Virgo Interferometer for the Detection of Gravitational Waves
The Virgo interferometer is a large interferometer designed to detect gravitational waves predicted by Einstein's general theory of relativity. Virgo is a Michelson interferometer that is isolated from external disturbances: its mirrors and instrumentation are suspended and its laser beam operates in a vacuum. The instrument's two arms are three kilometers long and located in Santo Stefano a Macerata, near the city of Pisa, Italy. The interferometer is named for the Virgo Cluster of about 1,500 galaxies in the Virgo constellation, about 50 million light-years from Earth.
Virgo is part of a scientific collaboration of laboratories from six countries: Italy and France, the Netherlands, Poland, Hungary and Spain. Other interferometers similar to Virgo have the same goal of detecting gravitational waves, including the two LIGO (Laser Interferometric Gravitational-wave Observatory) interferometers in the United States (at the Hanford Site in Washington State and in Livingston, Louisiana).
The gravitational force: Among all the forces of Nature, the gravitational force is the one that has been known to man for the longest time. One of its fundamental properties -that all bodies fall with the same acceleration- was recognized by Galileo at the beginning of the seventeenth century. Towards the end of the same century, Newton established the universal gravitation law connecting the force responsible of the fall of bodies to the gravitational force between planets. Finally, Einstein, with the theory of general relativity, connected the gravitational field with the structure of space-time. Nevertheless, we dispose of very few elements on properties of gravitational force in particular in extreme conditions such as during the primordial explosion or the collision of black holes. Contrarily to what one could believe the gravitational force is, among the fundamental forces, the less known. 1)
Einstein’s theory predicts the existence of gravitational waves which are perturbations of the gravitational field spreading out in space at the speed of light, like ripples on the surface of a pond. However, while electromagnetic radiations (for example visible light) can be absorbed completely by matter, gravitational waves can travel through space without being absorbed neither by stars, nor by interstellar matter.
This very low interaction, together with the weakness of the gravitational force makes the detection of gravitational waves extraordinarily difficult. Actually, after 30 years of active research, we only have an indirect proof of their existence. It has not yet been possible to detect gravitational waves directly, this remains one of the major challenges of experimental physics.
Some background: The Virgo project was approved in 1993 by the French CNRS and in 1994 by the Italian INFN, the two institutes at the origin of the experiment. The construction of the detector started in 1996 in the Cascina site near Pisa, Italy. 2)
In December 2000, CNRS and INFN created the European Gravitational Observatory (EGO consortium), later joined by the Netherlands, Poland, Hungary and Spain. EGO is responsible for the Virgo site, in charge of the construction, the maintenance and the operation of the detector, as well as of its upgrades. The goal of EGO is also to promote research and studies about gravitation in Europe. By December 2015, 19 laboratories plus EGO were members of the Virgo collaboration.
In the 2000s, the "initial" Virgo detector was built, commissioned and operated. The instrument reached its design sensitivity to gravitational wave signals. This long-term endeavor allowed the technical choices made to build Virgo to be validated; it also showed that giant interferometers are promising devices to detect gravitational waves in a wide frequency band. 3) However, the initial Virgo detector was not sensitive enough to achieve such a detection. Therefore, it was decommissioned from 2011 in order to be replaced by the "advanced" Virgo detector which aims at increasing its sensitivity by a factor of 10. The advanced Virgo detector benefits from the experience gained on the initial detector and from technological advances since it was made. 4)
The construction of the initial Virgo detector was completed in June 2003 and several data taking periods followed between 2007 and 2011. Some of these runs were done in coincidence with the two LIGO detectors. Then a long upgrade to the second generation detector, called Advanced Virgo, started; its aim is to reach a sensitivity one order of magnitude better than the initial Virgo detector, allowing it to probe a volume of the Universe 1,000 times larger, making detections of gravitational waves more likely.
Advanced Virgo started commissioning in 2016, joining the two advanced LIGO detectors ("aLIGO") for a first "engineering" observing period in May and June 2017. 5) On 14 August 2017, LIGO and Virgo detected a signal, GW170814, which was reported on 27 September 2017. It was the first binary black hole merger detected by both LIGO and Virgo. 6)
Goals: The first goal of Virgo is to directly observe gravitational waves, a straightforward prediction of Albert Einstein's general relativity. 7) The study over three decades of the binary pulsar 1913+16, whose discovery was awarded the 1993 Nobel Prize in Physics, led to indirect evidence of the existence of gravitational waves. The observed evolution over time of this binary pulsar's orbital period is in excellent agreement with the hypothesis that the system is losing energy by emitting gravitational waves. 8) The rotation motion is accelerating (its period, reported in 2004 to be 7.75 hours, is decreasing by 76.5 microseconds per year) and the two compact stars get closer by about three meters each year. They should coalesce in about 300 million years. But only the very last moments preceding that particular cosmic collision will generate gravitational waves strong enough to be visible in a detector like Virgo. This theoretical scenario for the evolution of Binary Pulsar B1913+16 would be confirmed by a direct detection of gravitational waves from a similar system, the main goal of giant interferometric detectors like Virgo and LIGO.
On the longer term, after accomplishing the primary goal of discovering gravitational waves, Virgo aims at being part of the birth of a new branch of astronomy by observing the Universe with a different and complementary perspective than current telescopes and detectors. Information brought by gravitational waves will be added to those provided by the study of the electromagnetic spectrum (microwaves, radio waves, infrared, the visible spectrum, ultraviolet, X-rays and gamma rays), of cosmic rays and of neutrinos. In order to correlate a gravitational wave detection with visible and localized events in the sky, the LIGO and Virgo collaborations have signed bilateral agreements with many teams operating telescopes to quickly inform (on the timescale of a few days or a few hours) these partners that a potential gravitational wave signal has been observed. These alerts must be sent before knowing whether the signal is real or not, because the source (if it is real) may only remain visible during a short amount of time.
The Gravitational Wave Universe
For centuries, mankind has observed the sky with the naked eye, and in recent times with bigger and bigger telescopes. Today we study the universe mainly by observing visible light and other forms of electromagnetic radiation, such as radio waves, X rays, and gamma rays. However, recently we have learnt to also exploit other cosmic “messengers”, such as high-energy particles including cosmic rays and neutrinos. With Advanced Virgo, we are attempting to detect a new type of astrophysical messenger, detected for the first time in September 2015: gravitational waves. 9)
Gravitational waves are ripples in the fabric of spacetime, and are expected to be emitted by spinning stars in binary systems, black holes, massive stellar explosions, and even shortly after the birth of the Universe, the Big Bang. Most likely there are also as yet unknown astrophysical sources, which must enlarge this list: General Relativity states that any accelerated motion of mass that does not have spherical nor cylindrical symmetry could be a source of gravitational waves.
Advanced Virgo can detect gravitational waves with frequencies between 10 Hz and 10000 Hz. These are the same frequencies as the sound waves that are audible by humans. Therefore, any signal measured by Advanced Virgo can be sent to a loudspeaker, and we can hear the symphony of the Universe.
Coalescences of black holes and neutron stars: When two compact and massive objects such as black holes and neutron stars spin one around the other, they slowly get closer and closer until they finally merge, forming a black hole. This phenomenon is known as coalescence. Such binary systems lose energy by the emission of gravitational waves with increasing frequency and increasing amplitude throughout their long lifetimes. The first experimental evidence for the emission of gravitational waves came from the study of the binary neutron star PSR 1913+16. Russel Hulse and Joseph Taylor were awarded the Nobel Prize for Physics in 1993 for observing that this binary star loses energy exactly as expected by the emission of gravitational waves. Several other binary stars discovered successively behave in the same way.
During the final stage of the merging phase, the gravitational waves are strong enough to be detected by Advanced Virgo just a few seconds before their collision, when they spin 10, 100, 1000 times per second around each other! Such collisions are very rare in a single galaxy, but Advanced Virgo will be searching for them in millions of galaxies. This should enable us to find a handful of them every year. Detecting binary systems will help us to understand how compact astrophysics objects interact, and if such violent collisions are related to the gamma-ray bursts detected by satellites since decades. The first ever detected gravitational wave (called GW150914) came from a binary black hole merger, and it already teached us that black holes as massive as 30 and 60 solar masses do exist!
Virgo is a Michelson laser interferometer with two orthogonal arms each 3 kilometers long. A beam splitter divides the incident laser beam into two equal components sent into the two arms of the interferometer. In each arm, a two mirrors Fabry-Perot resonant cavity extends the optical length from 3 to about 100 kilometers because of multiple reflections and therefore amplifies the tiny distance variation caused by a gravitational wave. The two beams of laser light coming from the two arms, are recombined out of phase on a detector so that, in principle, no light reaches the detector. The variation of the optical path’s length, caused by the changing distance between the mirrors, produces a very small phase shift between the beams and, thus, a variation of the luminous intensity, which is proportional to the wave’s amplitude. 10)
However, in this scheme, a large fraction of the light is sent back toward the laser. In order to further increase the power, this light is sent back to the interferometer by a recycling mirror, in phase with the incident beam thus increasing the light power that can reach several tens of kilowatts in the Fabry-Perot resonant cavities. A high light power is important because it allows to improve the sensitivity of the interferometer. With these resonant cavities coupled together, the interferometer can be seen as a giant light trap. If the optics would be perfect and the mirrors perfectly stable, no light should normally reach the detector except when the interferometer plane is crossed by a gravitational wave. The quality and stability of the optics represent therefore one of the major challenges of the interferometer.
Virgo is sensitive to gravitational waves in a wide frequency range, from 10 to 10,000 Hz. This should allow the detection of gravitational radiation caused by the coalescence of binary systems (stars or black holes), pulsars and those produced by supernovae in the milky way and in outer galaxies, for instance from the Virgo cluster, hence the name of the project.
Virgo runs day and night, listening to all signals that arrive at any time from any part of the universe. The data cominig from the interferometer as well as the ancillary data necessary to its control (4Mbytes/s) are subjected to a preliminary analysis for quality check and a quick detection of potentially interesting anomalous signals. The data is then put at the disposal of the scientific collaboration, for a deeper analysis.
A full description of the Virgo interferometer detection principles and its builtup is provided in references 4), 5) and NO TAG#. In addition, the Virgo interfrometer is based on the same principles as the LIGO interferometer, described in the LIGO file.
Virgo Network Status
• September 22, 2020: Quantum mechanics does not only describe how the world works on its smallest scales, but also affects the motion of macroscopic objects. An international research team, including four scientists from the MPI for Gravitational Physics (Albert-Einstein-Institut/AEI) and Leibniz University in Hannover, Germany, has shown how they can influence the motion of mirrors, each weighing more than 40 kg, in the Advanced Virgo gravitational-wave detector trough the deliberate use of quantum mechanics. At the core of their experiment published today in Physical Review Letters is a squeezed-light source, developed and built at the AEI in Hannover, which generates specially tuned laser radiation and improves the detector's measurement sensitivity during observing runs. 11) 12)
- The quantum mechanical world of probabilities and uncertainties also governs the behavior of the kilometer-sized gravitational wave detectors Advanced LIGO, Advanced Virgo, and GEO600. The sensitivity of these high-precision instruments to gravitational waves – caused, for example, by distant black hole mergers – is currently limited by quantum mechanical background noise.
Heisenberg's Uncertainty Limits the Detectors
- In the detectors, laser light is used to measure with highest precision the relative position of mirrors kilometers apart. Even in the absence of any gravitational-wave signals or noise sources, these mirror position measurements would show a slight jitter.
- The reason for this is Heisenberg's uncertainty principle. According to this cornerstone of quantum mechanics, simultaneous measurements of two related quantities are impossible with arbitrary accuracy; they are blurred, or uncertain. However, the measurement inaccuracy of one of the two quantities can be reduced – but only at the expense of a greater inaccuracy when measuring the other quantity.
- In gravitational wave detectors shot noise – the patter of the randomly and irregularly arriving light particles – is usually reduced. This trick is necessary because this quantum mechanical background noise limits the sensitivity of the detectors at high measuring frequencies with which they listen into the cosmos.
There Ain’t No Such Thing as a Free Lunch
- According to the uncertainty relation, however, reduced shot noise results in increased radiation pressure noise: The force with which the stream of light particles pushes on the mirrors fluctuates more strongly. As a result, the mirrors move back and forth more, simply because of the effects of quantum mechanics.
- “There ain’t no such thing as a free lunch: If you reduce the quantum mechanical background noise at high frequencies using current squeezed-light sources, you pay a price. And this price is increased quantum noise – and thus reduced measurement accuracy – at lower frequencies,” explains Moritz Mehmet, researcher at the AEI Hannover.
Massive Mirrors Move
- Until now, other technical noise sources have hidden this increase in radiation pressure noise in gravitational wave detectors. Only now, during Advanced LIGO’s and Advanced Virgo’s third observation run (April 2019 to March 2020) has this detection become a possibility using squeezed-light sources and reducing other noise sources.
- “If we use particularly strongly squeezed light, we clearly see an additional jitter of the 42 kilogram mirrors in the Advanced Virgo detector – really macroscopic objects – at low frequencies. This is due to quantum mechanical effects,” says Henning Vahlbruch, a researcher at the AEI Hannover.
- This new measurement is only possible because the researchers are able to determine fluctuations of the mirror positions to less than a thousandth of a proton diameter. Previous measurements of this effect in laboratory experiments used masses that were 10 million times lighter than the Advanced Virgo mirrors.
Squeezed-light Pioneer GEO600
- Since 2010, the German-British GEO600 detector has been using a squeezed-light source. GEO600 plays a pioneering role in this field. In the third joint observation run (April 2019 until end of March 2020), the two Advanced LIGO detectors and the Advanced Virgo detector also used squeezed light. At the Advanced Virgo instrument, a squeezed-light source developed and built at the AEI Hannover, based on the design tested at GEO600, is in use.
- In the future, squeezed-light sources will have to be modified to further increase the sensitivity of gravitational-wave detectors. The carefully tuned laser radiation they generate must no longer be the same at all frequencies. Its properties must be adjusted so that it reduces quantum mechanical noise at both high and low frequencies. The development of this frequency-dependent squeezing is already underway in the worldwide community of gravitational wave researchers including GEO600. Two groups have shown first successful experimental demonstrations in spring 2020.
• September 2, 2020: The fourth gravitational-wave detection from LIGO’s and Virgo’s third observing run published today is very big news: the most massive merger of two black holes ever observed to date. The black-hole collision formed a 142 solar-mass black hole when the Universe was half its current age. This is the first direct observation of the birth of an intermediate-mass black hole. Even more surprising is the heavier black hole in the pair: with 85 times the mass of our Sun, it should not exist according to the current understanding of stellar explosions, but it could be born from an earlier binary merger. It is unknown whether this signal, GW190521, is the first observed representative of a new class of binary black holes or is simply at the upper end of a wide mass spectrum. Scientists at the Max Planck Institute for Gravitational Physics in Potsdam and Hannover and at the Leibniz University Hannover have made crucial contributions to the discovery and its interpretation. 13) 14)
- Today the LIGO Scientific Collaboration and the Virgo Collaboration have published the latest observational results and their astrophysical implications in the journals Physical Review Letters and Astrophysical Journal Letters. GW190521 was observed by the twin LIGO detectors and the Virgo detector on May 21, 2019 – early on in their third-joint observing run O3, which began on April 1, 2019.
- “Right from the beginning this signal, which is only a tenth of a second long, challenged us in identifying its origin”, says Alessandra Buonanno, director at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute; AEI) in Potsdam and College Park professor at the University of Maryland. She adds, “But, despite its very short duration, we were able to match the signal to one expected of black-hole mergers, as predicted by Einstein’s theory of general relativity, and we realized we had witnessed, for the first time, the birth of an intermediate-mass black hole from a black-hole parent that most probably was born from an earlier binary merger.”
A Short Message from a Galaxy Far, Far Away
- GW190521 is the fourth gravitational-wave signal published from O3, and it is rather short: It lasted about a tenth of a second and has four gravitational-wave cycles (corresponding to two orbits of the black holes) in the frequency band of the detectors. During this short time, its frequency chirps up from 30 Hertz to 80 Hertz before the signal ends with the merger of the two black holes.
- GW190521 is not only the binary black hole merger with the highest total mass observed so far, it is also the most distant. Because of the high mass, very strong gravitational waves – with an energy equivalent to eight times the mass of the Sun – were emitted, making the signal loud and recognizable over large cosmological distances. The merger with a total mass of almost 150 Suns happened when the Universe was half its current age: about seven billion years ago.
Witnessing the Birth of an Intermediate Mass Black Hole
- The remnant of the merger of the two black holes, one with 66 and the other with 85 solar masses, is a black hole of 142 solar masses. This is heavier than any LIGO/Virgo black hole observed before and is the first direct observation of an intermediate mass black hole’s birth. This elusive, so far postulated, and previously only indirectly observed class of black holes is characterized by their masses of 100 to 100,000 times that of our Sun – more massive than the known lighter stellar mass black holes and less massive than the heavier supermassive black holes at the centers of galaxies.
A Black Hole that Shouldn’t Exist
- The heavier black hole in the pair is even more surprising: Its mass of 85 times our Sun does not fit at all into models of stellar evolution.
- “From our understanding of how stars age and evolve we expect to find black holes with either less than 65 solar masses or more than 120 solar masses, but none in between,” explains Frank Ohme, leader of an Independent Max Planck Research Group at AEI Hannover. “The 85 solar-mass black hole in the GW190521 origin system falls right in that gap where it shouldn’t be! This can mean two things: our understanding of stars evolution is incomplete or something different has happened here.”
A Gap in Black Hole Masses
- According to current understanding, stars which would give birth to black holes with masses between 65 and 120 solar masses do not explode as supernovae, and therefore no such black holes are formed. The stars rather experience one or more short episodes of instability in each of which they expel a significant fraction of their mass instead of exploding entirely. At the end of this process, a star is left that explodes in a supernova and creates a black hole of less than 65 solar masses. Stars that would form black holes of more than 120 solar masses are expected to directly collapse without the accompanying firework of a supernova.
- The resulting gap in the black hole mass spectrum is called the “pair instability” gap. It is named after the physical process causing the episodes of mass shedding.
A Merger of Merged Black Holes or Stars
- The binary system might have had a more complex origin story. Uncertainties in the understanding of how stars evolve might allow for black holes with more than 65 solar masses to be born from supernova explosions. However, LIGO and Virgo researchers think the most likely explanation for formation the 85 solar-mass object is the earlier merger of two smaller black holes or that of two massive stars.
Something Completely Different
- While the signal is well described by and agrees with what Einstein’s theory of general relativity predicts for a binary black hole merger, LIGO and Virgo scientists also look at other possible explanations for their observation in a companion paper. The origin from cosmic strings – a hypothetical object that could have formed in the early Universe – seems unlikely. The signal also is unlikely to come from a core collapse supernova, which would be accompanied by electromagnetic or neutrino signals.
- The GW190521 observation is also consistent with coming from a closer and less massive binary black hole merger, the gravitational waves of which have been distorted through a gravitational lens. It could also stem from primordial black holes that formed in the early Universe before stars were even born. However, LIGO and Virgo researchers have determined that both of these explanations as very unlikely compared to the regular merger scenario. Lastly, the signal could have been produced by a merger of two black holes on elliptic orbits. But to check that, accurate signal models including the fingerprints of elliptic orbits derived from general relativity have to be matched against the signal. They are not yet available.
A New Class of Binary Black Holes?
- “We don’t know yet whether GW190521, this surprising discovery and first observation of an intermediate mass black hole, is an entirely new class of binary black holes or just the high-mass end of the source spectrum we’ve seen so far,” says Karsten Danzmann, director at the AEI Hannover, and director of the Institute for Gravitational Physics at Leibniz University Hannover. “Soon, when we have analyzed all binary black hole mergers seen by LIGO and Virgo in their third observing run we might know more.”
- A future publication will analyze the larger sample of binary black hole mergers observed in the first half of O3 (O3a from 1 April through 1 October, 2019).
- AEI researchers contributed to detecting and analyzing GW190521. They have provided accurate models of the gravitational waves from coalescing black holes that included, for the first time, the precession of the black-holes’ spins, and multipole moments beyond the dominant quadrupole. Those features imprinted in the waveform are crucial to extract unique information about the source’s properties. The high-performance computer cluster “Hypatia” at AEI Potsdam was employed to develop the waveform models used for the analyses.
More than 50 Additional Gravitational-wave Candidates from O3
- The LIGO and Virgo researchers have issued alerts for 56 possible gravitational-wave events (candidates) in O3, which lasted from 1 April 2019 to 27 March 2020. So far, four candidates have been confirmed and made public. LIGO and Virgo scientists are examining all remaining 52 candidates and will publish all those for which detailed follow-up analyses confirm their astrophysical origin.
LIGO Scientific and Virgo Collaborations
- LIGO is funded by the National Science Foundation (NSF) and operated by Caltech and MIT, which conceived of LIGO and lead the project. Financial support for the Advanced LIGO project was led by the NSF with Germany (Max Planck Society), the U.K. (Science and Technology Facilities Council) and Australia (Australian Research Council-OzGrav) making significant commitments and contributions to the project. Approximately 1,300 scientists from around the world participate in the effort through the LIGO Scientific Collaboration, which includes the GEO Collaboration. A list of additional partners is available at https://my.ligo.org/census.php
- The Virgo Collaboration is currently composed of more than 500 scientists, engineers, and technicians from 99 institutes from Belgium, France, Germany, Hungary, Italy, the Netherlands, Poland, and Spain. The European Gravitational Observatory (EGO) hosts the Virgo detector near Pisa in Italy, and is funded by Centre National de la Recherche Scientifique (CNRS) in France, the Istituto Nazionale di Fisica Nucleare (INFN) in Italy, and Nikhef in the Netherlands. A list of the Virgo Collaboration members can be found at http://public.virgo-gw.eu/the-virgo-collaboration/. More information is available on the Virgo website at http://www.virgo-gw.eu.
• June 23, 2020: Another unprecedented discovery has just been unveiled by LIGO-Virgo scientists. Data from the third observation period (O3) of the Advanced LIGO and Advanced Virgo detectors reveal that, at 21:10 (UTC) on the 14th of August, 2019, the three instruments in the network detected a gravitational-wave signal, called GW190814. The signal originated from the merger of an enigmatic couple: a binary system composed of a black hole, 23 times heavier than our sun, and a much lighter object, about 2.6 times the mass of the Sun. The merger resulted in a final black hole about 25 times the mass of the sun. 15)
- It is this lighter object that makes GW190814 so special. It may just be either the lightest black hole or the heaviest neutron star ever discovered in a binary system. Another peculiar feature of GW190814 is the mass ratio of the objects in the binary system. The factor 9 ratio is even more extreme than was the case with the first detected merger of a binary with unequal masses, GW190412.
- "Once again, gravitational-wave observations are shedding light on the unknown. The lightest object in this system has a mass that has never before been observed", says Giovanni Losurdo, of Istituto Nazionale di Fisica Nucleare (Italy) and the spokesperson of the Virgo Collaboration. "A new discovery, which raises new questions. What is its nature? How did such a binary system form? Virgo, LIGO and, soon, KAGRA in Japan, will continue to search for the answers and push forward the frontier of what we know about the cosmos in which we live."
- The mass asymmetry causes the presence of higher multipoles in the gravitational radiation, a fact that allows stringent tests of General Relativity. Once again, all our tests confirm the prediction of Einstein’s theory. Moreover, the higher multiples allow us to disentangle the determination of the source distance from the inclination angle of the plane of the orbiting binary. We have found the source of the gravitational wave to be about 800 million light years away!
- The signal was clearly detected by the three instruments, with an overall signal-to-noise ratio as high as 25. Thanks mainly to the delay between the signal arrival times at the three, well separated detectors, the network was able to localize the origin of GW190814 to within about 19deg2 in the sky. This is similar to the localization achieved for the famous GW170817, which gave birth to multi-messenger astronomy with gravitational waves. In the case of GW190814, however, an electromagnetic counterpart has yet to be observed.
- "We are very satisfied with the performance of Advanced Virgo during O3," says Maddalena Mantovani, scientist at the European Gravitational Observatory (EGO). "We reached the target sensitivity with a very good duty cycle. This is the result of the hard work of the scientists and technicians that have fine-tuned the machine to provide its best performance. Scientific discoveries such as GW190814 are the best rewards for all those days and nights spent on improving the detector."
• April 20, 2020: The third LIGO-Virgo observing period (O3) is offering new insights into the late inspiral and merger phase of binary black hole (BBH) systems. The first gravitational wave event GW150914, detected back in 2015, originated from a binary black hole merger, and since then this class of events has become the most prominent. This allows us to advance in the characterization of the population of astrophysical BBHs. However, the systems observed so far were formed by black holes of nearly equal masses. This balance was broken by the observation of the merger of a very special BBH on the 12th of April, 2019 at 05:30:44 UTC, just a couple of weeks after the start of O3, on the 1st of April. 16)
- The signal, named GW190412, was detected by the Advanced Virgo and the two Advanced LIGO detectors, and it was produced by a coalescing BBH system with unequal masses, one component being more than 3 times heavier than the other one. More in detail, the merged black holes had masses respectively about 30 and 8 times the mass of the Sun. The mass difference produces specific signal modulations that were predicted by theory, but have now been observed for the first time. In fact, the mass unbalance produces an unusually high intensity of gravitational radiation in the so-called "Higher Order Modes", which are detectable in GW190412 and provide yet another confirmation of the validity of Einstein’s General Relativity. GW190412 also depends on other parameters of the binary system which cause modulations that enable us to constrain the inclination of the plane of the binary with respect to the line of sight and the distance of the source; two quantities that are otherwise highly correlated.
- "The Virgo and LIGO detectors are becoming more and more sensitive, the rate of detections increases and we expect new and unusual events. GW190412 is unusual and interesting, because of the large mass difference between the two coalescing black holes. We are learning that systems of this kind exist and how rare they are. This will allow us to deduce how they formed, which is something that I find exciting", says Giancarlo Cella, researcher at Istituto Nazionale di Fisica Nucleare (INFN) and the Virgo Data Analysis Coordinator.
- "The unequal masses of this source caused overtones of the main signal to be visible for the very first time. This provided us with an exciting new opportunity to test an important prediction of Einstein’s theory about what happens when black holes of unequal size collide", says Anuradha Samajdar, postdoc fellow at the Dutch National Institute for Subatomic Physics (Nikhef), and member of the Virgo Collaboration.
• April 18, 2020: Giovanni Losurdo, research director at the Institute for Nuclear Physics (INFN) in Italy, has been appointed as the new Spokesperson of the Virgo Collaboration. From 2009 to 2017, he was Project Leader of Advanced Virgo, the program of upgrades to the detector that made it possible for Virgo to participate alongside the two LIGO detectors, in the US, in the second observation period, called 'O2'. 17)
- Giovanni succeeds Jo van den Brand, from Nikhef, Amsterdam, and professor at Maastricht University in The Netherlands, who has served as Virgo Spokesperson from the 1st of May 2017 to the 30th of April 2020. Jo's tenure covered both the second and third joint-observation periods with the LIGO detectors, which have produced a wealth of scientific results.
- The Spokesperson represents the 550 scientists, engineers and technicians of the Virgo Collaboration, coming from more than 100 institutions in 10 different European countries. A map of the Virgo Collaboration can be found here.
- "Over the next few years we will face very important and exciting challenges," stated the newly-elected Spokesperson. "We will start with a substantial upgrade of the detector, which will allow us to explore a bigger and bigger portion of our universe. In the next data-taking period, for instance, we aim to observe coalescences of neutron stars that are at a distance of up to 300 million light years from us. Subsequently, our collaborations and relations with other astronomers and physicist communities will become even more intense and will have to become even more effective. This will enable us to achieve a deeper understanding of the physics behind the detected events, to further develop multi-messenger astronomy and to fine-tune technologies needed for the next generation of gravitational detectors, such as the Einstein Telescope."
- "It has been an honor serving the Virgo Collaboration these last three years," says Jo van den Brand. "Rapid commissioning of Virgo was of paramount importance and in the first three months we managed to increase Virgo's sensitivity from 30 kpc to about 30 Mpc. Then Virgo joined data taking with the LIGO detectors. We immediately made spectacular detections and kicked off the new field of multi-messenger astronomy with gravitational waves. After upgrading and commissioning Virgo to double the sensitivity up to 61 Mpc, we carried out observing run O3. Although COVID-19 forced us to suspend the run early, O3 was a big success. No less than 56 non-retracted alerts were released and the collaboration is now working enthusiastically to extract the science from the O3 data. I thank my colleagues in the Virgo Collaboration and at EGO for their dedication, their inspiring and critical discussions, and their creativity that allowed Virgo to succeed. I am certain that with Giovanni they are in good hands, and I wish him all the best!"
• March 25, 2020: The LIGO Scientific Collaboration and the Virgo Collaboration (the LVC) have agreed to suspend their third observation period, named O3, which has been running since the 1st of April, 2019. The suspension, which will be effective within one week, is motivated by the worldwide COVID-19 pandemic. Public health and worker safety are always the top priority for the LVC. 18)
- "It is certainly difficult to be obliged to suspend the run at the moment that Virgo had reached maximum sensitivity and a quasi-faultless operation", says Stavros Katsanevas, director of the European Gravitational Observatory (EGO) that hosts Virgo, "but the first priority of the worldwide collaboration and the EGO-Virgo managements in particular, is to preserve the health of the people; both those working at the site and the public at large. Here I cannot but praise the composure, the calmness and the dedication to the task, of the people on site, with the EGO operators first at the line-front, who have operated the detector these last few weeks, in the difficult conditions we all know. This is certainly a good augur for the restart of the operations, when the conditions permit it."
- "Even though we had suspend the run early, O3 has been tremendously successful, thanks to the collective efforts of the LVC", says Jo van den Brand, spokesperson of the Virgo Collaboration, from Nikhef, Amsterdam and professor at Maastricht University in The Netherlands. "The discovery of GW190425, the second observation of a gravitational-wave signal consistent with the merger of a binary-neutron-star system after GW170817, has already been reported."
- Much more is expected to be discovered as scientists work on the analysis of the data collected during the run: 56 detection candidates have already been announced as public alerts, as reported in the freely accessible Gravitational Wave Candidate Event Database. The alerts facilitate follow-up observations by other telescopes (e.g. electromagnetic and neutrino) and enhance the extraordinary potential of multi-messenger astronomy, pioneered with the GW170817 event.
- O3 had been planned to last for one full year and, taking into account a one-month break, in October 2019, which was dedicated to commissioning activities, had been due to end on the 30th of April, 2020.
• January 6, 2020: On April the 25th, 2019, the network of gravitational-wave (GW) detectors formed by the European Advanced Virgo, in Italy, and the two Advanced LIGO, in the US, detected a signal, named GW190425. This is the second observation of a gravitational-wave signal consistent with the merger of a binary-neutron-star system after GW170817. GW190425 was detected at 08:18:05 UTC; about 40 minutes later the LIGO Scientific Collaboration and the Virgo Collaboration sent an alert to trigger follow-up telescope observations. 19)
- The source of GW190425 is estimated to be at a distance of 500 million light years from the Earth. It is localized in the sky within an area about 300 times broader than was the case for the BNS (Binary Neutron Star) observed by LIGO and Virgo in 2017, the famous GW170817, which gave birth to multi-messenger astrophysics. However, unlike GW170817, no counterpart (electromagnetic signals, neutrinos or charged particles) has been found to date.
- There are a few explanations for the origin of GW190425. The most likely is the merger of a BNS system. Alternatively, it might have been produced by the merger of a system with a black hole (BH) as one or both components, even if light BHs in the mass-range consistent with GW190425 have not been observed. Yet, on the basis solely of GW data, these exotic scenarios cannot be ruled out. The estimated total mass of the compact binary is 3.4 times the mass of the Sun. Under the hypothesis that GW190425 originated from the merger of a BNS system, the latter would have been considerably different to all known BNS in our galaxy, the total mass range of which is between 2.5 and 2.9 times the mass of the Sun. This indicates that the NS system that originated GW190425 may have formed differently than known galactic BNSs.
- "After the surprise of the initial results", says Alessandro Nagar of the Istituto Nazionale di Fisica Nucleare (INFN) of Turin, Italy, "we have finally reached a reliable understanding of this event. Although predicted theoretically, heavy binary systems like those that might have originated GW190425 may be invisible through electromagnetic observations."
- "While we did not observe the object formed by the coalescence, our computer simulations based on general relativity predict that the probability that a BH (Black Hole) is formed promptly after the merger is high, about 96%", says Sebastiano Bernuzzi of the University of Jena, Germany.
• October 19, 2019: The world's three principal gravitational-wave detectors - LIGO in the US, VIRGO in Italy (VIRGO denotes the Virgo Collaboration and the European Gravitational Observatory (EGO) Consortium), and now KAGRA in Japan - have today signed a memorandum of agreement (MoA) that covers scientific collaboration. The agreement includes the joint observation of gravitational waves and the sharing of data over the coming years, while it also foresees the expansion of the collaboration through the welcoming of new partners in the future. 20)
- "With KAGRA joining, gravitational-wave science will become a global collaborative effort. The Virgo Collaboration looks forward to learning from the new and innovative approach of using an underground and cryogenic interferometer", says Jo van den Brand, Virgo Collaboration Spokesperson.
- KAGRA is a gravitational wave observatory developed in Kamioka, Japan under the leadership of the University of Tokyo Institute for Cosmic Ray Research (ICRR). Construction started in 2010 and the highly-sensitive instrument is now nearing readiness.
- In December of this year, KAGRA is expected to join the third observing run, called O3, which began on the 1st of April, 2019, and already involves the VIRGO detector and the two LIGO detectors.
- The addition of a fourth detector to the global network of gravitational-wave interferometers will help to improve the localization of gravitational-wave sources, further assisting follow-up astronomical observations and the process of understanding the characteristics of the signals.
- The main distinguishing feature of KAGRA, with respect to VIRGO and LIGO, is the fact that the mirrors are operated at cryogenic temperatures, in order to reduce thermal noise. The detector is installed underground in the Kamioka mine, which helps in the overcoming of seismic and wind noise.
- The cryogenics and underground-operation technologies are a significant development in the gravitational-wave field, as they are also being studied for the next-generation gravitational-wave detectors, such as the European Einstein Telescope.
• March 26, 2019: The Virgo and LIGO detectors are ready to start the new Observing run called O3, lasting a whole year. The hunt for gravitational waves is set to start on April 1st when the European Virgo detector, based in Italy at the European Gravitational Observatory (EGO), and the LIGO twin detectors, located in the state of Washington and Louisiana (USA), will start to take data becoming together the most sensitive gravitational wave observatory to date. 21) 22)
- During a one-year period the LIGO and Virgo Collaborations will register science data continuously, and the three detectors will operate as a global observatory. Since August 2017, the end of the second observation run O2, the two collaborations have intensively worked on their interferometers to improve the sensitivity and reliability. Scientists have also improved their offline and online data analysis and developed further the procedures for releasing Open Public Alerts: these will within minutes notify the physics and astronomy community when a potential gravitational-wave event is observed.
- “With our three detectors now operational at a significantly improved sensitivity, the global LIGO-Virgo detector network is expected to make several new detections. Moreover it will allow precise triangulation of the sources of gravitational waves. This will be an important step towards our quest of multi-messenger astronomy”, says Jo van den Brand of Nikhef (the Dutch National Institute for Subatomic Physics) and VU University Amsterdam, who is the spokesperson for the Virgo collaboration.
- “Going from the pioneering era that led to the historical discovery to the present observatory era, where the interferometer and the infrastructure will have to operate faultlessly for 24 hours, seven days in a week for a whole year was and continues to be a daunting challenge;” says Stavros Katsanevas, Director of EGO, “I have confidence however that we will face this challenge with the same success we faced the previous one."
- The detector sensitivity is commonly given in terms of the distance at which it can observe the merger of a binary neutron star system. “During O2 Advanced Virgo could observe neutron star events up to a distance of 88 million light years”, says Alessio Rocchi, researcher at INFN and Virgo’s commissioning coordinator. “Both LIGO and Virgo Collaborations have been working to improve the sensitivity of the detectors, also exploiting the upgrades installed on the interferometers. With respect to O2, the Virgo sensitivity has improved by about a factor of 2, which means that the volume of the observable Universe has increased by a factor of 8", concludes Rocchi.
- "The quality of the data collected by the instruments is a determining factor to detect gravitational-wave signals buried into noise and to measure their properties", says Nicolas Arnaud, CNRS researcher currently seconded to EGO and Virgo detector characterization coordinator. "A lot of progress has been made in that direction since O2, thanks to the combined effort of the collaboration as a whole, from the instrumentalists to the data analysts".
- The scientific output of observation run O3 is expected to be tremendous and it will potentially reveal new exciting signals coming from new sources such as the merger of mixed binaries made by a black hole and a neutron star. O3 will also target long lasting gravitational waves produced for instance by spinning neutron stars which are not symmetric with respect to their axis; however, the detection of such signals is still an enormous challenge and the LIGO and Virgo Collaborations are raising up to it.
- Furthermore, thanks to the upgrades of Virgo and LIGO, signals for the merger of binary black holes, such as for GW150914 the first gravitational-wave event ever detected, are expected to become quite common, perhaps up to one per week. Scientists also expect to observe several binary neutron star mergers, such as GW170817 which opened the era of multi-messenger astronomy as well as providing insights into binary evolution, nuclear physics, cosmology and fundamental physics.
- "The new software we have built is able to send Open Public Alerts within five minutes", says Sarah Antier, postdoc at the Université Paris Diderot and responsible of the low latency program for the Virgo Collaboration. "This will allow to follow-up the gravitational wave signal with neutrino and/or electromagnetic searches, that may lead to multimessenger discoveries. Observations of many signals as we expect during O3 will give us a census of the population of stellar mass remnants and a better understanding of the violent universe."
- Since August 2017 both LIGO and Virgo have been updated and tested. In particular Virgo has fully replaced the steel wires which were used in O2 to suspend the four main mirrors of the 3 km long interferometer: the mirrors are now suspended with thin fused-silica (‘glass’) fibres, a procedure which has allowed to increase the sensitivity in the lowmedium frequency region, and has a dramatic impact in the capabilities to detect mergers of compact binary systems. A second major upgrade was the installation of a more powerful laser source, which improves the sensitivity at high frequencies. Last but not least squeezed vacuum states are now injected into Advanced Virgo, thanks to a collaboration with the AEI (Albert Einstein Institute) in Hannover, Germany. This technique takes advantage of the quantum nature of light and improves the sensitivity at high frequencies.
- Squeezing is a major upgrade also implemented in the two LIGO interferometers in the US for this next observation run. Moreover, the laser power has been doubled to more precisely measure the effect of passing gravitational waves. Other upgrades were made to LIGO's mirrors at both locations, with a total of five of eight mirrors being swapped out for better-performing versions.
- “We had to break the fibers holding the mirrors and very carefully take out the optics and replace them," says Calum Torrie, LIGO's mechanical-optical engineering head at Caltech. "It was an enormous engineering undertaking."
- During O3 the LIGO and Virgo Collaborations will continue to communicate new findings to the scientific community as well as to the general public. Furthermore scientists will keep on extracting all possible physics results from the data.
- The global LIGO-Virgo network will provide prompt localizations of gravitational-wave signals and will release confident events publicly through the Open Public Alert system to maximize the science that the entire scientific community can do with the gravitational-wave detections and to minimize the chance of missing any electromagnetic or neutrino counterparts.
- The Japanese detector KAGRA (Kamioka Gravitational Wave Detector) is expected to join the global LIGO-Virgo network in the last part of O3, extending the detection and pointing capabilities of the global network.
• On March 4, 2019, the Advanced LIGO and Advanced Virgo detectors are starting their 14th Engineering Run. ER14 will last at least four weeks: it will be the final test before the start of the 3rd LIGO-Virgo Observation Run (O3). During the first half of the run activities will be scheduled that might still improve the three interferometres in the network. ER14 will allow scientists to perform long-term tests of the detector stability, as well as to check the readiness of the software that analyses data in real time. No automatic open public alerts will be issued during this period: any significant candidate trigger identified in the data would have to pass human vetting first. 23)
- The successful completion of ER14 will lead the path to the one year-long O3 science run: O3 will be the longest period during which the global network of advanced gravitational-wave detectors will be observing the Universe with unsurpassed sensitivity. Since the end of the O2 science run in August 2017, the LIGO and Virgo Collaborations have continued working on their instruments to improve their performance. The figure on the left shows how the sensitivity of Advanced Virgo has progressed steadily over the past months.
• February 28, 2019: The O2 observing run began on the 30th of November, 2016 and ended on the 25th of August, 2017. This was the second observing run of Advanced LIGO, and the first observing run of Advanced Virgo, which joined O2 on the 1st of August, 2017. 24)
- The release includes over 150 days of recorded data from each of the two LIGO observatories, as well as 20 days of recorded data from Virgo, making this the largest data set of 'advanced' gravitational-wave detectors to date. Observations in O2 include seven binary black hole mergers, as well as the first binary neutron star merger observed in gravitational waves, all recently published in the GWTC-1 catalogue. Along with the strain data, the release contains detailed documentation and links to open-source software tools. As with previous data releases, the O2 data set should be useful for both scientific investigations and educational activities.
• On 1 December 2018, scientists attending the Gravitational Wave Physics and Astronomy Workshop in College Park, Maryland, presented new results from searches for coalescing cosmic objects, such as pairs of black holes and pairs of neutron stars, by the LIGO and Virgo detectors. The LIGO and Virgo interferometers have now confidently detected gravitational waves from a total of 10 stellar-mass binary black hole mergers and one merger of neutron stars, which are the dense, spherical remains of stellar explosions. Seven of these events had been reported before, while four of the black hole detections are newly announced. 25) 26)
- From September 12, 2015, to January 19, 2016, during the first LIGO observing run since undergoing upgrades in a program called Advanced LIGO, gravitational waves from three binary black hole mergers were detected. The second observing run, which lasted from November 30, 2016, to August 25, 2017, yielded a binary neutron star merger and seven additional binary black hole mergers, including the four new gravitational wave events being reported now. The new events are known as GW170729, GW170809, GW170818 and GW170823 based on the dates on which they were detected.
- The Virgo interferometer joined the two LIGO detectors on August 1, 2017, while LIGO was in its second observing run. Although the LIGO-Virgo three-detector network was operational for only three-and-a-half weeks, five events were observed in this period. Two events detected jointly by LIGO and Virgo, GW170814 and GW170817, have already been reported.
- One of the new events, GW170818, detected by the global network formed by the LIGO and Virgo observatories, was precisely pinpointed in the sky. The sky position of the binary black holes, located about 2.5 billion light-years from Earth, was identified with a precision of 39 square degrees. That makes it the next best localized gravitational-wave source after the GW170817 neutron star merger.
• July 17, 2018: As planned, the Virgo and LIGO detectors stopped taking data for the ‘Observation Run 2’ - O2 - on the 25th of August, 2017. For both collaborations, this marked the beginning of a new and busy period, which is scheduled to last at least one year (see timelines on the left). During this time, the sensitivity of all three instruments (that is, their ability to detect signals even fainter than those observed in 2015 and 2017 or coming from similar sources, but located further away in the universe) should be improved significantly. Then, in early 2019, the data-taking period – O3 – will start and last for about one calendar year. 27)
- On the Virgo side, three phases were foreseen. First, commissioning activities were undertaken until mid-autumn, in order to improve our knowledge of the detector configuration that was used to take data, and to fix issues identified during the August 2017 run. Indeed, for all large facilities such as Virgo, the golden rule is to disturb the instrument as little as possible while it is running. Only issues preventing the taking of data are promptly fixed and only straightforward improvements are allowed. Therefore, it was only after the end of the O2 run that people working in the Virgo control room were able to carry out many different tests and modify the hardware and software configurations of the detector.
- Instrument upgrades were implemented from the end of November 2017 until the middle of March 2018. Several pieces of hardware were replaced or modified. Notable upgrades included:
1) The installation of a more powerful, ultra-stable input laser: the larger the power circulating in the detector, the more sensitive it is, in particular in the high-frequency range: above a few hundred hertz. With the new laser, the O3 input power is expected to increase by up to a factor of three in comparison with the O2 data-taking period.
2) The replacement of the steel wires suspending the mirrors forming the 3-km long Fabry-Perot cavities - four mirrors in total - with fused silica - ‘glass’ - wires. This lower-dissipation material helps in reducing friction at the anchor levels, hence the suspension thermal noise, which represents the dominant fundamental noise impacting upon the Virgo sensitivity in the medium-frequency region, where it is at its best. These fibers have high breaking strengths, but they are fragile, which makes the whole process - from the production of the fibers in a dedicated lab at EGO, to the suspension of the mirror from its superattenuator structure - challenging. In parallel, the vacuum quality has been improved. About a year and half ago, particle contamination of the vacuum caused some fused-silica fibers to break inside the detector. At that time, the mirrors were again suspended from steel wires and the upgrade to fused-silica fibers was postponed to the O2-O3 long shutdown.
3) The addition of a squeezed vacuum source - a ’squeezer’ - provided by the Albert Einstein Institute in Hannover, Germany. This instrument, installed at the output port of the interferometer - where the power exists that results from the interference between the laser beams circulating in the 3-km long arms - helps to ’beat’ the quantum noise limit, i.e. to reduce the laser shot-noise, which is dominant at high frequency, below its normal level. This counter-intuitive effect is due to the quantum nature of light: any electromagnetic wave, such as the Virgo laser beam, is defined by two quantities, an amplitude and a phase, both of which are fluctuating. The fluctuations of the phase – also known as ’phase noise’ – matter more than the amplitude fluctuations for Virgo. With a squeezer, one can move part of the phase noise to the amplitude noise – the Heisenberg principle states that one cannot decrease both fluctuations: if one goes down, the other should increase – and hence improve the instrument sensitivity. This technique has been successfully implemented in GEO 600 and LIGO: this is the first time it will be tried in Virgo.
- Following the completion of all of these upgrades, Virgo is now back in commissioning mode. The first aim is to learn how to control the detector, which has been significantly modified, and then to improve the sensitivity – by at least a factor of two by the end of the year. This will be challenging but the first results are promising: the best O2 sensitivity – the all-time record sensitivity for Virgo – was surpassed in early June.
• October 17, 2017: For the first time, scientists have directly detected gravitational waves — ripples in space and time — in addition to light from the spectacular collision of two neutron stars. This marks the first time that a cosmic event has been viewed in both gravitational waves and light. 28)
- The discovery was made using the U.S.-based Laser Interferometer Gravitational-Wave Observatory (LIGO); the Europe-based Virgo detector; and some 70 ground- and spaceborne observatories.
• September 27, 2017: A fourth gravitational-wave signal coming from the merger of two stellar mass black holes located about 1.8 billion light-years away was detected on the 14th of August 2017, at 10:30:43 UTC. GW170814 is the first event observed by the global 3-detector network, including not only the two twin Advanced LIGO detectors, but the Advanced Virgo detector as well (Ref. 6) 29) 30) 31)
Following a multi-year upgrade program and several months of commissioning, the Advanced Virgo detector joined the LIGO "Observation Run 2" data-taking period on the 1st of August. The three instruments worked together until the 25th of August.
Therefore, GW170814 holds great promise for the future of multi-messenger astronomy. Additional results, based on data from the three-detector network, will be announced in the near future by the LIGO-Virgo Collaboration; the analysis of the data is currently being finalized.
The detected waves—observed on August 14th, 2017 at 10:30:43 UTC (6:30AM EDT) —were produced by a pair of black holes with 31 and 25 solar masses. They merged to produce a spinning black hole of 53 solar masses. Combining the signal from Virgo with the signal observed in the two LIGO observatories improved the sky localization of the source by over a factor of 10.
The Virgo and LIGO Scientific Collaborations have been observing since November 30, 2016 in the second Advanced Detector Observing Run ‘O2’ , searching for gravitational-wave signals, first with the two LIGO detectors, then with both LIGO and Virgo instruments operating together since 1 August 2017. Some promising gravitational-wave candidates have been identified in data from both LIGO and Virgo during our preliminary analysis, and we have shared what we currently know with astronomical observing partners. We are working hard to assure that the candidates are valid gravitational-wave events, and it will require time to establish the level of confidence needed to bring any results to the scientific community and the greater public. We will let you know as soon we have information ready to share. 32) 33)
The era of gravitational-wave (GW) astronomy began with the detection of binary black hole (BBH) mergers, by the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors, during the first of the Advanced Detector Observation Runs. 34) Three detections, GW150914, GW151226, and GW170104, and a lower significance candidate, LVT151012, have been announced so far. The Advanced Virgo detector joined the second observation run on August 1, 2017.
• August 25, 2017: The Virgo and LIGO Scientific Collaborations have been observing since November 30, 2016 in the second Advanced Detector Observing Run ‘O2’, searching for gravitational-wave signals, first with the two LIGO detectors, then with both LIGO and Virgo instruments operating together since August 1, 2017. Some promising gravitational-wave candidates have been identified in data from both LIGO and Virgo during our preliminary analysis, and we have shared what we currently know with astronomical observing partners. We are working hard to assure that the candidates are valid gravitational-wave events, and it will require time to establish the level of confidence needed to bring any results to the scientific community and the greater public. We will let you know as soon we have information ready to share.
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The information compiled and edited in this article was provided by Herbert J. Kramer from his documentation of: ”Observation of the Earth and Its Environment: Survey of Missions and Sensors” (Springer Verlag) as well as many other sources after the publication of the 4th edition in 2002. - Comments and corrections to this article are always welcome for further updates (email@example.com).