Gravitational waves are transient displacements in a gravitational field – generated by the relative motion of gravitating masses – that radiate outward from their source at the speed of light . They were first proposed by Oliver Heaviside in 1893 and then later by Henri Poincaré in 1905 as the gravitational equivalent of electromagnetic waves . In 1916, Albert Einstein demonstrated that gravitational waves result from his general theory of relativity as ripples in spacetime .
194-532: The Virgo interferometer is a large-scale instrument for detecting gravitational waves . It is in Santo Stefano a Macerata , near the city of Pisa , Italy. The detector – a Michelson interferometer – has two arms that are 3 kilometres (1.9 mi) long and contain its mirrors and instrumentation in an ultra-high vacuum . Virgo is hosted by the European Gravitational Observatory (EGO),
388-438: A 5 σ {\displaystyle 5\sigma } -significance will be achieved by 2025 by combining the measurements of several collaborations. Gravitational waves are constantly passing Earth ; however, even the strongest have a minuscule effect and their sources are generally at a great distance. For example, the waves given off by the cataclysmic final merger of GW150914 reached Earth after travelling over
582-471: A 1 and a 2 denote the amplitude of the wave in the two components of the electric field vector, while θ 1 and θ 2 represent the phases. The product of a Jones vector with a complex number of unit modulus gives a different Jones vector representing the same ellipse, and thus the same state of polarization. The physical electric field, as the real part of the Jones vector, would be altered but
776-421: A birefringent substance, electromagnetic waves of different polarizations travel at different speeds ( phase velocities ). As a result, when unpolarized waves travel through a plate of birefringent material, one polarization component has a shorter wavelength than the other, resulting in a phase difference between the components which increases the further the waves travel through the material. The Jones matrix
970-776: A decay in the orbit by about 1 × 10 meters per day or roughly the diameter of a proton . At this rate, it would take the Earth approximately 3 × 10 times more than the current age of the universe to spiral onto the Sun. This estimate overlooks the decrease in r over time, but the radius varies only slowly for most of the time and plunges at later stages, as r ( t ) = r 0 ( 1 − t t coalesce ) 1 / 4 , {\displaystyle r(t)=r_{0}\left(1-{\frac {t}{t_{\text{coalesce}}}}\right)^{1/4},} with r 0 {\displaystyle r_{0}}
1164-426: A hyper-compact stellar system . Or it may carry gas, allowing the recoiling black hole to appear temporarily as a " naked quasar ". The quasar SDSS J092712.65+294344.0 is thought to contain a recoiling supermassive black hole. Polarization (waves) Polarization ( also polarisation ) is a property of transverse waves which specifies the geometrical orientation of the oscillations . In
1358-441: A master-slave laser system, where a "master" laser is used to stabilise a high-powered "slave" laser; the master laser was a Nd:YAG laser , and the slave laser was a Nd:YVO4 laser . The Advanced Virgo design uses a fibre laser , with an amplification stage also made of fibres, to improve the system's robustness; its final configuration is planned to combine the light of two lasers to reach the required power. The laser's wavelength
1552-516: A "cross"-polarized gravitational wave, h × , the effect on the test particles would be basically the same, but rotated by 45 degrees, as shown in the second animation. Just as with light polarization, the polarizations of gravitational waves may also be expressed in terms of circularly polarized waves. Gravitational waves are polarized because of the nature of their source. In general terms, gravitational waves are radiated by large, coherent motions of immense mass, especially in regions where gravity
1746-408: A "kick" with amplitude as large as 4000 km/s. This is fast enough to eject the coalesced black hole completely from its host galaxy. Even if the kick is too small to eject the black hole completely, it can remove it temporarily from the nucleus of the galaxy, after which it will oscillate about the center, eventually coming to rest. A kicked black hole can also carry a star cluster with it, forming
1940-465: A billion light-years , as a ripple in spacetime that changed the length of a 4 km LIGO arm by a thousandth of the width of a proton , proportionally equivalent to changing the distance to the nearest star outside the Solar System by one hair's width. This tiny effect from even extreme gravitational waves makes them observable on Earth only with the most sophisticated detectors. The effects of
2134-480: A changing quadrupole moment . That is, the system will give off gravitational waves. In theory, the loss of energy through gravitational radiation could eventually drop the Earth into the Sun . However, the total energy of the Earth orbiting the Sun ( kinetic energy + gravitational potential energy ) is about 1.14 × 10 joules of which only 200 watts (joules per second) is lost through gravitational radiation, leading to
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#17328448695872328-459: A cluster of about 1,500 galaxies in the Virgo constellation about 50 million light-years from Earth. It was conceived and built when gravitational waves were only a prediction of general relativity; the project was first approved in 1992 and the construction was completed in 2003. After several years of improvements without detection, it was shut down in 2011 for the "Advanced Virgo" upgrades. In 2015,
2522-492: A complete relativistic theory of gravitation. He conjectured, like Poincare, that the equation would produce gravitational waves, but, as he mentions in a letter to Schwarzschild in February 1916, these could not be similar to electromagnetic waves. Electromagnetic waves can be produced by dipole motion, requiring both a positive and a negative charge. Gravitation has no equivalent to negative charge. Einstein continued to work through
2716-552: A consortium founded by the French Centre National de la Recherche Scientifique (CNRS) and the Italian Istituto Nazionale di Fisica Nucleare (INFN). The Virgo Collaboration operates the detector, and defines the strategy and policy for its use and upgrades. The Collaboration consists of more than 850 members in 16 countries. The Virgo interferometer works in collaboration with other similar detectors, including
2910-400: A coordinate system and viewing the polarization ellipse in terms of the x and y polarization components, corresponds to the definition of the Jones vector (below) in terms of those basis polarizations. Axes are selected to suit a particular problem, such as x being in the plane of incidence. Since there are separate reflection coefficients for the linear polarizations in and orthogonal to
3104-406: A coupled oscillating electric field and magnetic field which are always perpendicular to each other; by convention, the "polarization" of electromagnetic waves refers to the direction of the electric field. In linear polarization , the fields oscillate in a single direction. In circular or elliptical polarization , the fields rotate at a constant rate in a plane as the wave travels, either in
3298-431: A dedicated building at the end of each arm. South of the west arm, additional buildings contains offices, workshops, as well as the site computing center and the instrument control room. The arm "tunnels" house pipes in which the laser beams travel in a vacuum. Virgo is Europe's largest ultra-high vacuum installation, with a volume of 6,800 cubic meters (1,800,000 U.S. gal). The two 3-km (1.9 mi) arms are made of
3492-490: A detailed version of the "sticky bead argument". This later led to a series of articles (1959 to 1989) by Bondi and Pirani that established the existence of plane wave solutions for gravitational waves. Paul Dirac further postulated the existence of gravitational waves, declaring them to have "physical significance" in his 1959 lecture at the Lindau Meetings . Further, it was Dirac who predicted gravitational waves with
3686-1253: A dielectric, η is real and has the value η 0 / n , where n is the refractive index and η 0 is the impedance of free space . The impedance will be complex in a conducting medium. Note that given that relationship, the dot product of E and H must be zero: E → ( r → , t ) ⋅ H → ( r → , t ) = e x h x + e y h y + e z h z = e x ( − e y η ) + e y ( e x η ) + 0 ⋅ 0 = 0 , {\displaystyle {\begin{aligned}{\vec {E}}\left({\vec {r}},t\right)\cdot {\vec {H}}\left({\vec {r}},t\right)&=e_{x}h_{x}+e_{y}h_{y}+e_{z}h_{z}\\&=e_{x}\left(-{\frac {e_{y}}{\eta }}\right)+e_{y}\left({\frac {e_{x}}{\eta }}\right)+0\cdot 0\\&=0,\end{aligned}}} indicating that these vectors are orthogonal (at right angles to each other), as expected. Knowing
3880-471: A factor of 10, allowing it to probe a volume of the universe 1,000 times larger and making detection of gravitational waves more likely. It benefited from the experience gained with the initial detector and technological advances. The Advanced Virgo detector kept the same vacuum infrastructure as the initial Virgo, but the rest of the interferometer was upgraded. Four additional cryotraps were added at both ends of each arm to trap residual particles coming from
4074-464: A form of radiant energy similar to electromagnetic radiation . Newton's law of universal gravitation , part of classical mechanics , does not provide for their existence, instead asserting that gravity has instantaneous effect everywhere. Gravitational waves therefore stand as an important relativistic phenomenon that is absent from Newtonian physics. In gravitational-wave astronomy , observations of gravitational waves are used to infer data about
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#17328448695874268-399: A frequency of f = c/λ where c is the speed of light), let us take the direction of propagation as the z axis. Being a transverse wave the E and H fields must then contain components only in the x and y directions whereas E z = H z = 0 . Using complex (or phasor ) notation, the instantaneous physical electric and magnetic fields are given by the real parts of
4462-446: A frequency of 0.5 Hz, and a wavelength of about 600 000 km, or 47 times the diameter of the Earth. In the above example, it is assumed that the wave is linearly polarized with a "plus" polarization, written h + . Polarization of a gravitational wave is just like polarization of a light wave except that the polarizations of a gravitational wave are 45 degrees apart, as opposed to 90 degrees. In particular, in
4656-403: A given path on those two components is most easily characterized in the form of a complex 2 × 2 transformation matrix J known as a Jones matrix : e ′ = J e . {\displaystyle \mathbf {e'} =\mathbf {J} \mathbf {e} .} The Jones matrix due to passage through a transparent material is dependent on the propagation distance as well as
4850-469: A long steel pipe 1.2 m (3.9 ft) in diameter, in which the target residual pressure is about one-thousandth of a billionth of an atmosphere (100 times thinner than in the original Virgo). The residual gas molecules, primarily hydrogen and water, have a limited impact on the laser beams' path. Large gate valves are at both ends of the arms so work can be done in the mirror-vacuum towers without breaking an arm's ultra-high vacuum. The towers containing
5044-509: A mirror at the end of each arm. As the gravitational wave passes, it alters the path of the two beams differently; they are then recombined, and the resulting interferometric pattern is measured with a photodiode . Since the induced deformation is extremely small, precision in mirror position, laser stability, measurements, and isolation from outside noise are essential. The laser , the instrument's light source, must be powerful and stable in frequency and amplitude. To meet these specifications,
5238-483: A more general formulation with propagation not restricted to the +z direction, then the spatial dependence kz is replaced by k → ∙ r → where k → is called the wave vector , the magnitude of which is the wavenumber. Thus the leading vectors e and h each contain up to two nonzero (complex) components describing the amplitude and phase of the wave's x and y polarization components (again, there can be no z polarization component for
5432-412: A pair of solar mass neutron stars in a circular orbit at a separation of 1.89 × 10 m (189,000 km) has an orbital period of 1,000 seconds, and an expected lifetime of 1.30 × 10 seconds or about 414,000 years. Such a system could be observed by LISA if it were not too far away. A far greater number of white dwarf binaries exist with orbital periods in this range. White dwarf binaries have masses in
5626-407: A passing gravitational wave, in an extremely exaggerated form, can be visualized by imagining a perfectly flat region of spacetime with a group of motionless test particles lying in a plane, e.g., the surface of a computer screen. As a gravitational wave passes through the particles along a line perpendicular to the plane of the particles, i.e., following the observer's line of vision into the screen,
5820-622: A plane wave with those given parameters can then be used to predict its response to a more general case, since a wave with any specified spatial structure can be decomposed into a combination of plane waves (its so-called angular spectrum ). Incoherent states can be modeled stochastically as a weighted combination of such uncorrelated waves with some distribution of frequencies (its spectrum ), phases, and polarizations. Electromagnetic waves (such as light), traveling in free space or another homogeneous isotropic non-attenuating medium, are properly described as transverse waves , meaning that
6014-434: A plane wave's electric field vector E and magnetic field H are each in some direction perpendicular to (or "transverse" to) the direction of wave propagation; E and H are also perpendicular to each other. By convention, the "polarization" direction of an electromagnetic wave is given by its electric field vector. Considering a monochromatic plane wave of optical frequency f (light of vacuum wavelength λ has
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6208-419: A purely polarized monochromatic wave the electric field vector over one cycle of oscillation traces out an ellipse. A polarization state can then be described in relation to the geometrical parameters of the ellipse, and its "handedness", that is, whether the rotation around the ellipse is clockwise or counter clockwise. One parameterization of the elliptical figure specifies the orientation angle ψ , defined as
6402-426: A random mixture of waves having different spatial characteristics, frequencies (wavelengths), phases, and polarization states. However, for understanding electromagnetic waves and polarization in particular, it is easier to just consider coherent plane waves ; these are sinusoidal waves of one particular direction (or wavevector ), frequency, phase, and polarization state. Characterizing an optical system in relation to
6596-467: A rotating mass at a specific distance from it. At the beginning of the second part of O4, Ncal became the main calibration method because it performed better than PCal; PCal is still used to validate NCal results and probe higher frequencies which are inaccessible to the NCal. The instrument requires an efficient data-acquisition system which manages data measured at the interferometer's output and from sensors on
6790-414: A short-term impact; bad weather or earthquakes may temporarily increase the noise level. Short-lived artefacts may appear in the data due to many possible instrumental issues, and are usually referred to as "glitches". It is estimated that about 20 per cent of detected events are impacted by glitches, requiring specific data-processing methods to mitigate their impact. Sensitivity depends on frequency , and
6984-431: A significant imaginary part (or " extinction coefficient ") such as metals; these fields are also not strictly transverse. Surface waves or waves propagating in a waveguide (such as an optical fiber ) are generally not transverse waves, but might be described as an electric or magnetic transverse mode , or a hybrid mode. Even in free space, longitudinal field components can be generated in focal regions, where
7178-487: A source at 50 Hz (and harmonics at 100, 150, and 200 Hz), corresponding to the frequency of the European power grid ; "violin modes" at 300 Hz (and several harmonics), corresponding to the resonant frequency of the suspension fibres (which can vibrate at a specific frequency, as the strings of a violin do); and calibration lines, appearing when mirrors are moved for calibration. Additional noise sources may have
7372-536: A superposition of right and left circularly polarized states, with equal amplitude and phases synchronized to give oscillation in a plane. Polarization is an important parameter in areas of science dealing with transverse waves, such as optics , seismology , radio , and microwaves . Especially impacted are technologies such as lasers , wireless and optical fiber telecommunications , and radar . Most sources of light are classified as incoherent and unpolarized (or only "partially polarized") because they consist of
7566-774: A total orbital lifetime that may have been billions of years. In August 2017, LIGO and Virgo observed the first binary neutron star inspiral in GW170817 , and 70 observatories collaborated to detect the electromagnetic counterpart, a kilonova in the galaxy NGC 4993 , 40 megaparsecs away, emitting a short gamma ray burst ( GRB 170817A ) seconds after the merger, followed by a longer optical transient ( AT 2017gfo ) powered by r-process nuclei. Advanced LIGO detectors should be able to detect such events up to 200 megaparsecs away; at this range, around 40 detections per year would be expected. Black hole binaries emit gravitational waves during their in-spiral, merger , and ring-down phases. Hence, in
7760-457: A transverse wave in the + z direction). For a given medium with a characteristic impedance η , h is related to e by: h y = e x η h x = − e y η . {\displaystyle {\begin{aligned}h_{y}&={\frac {e_{x}}{\eta }}\\h_{x}&=-{\frac {e_{y}}{\eta }}.\end{aligned}}} In
7954-420: A transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of a polarized transverse wave is vibrations traveling along a taut string (see image) , for example, in a musical instrument like a guitar string . Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to
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8148-476: A universal gravitational wave background . North American Nanohertz Observatory for Gravitational Waves states, that they were created over cosmological time scales by supermassive black holes, identifying the distinctive Hellings-Downs curve in 15 years of radio observations of 25 pulsars. Similar results are published by European Pulsar Timing Array, who claimed a 3 σ {\displaystyle 3\sigma } -significance . They expect that
8342-437: A vacuum. Superattenuator design is based on passive attenuation of seismic noise achieved by chaining several pendula , each a harmonic oscillator . They have a resonant frequency (diminishing with pendulum length) above which noise will be dampened; chaining several pendula reduces noise by twelve orders of magnitude, introducing resonant frequencies which are higher than a single long pendulum. The highest resonant frequency
8536-627: A way to measure the Hubble constant . The Virgo project was approved in 1992 by the French CNRS and the following year by the Italian INFN. Construction of the detector began in 1996 in Santo Stefano a Macerata in Cascina , near Pisa , Italy, and was completed in 2003. After several observation runs in which no gravitational waves were detected, the interferometer was shut down in 2011 for upgrading as part of
8730-540: A well defined energy density in 1964. After the Chapel Hill conference, Joseph Weber started designing and building the first gravitational wave detectors now known as Weber bars . In 1969, Weber claimed to have detected the first gravitational waves, and by 1970 he was "detecting" signals regularly from the Galactic Center ; however, the frequency of detection soon raised doubts on the validity of his observations as
8924-430: Is 1064 nanometres in the original and Advanced Virgo configurations. This laser beam is sent into the interferometer after passing through the injection system, which ensures its stability, adjusts its shape and power, and positions it correctly for entering the interferometer. The injection system includes the input mode cleaner, which is a 140-metre-long (460 ft) cavity designed to improve beam quality by stabilising
9118-534: Is a unitary matrix : | g 1 | = | g 2 | = 1 . Media termed diattenuating (or dichroic in the sense of polarization), in which only the amplitudes of the two polarizations are affected differentially, may be described using a Hermitian matrix (generally multiplied by a common phase factor). In fact, since any matrix may be written as the product of unitary and positive Hermitian matrices, light propagation through any sequence of polarization-dependent optical components can be written as
9312-424: Is about 130,000 seconds or 36 hours. The orbital frequency will vary from 1 orbit per second at the start, to 918 orbits per second when the orbit has shrunk to 20 km at merger. The majority of gravitational radiation emitted will be at twice the orbital frequency. Just before merger, the inspiral could be observed by LIGO if such a binary were close enough. LIGO has only a few minutes to observe this merger out of
9506-411: Is around 2 Hz, providing meaningful noise reduction starting at 4 Hz and reaching the level needed to detect gravitational waves around 10 Hz. The system is limited in that noise in the resonant-frequency band (below 2 Hz) is not filtered and can generate large oscillations; this is mitigated by an active damping system, including sensors measuring seismic noise and actuators controlling
9700-443: Is commonly referred to as transverse-magnetic (TM), and has also been termed pi-polarized or π -polarized , or tangential plane polarized . S -polarization is also called transverse-electric (TE), as well as sigma-polarized or σ-polarized , or sagittal plane polarized . Degree of polarization ( DOP ) is a quantity used to describe the portion of an electromagnetic wave which is polarized. DOP can be calculated from
9894-434: Is dependent on the polarization state of a wave, properties known as birefringence and polarization dichroism (or diattenuation ) respectively, then the polarization state of a wave will generally be altered. In such media, an electromagnetic wave with any given state of polarization may be decomposed into two orthogonally polarized components that encounter different propagation constants . The effect of propagation over
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#173284486958710088-416: Is depicted in the animation on the right. Note that circular or elliptical polarization can involve either a clockwise or counterclockwise rotation of the field, depending on the relative phases of the components. These correspond to distinct polarization states, such as the two circular polarizations shown above. The orientation of the x and y axes used in this description is arbitrary. The choice of such
10282-413: Is identical to one of those basis polarizations. Since the phase shift, and thus the change in polarization state, is usually wavelength-dependent, such objects viewed under white light in between two polarizers may give rise to colorful effects, as seen in the accompanying photograph. Circular birefringence is also termed optical activity , especially in chiral fluids, or Faraday rotation , when due to
10476-462: Is low). From the air, the Virgo detector has an "L" shape with its two 3-km-long (1.9 mi) perpendicular arms. At the intersection of the two arms, the central building is found, containing most of Virgo's key components including the laser, the beamsplitter and the input mirrors. Alongside the west arm, a shorter cavity and the associated building host the input mode-cleaner. The end mirrors are contained in
10670-439: Is more commonly called in astronomy to avoid confusion with the horizontal coordinate system ) corresponding to due north. Another coordinate system frequently used relates to the plane of incidence . This is the plane made by the incoming propagation direction and the vector perpendicular to the plane of an interface, in other words, the plane in which the ray travels before and after reflection or refraction. The component of
10864-402: Is normally not even mentioned. On the other hand, sound waves in a bulk solid can be transverse as well as longitudinal, for a total of three polarization components. In this case, the transverse polarization is associated with the direction of the shear stress and displacement in directions perpendicular to the propagation direction, while the longitudinal polarization describes compression of
11058-491: Is not fully understood, it is not easy to model the gravitational radiation emitted by them. As noted above, a mass distribution will emit gravitational radiation only when there is spherically asymmetric motion among the masses. A spinning neutron star will generally emit no gravitational radiation because neutron stars are highly dense objects with a strong gravitational field that keeps them almost perfectly spherical. In some cases, however, there might be slight deformities on
11252-470: Is part of the larger LIGO-Virgo-KAGRA (LVK) Collaboration, which gathers scientists from the other major gravitational-waves experiments to jointly analyse the data; this is crucial for gravitational-wave detection. LVK began in 2007 as the LIGO-Virgo Collaboration, and was expanded when KAGRA joined in 2019. Virgo is designed to look for gravitational waves emitted by astrophysical sources across
11446-532: Is passed through an ideal polarizer (where g 1 = 1 and g 2 = 0 ) exactly half of its initial power is retained. Practical polarizers, especially inexpensive sheet polarizers, have additional loss so that g 1 < 1 . However, in many instances the more relevant figure of merit is the polarizer's degree of polarization or extinction ratio , which involve a comparison of g 1 to g 2 . Since Jones vectors refer to waves' amplitudes (rather than intensity ), when illuminated by unpolarized light
11640-627: Is polarized. In a vacuum , the components of the electric field propagate at the speed of light , so that the phase of the wave varies in space and time while the polarization state does not. That is, the electric field vector e of a plane wave in the + z direction follows: e ( z + Δ z , t + Δ t ) = e ( z , t ) e i k ( c Δ t − Δ z ) , {\displaystyle \mathbf {e} (z+\Delta z,t+\Delta t)=\mathbf {e} (z,t)e^{ik(c\Delta t-\Delta z)},} where k
11834-407: Is so strong that Newtonian gravity begins to fail. The effect does not occur in a purely spherically symmetric system. A simple example of this principle is a spinning dumbbell . If the dumbbell spins around its axis of symmetry, it will not radiate gravitational waves; if it tumbles end over end, as in the case of two planets orbiting each other, it will radiate gravitational waves. The heavier
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#173284486958712028-446: Is the wavenumber . As noted above, the instantaneous electric field is the real part of the product of the Jones vector times the phase factor e − i ω t {\displaystyle e^{-i\omega t}} . When an electromagnetic wave interacts with matter, its propagation is altered according to the material's (complex) index of refraction . When the real or imaginary part of that refractive index
12222-452: Is the horizon distance, defined as the distance at which a reference target produces a signal-to-noise ratio of 8 in the detector. The reference is usually a binary neutron star with both components having a mass of 1.4 solar masses ; the distance is generally expressed in megaparsecs. The range for Virgo during the O3 run was between 40 and 50 Mpc. This range is an indicator, not a maximal range for
12416-402: Is the wavelength in the medium (whose refractive index is n ) and T = 1/ f is the period of the wave. Here e x , e y , h x , and h y are complex numbers. In the second more compact form, as these equations are customarily expressed, these factors are described using the wavenumber k = 2π n / λ 0 and angular frequency (or "radian frequency") ω = 2π f . In
12610-664: Is under development. A space-based observatory, the Laser Interferometer Space Antenna (LISA), is also being developed by the European Space Agency . Gravitational waves do not strongly interact with matter in the way that electromagnetic radiation does. This allows for the observation of events involving exotic objects in the distant universe that cannot be observed with more traditional means such as optical telescopes or radio telescopes ; accordingly, gravitational wave astronomy gives new insights into
12804-605: Is used for joint observing runs with the other detectors, separated by commissioning periods during which it is upgraded to increase its sensitivity and scientific output. The Virgo project is managed by the European Gravitational Observatory (EGO) consortium, which was created in December 2000 by the French National Centre for Scientific Research (CNRS) and the Istituto Nazionale di Fisica Nucleare (INFN). Nikhef ,
12998-411: Is usually represented as a curve corresponding to the noise power spectrum (or amplitude spectrum, the square root of the power spectrum); the lower the curve, the greater the sensitivity. Virgo is a wide-band detector whose sensitivity ranges from a few Hz to 10 kHz; a 2011 Virgo sensitivity curve is plotted with a log-log scale . The most common measure of gravitational-wave-detector sensitivity
13192-630: The COVID-19 pandemic . The upgrades following O3 are part of the Advanced Virgo + program, divided into two phases; the first preceded the O4 run, and the second precedes the O5 run. The first phase focused on the reduction of quantum noise by introducing a more powerful laser, improving the squeezing introduced in O3, and implementing a new technique known as signal recycling ; seismic sensors were also installed around
13386-458: The LIGO and Virgo detectors received gravitational wave signals at nearly the same time as gamma ray satellites and optical telescopes saw signals from a source located about 130 million light years away. The possibility of gravitational waves and that those might travel at the speed of light was discussed in 1893 by Oliver Heaviside , using the analogy between the inverse-square law of gravitation and
13580-459: The Stokes parameters . A perfectly polarized wave has a DOP of 100%, whereas an unpolarized wave has a DOP of 0%. A wave which is partially polarized, and therefore can be represented by a superposition of a polarized and unpolarized component, will have a DOP somewhere in between 0 and 100%. DOP is calculated as the fraction of the total power that is carried by the polarized component of
13774-459: The complexity of the equations of general relativity to find an alternative wave model. The result was published in June 1916, and there he came to the conclusion that the gravitational wave must propagate with the speed of light, and there must, in fact, be three types of gravitational waves dubbed longitudinal–longitudinal, transverse–longitudinal, and transverse–transverse by Hermann Weyl . However,
13968-405: The electric displacement D and magnetic flux density B still obey the above geometry but due to anisotropy in the electric susceptibility (or in the magnetic permeability ), now given by a tensor , the direction of E (or H ) may differ from that of D (or B ). Even in isotropic media, so-called inhomogeneous waves can be launched into a medium whose refractive index has
14162-513: The electrostatic force . In 1905, Henri Poincaré proposed gravitational waves, emanating from a body and propagating at the speed of light, as being required by the Lorentz transformations and suggested that, in analogy to an accelerating electrical charge producing electromagnetic waves , accelerated masses in a relativistic field theory of gravity should produce gravitational waves. In 1915 Einstein published his general theory of relativity ,
14356-405: The ellipticity angle , χ = arctan b / a {\textstyle \chi =\arctan b/a} = arctan 1 / ε {\textstyle =\arctan 1/\varepsilon } as is shown in the figure. The angle χ is also significant in that the latitude (angle from the equator) of the polarization state as represented on
14550-499: The first observation of gravitational waves was made by the two LIGO detectors, while Virgo was still being upgraded. It resumed observations in early August 2017, making its first detection on 14 August (together with the LIGO detectors); this was quickly followed by the detection of the GW170817 gravitational wave, the only one observed with classical methods ( optical , gamma-ray , X-ray and radio telescopes) as of 2024. The detector
14744-404: The quadrupole moment (or the l -th time derivative of the l -th multipole moment ) of an isolated system's stress–energy tensor must be non-zero in order for it to emit gravitational radiation. This is analogous to the changing dipole moment of charge or current that is necessary for the emission of electromagnetic radiation . Gravitational waves carry energy away from their sources and, in
14938-462: The right-hand or in the left-hand direction. Light or other electromagnetic radiation from many sources, such as the sun, flames, and incandescent lamps , consists of short wave trains with an equal mixture of polarizations; this is called unpolarized light . Polarized light can be produced by passing unpolarized light through a polarizer , which allows waves of only one polarization to pass through. The most common optical materials do not affect
15132-427: The xy -plane, along the page, with the wave propagating in the z direction, perpendicular to the page. The first two diagrams below trace the electric field vector over a complete cycle for linear polarization at two different orientations; these are each considered a distinct state of polarization (SOP). The linear polarization at 45° can also be viewed as the addition of a horizontally linearly polarized wave (as in
15326-463: The Advanced Virgo project. It began making observations again in 2017, quickly making its first detections with the LIGO detectors. Although the concept of gravitational waves was presented by Albert Einstein in 1916, serious projects for detecting them only began during the 1970s. The first were the Weber bars , invented by Joseph Weber ; although they could detect gravitational waves in theory, none of
15520-582: The BICEP2 collaboration claimed that they had detected the imprint of gravitational waves in the cosmic microwave background . However, they were later forced to retract this result. In 2017, the Nobel Prize in Physics was awarded to Rainer Weiss , Kip Thorne and Barry Barish for their role in the detection of gravitational waves. In 2023, NANOGrav, EPTA, PPTA, and IPTA announced that they found evidence of
15714-493: The CNRS and the INFN, construction of the interferometer began in 1996 with the aim of beginning observations by 2000. Virgo's first goal was to directly observe gravitational waves, whose existence was already indirectly evidenced by the three-decade study of the binary pulsar 1913+16 : the observed decrease of this binary pulsar 's orbital period was in agreement with the hypothesis that
15908-692: The Dutch Institute for Nuclear and High-Energy Physics, later joined as an observer and eventually became a full member. EGO is responsible for the Virgo site and is in charge of the commissioning, maintenance, and operation of the detector and its upgrades. By metonymy , the site itself is sometimes referred to as EGO, as it represents its headquarters. One of EGO's goals is to promote research on gravity in Europe. The budget of EGO fluctuates between 9 and 11.5 million euros per year (2018-2024 period), employing around 60 people. The Virgo Collaboration consists of all
16102-421: The Jones matrix can be written as J = T [ g 1 0 0 g 2 ] T − 1 , {\displaystyle \mathbf {J} =\mathbf {T} {\begin{bmatrix}g_{1}&0\\0&g_{2}\end{bmatrix}}\mathbf {T} ^{-1},} where g 1 and g 2 are complex numbers describing the phase delay and possibly
16296-496: The O4 run during its first part (O4a, which ended on 16 January 2024), since it only reached a peak sensitivity of 45 Mpc instead of the 80 to 115 Mpc initially expected; it joined the second part of the run (O4b), which began on 10 April 2024, with a sensitivity of 50 to 55 Mpc. In June 2024, it was announced that the O4 run would last until 9 June 2025 to further prepare for the O5 upgrades. The detector will again be shut down for upgrades, including mirror-coating improvement, after
16490-403: The O4 run. A fifth observing run (O5) is planned to begin around June 2027. Virgo's target sensitivity, originally set at 150–260 Mpc, is being redefined in light of its performance during O4. Plans to enter the O5 run are expected to be known before the end of 2024. No official plans have been announced for the future of the Virgo installations after the O5 period, although projects for improving
16684-458: The Poincaré sphere (see below) is equal to ±2 χ . The special cases of linear and circular polarization correspond to an ellipticity ε of infinity and unity (or χ of zero and 45°) respectively. Full information on a completely polarized state is also provided by the amplitude and phase of oscillations in two components of the electric field vector in the plane of polarization. This representation
16878-628: The Universe when space expanded by a large factor in a very short amount of time. If this expansion was not symmetric in all directions, it may have emitted gravitational radiation detectable today as a gravitational wave background . This background signal is too weak for any currently operational gravitational wave detector to observe, and it is thought it may be decades before such an observation can be made. Water waves, sound waves, and electromagnetic waves are able to carry energy , momentum , and angular momentum and by doing so they carry those away from
17072-427: The amplitude attenuation due to propagation in each of the two polarization eigenmodes . T is a unitary matrix representing a change of basis from these propagation modes to the linear system used for the Jones vectors; in the case of linear birefringence or diattenuation the modes are themselves linear polarization states so T and T can be omitted if the coordinate axes have been chosen appropriately. In
17266-439: The angle between the major axis of the ellipse and the x -axis along with the ellipticity ε = a/b , the ratio of the ellipse's major to minor axis. (also known as the axial ratio ). The ellipticity parameter is an alternative parameterization of an ellipse's eccentricity e = 1 − b 2 / a 2 , {\textstyle e={\sqrt {1-b^{2}/a^{2}}},} or
17460-445: The baffles from affecting interferometer operation. Calibration is required to estimate the detector's response to gravitational waves and correctly reconstruct the signal. It involves moving the mirrors in a controlled way and measuring the result. During the initial Virgo era, this was primarily achieved by agitating a pendulum on which the mirror is suspended with coils to generate a magnetic field interacting with magnets fixed to
17654-435: The beam starts from a low-power, stable laser. Light from the laser passes through several amplifiers, which enhance its power by a factor of 100. A 50 watt (W) output power was achieved for the last configuration of the initial Virgo detector (reaching 100 W during the O3 run after the Advanced Virgo upgrades), and is expected to be upgraded to 130 W at the beginning of the O4 run. The original Virgo detector had
17848-451: The birefringence. The birefringence (as well as the average refractive index) will generally be dispersive , that is, it will vary as a function of optical frequency (wavelength). In the case of non-birefringent materials, however, the 2 × 2 Jones matrix is the identity matrix (multiplied by a scalar phase factor and attenuation factor), implying no change in polarization during propagation. For propagation effects in two orthogonal modes,
18042-480: The case of linear birefringence (with two orthogonal linear propagation modes) with an incoming wave linearly polarized at a 45° angle to those modes. As a differential phase starts to accrue, the polarization becomes elliptical, eventually changing to purely circular polarization (90° phase difference), then to elliptical and eventually linear polarization (180° phase) perpendicular to the original polarization, then through circular again (270° phase), then elliptical with
18236-513: The case of orbiting bodies, this is associated with an in-spiral or decrease in orbit. Imagine for example a simple system of two masses – such as the Earth–Sun system – moving slowly compared to the speed of light in circular orbits. Assume that these two masses orbit each other in a circular orbit in the x – y plane. To a good approximation, the masses follow simple Keplerian orbits . However, such an orbit represents
18430-1575: The complex quantities occurring in the following equations. As a function of time t and spatial position z (since for a plane wave in the + z direction the fields have no dependence on x or y ) these complex fields can be written as: E → ( z , t ) = [ e x e y 0 ] e i 2 π ( z λ − t T ) = [ e x e y 0 ] e i ( k z − ω t ) {\displaystyle {\vec {E}}(z,t)={\begin{bmatrix}e_{x}\\e_{y}\\0\end{bmatrix}}\;e^{i2\pi \left({\frac {z}{\lambda }}-{\frac {t}{T}}\right)}={\begin{bmatrix}e_{x}\\e_{y}\\0\end{bmatrix}}\;e^{i(kz-\omega t)}} and H → ( z , t ) = [ h x h y 0 ] e i 2 π ( z λ − t T ) = [ h x h y 0 ] e i ( k z − ω t ) , {\displaystyle {\vec {H}}(z,t)={\begin{bmatrix}h_{x}\\h_{y}\\0\end{bmatrix}}\;e^{i2\pi \left({\frac {z}{\lambda }}-{\frac {t}{T}}\right)}={\begin{bmatrix}h_{x}\\h_{y}\\0\end{bmatrix}}\;e^{i(kz-\omega t)},} where λ = λ 0 / n
18624-501: The construction of GEO600 , LIGO , and Virgo . After years of producing null results, improved detectors became operational in 2015. On 11 February 2016, the LIGO-Virgo collaborations announced the first observation of gravitational waves , from a signal (dubbed GW150914 ) detected at 09:50:45 GMT on 14 September 2015 of two black holes with masses of 29 and 36 solar masses merging about 1.3 billion light-years away. During
18818-428: The crystal. It was this effect that provided the first discovery of polarization, by Erasmus Bartholinus in 1669. Media in which transmission of one polarization mode is preferentially reduced are called dichroic or diattenuating . Like birefringence, diattenuation can be with respect to linear polarization modes (in a crystal) or circular polarization modes (usually in a liquid). Devices that block nearly all of
19012-504: The data-acquisition software and tools for distributing the data, the effort is shared with members of the LIGO and KAGRA collaborations as part of the LIGO-Virgo-KAGRA (LVK) collaboration. Data from the detector is initially only available to LVK members. Segments of data surrounding detected events are released at the publication of the related paper, and the full data is released after a proprietary period (currently 18 months). During
19206-645: The decay predicted by general relativity as energy is lost to gravitational radiation. In 1993, Russell A. Hulse and Joseph Hooton Taylor Jr. received the Nobel Prize in Physics for this discovery. The first direct observation of gravitational waves was made in September 2015, when a signal generated by the merger of two black holes was received by the LIGO gravitational wave detectors in Livingston, Louisiana, and in Hanford, Washington. The 2017 Nobel Prize in Physics
19400-455: The detection of gravitational waves using laser interferometers. The idea of using a laser interferometer for this seems to have been floated independently by various people, including M.E. Gertsenshtein and V. I. Pustovoit in 1962, and Vladimir B. Braginskiĭ in 1966. The first prototypes were developed in the 1970s by Robert L. Forward and Rainer Weiss. In the decades that followed, ever more sensitive instruments were constructed, culminating in
19594-428: The detector; signals from more massive sources will have a larger amplitude, and can be detected from further away. Calculations indicate that the detector sensitivity roughly scales as 1 L × P {\displaystyle {\frac {1}{L\times {\sqrt {P}}}}} , where L {\displaystyle L} is the arm-cavity length and P {\displaystyle P}
19788-484: The detectors have been suggested. The collaboration's current plans are known as the Virgo_nEXT project. In general relativity, a gravitational wave is a space-time perturbation which propagates at the speed of light. It slightly curves spacetime, changing the light path. This can be detected with a Michelson interferometer , in which a laser is divided into two beams travelling in orthogonal directions, bouncing on
19982-412: The different propagation of waves in two such components in circularly birefringent media (see below) or signal paths of coherent detectors sensitive to circular polarization. Regardless of whether polarization state is represented using geometric parameters or Jones vectors, implicit in the parameterization is the orientation of the coordinate frame. This permits a degree of freedom, namely rotation about
20176-457: The distance (not distance squared) from the source. Inspiraling binary neutron stars are predicted to be a powerful source of gravitational waves as they coalesce , due to the very large acceleration of their masses as they orbit close to one another. However, due to the astronomical distances to these sources, the effects when measured on Earth are predicted to be very small, having strains of less than 1 part in 10 . Scientists demonstrate
20370-401: The dumbbell, and the faster it tumbles, the greater is the gravitational radiation it will give off. In an extreme case, such as when the two weights of the dumbbell are massive stars like neutron stars or black holes, orbiting each other quickly, then significant amounts of gravitational radiation would be given off. Some more detailed examples: More technically, the second time derivative of
20564-486: The early 1990s the physics community rallied around a concerted effort to predict the waveforms of gravitational waves from these systems with the Binary Black Hole Grand Challenge Alliance . The largest amplitude of emission occurs during the merger phase, which can be modeled with the techniques of numerical relativity. The first direct detection of gravitational waves, GW150914 , came from
20758-528: The effects of heating induced by the laser (despite extremely low absorption ). These effects can cause deformation of the surface due to dilation or a change in refractive index of the substrate , resulting in power escaping from the interferometer and perturbations of the signal. These effects are accounted for by a thermal compensation system (TCS) which includes Hartmann wavefront sensors to measure optical aberration through an auxiliary light source, and two actuators : CO 2 lasers (which heat parts of
20952-406: The electric field parallel to this plane is termed p-like (parallel) and the component perpendicular to this plane is termed s-like (from senkrecht , German for 'perpendicular'). Polarized light with its electric field along the plane of incidence is thus denoted p-polarized , while light whose electric field is normal to the plane of incidence is called s-polarized . P -polarization
21146-510: The end of the O2 run. LIGO and Virgo detected the GW170814 signal on 14 August 2017, which was reported on 27 September of that year. It was the first binary black hole merger detected by both LIGO and Virgo, and the first for Virgo. GW170817 was detected by LIGO and Virgo on 17 August 2017. The signal, produced by the final minutes of two neutron stars spiralling closer to each other and merging ,
21340-537: The ends of the 3-km (1.9 mi) interferometer arms and the two input mirrors near the beginning of the arms. These mirrors make a resonant optical cavity in each arm in which the light bounces thousands of times before returning to the beam splitter, maximising the signal's effect on the laser path and allowing the power of the light circulating in the arms to be increased. These mirrors (designed for Virgo) are cylinders 35 cm (14 in) in diameter and 20 cm (7.9 in) thick, made from extremely pure glass. During
21534-482: The existence of these waves with highly-sensitive detectors at multiple observation sites. As of 2012 , the LIGO and VIRGO observatories were the most sensitive detectors, operating at resolutions of about one part in 5 × 10 . The Japanese detector KAGRA was completed in 2019; its first joint detection with LIGO and VIRGO was reported in 2021. Another European ground-based detector, the Einstein Telescope ,
21728-515: The experiments succeeded. However, they sparked the creation of research groups dedicated to gravitational waves. The idea of a large interferometric detector began to gain credibility during the early 1980s, and the Virgo project was conceptualised by Italian researcher Adalberto Giazotto and French researcher Alain Brillet in 1985 after they met in Rome . A key idea that set Virgo apart from other projects
21922-426: The final fraction of a second of the merger, it released more than 50 times the power of all the stars in the observable universe combined. The signal increased in frequency from 35 to 250 Hz over 10 cycles (5 orbits) as it rose in strength for a period of 0.2 second. The mass of the new merged black hole was 62 solar masses. Energy equivalent to three solar masses was emitted as gravitational waves. The signal
22116-410: The frequency, removing unwanted light propagation and reducing the effect of laser misalignment. It also features a Faraday isolator preventing light from returning to the laser, and a mode-matching telescope which adapts the size and position of the beam before it enters the interferometer. The large mirrors in each arm are the interferometer's most critical optics. They include the two end mirrors at
22310-528: The general theory of relativity. In principle, gravitational waves can exist at any frequency. Very low frequency waves can be detected using pulsar timing arrays. In this technique, the timing of approximately 100 pulsars spread widely across our galaxy is monitored over the course of years. Detectable changes in the arrival time of their signals can result from passing gravitational waves generated by merging supermassive black holes with wavelengths measured in lightyears. These timing changes can be used to locate
22504-500: The implied rate of energy loss of the Milky Way would drain our galaxy of energy on a timescale much shorter than its inferred age. These doubts were strengthened when, by the mid-1970s, repeated experiments from other groups building their own Weber bars across the globe failed to find any signals, and by the late 1970s consensus was that Weber's results were spurious. In the same period, the first indirect evidence of gravitational waves
22698-510: The initial Virgo detector was completed in June 2003, and several data collection periods ("science runs") followed between 2007 and 2011, after 4 years of commissioning. Some of the runs were performed with the two LIGO detectors (which are located in Hanford , Washington and in Livingston, Louisiana ). There was a shut-down of a few months in 2010 for an upgrade of the Virgo suspension system, and
22892-537: The initial radius and t coalesce {\displaystyle t_{\text{coalesce}}} the total time needed to fully coalesce. More generally, the rate of orbital decay can be approximated by where r is the separation between the bodies, t time, G the gravitational constant , c the speed of light , and m 1 and m 2 the masses of the bodies. This leads to an expected time to merger of Compact stars like white dwarfs and neutron stars can be constituents of binaries. For example,
23086-404: The injection optics used to shape the laser beam, such as the optical benches used for the light detection, are also suspended in a vacuum to limit seismic and acoustic noise. In the Advanced Virgo configuration, the instrumentation used to detect gravitational-wave signals and steer the interferometer ( photodiodes , cameras, and associated electronics) is installed on several benches suspended in
23280-404: The interferometer's designated path) by scattering on a surface or from unwanted reflection. Recombination of stray light with the interferometer's main beam can be a significant noise source, often difficult to track and model. Most efforts to mitigate stray light are based on absorbing plates (known as baffles) placed near the optics and within the tubes; additional precautions are taken to prevent
23474-401: The kind of oscillations associated with gravitational waves as produced by a pair of masses in a circular orbit . In this case the amplitude of the gravitational wave is constant, but its plane of polarization changes or rotates at twice the orbital rate, so the time-varying gravitational wave size, or 'periodic spacetime strain', exhibits a variation as shown in the animation. If the orbit of
23668-420: The laser power on the beam splitter. To improve it, these quantities must be increased. This is achieved with long arms, optical cavities inside the arm to maximise exposure to the signal, and power recycling to increase power in the arms. An important part of Virgo collaboration resources is dedicated to the development and deployment of data-analysis software designed to process the detector's output. Apart from
23862-414: The leftmost figure) and a vertically polarized wave of the same amplitude in the same phase . [REDACTED] [REDACTED] [REDACTED] Now if one were to introduce a phase shift in between those horizontal and vertical polarization components, one would generally obtain elliptical polarization as is shown in the third figure. When the phase shift is exactly ±90°, and the amplitudes are
24056-506: The length of the vector measured from the center of the sphere. Unpolarized light is light with a random, time-varying polarization . Natural light, like most other common sources of visible light, is produced independently by a large number of atoms or molecules whose emissions are uncorrelated . Unpolarized light can be produced from the incoherent combination of vertical and horizontal linearly polarized light, or right- and left-handed circularly polarized light. Conversely,
24250-437: The manufacturing process, the mirrors are polished to the atomic level to avoid diffusing (and losing) any light. A reflective coating (a Bragg reflector made with ion-beam sputtering ) is then added. The mirrors at the end of the arms reflect almost all incoming light, with less than 0.002 per cent lost at each reflection. Two other mirrors are also in the final design: To mitigate seismic noise which could propagate up to
24444-489: The masses is elliptical then the gravitational wave's amplitude also varies with time according to Einstein's quadrupole formula . As with other waves , there are a number of characteristics used to describe a gravitational wave: The speed, wavelength, and frequency of a gravitational wave are related by the equation c = λf , just like the equation for a light wave . For example, the animations shown here oscillate roughly once every two seconds. This would correspond to
24638-449: The merger of two black holes. A supernova is a transient astronomical event that occurs during the last stellar evolutionary stages of a massive star's life, whose dramatic and catastrophic destruction is marked by one final titanic explosion. This explosion can happen in one of many ways, but in all of them a significant proportion of the matter in the star is blown away into the surrounding space at extremely high velocities (up to 10% of
24832-486: The mirror to correct the defects) and ring heaters, which adjust the mirror's radius of curvature . The system also corrects "cold defects": permanent defects introduced during mirror manufacture. During the O3 run, the TCS increased power inside the interferometer by 15 per cent and decreased power leaving the interferometer by a factor of two. Another important component is the system for controlling stray light (any light leaving
25026-405: The mirror towers. The new mirrors were larger, with a diameter of 35 cm (14 in) and a weight of 40 kg (88 lb), and their optical performance was improved. The optical elements used to control the interferometer were under vacuum on suspended mountings. A system of adaptive optics were installed to correct the mirror aberrations in situ . In the original plan, the laser power
25220-425: The mirrors and attenuators are split into two sections, with different pressures. The tubes undergo a process, known as baking, in which they are heated to 150 °C (302 °F) to remove unwanted particles from their surfaces; although the towers were also baked in the initial Virgo design, cryogenic traps are now used to prevent contamination. Due to the interferometer's high power, its mirrors are susceptible to
25414-457: The mirrors, shaking them and obscuring potential gravitational-wave signals, the mirrors are suspended by a complex system. The main mirrors are suspended by four thin fibres made of silica which are attached to a series of attenuators. This superattenuator, nearly 8 metres (26 ft) high, is in a vacuum. The superattenuators limit disturbances to the mirrors and allow mirror position and orientation to be precisely steered. The optical table with
25608-416: The mirrors. The second phase will attempt to reduce the mirror thermal noise by changing the geometry of the laser beam to increase its size on the mirrors (spreading the energy on a larger area and thus reducing the temperature) and improving the coating of the mirrors; the end mirrors will be larger, requiring improvements to the suspension. Further improvements for quantum noise reduction are also expected in
25802-429: The motion is not spherically symmetric, the motion can cause gravitational waves which propagate away at the speed of light . As a gravitational wave passes an observer, that observer will find spacetime distorted by the effects of strain . Distances between objects increase and decrease rhythmically as the wave passes, at a frequency equal to that of the wave. The magnitude of this effect is inversely proportional to
25996-400: The nature of Einstein's approximations led many (including Einstein himself) to doubt the result. In 1922, Arthur Eddington showed that two of Einstein's types of waves were artifacts of the coordinate system he used, and could be made to propagate at any speed by choosing appropriate coordinates, leading Eddington to jest that they "propagate at the speed of thought". This also cast doubt on
26190-421: The only type of source detected until now. Analysis software is running the data in search of this type of event, and a dedicated infrastructure is used to alert the online community. Other efforts are carried out after the data-acquisition period (offline), including searches for continuous sources, a stochastic background , or deeper analysis of detected events. Virgo first detected a gravitational signal during
26384-437: The order of the Sun , and diameters in the order of the Earth. They cannot get much closer together than 10,000 km before they will merge and explode in a supernova which would also end the emission of gravitational waves. Until then, their gravitational radiation would be comparable to that of a neutron star binary. When the orbit of a neutron star binary has decayed to 1.89 × 10 m (1890 km), its remaining lifetime
26578-472: The original azimuth angle, and finally back to the original linearly polarized state (360° phase) where the cycle begins anew. In general the situation is more complicated and can be characterized as a rotation in the Poincaré sphere about the axis defined by the propagation modes. Examples for linear (blue), circular (red), and elliptical (yellow) birefringence are shown in the figure on the left. The total intensity and degree of polarization are unaffected. If
26772-423: The original steel suspension wires were replaced by glass fibres to reduce thermal noise. Even after several months of data collection with the upgraded suspension system, no gravitational waves were observed, and the detector was shut down in September 2011 for the installation of Advanced Virgo. The Advanced Virgo detector aimed to increase the sensitivity (and the distance from which a signal can be detected) by
26966-475: The overall magnitude and phase of that wave. Specifically, the intensity of the light wave is proportional to the sum of the squared magnitudes of the two electric field components: I = ( | e x | 2 + | e y | 2 ) 1 2 η {\displaystyle I=\left(\left|e_{x}\right|^{2}+\left|e_{y}\right|^{2}\right)\,{\frac {1}{2\eta }}} However,
27160-441: The paper was rewritten with the opposite conclusion and published elsewhere. In 1956, Felix Pirani remedied the confusion caused by the use of various coordinate systems by rephrasing the gravitational waves in terms of the manifestly observable Riemann curvature tensor . At the time, Pirani's work was overshadowed by the community's focus on a different question: whether gravitational waves could transmit energy . This matter
27354-478: The particles will follow the distortion in spacetime, oscillating in a " cruciform " manner, as shown in the animations. The area enclosed by the test particles does not change and there is no motion along the direction of propagation. The oscillations depicted in the animation are exaggerated for the purpose of discussion – in reality a gravitational wave has a very small amplitude (as formulated in linearized gravity ). However, they help illustrate
27548-447: The path length in the birefringent medium is sufficient, the two polarization components of a collimated beam (or ray ) can exit the material with a positional offset, even though their final propagation directions will be the same (assuming the entrance face and exit face are parallel). This is commonly viewed using calcite crystals , which present the viewer with two slightly offset images, in opposite polarizations, of an object behind
27742-453: The pendulum. This technique was used until O2. For O3, the primary calibration method was photon calibration (PCal); it had been a secondary method to validate the results, using an auxiliary laser to displace the mirror with radiation pressure . A method known as Newtonian calibration (NCal) was introduced at the end of O2 to validate the PCal results; it relies on gravity to move the mirror, placing
27936-545: The phase of e x is zero; in other words e x is a real number while e y may be complex. Under these restrictions, e x and e y can be represented as follows: e x = 1 + Q 2 e y = 1 − Q 2 e i ϕ , {\displaystyle {\begin{aligned}e_{x}&={\sqrt {\frac {1+Q}{2}}}\\e_{y}&={\sqrt {\frac {1-Q}{2}}}\,e^{i\phi },\end{aligned}}} where
28130-510: The physicality of the third (transverse–transverse) type that Eddington showed always propagate at the speed of light regardless of coordinate system. In 1936, Einstein and Nathan Rosen submitted a paper to Physical Review in which they claimed gravitational waves could not exist in the full general theory of relativity because any such solution of the field equations would have a singularity. The journal sent their manuscript to be reviewed by Howard P. Robertson , who anonymously reported that
28324-458: The plane of incidence ( p and s polarizations, see below), that choice greatly simplifies the calculation of a wave's reflection from a surface. Any pair of orthogonal polarization states may be used as basis functions, not just linear polarizations. For instance, choosing right and left circular polarizations as basis functions simplifies the solution of problems involving circular birefringence (optical activity) or circular dichroism. For
28518-409: The plane wave approximation breaks down. An extreme example is radially or tangentially polarized light, at the focus of which the electric or magnetic field respectively is entirely longitudinal (along the direction of propagation). For longitudinal waves such as sound waves in fluids , the direction of oscillation is by definition along the direction of travel, so the issue of polarization
28712-457: The polarization of a coherent wave cannot be described simply using a Jones vector, as we have just done. Just considering electromagnetic waves, we note that the preceding discussion strictly applies to plane waves in a homogeneous isotropic non-attenuating medium, whereas in an anisotropic medium (such as birefringent crystals as discussed below) the electric or magnetic field may have longitudinal as well as transverse components. In those cases
28906-440: The polarization of an electromagnetic wave is determined by a quantum mechanical property of photons called their spin . A photon has one of two possible spins: it can either spin in a right hand sense or a left hand sense about its direction of travel. Circularly polarized electromagnetic waves are composed of photons with only one type of spin, either right- or left-hand. Linearly polarized waves consist of photons that are in
29100-456: The polarization of light, but some materials—those that exhibit birefringence , dichroism , or optical activity —affect light differently depending on its polarization. Some of these are used to make polarizing filters. Light also becomes partially polarized when it reflects at an angle from a surface. According to quantum mechanics , electromagnetic waves can also be viewed as streams of particles called photons . When viewed in this way,
29294-481: The polarization state is now fully parameterized by the value of Q (such that −1 < Q < 1 ) and the relative phase ϕ . In addition to transverse waves, there are many wave motions where the oscillation is not limited to directions perpendicular to the direction of propagation. These cases are far beyond the scope of the current article which concentrates on transverse waves (such as most electromagnetic waves in bulk media), but one should be aware of cases where
29488-403: The polarization state itself is independent of absolute phase . The basis vectors used to represent the Jones vector need not represent linear polarization states (i.e. be real ). In general any two orthogonal states can be used, where an orthogonal vector pair is formally defined as one having a zero inner product . A common choice is left and right circular polarizations, for example to model
29682-420: The presence of a magnetic field along the direction of propagation. When linearly polarized light is passed through such an object, it will exit still linearly polarized, but with the axis of polarization rotated. A combination of linear and circular birefringence will have as basis polarizations two orthogonal elliptical polarizations; however, the term "elliptical birefringence" is rarely used. One can visualize
29876-500: The product of these two basic types of transformations. In birefringent media there is no attenuation, but two modes accrue a differential phase delay. Well known manifestations of linear birefringence (that is, in which the basis polarizations are orthogonal linear polarizations) appear in optical wave plates /retarders and many crystals. If linearly polarized light passes through a birefringent material, its state of polarization will generally change, unless its polarization direction
30070-418: The propagation direction ( + z in this case) and η , one can just as well specify the wave in terms of just e x and e y describing the electric field. The vector containing e x and e y (but without the z component which is necessarily zero for a transverse wave) is known as a Jones vector . In addition to specifying the polarization state of the wave, a general Jones vector also specifies
30264-420: The propagation direction. When considering light that is propagating parallel to the surface of the Earth, the terms "horizontal" and "vertical" polarization are often used, with the former being associated with the first component of the Jones vector, or zero azimuth angle. On the other hand, in astronomy the equatorial coordinate system is generally used instead, with the zero azimuth (or position angle, as it
30458-437: The radiation in one mode are known as polarizing filters or simply " polarizers ". This corresponds to g 2 = 0 in the above representation of the Jones matrix. The output of an ideal polarizer is a specific polarization state (usually linear polarization) with an amplitude equal to the input wave's original amplitude in that polarization mode. Power in the other polarization mode is eliminated. Thus if unpolarized light
30652-456: The remaining power in the unwanted polarization will be ( g 2 / g 1 ) of the power in the intended polarization. In addition to birefringence and dichroism in extended media, polarization effects describable using Jones matrices can also occur at (reflective) interface between two materials of different refractive index . These effects are treated by the Fresnel equations . Part of the wave
30846-638: The researchers working on various aspects of the detector. About 880 members, representing 182 institutions in 21 countries, were part of the Collaboration in October 2024. This includes institutions in France, Italy, the Netherlands, Poland, Spain, Belgium, Germany, Hungary, Portugal, Greece, Czechia, Denmark, Ireland, Monaco, Switzerland, Brazil, Burkina Faso, China, Israel, Japan and South Korea. The Virgo Collaboration
31040-402: The rest is collected by the detection system. It first passes through the output mode cleaner, which filters the "high-order modes" (light propagating in an unwanted way, typically from small defects in the mirrors) before reaching the photodiodes which measure the light intensity. The output mode cleaner and the photodiodes are suspended in a vacuum. With the O3 run, a squeezed vacuum source
31234-413: The same, then circular polarization is produced (fourth and fifth figures). Circular polarization can be created by sending linearly polarized light through a quarter-wave plate oriented at 45° to the linear polarization to create two components of the same amplitude with the required phase shift. The superposition of the original and phase-shifted components causes a rotating electric field vector, which
31428-631: The second observation run (O2) of the "advanced" era; only the LIGO detectors were operating during the first observation run. The event, named GW170814 , was a coalescence between two black holes. It was the first event detected by three different detectors, allowing for greatly-improved localisation compared to events from the first observation run. It also allowed for the first conclusive measure of gravitational-wave polarisation , providing evidence against polarisations other than those predicted by general relativity. Gravitational wave Gravitational waves transport energy as gravitational radiation ,
31622-500: The second phase, building on the changes in the first. The fourth observation run (O4) was scheduled to begin in May 2023 and was planned to last for 20 months, including a commissioning break of up to two months. On 11 May 2023, Virgo announced that it would not join the beginning of O4; the interferometer was not stable enough to reach the expected sensitivity and one mirror needed replacement, requiring several weeks of work. Virgo did not join
31816-457: The singularities in question were simply the harmless coordinate singularities of the employed cylindrical coordinates. Einstein, who was unfamiliar with the concept of peer review, angrily withdrew the manuscript, never to publish in Physical Review again. Nonetheless, his assistant Leopold Infeld , who had been in contact with Robertson, convinced Einstein that the criticism was correct, and
32010-470: The site, writing it in files and distributing the files for data analysis. Dedicated electronic hardware and software have been developed for this purpose. The Virgo detector is sensitive to several noise sources which limit its ability to detect gravitational-wave signals. Some have large frequency ranges and limit the overall sensitivity of the detector, such as: In addition to these broad noise sources, others may affect specific frequencies. These include
32204-505: The solid and vibration along the direction of propagation. The differential propagation of transverse and longitudinal polarizations is important in seismology . Polarization can be defined in terms of pure polarization states with only a coherent sinusoidal wave at one optical frequency. The vector in the adjacent diagram might describe the oscillation of the electric field emitted by a single-mode laser (whose oscillation frequency would be typically 10 times faster). The field oscillates in
32398-443: The source of the waves. Using this technique, astronomers have discovered the 'hum' of various SMBH mergers occurring in the universe. Stephen Hawking and Werner Israel list different frequency bands for gravitational waves that could plausibly be detected, ranging from 10 Hz up to 10 Hz. The speed of gravitational waves in the general theory of relativity is equal to the speed of light in vacuum, c . Within
32592-457: The source. Gravitational waves perform the same function. Thus, for example, a binary system loses angular momentum as the two orbiting objects spiral towards each other – the angular momentum is radiated away by gravitational waves. The waves can also carry off linear momentum, a possibility that has some interesting implications for astrophysics . After two supermassive black holes coalesce, emission of linear momentum can produce
32786-540: The sources of gravitational waves. Sources that can be studied this way include binary star systems composed of white dwarfs , neutron stars , and black holes ; events such as supernovae ; and the formation of the early universe shortly after the Big Bang . The first indirect evidence for the existence of gravitational waves came in 1974 from the observed orbital decay of the Hulse–Taylor binary pulsar , which matched
32980-459: The speed of gravitational waves, and, further, the speed of any massless particle. Such particles include the gluon (carrier of the strong force), the photons that make up light (hence carrier of electromagnetic force), and the hypothetical gravitons (which are the presumptive field particles associated with gravity; however, an understanding of the graviton, if any exist, requires an as-yet unavailable theory of quantum gravity). In August 2017,
33174-414: The speed of light). Unless there is perfect spherical symmetry in these explosions (i.e., unless matter is spewed out evenly in all directions), there will be gravitational radiation from the explosion. This is because gravitational waves are generated by a changing quadrupole moment , which can happen only when there is asymmetrical movement of masses. Since the exact mechanism by which supernovae take place
33368-475: The string. In contrast, in longitudinal waves , such as sound waves in a liquid or gas, the displacement of the particles in the oscillation is always in the direction of propagation, so these waves do not exhibit polarization. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves , gravitational waves , and transverse sound waves ( shear waves ) in solids. An electromagnetic wave such as light consists of
33562-400: The superattenuator to counteract the noise. Part of the light in the arm cavities is sent towards the detection system by the beam splitter. The interferometer works near the "dark fringe", with very little light sent towards the output; most is sent back to the input, to be collected by the power-recycling mirror. A fraction of this light is reflected back by the signal-recycling mirror, and
33756-403: The surface called "mountains", which are bumps extending no more than 10 centimeters (4 inches) above the surface, that make the spinning spherically asymmetric. This gives the star a quadrupole moment that changes with time, and it will emit gravitational waves until the deformities are smoothed out. Many models of the Universe suggest that there was an inflationary epoch in the early history of
33950-434: The system was losing energy by emitting gravitational waves. The Virgo detector was first built, commissioned and operated during the 2000s, and reached its expected sensitivity. This validated its design choices, and demonstrated that giant interferometers were promising devices for detecting gravitational waves in a broad frequency band. This phase is sometimes called the "initial Virgo" or "original Virgo". Construction of
34144-400: The theory of special relativity , the constant c is not only about light; instead it is the highest possible speed for any interaction in nature. Formally, c is a conversion factor for changing the unit of time to the unit of space. This makes it the only speed which does not depend either on the motion of an observer or a source of light and/or gravity. Thus, the speed of "light" is also
34338-515: The third observing run (O3), this resulted in two separate data releases (O3a and O3b) corresponding to the first and last six months of the run. The data is then generally available on the Gravitational Wave Open Science Center (GWOSC) platform. Analysis of the data requires a variety of techniques targeting different types of sources. Most of the effort is dedicated to the detection and analysis of mergers of compact objects,
34532-570: The two LIGO interferometers in the United States and the Japanese interferometer KAGRA . Cooperation between several detectors is crucial for detecting gravitational waves and pinpointing their origin; the LIGO and Virgo collaborations have shared their data since 2007, and with KAGRA since 2019, to form the LIGO-Virgo-KAGRA (LVK) collaboration. The interferometer is named after the Virgo Cluster ,
34726-452: The two constituent linearly polarized states of unpolarized light cannot form an interference pattern , even if rotated into alignment ( Fresnel–Arago 3rd law ). A so-called depolarizer acts on a polarized beam to create one in which the polarization varies so rapidly across the beam that it may be ignored in the intended applications. Conversely, a polarizer acts on an unpolarized beam or arbitrarily polarized beam to create one which
34920-429: The universe which can be classified into three types: Detection of these sources is a new way to observe them (often with different information than classical methods such as telescopes) and to probe fundamental properties of gravity such as the polarisation of gravitational waves, possible gravitational lensing , or determining whether the observed signals are correctly described by general relativity. It also provides
35114-425: The wave's state of polarization is only dependent on the (complex) ratio of e y to e x . So let us just consider waves whose | e x | + | e y | = 1 ; this happens to correspond to an intensity of about 0.001 33 W /m in free space (where η = η 0 ). And because the absolute phase of a wave is unimportant in discussing its polarization state, let us stipulate that
35308-495: The wave. DOP can be used to map the strain field in materials when considering the DOP of the photoluminescence . The polarization of the photoluminescence is related to the strain in a material by way of the given material's photoelasticity tensor . DOP is also visualized using the Poincaré sphere representation of a polarized beam. In this representation, DOP is equal to
35502-401: The workings of the universe. In particular, gravitational waves could be of interest to cosmologists as they offer a possible way of observing the very early universe. This is not possible with conventional astronomy, since before recombination the universe was opaque to electromagnetic radiation. Precise measurements of gravitational waves will also allow scientists to test more thoroughly
35696-653: Was discovered. In 1974, Russell Alan Hulse and Joseph Hooton Taylor, Jr. discovered the first binary pulsar , which earned them the 1993 Nobel Prize in Physics . Pulsar timing observations over the next decade showed a gradual decay of the orbital period of the Hulse–Taylor pulsar that matched the loss of energy and angular momentum in gravitational radiation predicted by general relativity. This indirect detection of gravitational waves motivated further searches, despite Weber's discredited result. Some groups continued to improve Weber's original concept, while others pursued
35890-549: Was expected to reach 200 W in its final configuration. Advanced Virgo began the commissioning process in 2016, joining the two LIGO detectors (which had gone through similar upgrades with Advanced LIGO) on 1 August 2017. Observation "runs" for the Advanced detector era are planned by the LVK collaboration with the goal to maximise the observing time with several detectors, and are labelled O1 to O5; Virgo began participating in these near
36084-401: Was introduced to reduce the quantum noise which is one of the main limitations to sensitivity. When replacing the standard vacuum with a squeezed vacuum, the fluctuations of a quantity are decreased at the expense of increasing the fluctuations of the other quantity due to Heisenberg's uncertainty principle . In Virgo, the quantities are the amplitude and phase of the light. A squeezed vacuum
36278-443: Was proposed in 1981 by Carlton Caves during the infancy of gravitational-wave detectors. During the O3 run, frequency-independent squeezing was implemented; squeezing is identical at all frequencies, reducing shot noise (dominant at high frequencies) and increasing radiation pressure noise (dominant at low frequencies, and not limiting the instrument's sensitivity). Due to the addition of the squeezed vacuum injection, quantum noise
36472-468: Was reduced by 3.2 dB at high frequencies and the detector's range was increased by five to eight per cent. More sophisticated squeezed states are produced by combining the technology from O3 with a new 285-m-long (935 ft) filter cavity. This technology, known as frequency-dependent squeezing , helps to reduce shot noise at high frequencies (where radiation pressure noise is irrelevant) and reduce radiation-pressure noise at low frequencies (where shot noise
36666-534: Was seen by both LIGO detectors in Livingston and Hanford, with a time difference of 7 milliseconds due to the angle between the two detectors and the source. The signal came from the Southern Celestial Hemisphere , in the rough direction of (but much farther away than) the Magellanic Clouds . The confidence level of this being an observation of gravitational waves was 99.99994%. A year earlier,
36860-439: Was settled by a thought experiment proposed by Richard Feynman during the first "GR" conference at Chapel Hill in 1957. In short, his argument known as the " sticky bead argument " notes that if one takes a rod with beads then the effect of a passing gravitational wave would be to move the beads along the rod; friction would then produce heat, implying that the passing wave had done work . Shortly after, Hermann Bondi published
37054-419: Was subsequently awarded to Rainer Weiss , Kip Thorne and Barry Barish for their role in the direct detection of gravitational waves. In Albert Einstein 's general theory of relativity , gravity is treated as a phenomenon resulting from the curvature of spacetime . This curvature is caused by the presence of mass. (See: Stress–energy tensor ) If the masses move, the curvature of spacetime changes. If
37248-472: Was the first binary neutron-star merger observed and the first gravitational-wave observation confirmed by non-gravitational means. The resulting gamma-ray burst was also detected, and optical telescopes later discovered a kilonova corresponding to the merger. After further upgrades, Virgo began its third observation run (O3) in April 2019. Planned to last one year, the run ended early on 27 March 2020 due to
37442-489: Was the targeting of low frequencies (around 10 Hz); most projects focused on higher frequencies (around 500 Hz). Many believed at the time that low-frequency observations were not possible; only France and Italy began work on the project, which was first proposed in 1987. The name Virgo was coined shortly after, in reference to the Virgo galaxy cluster ; it symbolizes the aim of the project to detect gravitational waves originating from beyond our galaxy. After approval by
37636-566: Was used above to show how different states of polarization are possible. The amplitude and phase information can be conveniently represented as a two-dimensional complex vector (the Jones vector ): e = [ a 1 e i θ 1 a 2 e i θ 2 ] . {\displaystyle \mathbf {e} ={\begin{bmatrix}a_{1}e^{i\theta _{1}}\\a_{2}e^{i\theta _{2}}\end{bmatrix}}.} Here
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