Gravitational wave, in physics, refers to the ripples in the curvature of space-time, which propagate outward from the radiation source in the form of waves, and this wave transmits energy in the form of gravitational radiation.In other words, gravitational wave is a kind of matter wave generated by the violent movement and change of matter and energy.
In 1916, Albert Einstein based hisGeneral relativityThe existence of gravitational waves is predicted.The existence of gravitational waves is general relativityLorentz invarianceBecause it introduces the concept that the propagation speed of interaction is limited.In contrast, gravitational waves do not exist in Newton's classical theory of gravity, because Newton's classical theory assumes that the interaction of matter propagates at an infinite speed.[1]
The cooperation group composed of various ground gravitational wave detectors in the world is sparing no effort to find gravitational waves propagating to the earth.The advanced Laser Interferometer Gravitational wave Observatory (aLIGO) of the United States began its first operational observation (O1) in September 2015 and its fourth operation (O4) in May 2023.LIGO includes two detectors, one located in Hanford, Washington, USA,Washington，USA），The other is located in Livingston, Louisiana,Louisiana, USA）。The GEO600 gravitational wave detector in Hanover, Germany, carried out synchronous observation with LIGO in September 2015, and the "advanced Virgo" gravitational wave detector in Cassina, Italy, joined LIGO in August 2017 (the last month of O2) for cooperative observation. The Shengang gravitational wave detector (KAGRA) located under the Shengang Mountain in NihonAfter the end of O3 (LIGO Virgo ended O3 observation in advance due to COVID-19 epidemic), it also joined the cooperative observation.The next generation of gravitational wave detectors, such as the Space Laser Interferometer (LISA) jointly built by the European Space Agency (ESA) and the United States Space Agency (NASA), China's Taiji Program and Tianqin Program, and Europe's Einstein Telescope (ET), will bring higher sensitivity and frequency detection range to the current gravitational wave detection.
Possible gravitational wave sources include the rotation, spin or merger of compact binary system (white dwarf, neutron star or black hole), supernova explosion, remnants of cosmic inflation, etc.On February 11, 2016, the LIGO Scientific Cooperation Organization (LSC) and the Virgo cooperation team announced that LIGO's two gravitational wave detectors located in Hanford District, Washington and Livingston, Louisiana, the United States, detected the gravitational wave signal from the merger of two black holes for the first time[2]。The first gravitational wave signal detected by humans is called GW150914, which was observed by LIGO at 09:50:45 (UTC) on September 14, 2015.In the early morning of June 16, 2016, the LIGO cooperation team announced that at 03:38:53 (UTC) on December 26, 2015, LIGO once again detected the gravitational wave signal of the merger of two black holes;This is the second gravitational wave signal detected by humans.[3]On October 3, 2017, Rainer Weiss, Barry C. Barish and Kip S. Thorne won the 2017 Nobel Prize for Physics for their "decisive contribution to LIGO detector and gravitational wave observation".
On October 16, 2017, the LIGO Virgo cooperation group announced that for the first time, humans directly detected gravitational waves (called GW170817) from the merger of two neutron stars. Two seconds later, the Fermi Space Telescope of the United States observed short gamma ray bursts (called GRB170817A) from the same source.About 11 hours later, the 1-meter diameter Swope telescope team in Chile and several other teams successively observed a thousand nova burst (called AT 2017gfo) in optical, infrared and ultraviolet bands, which was confirmed to be the electromagnetic counterpart of GW170817.Nine days later, the Chandra X-ray Observatory observed the combined X-ray for the first time.After 16 days of merging, the corresponding radio afterglow was observed by the Very Large Array (VLA) in the United States.[19]This is the first time in human history that the same astrophysical event was observed simultaneously with the Gravitational Wave Observatory and the Electromagnetic Wave Telescope, marking the arrival of the age of multi messenger astronomy.[4]
On June 29, 2023, the Chinese Pulsar Timing Array (CPTA) team, the NANOGrave team in North America, the EPTA InPTA joint team in Europe and India, and the PPTA team in Australia announced that the Pulsar Timing Array (PTA) observed an indiscernible random gravitational wave background for the first time.[6][14-16]This is the low-frequency NaHz gravitational wave signal from the supermassive double black holes at the center of many star systems in the distant universe.
In Einstein's general theory of relativity, gravity is considered as an effect of space-time bending, which is caused by the existence of mass.Generally speaking, in a given volume, the greater the mass contained, the greater the spatiotemporal curvature at the boundary of the volume.When a mass object moves in space-time, the change of curvature reflects the change of the spatial position of these objects.Under certain circumstances, accelerating objects can change the curvature, and can propagate outward at the speed of light in the form of waves, which is called gravitational waves.It can also be understood that the transfer of gravitational field around a massive binary star creates ripples, just like the ripples aroused by a stone falling into the water, which will continue to spread around.Unlike electromagnetic waves generated by dipole radiation, gravitational waves are quadrupole radiation, which can only be caused by the acceleration of quadrupole moment.
When a gravitational wave passes through an observer, the observer will find that space-time is distorted due to the strain effect.When the gravitational wave passes through, the distance between objects will increase or decrease rhythmically, and this frequency is equal to the frequency of the gravitational wave.The intensity of this effect is inversely proportional to the distance between sources of gravitational waves.When the rotating binary neutron star system merges, it is a very strong gravitational wave source because of the huge acceleration generated when they close to each other and rotate.Usually we are very far away from these sources, so the effect is very small when we observe on the earth, and the deformation effect is usually less than.At present, LIGO Virgo KAGRA, the most sensitive gravitational wave detector network, can see binary neutron stars with a signal noise ratio (SNR) greater than 8 at a distance of 140~165Mpc at the farthest.[7]
Gravitational waves can generally penetrate places that are difficult to penetrate by electromagnetic waves, such as plasma or gas clouds, so they can provide observers on the earth with information about black holes and other strange celestial bodies in the distant universe.These objects cannot be observed by traditional means, such as optical telescopes and radio telescopes, so gravitational wave astronomy will give us new knowledge about the evolution of the universe and celestial bodies.More interestingly, it can provide a way to directly observe the very early universe, which is impossible in traditional astronomy, because before the cosmic recombination, the universe was opaque to electromagnetic radiation.Therefore, the accurate measurement of gravitational waves can enable scientists to verify the general theory of relativity more comprehensively.
Gravitational spectrum
Figure: Gravityspectrum；Corresponding to different gravitational wave sourcesfrequency range (Note that the frequency islogarithmValue after), period.And the corresponding detection mode.
Gravitational waves travel at the speed of light. The frequency of gravitational waves multiplied by the wavelength equals the speed of light.The lowest frequency gravitational wave is a relic left by quantum fluctuations during the inflationary period of the universe. The wavelength is equivalent to the visible cosmic scale. Because the signal is too weak, it is difficult to observe directly;There is no reliable gravitational wave source for extremely high frequency gravitational waves.Stephen Hawking and Werner Israel believe that the frequency of gravitational waves that may be detected is between Hz and Hz [MOU1].
Even the strongest gravitational waves have very little effect after reaching the earth, because these sources are very far away from us.For example, the gravitational wave generated by GW150914 in the final severe merger stage reached the Earth after passing 1.3 billion light years, which only changed the 4-km arm length of the LIGO detector by one ten thousandth of the proton diameter, which is equivalent to changing the distance between the solar system and our nearest star by one hair width.This extremely small change, if we do not borrow the extremely precise detector, we can not detect it at all.
Gravitational wave
chart: Two LIGOObservation stationThe same gravitational wave event was detected.The above is the observed curve, and the following is the fitting result after comparison with the theory.(From LIGO articles[2]）
Detection history
Announce
edit
Many physicists and astronomers have made countless efforts to prove the existence of gravitational waves.The indirect experimental evidence for the existence of gravitational waves for the first time comes from the pulsar binary PSR1913+16.In 1974, Professor Joseph Taylor, a physicist at the University of Massachusetts in the United States, and his student Russell Hulse, using the 305 meter aperture radio telescope at the Arecibo Observatory in the United States, discovered two neutron stars with a mass roughly equal to 1.4 suns (with a radius of less than 10km)A binary system consisting of rotating stars.Since one of the two neutron stars is a pulsar, using its precise periodic radio pulse signal, we can know the semi major axis and period of the orbits of the two compact stars when they rotate around their center of mass with great accuracy.According to general relativity, when two compact stars revolve around each other, the system will produce gravitational radiation.The gravitational wave radiated carries energy away, so the total energy of the system will be less and less, and the orbital radius and period will also be shorter.
Taylor et al. made continuous observations on PSR1913+16 over the next 30 years, and the observation results are exactly as predicted by general relativity: the periodic change rate is reduced by 76.5 microseconds per year, and the semi major axis is shortened by 3.5 meters per year.General relativity can even predict that the binary system will merge in 300 million years.This is the first time that humans have obtained indirect evidence for the existence of gravitational waves, and it is also an important verification of the gravitational theory of general relativity.Taylor and Hulls won the 1993 Nobel Prize in Physics.
In terms of experiments, Joseph Weber was the first person who made a great attempt to directly detect gravitational waves.As early as the 1950s, he realized with foresight that it is not impossible to detect gravitational waves.From 1957 to 1959, Weber devoted himself to the design of gravitational wave detection scheme.In the end, Weber chose a cylindrical aluminum bar 2 meters long, 0.5 meters in diameter, and weighing about 1 ton, with its side pointing in the direction of gravitational waves.This type of detector is called bar shaped gravitational wave detector, also called resonance rod: when the gravitational wave arrives, the two ends of the aluminum rod will be alternately squeezed and stretched. When the frequency of the gravitational wave is consistent with the design frequency of the aluminum rod, the aluminum rod will resonate.The wafer attached to the surface of the aluminum bar will generate the corresponding voltage signal.Resonant rod detector has obvious limitations, such as its resonant frequency is determined, although we can adjust the resonant frequency by changing the length of the resonant rod.But for the same detector, it can only detect the gravitational wave signal of its corresponding frequency. If the frequency of the gravitational wave signal is inconsistent, the detector can do nothing.In addition, the resonance rod detector has a serious limitation: gravitational waves will produce spatiotemporal distortion. The longer the detector does, the greater the variation of gravitational waves on the length.Weber's resonant rod detector is only 2 meters long, and the gravitational wave of strength is too small in this length strain (2 × m). For physicists in the 1950s and 1960s, it is almost impossible to detect such a small length change.Although the resonant rod detector failed to find gravitational waves, Weber pioneered the experimental science of gravitational waves. After him, many young and talented physicists devoted themselves to the experimental science of gravitational waves.
At the same time when Weber designed and built the resonance rod, some physicists realized the limitations of the resonance rod, and then gave birth to the gravitational wave laser interferometer detection scheme based on the principle of Michelson interferometer.It was built in the 1970s by Rainer Weiss of MIT and Robert Forward of Malibu Hughes Laboratory.By the late 1970s, these interferometers had become important substitutes for resonant rod detectors.The advantages of laser interferometer for resonant rod are obvious: first, laser interferometer can detect gravitational wave signals in a certain frequency range;Secondly, the arm length of the laser interferometer can be very long. For example, the arm length of the ground gravitational wave interferometer is generally on the order of kilometers, far exceeding that of the resonance rod.
In addition to the LIGO we mentioned earlier, there are many other gravitational wave observatories.VIRGO, located near Pisa, Italy, with an arm length of 3km;GEO with arm length of 600m in Hanover, Germany;TAMA300 with an arm length of 300 meters at the National Astronomical Observatory in Tokyo, Japan.These detectors used to observe together from 2002 to 2011, but did not detect gravitational waves.Therefore, these detectors have been upgraded significantly since then. Two high-tech LIGO (upgraded LIGO) detectors have been observed as pioneers in the high-tech detector network with significantly improved sensitivity since 2015, and high-tech VIRGO (upgraded VIRGO) has also been put into operation since 2017.The Japanese project TAMA300 has been comprehensively upgraded, and the arm length has been increased to 3 km, renamed KAGRA, and will be put into operation in 2020.
Because ground detectors are easily disturbed by natural phenomena such as earthquakes, physicists are also marching into space.European space gravitational wave project LISA (laser interference space antenna).LISA will consist of three identical detectors to form an equilateral triangle with a side length of five million kilometers, and will also use laser interferometry to detect gravitational waves.This project has been approved by the European Space Agency and officially established. It is in the design stage and is planned to launch in 2034.As a pilot project, two test satellites were successfully launched on December 3, 2015 and are under commissioning.In addition to actively participating in international cooperation, Chinese researchers are also preparing their own gravitational wave detection projects - Taiji Plan and Tianqin Plan.
The above detectors all use laser interference to detect high-frequency gravitational waves (10 ^ - 3~10 ^ 2Hz).Our universe itself has "created" a detection tool - millisecond pulsars, which are high-speed rotating neutron stars formed by the supernova explosion of massive stars.These extremely stable neutron stars are the most accurate clocks in nature. Like lighthouses, they send a signal to the earth every time they "tick". This is the method of pulsar timing.In 1983, Ronald Ward Hellings and George S. Downs of California Institute of Technology put forward the principle of measuring the gravitational waves of NaHz through pulsar timing array (PTA).[13]When the Earth and pulsar are taken as the two ends of the baseline for detecting gravitational waves, the distance of this baseline will change after the gravitational waves pass through, which can be observed through the fluctuation of the pulse period.Although the periodic fluctuations of a pulsar may be caused by noise, the synchronous fluctuations of a group of pulsar arrays will provide strong evidence for the random gravitational wave background in the universe.European PTA (EPTA), the pulsar timing array team in Europe, Indian PTA (InPTA) in India, North American Nanohertz Observatory for Gravitational Waves (NANOGrave for short), Australia based Parkes PTA (PPTA) in Australia, MeerKAT PTA in South Africa and CPTA in China,Both use their own radio telescopes (such as China's Celestial Eye Telescope FAST) to monitor ten pulsars for many years to detect the background of random gravitational waves.The Square Kilometer Array (SKA), which was built in 2021, plans to build giant radio telescope arrays in South Africa and Australia, which will search and monitor pulsars with unprecedented accuracy.
In addition, the original gravitational wave, the relic of the very early cosmic inflation, will also leave traces on the polarization mode of the cosmic microwave background radiation (CMB).However, because the signal is too weak, there is no evidence of the existence of the original gravitational wave.The next generation of CMB telescopes, such as CMBS4 in the United States, LiteBIRD in Japan, and Ali Experiment Program in China, will take finding primary gravitational waves as one of the main scientific goals.
Gravitational wave detection in China
Announce
edit
From Einstein's prediction of gravitational waves in 1916 to LIGO's acquisition of direct observational evidence in 2015, it has spanned a hundred years.In this process, Chinese scientists are also constantly seeking and pursuing.As early as the 1970s, Chinese scientists began to study gravitational waves. Unfortunately, it has stagnated for more than ten years due to various reasons, resulting in a talent gap.Until 2008, under the promotion of Academician Hu Wenrui of the National Microgravity Laboratory of the Institute of Mechanics, Chinese Academy of Sciences, the space gravitational wave detection working group of Chinese Academy of Sciences was established, and the Chinese research of gravitational waves began again.
There are three major gravity wave detection projects in China. One is the Taiji Program, which is led by Academicians Hu Wenrui and Wu Yueliang of the Chinese Academy of Sciences. It is very similar to the European LISA Program.The other space program is the "Tianqin Program" led by Academician Luo Jun of Sun Yat sen University. Compared with Taiji, it will be located in an orbit of 100000 kilometers above the earth, and the distance between the three satellites is also about 100000 kilometers.The third is the "Ali Experiment Plan" led by the Institute of High Energy Physics of the Chinese Academy of Sciences. The Ali Experiment Plan is to place a small radio telescope with a large field of view in Ali, Tibet, China, to enjoy the rainbow left by the original gravitational waves on the cosmic micro wave background radiation (CMB) from the ground in the northern hemisphere.The Tai Chi and Tianqin plans are still in the pre research stage.Ali plans to start operation at the end of 2023.
On June 29, 2023, the China Pulsar Timing Array (CPTA) research team released the latest results. They used the "China Celestial Eye" telescope FAST to detect the evidence of the existence of the NaHz gravitational wave background. At the same time, other international pulsar timing array teams also published similar observation results.[6]China is the most junior in this international cooperation. The longest observation time of pulsar timing array in other countries is nearly 30 years, while China only has more than three years.Curiously, although the observation time in China is the shortest, the conclusion is the strongest, and the degree of determination of gravitational wave correlation is the highest among all pulsar time measurement arrays in the world.Statistical analysis shows that the confidence level of the observed value of the CPTA correlation curve in line with the theoretical value reaches 4.6, which is the highest confidence level in each international cooperation group.
Astronomical significance
Announce
edit
In the past century, astronomy has undergone tremendous changes because of the use of new methods of observing the universe.Since Galileo first used telescope for astronomical observation more than 400 years ago, astronomical observation only used visible light at first.However, visible light is only a small part of the electromagnetic spectrum. In the distant universe, not all celestial beings can generate strong radiation in this special band. For example, more useful information may be available in the radio band.Using radio telescopes, astronomers have discovered pulsars, quasars and other extreme celestial phenomena, pushing our understanding of some physics to the limit.Using gamma ray, X-ray, ultraviolet and infrared observations, we have also made similar progress, bringing new knowledge to astronomy.Every opening of the electromagnetic spectrum will bring us unprecedented discoveries.Astronomers expect gravitational waves to do the same.
Gravitational waves have two very important and unique properties.First: It does not need any matter to exist around the gravitational wave source, that is, it does not need to generate electromagnetic radiation.Second: Gravitational waves can pass through the moving objects almost unstopped. For example, light from distant stars will be blocked by interstellar media, and gravitational waves can pass through unimpeded.These two characteristics allow gravitational waves to carry more information about astronomical phenomena that have never been observed before.
propagation velocity
Announce
edit
In general relativity, the propagation speed of gravitational waves is equal to the speed of light c in vacuum.In special relativity, the constant c is not only related to the speed of light, but also the upper limit of the speed of any interaction in nature.The speed of light c is actually a conversion factor that changes the time unit into the space unit, which makes it the only speed that does not depend on the motion of the observer, nor on the light source and gravitational wave source.Therefore, the speed of "light" is the speed of gravitational waves, but also the speed of any zero mass particles, including gluons (carriers of strong interaction), photons (carriers of electromagnetic force) and gravitons (field particles assumed by the gravitational theory, if any, need to invent a new quantum gravitational theory).
In August 2017, the LIGO Virgo detector, the gamma ray satellite and the optical telescope received gravitational waves and optical signals from the same direction within 2 seconds, which confirmed that the speed of gravitational waves is the same as that of light.[8]
Effect during passage
Announce
edit
To understand the effect of gravitational waves when passing through the observer, we can imagine a completely flat space-time area, with a bunch of static test particles placed on a plane.When gravitational waves pass through these particles in a direction perpendicular to the plane, they will swing in a cross shape with the warped space-time (see the left figure in the animation).The area enclosed by the test particle is unchanged, and the particle will not move in the direction of wave transmission.When the transverse particle distance is the largest, the longitudinal particle distance is the smallest;On the contrary, when the transverse particle distance is the smallest, the longitudinal particle distance is the largest.
Animation greatly exaggerates the swing of particles, and the amplitude of gravitational waves is actually very small.This effect can be produced when two masses move in circular orbits with each other.In this case, the amplitude of the gravitational wave is unchanged, but its polarization plane will rotate twice the revolution period.Therefore, the size of gravitational waves (periodic space-time strain) will change with time, as shown in the animation.If the orbit is elliptical, the amplitude itself will change with time.
Like other waves, gravitational waves also have several characteristics:
Amplitude: usually recorded as h, a scalar describing the wave size, which is the ratio of the maximum squeezing degree of the distance between two particles to the original distance.The amplitude in the animation is approximately h=0.5 (50%).The gravitational wave generated by the merger of two black holes passes through the earth with only h amplitude~
。
Frequency: usually recorded as f, the frequency of wave vibration (1 divided by the time interval between the two largest squeezes, the reciprocal of the cycle).
Wavelength: usually recorded as λ, the space interval between the two maximum squeezing points of the wave.
Speed: the speed of wave propagation.In general relativity, gravitational waves travel at the speed of light c.
The relationship between the velocity, wavelength and frequency of gravitational wave is c=λ f, which is the same as the corresponding equation of electromagnetic wave.For example, the particles in the animation swing about once every 2 seconds, that is, the frequency is 0.5 Hz, and the wavelength can be calculated to be about 600000 km, that is, about 47 times the diameter of the earth.
The above example assumes that the wave has a "cross" linear polarization, denoted as.Unlike the polarization of light waves, the polarization of gravitational waves is 45 degrees instead of 90 degrees.If the polarization is "cross type", the waves of the test particles are very similar, but the direction is rotated 45 degrees, as shown in the second animation.Like light waves, gravitational wave polarization can also be represented by circularly polarized waves.The polarization of gravitational waves depends on the nature and angle of the wave source.
Left: The role of a ring composed of particles under cross polarized gravitational waves
Figure right: The role of a ring composed of particles under cross polarized gravitational waves
Gravitational wave source
Announce
edit
Figure: Frequency domain distribution of wave sources mainly detected by LIGO and LISA.The horizontal axis is the frequency, and the vertical axis is the amplitude of gravitational wave
Gravitational waves are generated due to acceleration motion and its change, and cannot be perfectly spherically symmetric motion (such as a sphere in expansion or contraction) or symmetric rotation (such as a disk or sphere in rotation).For example, if a dumbbell rotates around its axis of symmetry (iron bar), it will not produce gravitational waves. However, if it is placed flat on the ground, and the axis of rotation is perpendicular to the handle connecting the two ends of the dumbbell (analogous to the twin stars rotating around each other), it will produce gravitational waves. If the two ends of the dumbbell have high mass, it can simulate a neutron star or black hole binary system.The greater the mass at both ends of the dumbbell, the higher the speed of movement, and the stronger the gravitational waves it emits.For another example, whether the rotation of a pencil will produce gravitational waves depends on its rotation axis. There is no gravitational wave along the pencil, and there is gravitational wave perpendicular to the pencil.
Here are some examples:
Two celestial bodies circle each other. If a planet moves around a star, it will radiate gravitational waves.
The rotation of an axially asymmetric asteroid - for example, its equator is uneven - will radiate gravitational waves.
Supernovae usually generate gravitational waves, unless their explosion shape is perfect spherical symmetry, which is almost impossible.
A non rotating solid moving at a constant speed will not produce gravitational waves.(This is the law of conservation of momentum)
A rotating disk does not radiate gravitational waves.(This is the conservation law of angular momentum, but it will have gravitational magnetic effect)
Spherical bodies with spherically symmetric pulsations (monopole moment is not 0, but quadrupole moment is 0) will not radiate gravitational waves.(Berkhov's theorem)
The frequency of gravitational waves depends on the characteristic time scale of the dynamic system.For a binary system, the frequency at which two celestial bodies revolve around each other is the frequency of gravitational waves.Gravitational wave sources are generally classified by frequency band.1 to 10 kHz are classified as high-frequency wave sources, which come from neutron binaries, double black holes, supernovae, etc. This frequency band is within the detection accuracy range of ground-based gravitational wave detectors.1 mHz to 1 Hz are classified as low-frequency wave sources, which come from supermassive black holes, dwarf binaries, white dwarf binaries, etc., and can be detected by space laser interferometer and spacecraft Doppler tracking method.1 nHz to 1 mHz are classified as VLF wave sources, which come from supermassive black holes, cosmic string cusps, etc., which are the frequency bands studied by pulsar timing experiments.The last one to Hz is classified as the extremely low frequency wave source, which corresponds to the characteristics of gravitational waves that can be detected in the cosmic microwave background.
binary star
Announce
edit
Figure: Schematic diagram of the motion of a binary star system around the center of mass. In Newtonian mechanics, this orbit is always stable, but under relativistic mechanics, gravitational radiation will cause slow contraction of the orbit
Close binary systems capable of radiating observable gravitational waves include binary systems composed of white dwarfs, neutron stars, black holes and other compact stars, such as black hole binaries, black hole neutron stars, double neutron stars, double white dwarfs and so on.They have large and time varying quadrupole moments, which are important gravitational wave sources for LIGO and other ground detectors and space detectors LISA, and are the only gravitational wave source confirmed by indirect observation (pulsar binary system PSR 1913+16).On the whole, the gravitational radiation process of the binary system is actually a process of the binary gradually approaching the combination, which is divided into three phases in order: spinning, merging, and slow rotation.
Gravitational radiation will cause the binary stars in the approaching state to lose kinetic energy, causing their orbits to decay at a very slow speed, and the two stars will gradually approach.In other words, the time scale of their gravitational radiation is far larger than their revolution period, so this process is considered to be adiabatic. The most commonly used method to predict the waveform is the post Newtonian approximation method.From the frequency estimation method of gravitational waves, it can be seen that the radiation frequency of a binary system is proportional to the square root of its own density.The binaries that can be detected by ground detectors include neutron stars and stellar mass black holes, while LISA is responsible for detecting unknown binaries such as white dwarfs and supermassive black holes.
The energy radiated by the orbital movement will cause the orbital contraction, and the result is that the frequency of the emitted gravitational wave increases with time, which is called chirp signal.If the time scale of chirp can be observed, the chirp quality of binary stars can be calculated;Furthermore, the distance from the binary star to the earth can be calculated from the chirp mass and the observed gravitational wave amplitude, which means that it will be possible to further measure the Hubble constant and other cosmological constants.
As the orbital decay of the binary star system gradually accelerates, the adiabatic approximation is no longer applicable, so the binary star system enters the merging state: two stars close together and merge into a black hole violently,And a considerable part of the mass is released in the form of gravitational waves (but a large part of the mass cannot leave the horizon of the black hole due to the restriction of the conservation of angular momentum, thus forming an accretion disk near the black hole, which is generally believed to lead to the formation of gamma ray bursts), where the post Newtonian approximation method is not applicable (see the section on stellar mass black holes);The merging black hole then enters a slow rotation state, and the rotation frequency of the gravitational radiation black hole gradually decreases, finally stabilizing into a Kerr black hole.
In essence, the number of double neutron stars in the universe is relatively rare. In the observable range, their number is less than that of the double star system composed of neutron stars and white dwarfs, and even less than the low frequency (to Hz) double white dwarfs system that widely exists in the universe.The number and lifetime of these double white dwarfs are much larger than those of binary neutron stars in orbital contraction state such as PSR B1913+16.This is because most stars have smaller masses, and most stars are binary stars.It is estimated that LISA is likely to find thousands of such double white dwarf systems, and its detection probability is far greater than the detection expectation of ground detectors for double neutron stars.However, in fact, too many double white dwarf star systems in the Milky Way will form a background noise with a frequency lower than 1 millihertz. This background noise is called "confusion noise". It will be higher than the instrument noise of LISA itself, but these noises will not affect the detection of strong black hole signals.However, due to the low amplitude of the double white dwarfs of the river alien system, although they can also form the background noise with a frequency as high as 1 Hz, the degree is still far below the instrument noise of LISA.
Pulsar
Announce
edit
Figure: Crab Nebula, the blue part is the X-ray image taken by Chandra X-ray Observatory[17]The red part is the visible light image. There is a young pulsar PSR J0534+2200 near the nebula center, which is very likely to be confirmed as one of the objects of gravitational wave source
For a neutron star (pulsar) to be a gravitational wave source, its mass (or mass flow) distribution must be asymmetric.The source mechanism of asymmetry includes two types.
The first case is the asymmetry relative to the fixed star, and the possible mechanisms include:
The star itself is an asymmetrical quasi sphere (for example, the pulsar PSR J1748-2446ad inside the globular cluster Terzan 5, with a rotation frequency of 716 Hz, is the fastest known pulsar)
The direction of the pulsar's magnetic field is inconsistent with its rotation axis (e.g. PSR 1828-11)
Asymmetry caused by star accretion (typical example is low mass X-ray binary, such as Cygnus X-1)
It is now generally believed that the shell of a neutron star is not enough to support the asymmetry of mass more than times the mass of the sun.For example, it is estimated that the upper limit of asymmetry of the expected wave source PSR J2124-3358 of LIGO accounts for 1.1 × of the total mass.The estimated time scale of the slow rotation state from this point is much longer than the actual one.Therefore, it seems that gravitational radiation is not enough to be the main reason for the slow rotation of neutron stars.Taking the young pulsar PSR J0534+2200 in the Crab Nebula as an example, its asymmetry is less than 3 × of the total mass, and the upper limit of the gravitational wave amplitude is about 6 ×;For older millisecond pulsars, the asymmetry is only about the total mass. If the distance from the earth is 1 second, the upper limit of the estimated amplitude is.Although these typical amplitudes are far lower than the sensitivity of LIGO, their corresponding relevant signals can be found as long as they are measured for a long time.
The second case is that the asymmetric part is moving relative to the star. A typical example is the instability of the r-mode of the neutron star, also known as the Rossby Wave on the neutron star. This name comes from its mechanism similar to the Coriolis force on the earth's surface.In this case, the gravitational radiation frequency calculated theoretically is 4/3 times of the rotation frequency.
Supernovae and gamma ray bursts
Announce
edit
The formation of neutron stars comes from the gravitational collapse of supernovae. The collapse rate of the core of supernovae can reach 70000 kilometers per second.This gravitational collapse is not highly symmetric, which has been confirmed in the observation of supernova SN 1987A.Therefore, this gravitational collapse will produce a short-lived and aperiodic gravitational wave burst signal, accompanied by the process of electron capture and neutrino transport.However, the waveform and amplitude of gravitational radiation are difficult to predict theoretically, and it is generally believed that only numerical simulation can be used.The frequency band of this burst signal may be very wide, with the center frequency at 1 kHz;Or it may be a periodic chirped signal at any frequency between 100 Hz and 10 kHz.Theoretically, it is estimated that if a supernova collapses in the Virgo Galaxy Cluster and its emitted energy is greater than 0.01 times the mass of the sun, it is possible for current ground-based detectors to observe such events.But in fact, how much of the energy is released by radiation is still an unsolved problem. Now it is generally believed that the radiation energy will not exceed the total mass of the supernova. The current gravitational wave detectors are not able to detect supernova explosions in extragalactic galaxies.The probability of such events occurring in the Milky Way is about once every few decades. According to the calculation, the amplitude of gravitational radiation from the gravitational collapse of the 10 thousand second gap is about, and the duration is several milliseconds.The sensitivity of the new generation of ground detectors should reach the corresponding level.
Gamma ray bursts are sudden bursts of extremely intense gamma ray radiation in a short time (from a few milliseconds to a few minutes), which can be divided into two categories according to the duration.According to the conclusions obtained from most observations, gamma ray bursts are likely to be generated when the high-speed rotating black hole was born.If so, compared with gravitational collapse, this asymmetric structure of high-speed rotation will form highly stable gravitational radiation, so it is possible to detect the corresponding gravitational radiation while observing its electromagnetic radiation explosion.However, such events should be rare, so it requires a wide observation distance (at least about 3 gigabit seconds difference) and a considerable proportion of radiation energy.However, in February 2007, a GRB 070201 short gamma ray burst from the Andromeda galaxy occurred, and LIGO did not detect the existence of gravitational radiation.This may be because GRB 070201 is more distant than the Andromeda galaxy, but it may also imply that the gamma ray bursts are not from the formation process of black holes or neutron stars, but from repeated soft gamma ray bursts with extremely strong magnetic fields such as magnetostars.
Stellar mass black hole
Announce
edit
NASA Supercomputer Simulations of Black Hole Binary Stars Starting to Merge
Astronomers now realize that there are abundant black holes in the universe, which can be divided into stellar black holes (3~100 times the mass of the sun) and medium mass black holes according to their masses（
Times the mass of the sun) and supermassive black holes at the center of extragalactic galaxies（
Times the mass of the sun).The mass of these two kinds of black holes is very different, so there are great differences in the mechanism and frequency of their gravitational radiation: stellar mass black holes are formed in the gravitational collapse of the interior of a red giant or supernova explosion;The mass of medium mass black holes may result from the merger of stellar mass black holes or the collapse of supermassive stars;The supermassive black hole may originate from the direct collapse of the giant gas cloud in the early universe.The rotation frequency of black hole binaries is inversely proportional to their mass, which indicates that the gravitational wave frequency of star mass black holes and medium mass black holes is within the detection range of ground detectors, while the gravitational wave of supermassive black holes can only be captured by space detectors such as LISA.
The gravitational radiation of stellar mass black holes is generally believed to originate from a series of processes of approaching merging slowing down rotation of binary star systems (at least one of which is a black hole), which is the same as the gravitational wave radiation mechanism of other binary star systems such as binary neutron stars.In the spin near state, the distance between the two black holes is quite far（
）And gradually approach at a very slow speed.In this case, as in all binary systems, the post Newtonian approximation is sufficient to solve such problems.However, when the distance between black hole binaries gradually narrows, until their orbits are reduced to the minimum stable circular orbit (ISCO), black holes fall into each other's event horizons, and the binaries change from the approaching state to the merging state.This phase transition is completely a relativistic effect, so the post Newtonian approximation is completely inapplicable here.The merging of black holes will inevitably be accompanied by the sudden emission of gravity wave signals. At present, such signals can only be analyzed by the method of numerical relativistic simulation, and there are many difficulties in practical calculation.Moreover, for a black hole with a mass greater than 50 times the mass of the sun, the frequency at the end of the spin state is the revolution frequency of the final stable orbit, which is about 0.06 times the natural frequency of the black hole, about 30 Hz.This frequency is close to the low frequency limit of ground detectors, and even if only such events are detected, it is also necessary to make some predictions on the waveform. Therefore, the results of the numerical simulation of black hole mergers are of great significance for the detection of such gravitational waves.After merging, the system enters into a slow rotation state, and the event horizons of the two black holes merge into one. The black hole binaries emit gravitational radiation in the form of similar damped vibrations, and gradually stabilize into a single Kerr black hole. The space-time metric of this process can be solved by the linear perturbation theory of Kerr spacetime.One of the characteristics of the slow rotation state is that it has a complex rotation frequency mathematically, that is, the real part of the complex frequency is the characteristic frequency, and the imaginary part is the damping factor.Theoretically, the mass and angular momentum of the Kerr black hole completely determine all possible complex frequencies. These frequencies are discrete and have an infinite number, which are collectively called quasi normal modes of the black hole. The rotation of the black hole can be described by the linear superposition of these quasi normal modes.
Although the number of black holes in the universe is lower than that of neutron stars, it is estimated that the number of binary star systems composed of two black holes is more than that of neutron stars in space scale, mainly because the binary star systems of neutron stars are not easy to form compared with black hole binary star systems.It is said that globular clusters are places where black hole binaries are formed with high efficiency. If this is the case, the number of black hole binaries in the universe may be about ten times higher than that of neutron star binaries.Since the mass of the black hole inside the globular cluster is greater than the average mass of the star, the black hole will gradually move towards the center of the cluster. The interaction of three bodies in the center is the main mechanism for the formation of binary stars.It is worth noting that the gravitational binding between such binary star systems and globular clusters is not strong. As a result, binary stars may start to evolve independently from clusters, and their stable time is generally within years.Current research is not sure about the merging probability of stellar mass black holes, but it is generally believed that within the range of 15 trillion seconds, it will occur at least several times a year.
Medium mass black hole
Announce
edit
On May 21, 2019, the LIGO Virgo cooperation team first detected the gravitational waves generated by the intermediate mass black holes formed by the merger of two black holes, with the mass of 85 times and 66 times of the solar mass respectively, and combined a 142 times solar mass black hole. This event is called GW190521.[20-21]This discovery has two milestone significance: first, astronomers collected clear gravitational wave data of medium mass black holes for the first time;Second, we found a black hole with a mass between the "gray zone", that is, a medium mass black hole.Previously, scientists had no clear physical picture of the formation of intermediate mass black holes.They may originate in the center of globular clusters or dwarf galaxies, which are formed by collapsing of continuously merging supermassive stars, or by merging two stellar mass black holes.GW190521 belongs to the latter event, but how these two stellar mass black holes came into being has not been determined yet.Up to the third operation (O3), LIGO Virgo has found eight cases of gravitational waves generated by black holes with mass more than 100 times the mass of the sun.[22-23]With the discovery of more medium mass black holes in the future, the mystery of their formation will be gradually revealed.
Figure: Mass of black hole or neutron star corresponding to gravitational wave detected by LIGO Virgo KAGRA cooperation group as of O3[23]
Supermassive black hole
Announce
edit
Figure: NGC 4038 and NGC4039, two tentacle galaxies photographed by the Hubble Space Telescope[18]https://science.nasa.gov/image-detail/antennae-galaxies-reloaded/The collision of galaxies is likely to lead to the merger of supermassive black holes at their centers
There are two forms of gravitational radiation from supermassive black holes: one is the merger of supermassive black holes, and the other is the gravitational radiation released by the capture of small dense objects by massive black holes.The merging mode of the two is different, so the gravitational waveform, theoretical prediction ability and detection method are different.
Galaxy merging
Announce
edit
The merger of two supermassive black holes is an enhanced version of the merger of stellar mass black holes.Due to the large mass of participation, the frequency of its gravitational radiation is very low, but the amplitude is quite high.Because the effective signal amplitude is approximately linear with the black hole mass, the mass is
The gravitational radiation amplitude of supermassive black holes with solar mass is about 10 times that of black holes with solar mass
Times（
）。This means that space detectors will have a very high signal to noise ratio for such signals, no matter where such wave sources are located in the universe.Now it is generally believed that there is mass at the center of most galaxies at least
There is evidence that the mass of a supermassive black hole is proportional to the mass of its host galaxy nucleus.Different from stars, the probability of collisions between galaxies is quite high. For example, NGC 6240, a galactic collision remnant in Ophiuchus, contains two supermassive black holes from protogalaxies.After the merger of the two galaxies, the black holes at the center of the two galaxies will gradually drift towards the center of the newly formed galaxy and eventually collide. This mechanism shows that the probability of merging supermassive black holes in the universe is quite high.
Extreme mass proportional approximation
Announce
edit
Figure: EMRI formed by small compact objects and massive black holes at the center of galaxies is one of the important detection wave sources of LISA
The supermassive black hole merges with white dwarfs, neutron stars, stellar mass black holes, medium mass black holes and other compact objects with smaller mass, which is called extreme mass ratio inward (EMRI).When a compact star happens to be close to the supermassive black hole at the center of the galaxy, it may be captured and emit gravitational radiation while orbiting the supermassive black hole, so this is also a kind of approaching state.However, due to the huge difference in the mass ratio between the two, the change of this near spin state is slower than that of ordinary binary systems. From the perspective of observation, this means that the same waveform can be observed for several years.This gravitational radiation can be approximated as a chirped signal emitted from a particle near a Kerr black hole, and the orbit of the particle may be highly eccentric (eccentricity close to 1).As the kinetic energy of the gravitational radiation system continues to decrease, the eccentricity of the orbit gradually decreases, which may be reduced to about 0.4 in the later period of the spin near state. During this period, the radiation frequency of EMRI is stable in the measurement frequency domain of LISA.Its waveform contains the spatiotemporal geometric information near the black hole, and it is especially possible to verify the black hole hairless theorem by observing the mass and spin of the black hole.
The incidence of EMRI has little to do with the way galaxies are formed, so LISA has the ability to observe hundreds of such events in a year.The nearest event may be within the red shift of less than 0.1, provided that theoretical research can make a more accurate prediction of the trajectory of particle motion in dozens of cycles.However, it is not so easy to predict this kind of orbit in theory, mainly because the highly eccentric orbit around the Kerr black hole may be chaotic. If the trajectory of the particle is far away from the equatorial plane orbit of the black hole, it will become very complex, and it may wander at a high speed throughout the event horizon.In order to accurately predict the orbital motion within dozens of cycles, it is necessary to define the initial conditions and as many as 14 parameters that are accurate enough to distinguish different motions, which leads to the detection and screening of such signals requiring a large number of waveform templates, and the complete calculation of these templates even exceeds the computing power of existing computers,This leads to the possibility that the simple pattern matching algorithm is not suitable for this.So far, the most common numerical solution of EMRI waveform is the Turksky equation founded by Sol Turksky of Cornell University in the 1970s.[9]
Inflation
Announce
edit
Figure: The origin of galaxies based on the inflation theory. The galaxies originated from the perturbation of the initial mass density, which forms today's random gravitational wave background radiation
Since its birth, gravitational waves have almost no attenuation or scattering in the universe. From the perspective of gravitons, it is because gravitons have very small scattering cross sections.The cosmic microwave background radiation reveals the cosmic picture 100000 years after the Big Bang, and the research on Taichu nuclear synthesis reveals the cosmic situation within a few minutes after the Big Bang, while the birth of gravitational waves can be traced back to less than
Seconds.The observation of this gravitational random background radiation is one of the most important topics in gravitational wave astronomy.
Unlike gravitational waves in general cases, which are described by average amplitude, the random background radiation of gravitational waves is usually described by the energy density of the wave field. This random background radiation can come from any celestial body (such as the confusing noise emitted by binary stars such as double white dwarfs), or from a big explosion.For the field in cosmology, the energy density of the field is generally normalized to the critical density of the universe.Although the specific value of the energy density of the gravitational wave field is still uncertain, under the framework of contemporary cosmology, the energy density of the background radiation is constrained by the primordial nucleosynthesis, microwave background radiation and pulsar timing: too high energy flow density will destroy the establishment of the primordial nucleosynthesis theory,Too high energy fluctuations are inconsistent with the actual microwave background radiation with very small anisotropy, and the observation of millisecond pulsar timing confirmed that the background radiation intensity of gravitational waves is not high enough to make the pulsar signal interval observable.
In the inflationary model describing the early universe, gravitons were generated during the Planck period and may be evenly divided according to the degrees of freedom of gravitational field and other fields, which formed the thermal background radiation of gravitational waves whose temperature is equivalent to the microwave background radiation.Later, the universe entered the period of inflation, which provided enough perturbation to the formation of the initial mass density, and this mechanism enabled the formation of galaxies.These perturbations spread to the whole universe in the form of gravitational field perturbations, forming a random background radiation.The random background radiation generated by gravitational waves is considered to be isotropic, static and unpolarized.The spectrum predicted by inflation theory is flat, that is, the energy density is independent of frequency.The Cosmic Background Explorer (COBE) observed the microwave background radiation and found that
The upper limit of energy density at hertz is
[10]。If the inflation theory is correct, it means that the background radiation at all frequencies has the same energy density.Such a low energy density makes it impossible for any existing detector to capture the gravitational wave signal of inflation.In other models different from inflation, for example, the vibration of the cosmic string will also produce gravitational radiation with energy density independent of frequency, and the energy density predicted by the cosmic string has reached the current observable level.
For this signal, LIGO's sensitivity at 100 Hz is
However, the cross correlation calculation of the results obtained from the coincidence measurement of two detectors (such as two detectors LHO and LLO of LIGO, or LIGO and VIRGO, GEO600, etc.) can be improved to
Therefore, cross correlation is an important means to search for this signal.The sensitivity of Advanced LIGO at this frequency is expected to reach
；The sensitivity of LISA at the frequency of 1mHz can be reached, but whether this value can be reached in actual observation depends on whether the background noise generated by double white dwarfs will submerge the random cosmic background radiation.In addition, neutron stars, double neutron stars, black holes and some supernova bursts in the r mode may submerge the cosmic background radiation with frequencies higher than 0.1 millihertz.It is generally believed that the background noise from binary stars decreases rapidly at a frequency lower than 10 microhertz, so space detectors of the order of microhertz may be the best means to detect the cosmic random background radiation.
Advanced theory
Announce
edit
Linear Einstein equation
Gravitational wave ripples in space-time (schematic diagram)
Gravitational waves predicted by general relativity are spatiotemporal disturbances propagating in the form of waves, which are vividly called "spatiotemporal ripples".The weak gravitational field under general relativity can be written as a linear perturbation to flat spacetime: (natural units are used below, and the gravitational constant G and the speed of light c are both set to 1)[4]
, where
here
It is the Minkowski metric of flat space-time,
It is the perturbation caused by weak gravitational field.The Riemann tensor calculated under this metric is
Einstein tensor is
here
，
，
It is called trace reverse metric perturbation.
If the Lorentz gauge is adopted, the last three terms of Einstein tensor will be zero. Here, the Lorentz gauge is in the form of
In fact, such a gauge condition can always be selected, and the Lorentz gauge is not unique, which means that the coordinates still meet the Lorentz gauge under an infinitesimal linear coordinate transformation. For this, please refer to the content about gauge transformation.
Under Lorentz gauge, Einstein tensor is
Substitution into Einstein's gravitational field equation
，
This equation is also called the linear Einstein equation in the weak gravitational field.At far source（
）In the case of, the four-dimensional wave equation with the d'Alembert operator is obtained:
Propagation of gravitational waves
The general solution of the wave equation above is the linear superposition of the following eigenfunctions:[11]
Where is the four-dimensional amplitude, is the four-dimensional wave vector,
, where
Is the angular frequency of the wave,
It is a classical three-dimensional wave vector, meeting the conditions
, which indicates that the geodesic line through which the gravitational wave propagates is zero, that is, its propagation speed is the speed of light.
Since the Lorentz gauge is not unique, the coordinates are not completely determined at this time.If conditions are added:
The first condition indicates that all the components related to time t in the gravitational wave tensor are zero, and the second condition indicates that the trace of the gravitational wave tensor matrix is zero.Therefore, this set of specification conditions is called the transverse traceless gauge, or TT specification for short.Under the TT specification,
。Only two components of gravitational wave tensor determined by Lorentz gauge and TT gauge are independent, and they actually correspond to two polarization states of gravitational wave.For wave vector propagating in z direction
These two vibration components are perpendicular to the propagation direction, which indicates that gravitational waves are shear waves like electromagnetic waves, and their tensor forms are written
among
and
They are respectively the "cross" and "cross" polarization states of the gravitational wave. The two animations in the section "Effects when the gravitational wave passes" above show the different vibration forms of the two polarization states.
Radiation of gravitational waves
The active linear Einstein equation explains how the motion of the wave source generates gravitational radiation:
Similarly, the Poisson equation is used to solve the Newton gravitational potential, and the Green function can be used to obtain a general solution with delayed potential:[11]
here
At the time
, indicating that the gravitational wave comes from the source point
Propagate to site
Time elapsed for
Delay of.
Under the far field approximation and the long wave limit, the Green's function solution is approximately
Where scalar
Is the distance from the source point to the field point.
The Conservation of Mass and Energy and the Conservation of Momentum of Wave Sources in Relativity
So momentum energy tensor
In
(mass energy density) and all other components related to time t
The partial derivatives of (momentum density) with respect to time are all zero, and the solution of the equation can be further simplified as
This is the quadrupole approximation formula of gravitational radiation, which describes the most basic situation of gravitational radiation of a weak relativistic system.It describes the mass energy distribution of the wave source
Tensor here
Is the mass quadrupole moment (moment of inertia tensor) of the system, and
Is the mass energy density of the wave source, and the integral range is within the whole wave source.
The physical meaning of the quadrupole moment formula is that gravitational radiation starts from the quadrupole moment that changes with the second order of time (such as resonance), which is different from electromagnetic radiation: electromagnetic radiation starts from the dipole moment that changes with the second order of time.The source of this difference is that an electric dipole moment or a magnetic dipole moment that changes in the second order with time corresponds to the vibration of the charge density center, which is free and unrestricted;The dipole moment of a mass that changes with the second order of time corresponds to the vibration of the center of mass. This vibration cannot meet the law of conservation of momentum, so there is no such mass dipole moment that the second order partial derivative of time is not zero.Since quadrupole moment is a higher order term of dipole moment, this is also the reason why gravitational radiation is much weaker than electromagnetic radiation.
Energy of gravitational waves
The luminosity (total radiation power) of gravitational wave under quadrupole moment approximation is:[11]
here
Is a tensor matrix
Trace of.The energy flux (radiant power per unit area) of gravitational waves is approximately
Here f is the frequency of monochromatic gravitational waves.
Consider the weak radiation storm that can be sensed by a ground detector, its frequency is 1000 Hz, and the gravitational strength when reaching the earth is
And its energy flux is about
W/
This is twice the electromagnetic radiation energy flux received by the earth from the moon at the full moon, about 1ms long. This gravitational wave source is the brightest star in the night sky.This shows that gravitational waves can actually carry a lot of energy, but the interaction with matter is very small, which is the fundamental reason why gravitational waves are difficult to detect.
Gravitational waves in science fiction
Announce
edit
A chapter of the science fiction "Space Apprenticece" published by former Soviet writers Arkady and Boris Strugatsky in 1962 described the experiment of observing the propagation of gravitational waves, and for this reason destroyed an asteroid 15 Eunomia the size of Mount Everest.[12]
In his 1986 novel Fiasco, Stanislaw Lem invented a "gravity gun" (to enhance gravity by collimating resonance emission) to reshape collapsed stars so that the protagonist can use extreme relativistic effects to travel between stars.
In his 1997 novel Diaspora, Greg Egan analyzed the gravitational wave signals of a group of neighboring neutron stars and found that their collision and merging were imminent, which meant that a large gamma ray burst was about to hit the Earth.
In the "Three Bodies" series created by Chinese science fiction writer Liu Cixin in 2006, gravitational waves are used as interstellar radio communication as the key plot of the conflict between civilizations in the Milky Way.
social influence
Announce
edit
In December 2017, it was selected as one of the five candidate international words of the year in the "Chinese Inventory 2017" activity.[5]
