure 6
Where is defined as the volume mass density along the radial direction (ray direction γthree）Surface mass density after integration, (ξone，ξtwo）Is the collision vector on the lens.
Take "Source 1" in the schematic diagram as an example to discuss the ray path equation.In the diagram, DdIs the distance from the observer to the lens, DdsIs the distance from the source to the lens, DsIs the distance between the observer and the source.D in principled、Dds、DsIt is not on the z-axis of the straight line (the reference direction selected for measuring angle), but considering that its transverse distance is far less than the longitudinal distance, it ignores the transverse deviation and takes the longitudinal distance as its spatial distance.
The meanings of the angles in the diagram are: β is the angle between the direction of the source and the z-axis when the gravitational lens does not exist;θ is the angle between the observed light direction and the z-axis in the presence of a gravitational lens;α is the deflection angle of light.It is worth mentioning that, due to the curvature of space-time, Ds≠Dd+ Dds。Under the condition of small angle approximation (α, β, θ<<1), using simple geometric relations, we can get: (see Figure 7)
Figure 7
This is the ray path equation, also known as the lens equation.There may be multiple values for the given β and θ.
The formula of known defined constant deflection angle is: (see Figure 8)
Figure 8
functionk(θ) It is a dimensionless surface density related to angle θ, and its value can be used to judge the type of gravitational lens: when κ>1, it is a strong lens, when κ<1, it is a weak lens, and when κ<<1, it is a microlens.When κ=1, there will be a strange phenomenon of gravitational lens, namely Einstein ring.At this time, the ray path equation can be reduced to:
The diameter of the corresponding Einstein ring is: (see Figures 9 and 10)
Figure 9
Figure 10
It can be estimated thatElliptical galaxyEinstein ring θ ofEThe maximum can reach 2 ″, Einstein ring θ of small mass elliptical galaxies and rotating galaxiesEFor stellar microlens, θEIt is about 0.001 ″, which is important for theOptical telescopeIs indistinguishable.[2]
Standard approximation
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Weak field approximation
Except that the light is close to the Schwarzschild radius, the gravitational force corresponding to the general gravitational lens is weak, so GMm/r<<mctwoThe weak field condition is tenable.So it can be approximately described by Newton's theory.The above derivation is carried out under the condition of weak field approximation.It is worth mentioning that the weak field approximation does not mean weak lens.For a strong lens, the weak field approximation is also applicable, because GMm/r<<mc is far away from the Schwarzschild radiustwoIt is also established.[3]
Thin mirror approximation
In the real world, no lens has no thickness.In the imaging analysis of gravitational lens, it is quite troublesome and unnecessary to take the scale of the lens itself into account.When the distance from the source to the lens and the distance from the observer to the lens are far greater than the scale of the lens itself, the mass density along the line of sight direction is often ignored and compressed to a two-dimensional plane perpendicular to the line of sight.When the lens scale is small, such as the gravitational lens of stars, galaxies and galaxy clusters, the thin mirror approximation is obviously true.For large-scale gravitational lens, this approximation is also applicable.For low redshift objects, gravitational lensing effect cannot be reflected;For objects with high redshift, the scale of the dark halo can be ignored compared with the distance from the observer to the background source, so the large-scale structure generally only produces weak gravitational lens, and the thin mirror approximation is also reasonable.[4]
Small angle approximation
Small angle approximation is a mathematical method.The observation results show that the observation angle (θ) and the light deflection angle (α) are on the order of "seconds" or even "milliseconds", which can be regarded as small angles.Therefore, after approximating sin θ ≈ θ and tan θ ≈ θ (the same for α and β) for the trigonometric function used in derivation, the expression is greatly simplified, and some integrals can also yield analytical expressions.[5]
Geometric approximation
according toWave particle dualityPhotons do not always travel in straight lines.When encountering obstacles, light waves will be diffracted, and the propagation direction of this light will be significantly deflected.But the wave of light is not considered when dealing with gravitational lens phenomenon.The reason is that the scale of the lens is far larger than the wavelength of the light wave, and there is almost no diffraction at this time. Therefore, geometric optics can be used to deal with lens problems.[6]
classification
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Strong gravitational lens
A strong gravitational lens is one that can significantly change the star image to form double images, multiple images, and annular half arcs and arcs.The strong gravitational lens mainly exists in two cases. The line between the source and the observer is located in the central region of the galaxy cluster or the core region of the galaxy, and the magnification of the strong gravitational lens is very large.
Because of its strong brightening effect, strong gravitational lens can be used to study distant and dark background galaxies.For example, the baby galaxy in the galaxy cluster Abell 2218 was discovered through a strong gravitational lens.In addition, the strong gravitational lens is also used to measure the mass of galaxies, galaxy clusters and the Hubble constant.[7]
Weak gravitational lens
The weak gravitational lens is due to the perturbation of the density field of cosmic matterGeneral relativistic effectAn optical phenomenon caused by space bending.In general, weak gravitational lens will no longer obviously form a virtual image, but will brighten the star image, thus increasing the number of observable objects.
In the absence of weak gravitational lensing, the distribution of galaxies is theoretically known.The properties of this weak lens can be obtained by observing the distribution of distorted images.The mass of galaxies or galaxy clusters can be estimated from the properties of weak lenses, which is a very important method for measuring the mass of celestial bodies in cosmology.[8]
Micro gravitational lens
Micro gravitational lensThe phenomenon is a lens phenomenon produced by the moving objects in the foreground.Compared with the gravitational lens phenomenon on the galactic scale, the source object mass of the micro gravitational lens is very small, so the deflection of light is much smaller.Generally, only the instantaneous brightness of luminosity can be observed through the micro gravitational lens.
An important application of micro gravitational lens is that the number, mass and other relevant information of moving objects (especially planets) in the sky can be estimated by studying the occurrence rate and characteristics of micro gravitational lens.[9]
purpose
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The leading objects producing gravitational lensing effect may be galaxies, galaxy clusters with giant black holes, or non baryonic dark matter.Dark matter does not emit any radiation and cannot be directly observed, but its spatial distribution can be analyzed through gravitational lens effect.Therefore, gravitational lens effect becomes a probe for discovering dark matter in the universe.On May 15, 2007,hubble space telescope The image of the galaxy cluster CL0024+17 with a dark matter ring with a diameter of 2.6 million light-years was released.Galaxy cluster CL0024+17 is located in Pisces, 5 billion light years away.Dark matter ring is analyzed and depicted according to the photos of gravitational lens effect it produces.The photo was taken by the Hubble Space Telescope in November 2004. It was exposed for 14 hours using six different wavelength filters.The picture shows many blue arcs, which are more distant galaxies distorted by gravitational lensing effect.
One of the world's top ten scientific and technological achievements in 2006 selected by academicians of the Chinese Academy of Sciences and the Chinese Academy of Sciences is that American astronomers first found direct evidence for the existence of dark matter in the universe.August 21, 2006 Hubble and ChandraSpace telescopeA comprehensive image of the "bullet cluster" of galaxy cluster 1E0657-56 was released.Located at the base of the ship, the cluster is 3.4 billion light-years away and formed by the merger of two large galaxy clusters after collision.The red area is the hot gas generated by the collision, and the X image taken by Chandra telescope;The numerous white and yellow galaxies are optical images taken by the Hubble Telescope and the 6.5m Magellan Telescope in the United States;The blue region belongs to the dark matter in the galaxy cluster, which is analyzed and described according to the gravitational lens effect caused by the galaxy cluster.The image clearly shows that in the process of galaxy cluster collision, the high-temperature gas composed of ordinary (baryon) matter and dark (non baryon) matter are symmetrically separated, while dark matter is further separated than ordinary matter.The reason is that there is an interaction between baryonic matter, which plays a blocking role, but there is no interaction between non baryonic matter.The image was taken from August 10 to 15, 2004, with a total time of 140 hours.On August 16, 2007 and August 27, 2008, the Hubble and Chandra telescopes released two similar pictures: the Abell 520 galaxy cluster in Orion, 2.4 billion light-years away;MACSJ0025.4-1222 galaxy cluster in the constellation Cetus, 5.9 billion light-years away.These are direct evidences for the existence of dark matter in the universe.
In January 2007, scientists from Europe and the United States released the three-dimensional map of dark matter distribution in local space for the first time, which was listed as one of the world's top ten scientific and technological achievements in 2007 by academicians of the Chinese Academy of Sciences and the Chinese Academy of Sciences.This is located atSextant holderThe area of the sky is 2.2 square degrees, which is equivalent to the area of nine full moons.The distance is divided into three levels: 3.5 billion light years, 5 billion light years and 6.5 billion light years.The breadth of local space is 0.6 × 100 million light years, and the depth is 3 billion light years.This achievement was jointly completed by 70 astronomers.They analyzed 575 pictures taken by the Hubble Space Telescope for 1000 hours and found 500000 galaxies distorted by gravitational lens effect.The distance between galaxies was measured using the Japanese 8.3m telescope in Hawaii, the ESA-XMM space telescope in Europe, the ESO-VLT4 × 8.2m ground telescope in Chile, and the VLA in the United StatesRadio telescope arrayInformation.From the research progress of contemporary precise cosmology, people are surprised to find that: with the development of natural science, only less than 5% of the bright matter has been understood clearly;22.8% of the dark matter is still in the haze to be measured;The other 72.6% belongs to dark energy, which makes people more confused.Dark matter and dark energy are known as two dark clouds in the sky of physics in the 21st century.At the end of the 19th century and the beginning of the 20th century, there were two small dark clouds, which unexpectedly brewed a raging wind, shaking the physics building built over the centuries.After rain, the two theoretical frameworks of modern physics, relativity and quantum mechanics, stand tall, and human society has entered a new era of rapid development of science and technology.People expect that the two dark clouds of the 21st century will also brew new storms, as they did 100 years ago, and push the ability of human beings to understand the universe and nature to a new height.[1]
Social evaluation
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Gravitational lensing effect has been developed for only a few decades, but now it has become an important measurement method in cosmology.For objects with different scales, distances and masses, the three types of gravitational lenses play an alternate role, providing a lot of information, which also makes a significant contribution to the development of cosmology.It can be predicted that the research and application of gravitational lens effect will have great prospects in the future.[10]
