Astronomy

Would LIGO Detect Head-On Collision?

Would LIGO Detect Head-On Collision?


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Assume two black holes collide head-on. In other words, they were not orbiting one another before the collision. I know this is unlikely. Further assume that their sizes and distance from Earth are similar to past collisions detected by LIGO.

My understanding is that detectable gravitational waves are caused by massive objects undergoing massive accelerations and that detections so far have been of colliding objects orbiting one another many times within a fraction of a second.

I assume that a head-on collision would create a single gravitational "pulse" instead of a wave. I don't know if "pulse" is the right word for this. Would this pulse be detectable by LIGO?


There are two issues: Would there be gravitational waves to be detected and would LIGO detect them.

On the first issue, gravitational waves are quadrupolar, and a cylindrically symmetric system will not produce any. (Specifically, the second time derivative of the quadrupole moment of an isolated system's stress-energy tensor must be non-zero in order for it to emit gravitational radiation.) So a head-on collision of equally massive black holes would not produce significant gravitational waves. If the BHs were of different masses, or the collision not quite head-on, gravitational waves would be produced.

On the second issue there are at least three ways LIGO might might miss them. First, they might simply be too faint. A merger through rotation is one of the best ways to produce gravitational waves, and a head-on collision is one of the worst (during a BH merger, of course).

A second way it might miss is if the merger is in one of its blind spots. Each LIGO detector has blind spots and there's no rule that says a BH merger can't be in one of them. (In fact, the neutron star merger was located by use of the blind spots. The third gravitational wave (GW) detector, Virgo, in Italy, didn't pick up the neutron star merger. It was bright/loud enough that it should have, which meant that the merger was in one of Virgo's blind spots, which helped to narrow down its location. A GW detected in only one detector would be listed as a possible GW, but not as a detection, because it might simply be terrestrial interference.

But another way it might miss is if LIGO had not been looking for the waveform of that kind of merger. General Relativity allows us to compute in very good detail the GW signal from any type of collision that we think likely. Because the GW signals are so faint, the first step of detection is matching computed GW waveforms to the data and looking for matches. Once a match is found, the signal is analyzed in more detail, but they have to know where to look. If no one expected the waveform and it was not strong enough to pop out of the data and yell "Here I am, dummy!" it might be missed. Since head-on collisions are expected to be very rare, it's possible that they are not in the library of waveforms that LIGO checks.


The waveform of binary inspiral was about 100ms with a peak for every rotation, about 10 waves/rotations were measured, ranging from 30 to 200Hz. The average female voice has a fundamental frequency of about 200hz, to have some idea, and a typical pitchfork is about 440Hz.

The waveform for a head on collision would about 5ms, probably less, kindof like a snap sound.

It would be indistinguishable from background noise. Sounds that consist of a single peak are like snaps on a vynil. you would challenge LIGO to detect a snap on a vynil record every hextillion years.

A direct collision of solar mass bh's is something like 1 in a hextillion years for the entire universe, because the singularities are as big as atoms, distanced by 100ds of kms travelling in the 20kmps kind of range.


Gravitational waves detected 100 years after Einstein’s prediction | News | Industry

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Watch a video of former NCSA Director Larry Smarr and current NCSA Director Ed Seidel discussing their work on colliding black holes.

The LIGO detectors in Livingston, La., and Hanford, Wash, separated 1,865 miles. It took about 7 milliseconds for the gravitational wave to cover the distance between the two.

The panels show the gravitational wave (GW) event GW150914 (after its detection on September 14, 2015) as observed by the LIGO Hanford (H1) and Livingston (L1) detectors.

Top panel: Time series filtered with a 35-350 Hz band-pass filter to suppress large fluctuations outside the detectors’ most sensitive frequency band. The panels show the GW strain in H1 and L1. GW150914 arrived first at L1 and about 7 milliseconds later at H1.

Second panel: various reconstructions of the waveforms in the 35-350Hz band.

Third panel: residual noise after the filtered numerical relativity waveform is subtracted from the filtered detection time series.

Bottom panel: The plots show how the gravitational wave strain in each LIGO detector varies as a function of time and frequency. The time is measured in seconds and the frequency in Hertz, or number of waveform cycles per second. The plots show how the gravitational wave event GW150914 sweeps from 35 Hz to 150 Hz over two tenths of a second.

Stats about the detected gravitational wave.

Gravitational waves detected 100 years after Einstein’s prediction

For the first time, scientists have observed ripples in the fabric of spacetime called gravitational waves, arriving at the earth from a cataclysmic event in the distant universe. This confirms a major prediction of Albert Einstein’s 1915 general theory of relativity and opens an unprecedented new window onto the cosmos.

Gravitational waves carry information about their dramatic origins and about the nature of gravity that cannot otherwise be obtained. Physicists have concluded that the detected gravitational waves were produced during the final fraction of a second of the merger of two black holes to produce a single, more massive spinning black hole. This collision of two black holes had been predicted but never observed.

The gravitational waves were detected on Sept. 14, 2015, at 5:51 a.m. Eastern Daylight Time (9:51 UTC) by both of the twin Laser Interferometer Gravitational-wave Observatory (LIGO) detectors, located in Livingston, La., and Hanford, Wash. The LIGO Observatories are funded by the National Science Foundation, and were conceived, built, and are operated by Caltech and Massachusetts Institute of Technology. The discovery, accepted for publication in the journal Physical Review Letters, was made by the LIGO Scientific Collaboration (which includes the GEO Collaboration and the Australian Consortium for Interferometric Gravitational Astronomy) and the Virgo Collaboration using data from the two LIGO detectors.

NCSA's role in this discovery

Thirty years ago, the National Center for Supercomputing Applications (NCSA) was founded at the University of Illinois at Urbana-Champaign by Larry Smarr based on the premise that numerically modeling scientific problems, such as the colliding of black holes, required high-performance computing to make progress. Smarr’s doctoral thesis had itself been on the modeling of the head-on collision of two black holes. In 2014, Smarr was honored with the Golden Goose award to highlight the impact that his black hole research had on creating NCSA and the NSF supercomputing centers program which led to the public Internet revolution via the creation of the NCSA Mosaic web browser, the first browser to have visual features like icons, bookmarks, and pictures, and was easy to use.

At NCSA, Smarr formed a numerical group, led by Edward Seidel&mdashthe current NCSA director. The group quickly became a leader in applying supercomputers to black hole and gravitational wave problems. For example, in 1994 the very first 3-dimension simulation of two colliding black holes providing computed gravitational waveforms was carried out at NCSA by this group in collaboration with colleagues at Washington University.

NCSA as a center has continued to support the most complex problems in numerical relativity and relativistic astrophysics, including working with several groups addressing models of gravitational waves sources seen by LIGO in this discovery. Even more complex simulations will be needed for anticipated future discoveries such as colliding neutron stars and black holes or supernovae explosions.

NCSA has also played a role in developing the tools needed for simulating relativistic systems. The work of Seidel’s NCSA group led to the development of the Cactus Framework, a modular and collaborative framework for parallel computing which since 1997 has supported numerical relativists as well as other disciplines developing applications to run on supercomputers at NCSA and elsewhere. Built on the Cactus Framework, the NSF-supported Einstein Toolkit developed at Georgia Tech, RIT, LSU, AEI, Perimeter Institute and elsewhere now supports many numerical relativity groups modeling sources important for LIGO on the NCSA Blue Waters supercomputer.

"This historic announcement is very special for me. My career has centered on understanding the nature of black hole systems, from my research work in numerical relativity, to building collaborative teams and technologies for scientific research, and then also having the honor to be involved in LIGO during my role as NSF Assistant Director of Mathematics and Physical Sciences. I could not be more excited that the field is advancing to a new phase," said Seidel, who is also Founder Professor of Physics and professor of astronomy at Illinois.

Gabrielle Allen, professor of astronomy at Illinois and NCSA associate director, previously led the development of the Cactus Framework and the Einstein Toolkit. "NCSA was a critical part of inspiring and supporting the development of Cactus for astrophysics. We held our first Cactus workshop at NCSA and the staff’s involvement in our projects was fundamental to being able to demonstrate not just new science but new computing technologies and approaches," said Allen.

Eliu Huerta, member of the LIGO Scientific Collaboration since 2011 and current leader of the relativity group at NCSA, is a co-author of the paper to be published in Physical Review Letters. Huerta works at the interface of analytical and numerical relativity, specializing in the development of modeled waveforms for the detection and interpretation of gravitational wave signals. Huerta uses these models to infer the astrophysical properties of compact binary systems, and shed light on the environments in which they form and coalesce.

"The first direct observation of gravitational waves from a binary black hole system officially inaugurates the field of gravitational wave astronomy. There can be no better way to celebrate the first centenary of Einstein’s prediction of gravitational waves. We can gladly say that Einstein is right, and that the beautiful mathematical framework he developed to describe gravity is valid even in the most extreme environments. A new era has begun, and we will be glad to discover astrophysical objects we have never dreamt of," said Huerta.

Stuart Shapiro, a professor of physics and astronomy at Illinois, was appointed an NCSA research scientist by Smarr two decades ago. A leading expert in the theory that underpinned the search for gravitational waves, he has developed software tools that can simulate on NCSA supercomputers like Blue Waters the very binary black hole merger and gravitational waves now detected by LIGO. Shapiro said he is thrilled by the discovery.

"This presents the strongest confirmation yet of Einstein's theory of general relativity and the cleanest evidence to date of the existence of black holes. The gravitational waves that LIGO measures can only be generated by merging black holes&mdashexotic relativistic objects from which nothing, including light, can escape from their interior,'' said Shapiro.

"Work at NCSA helps open windows into the universe," said Peter Schiffer, vice chancellor for research at the University of Illinois at Urbana-Champaign. "This is a wonderful fundamental discovery, and it’s exciting that the high performance computing capabilities that we developed to address challenges like this one are also being used to solve other significant societal problems."

Black holes are formed when massive stars undergo a catastrophic gravitational collapse. The gravitational field of these ultra compact objects is so strong that not even light can escape from them.

Gravitational waves are generated when ultra compact objects&mdashblack holes, neutron stars or white dwarfs&mdashare accelerated to velocities that are a significant fraction of the speed of light. Gravitational waves couple weakly to matter, which means that they can travel unimpeded throughout the Universe and that only extremely sensitive detectors such as LIGO can detect them.

LIGO research is carried out by the LIGO Scientific Collaboration, a group of more than 1,000 scientists from universities around the United States and in 14 other countries. More than 90 universities and research institutes in the collaboration develop detector technology and analyze data approximately 250 students are strong contributing members of the collaboration.

The LIGO Scientific Collaboration’s detector network includes the LIGO interferometers and the GEO600 detector. The GEO team includes scientists at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute, AEI), Leibniz Universität Hannover, along with partners at the University of Glasgow, Cardiff University, the University of Birmingham, other universities in the United Kingdom, and the University of the Balearic Islands in Spain.

LIGO was originally proposed as a means of detecting these gravitational waves in the 1980s by Rainer Weiss, professor of physics, emeritus, from MIT Kip Thorne, Caltech’s Richard P. Feynman Professor of Theoretical Physics, emeritus and Ronald Drever, professor of physics, emeritus, also from Caltech.

Virgo research is carried out by the Virgo Collaboration, consisting of more than 250 physicists and engineers belonging to 19 different European research groups: six from Centre National de la Recherche Scientifique (CNRS) in France eight from the Istituto Nazionale di Fisica Nucleare (INFN) in Italy two in the Netherlands with Nikhef the Wigner RCP in Hungary the POLGRAW group in Poland and the European Gravitational Observatory (EGO), the laboratory hosting the Virgo detector near Pisa in Italy.

The discovery was made possible by the enhanced capabilities of Advanced LIGO, a major upgrade that increases the sensitivity of the instruments compared to the first generation LIGO detectors, enabling a large increase in the volume of the universe probed&mdashand the discovery of gravitational waves during its first observation run.

The U.S. National Science Foundation leads in financial support for Advanced LIGO. Funding organizations in Germany (Max Planck Society), the U.K. (Science and Technology Facilities Council, STFC) and Australia (Australian Research Council) also have made significant commitments to the project. Several of the key technologies that made Advanced LIGO so much more sensitive have been developed and tested by the German UK GEO collaboration.

Significant computer resources have been contributed by the AEI Hannover Atlas Cluster, the LIGO Laboratory, Syracuse University, and the University of Wisconsin-Milwaukee. Several universities designed, built, and tested key components for Advanced LIGO: The Australian National University, the University of Adelaide, the University of Florida, Stanford University, Columbia University in the City of New York and Louisiana State University.


Black Holes Collide, and Gravity Quivers

In the most precise effort yet to detect gravitational waves — the quiverings of space-time predicted by Einstein's theory of general relativity — the National Science Foundation in the late 1990's carved two large V's, one in the barren landscape of central Washington State, the other among the pines outside Baton Rouge, La.

The tunnels are part of the Laser Interferometer Gravitational-Wave Observatory, known as LIGO. If something astronomically violent, like a collision of two black holes, shakes the fabric of the universe within 300 million light-years of Earth, an expanse that encompasses several thousand galaxies, LIGO should see the resulting gravitational ripples.

The observatory is sensitive enough to detect a change of less than one ten-quadrillionth of an inch, or about a thousandth of the diameter of a proton, in the length of the 2.5-mile-long tunnels.

After several years of testing and fine-tuning — special dampers had to be installed at the Louisiana site to counteract vibrations generated when nearby loggers cut down trees, for instance — the observatory began full operation in November. The centers cost nearly $300 million to build and $30 million a year to operate.

The data so far, reported last week at a meeting of the American Physical Society in Dallas, contain nothing of interest. In fact, scientists would not be surprised if the initial run of the experiment over the next year or so found nothing at all.

"I would still sleep well about general relativity," said Peter R. Saulson, a physics professor at Syracuse and an observatory spokesman.

Jay Marx, LIGO's executive director, estimated that the chance of success was "25 percent, if nature's kind."

General relativity, formulated 90 years ago by Einstein to explain the properties of space and time, fits well with measurements of gravity in and around the solar system. But predictions about what happens around black holes and other places where gravity is extremely strong remain largely untested. One of the predictions is that in such conditions, sizable gravitational waves will be produced.

With new research, scientists have a better idea of what LIGO should look for. Researchers led by Joan M. Centrella, chief of the Gravitational Astrophysics Laboratory at NASA's Goddard Space Flight Center, announced last month that they had succeeded in calculating the shape of the gravitational waves that should result when two black holes, orbiting one another, merge.

"This is not something made up like in a science fiction movie," Dr. Centrella said in a news conference announcing the findings. "Rather, we have confidence that these results are the real deal, that we have the true gravitational wave fingerprint predicted by Einstein for the black hole merger."

The equations of general relativity can be easily written down but are notoriously hard to solve. Astrophysicists were able to simulate the head-on collision of two black holes three decades ago, but computing the paths of orbiting black holes and their violent merger proved much harder.

"This has been a holy grail type of quest for the last 30 years," Dr. Centrella said.

Dr. Centrella's simulations still contain some simplifications that do not reflect attributes of actual black hole pairs: the two black holes have the same mass, and neither is spinning. The calculations predicted, for example, that 4 percent of the mass of the black holes should be converted into gravitational waves.

"That's a very important number," Dr. Saulson said. "That tells us that these gravitational waves are going to be about as strong as we hoped they could be." He added, "And that's got those of us working on the detectors very excited, making it seem more likely we'll bump into something."

Einstein's theory of general relativity changed the idea of gravity from a simple force dragging apples from a tree to a puzzle of geometry. Imagine a rubber sheet pulled taut horizontally and then tossing a bowling ball and a tennis ball onto it. The heavier bowling ball sinks deeper, and the tennis ball will move toward the bowling ball not because of a direct attraction between the two, but because the tennis ball rolls into the depression around the bowling ball.

In this two-dimensional analogy of space-time, one can also imagine a sudden collision of objects creating ripples that skitter across the sheet. Those are the gravitational waves LIGO hopes to detect.

At each site, a laser beam generated at the base of the V is split in two and shot through tunnels buried along each 2.5-mile-long arm. The light bounces back and forth in the two tunnels. When a gravitational wave speeds past, it should stretch and shrink the distance that the laser beams travel, causing the laser light to flicker into a detector at the base of the V.

Because the instruments are susceptible to tiny disturbances, only signals seen by both LIGO detectors, nearly 2,000 miles apart, would likely be convincing to scientists.

The skepticism about whether LIGO will actually spot gravitational waves comes not from questions about general relativity — "People would be incredibly surprised if it wasn't right," Dr. Marx said — but uncertainty about how often events that create gravitational waves occur in the universe.

Pairs of orbiting black holes should be the end result of star systems consisting of two massive stars. Over time, the black holes would spiral inward and eventually collide. Astronomers can see plenty of pairs of massive stars twirling in the sky, but they cannot be sure that they ultimately collapse into pairs of black holes.

Because astrophysicists do not fully understand how stars age, "There are multiple factors of uncertainty," said Vassiliki Kalogera, a professor of physics and astronomy at Northwestern University. "We don't know that binary black holes exist."

At the optimistic end, her calculations suggest that LIGO could detect up to 10 black hole mergers a year. But the calculations are still uncertain by a factor of 100, which means that at the pessimistic end, the rate of detectable black hole mergers may be just one every 50 years or so.

A more common event is the merger of neutron stars, the dense, burned-out cores left over by some exploding stars. The most convincing evidence so far for gravitational waves was the observation in 1974 by two Princeton physicists, Joseph H. Taylor and his student Russell A. Hulse. They saw a pair of pulsating neutron stars spiraling inward toward each other. The amount of energy lost in the decaying orbits turned out to match the amount of energy expected to be emitted in gravitational waves.

However, the gravitational waves produced by orbiting neutron stars are too weak to be detected by LIGO. And even when the neutron stars slam into each other, the cataclysm is not nearly as violent as the merger of black holes, so a neutron star collision would have to occur much closer in order for LIGO to see it. Dr. Kalogera's calculations suggest that the observatory will see a neutron star merger once every seven or eight years, at best.

For LIGO to detect gravitational waves routinely, the instruments will need a proposed $200 million upgrade, which includes more powerful lasers, to increase their sensitivity by a factor of 10, Dr. Marx said.

Astronomers hope that LIGO and its successors, as well as similar detectors in Europe and Japan, will become a new type of telescope. If the detection of gravitational waves becomes common, astronomers should be able to deduce many physical properties of black holes and neutron stars. They may also find that such objects are more common in certain types of galaxies.

The upgraded observatory may also be able to detect gravitational waves produced by exploding stars or even reverberations of the Big Bang 13.6 billion years ago.

Sometime in the next decade, NASA and the European Space Agency hope to launch a space-based gravitational wave detector called the Laser Interferometer Space Antenna, or LISA. Consisting of three satellites flying around the sun in the formation of an equilateral triangle 3.1 million miles apart, LISA would be able to detect gravitational waves with much larger wavelengths, like those produced when mega-black holes at the center of galaxies merge.

For now, the scientists await their first gravitational wave.

"We are all hoping we are lucky," said Gabriela González, a physics professor at Louisiana State and a LIGO scientist. "Even if we are not, we will know more about nature."


What is LIGO?

Unlike other astronomical observatories, which collect starlight through round lenses, LIGO is what CalTech calls a “blind” observatory, meaning it doesn’t need light to make its observations. LIGO is broken up into two separate observatory sites — one in Washington state and one in Louisana — that both feature a super-sensitive instrument called a Michelson interferometer.

Here’s what happens when a gravitational wave hits LIGO, according to NASA:

  • A gravitational wave caused by a cosmic collision passes by Earth
  • As it passes by, it squeezes and stretches space
  • LIGO has two outstretched arms (each 4 kilometers long) that cross each other asymmetrically — this is the Michelson Interferometer
  • This stretching of space causes LIGOs arms to change in length slightly, which it detects using lasers and reflecting mirrors

Michelson interferometers can be small enough to fit inside a lab but in LIGOs case it is larger than a football field and covered in steel and concrete.

In addition to detecting gravitational waves in 2015, LIGO has also helped scientists detect a “kilonova” (i.e. a black hole merger) in 2017.

What they did — When it comes to actually cooling an object down to near absolute zero — which also corresponds to its lowest-energy or ground state — Sudhir says that the team faced a “chicken and the egg” problem.

“If you need to cool [something] down, you need to extract energy from the object and do that faster than the rate at which energy gets into the object from its surroundings,” says Sudhir.

“However as the object gets colder, smaller perturbations of energy from the surrounding can cause a proportionately larger injection of energy into the object. So, as you get colder, you need to be extracting energy even faster to even be able to maintain that temperature.”

This is complicated further by first needing a cooler object to extract energy in the first place. To solve this problem, Sudhir says their team used something called “feedback cooling.”

“The idea is to use lasers to monitor very precisely how the object jiggles around in response to energy coming in from the surroundings, and then use that information to immediately cancel out that random motion — somewhat like a noise-canceling headphone,” says Sudhir.

Using this technique, the researchers were able to cool the 10-kilogram oscillator down to a temperature that Sudhir says could be used to help detect the effects of gravity on quantum mechanics.

What’s next — While the team’s results are incredibly promising, Sudhir says that future incarnations of LIGO — which would have a 40 km long interferometer and cryogenically cooled mirrors — will be an even greater asset to this exploration.

Ultimately, Sudhir hopes that experiments like these can bring him one step closer to answering questions that he once puzzled over as a young physics student.

“Some of the questions that are probed by these experiments are fairly fundamental — in fact questions that most students of physics might be prompted to ask when they encounter quantum physics for the first time,” he says. “I did too, a decade ago now I get the chance to ask nature the same question through an experiment.”

Abstract: The motion of a mechanical object, even a human-sized object, should be governed by the rules of quantum mechanics. Coaxing them into a quantum state is, however, difficult because the thermal environment masks any quantum signature of the object’s motion. The thermal environment also masks the effects of proposed modifications of quantum mechanics at large mass scales. We prepared the center-of-mass motion of a 10-kilogram mechanical oscillator in a state with an average phonon occupation of 10.8. The reduction in temperature, from room temperature to 77 nanokelvin, is commensurate with an 11 orders-of-magnitude suppression of quantum back-action by feedback and a 13 orders-of-magnitude increase in the mass of an object prepared close to its motional ground state. Our approach will enable the possibility of probing gravity on massive quantum systems.


Astronomers See Light Show Associated With Gravitational Waves

Marking the beginning of a new era in astrophysics, scientists have detected gravitational waves and electromagnetic radiation, or light, from the same event for the first time. This historic discovery reveals the merger of two neutron stars, the dense cores of dead stars, and resolves the debate about how the heaviest elements such as platinum and gold were created in the Universe.

To achieve this remarkable result, thousands of scientists around the world have worked feverishly using data from telescopes on the ground and in space. Researchers at the Harvard-Smithsonian Center for Astrophysics (CfA) in Cambridge, Mass., have played a pivotal role. A series of eight papers led by CfA astronomers and their colleagues detail the complete story of the aftermath of this event and examine clues about its origin.

"It's hard to describe our sense of excitement and historical purpose over the past couple of months," said the leader of the team, CfA's Edo Berger. "This is a once in a career moment -- we have fulfilled a dream of scientists that has existed for decades."

Gravitational waves are ripples in space-time caused by the accelerated motion of massive celestial objects. They were first predicted by Einstein’s General Theory of Relativity. The Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) made the first direct detection of gravitational waves in September 2015, when the merger of two stellar-mass black holes was discovered.

On 8:41 am EDT August 17, 2017, LIGO detected a new gravitational wave source, dubbed GW170817 to mark its discovery date. Just two seconds later NASA's Fermi satellite detected a weak pulse of gamma rays from the same location of the sky. Later that morning, LIGO scientists announced that two merging neutron stars produced the gravitational waves from GW170817.

"Imagine that gravitational waves are like thunder. We've heard this thunder before, but this is the first time we’ve also been able to see the lightning that goes with it," said Philip Cowperthwaite of the CfA. "The difference is that in this cosmic thunderstorm, we hear the thunder first and then get the light show afterwards."

A few hours after the announcement, as night set in Chile, Berger's team used the powerful Dark Energy Camera on the Blanco telescope to search the region of sky from which the gravitational waves emanated. In less than an hour they located a new source of visible light in the galaxy NGC 4993 at a distance of about 130 million light years.

"One of the first giant galaxies we looked at had an obvious new source of light popping right out at us, and this was an incredible moment," said Matt Nicholl of the CfA. “We thought it would take days to locate the source but this was like X marks the spot."

The CfA team and collaborators then launched a series of observations that spanned the electromagnetic spectrum from X-rays to radio waves to study the aftermath of the neutron star merger.

In their set of papers, the CfA scientists report their studies of the brightness and spectrum of the optical and infrared light and how it changed over time. They show that the light is caused by the radioactive glow when heavy elements in the material ejected by the neutron star merger are produced in a process called a kilonova.

"We've shown that the heaviest elements in the periodic table, whose origin was shrouded in mystery until today are made in the mergers of neutron stars,” said Edo Berger. "Each merger can produce more than an Earth’s mass of precious metals like gold and platinum and many of the rare elements found in our cellphones."

The material observed in the kilonova is moving at high speeds, suggesting that it was expelled during the head-on collision of two neutron stars. This information, independent of the gravitational wave signature, suggests that two neutron stars were involved in GW170817, rather than a black hole and a neutron star.

Radio observations with the Very Large Array in New Mexico helped confirm that the merger of the two neutron stars triggered a short gamma ray burst (GRB), a brief burst of gamma rays in a jet of high-energy particles. The properties match those predicted by theoretical models of a short GRB that was viewed with the jet initially pointing at a large angle away from Earth. Combining the radio data with observations from NASA’s Chandra X-ray Observatory shows that the jet pointed about 30 degrees away from us.

"This object looks far more like the theories than we had any right to expect," said the CfA's Kate Alexander who led the teams' VLA observations. "We will continue to track the radio emission for years to come as the material ejected from the collision slams into the surrounding medium," she continued.

An analysis of the host galaxy, NGC 4993, and the environment of the cataclysmic merger shows that the neutron star binary most likely formed more than 11 billion years ago.

"The two neutron stars formed in supernova explosions when the universe was only two billion years old, and have spent the rest of cosmic history getting closer and closer to each other until they finally smashed together," said Peter Blanchard of the CfA.

A long list of observatories were used to study the kilonova, including the SOAR and Magellan telescopes, the Hubble Space Telescope, the Dark Energy Camera on the Blanco, and the Gemini-South telescope.

The series of eight papers describing these results appeared in the Astrophysical Journal Letters on October 16th. The four papers with first authors from CfA are led by Philip Cowperthwaite about the changes with time of light from the kilonova, one led by Matt Nicholl about the changes with time of the kilonova's spectrum, another led by Kate Alexander about the VLA observations, and another led by Peter Blanchard about how long the merger took to unfold and the properties of the host galaxy.

Completing the series of eight papers, Marcelle Soares-Santos from Brandeis University in Waltham MA led a paper about the discovery of the optical counterpart Ryan Chornock from Ohio University in Athens, OH, led a paper about the kilonova's infrared spectra, Raffaella Margutti from Northwestern University in Evanston, IL, led a paper about the Chandra observations of the jet, and Wen-fai Fong also from Northwestern led a paper about the comparison between GW170817 and previous short GRBs.

Graphics and other additional information on this result can be found at http://www.kilonova.org.

Headquartered in Cambridge, Mass., the Harvard-Smithsonian Center for Astrophysics (CfA) is a collaboration between the Smithsonian Astrophysical Observatory and the Harvard College Observatory. CfA scientists, organized into six research divisions, study the origin, evolution and ultimate fate of the universe.


Theorists’ Contributions to Understanding and Controlling Noise in the LIGO Interferometers

A major aspect of the LIGO experiment is understanding and controlling a huge range of phenomena that produce noise which can hide gravitational-wave signals. Theorists have contributed to scoping out some of these phenomena. This has been highly enjoyable, and it has broadened the education of theory students. I will give several interesting examples:

Scattered-Light Noise

In each arm of a LIGO interferometer the light beam bounces back and forth between mirrors. A tiny portion of the light scatters off one mirror, then scatters or reflects from the inner face of the vacuum tube that surrounds the beam, then travels to the other mirror, and there scatters back into the light beam (Figure 15, top). The tube face vibrates with an amplitude that is huge compared to the gravitational wave's influence, and those vibrations put a huge, oscillating phase shift onto the scattered light. That huge phase shift on a tiny fraction of the beam's light can produce a net phase shift in the light beam that is bigger than the influence of a gravitational wave.

This light-scattering noise can be controlled by placing baffles in the beam tube (dashed lines in Figure 15) to block the scattered light from reaching the far mirror. A bit of the scattered light, however, can still reach the far mirror by diffracting off the edges of the baffles.

Baffles and their diffraction of light are a standard issue in optical telescopes and other devices. But not standard, and unique to gravitational interferometers, is the danger that there might be coherent superposition of the oscillating phase shift for light that travels by different routes from one mirror to the other such coherence could greatly increase the noise. In 1988 Rai Weiss recruited me and my theory students to look at this, determine how serious it is, and devise a way to mitigate it. Eanna Flanagan and I did so. To break the coherence, we gave the baffles deep saw teeth with random heights (Figure 15, bottom), and to minimize the noise further we chose the teeth pattern optimally and optimized the locations of the baffles in the beam tube. 31 A segment of one of our random-saw-toothed baffles is my contribution to the Nobel Museum in Stockholm.

Gravitational Noise

Humans working near a LIGO mirror create oscillating gravitational forces that might move the mirror more than does a gravitational wave. My wife, Carolee Winstein, is a biokinesiologist (expert on human motion). Using experimental data on human motion from her colleagues, we computed the size of this noise and concluded that, if humans are kept more than 10 meters from a LIGO mirror, the noise is acceptably small. 32 This was used as a specification for the layout of the buildings that house the LIGO mirrors. Theory students scoped out noise produced by the gravitational forces of seismic waves in the Earth, 33 and of airborne objects such as tumbleweeds. 34

Thermal Noise

Thermal vibrations (vibrations caused by finite temperature) make LIGO's mirrors jiggle. These vibrations can arise in many different ways. Theory student Yuri Levin devised a new method to compute this thermal noise and to identify its many different origins. 35 Most importantly he used his method to discover that thermal vibrations in the coatings of LIGO's mirrors (which previously had been overlooked) might be especially serious. This has turned out to be true: In the Advanced LIGO interferometers, and likely in the next generation of gravitational interferometers, coating thermal noise is one of the two most serious noise sources the other is quantum noise.

Quantum Noise and the Standard Quantum Limit for a Gravitational Interferometer

Quantum noise is noise due to the randomness of the photon distribution in an interferometer's light beams. In each initial LIGO interferometer (Parts I and II of this lecture), the quantum noise had two parts: photon shot noise, caused by randomness in the arrival of photons at the photodetector (the interferometer's output) and radiation pressure noise, caused by randomness in the bouncing of photons off the interferometers’ mirrors, which makes the mirrors jiggle.

Both forms of quantum noise must arise from light-beam differences in the interferometers’ two arms, since the interferometer output is sensitive only to differences.

In the late 1970s, there was much debate among gravitational wave scientists over the physical origin of these differences. Theory postdoc Carlton Caves found the surprising answer: 36 Both the radiation pressure noise and the shot noise arise, he realized, from electromagnetic (quantum electrodynamical) vacuum fluctuations that enter the interferometer backwards, from the direction of its output photodetector. These fluctuations beat against the laser light in the two arms to produce 1. radiation-pressure fluctuations (noise) that are opposite in the two arms, and 2. intensity fluctuations that also are also opposite and that therefore exit from the interferometer into the output photodetector as shot noise Figure 17.

Here Sh is the spectral density of the noise superposed on the gravitational wave signal, ħ is Planck's constant, m is the mass of each of the interferometer's mirrors, L is the length of the interferometer's two arms and ω is the gravitational wave's angular frequency.

In the late 1980s, Brian Meers at U. Glasgow (building on an idea of Ron Drever) proposed adding a signal recycling mirror to gravitational interferometers, in order to make them more versatile (see Weiss's and Barish's Parts I and II of this lecture), and by the late 1990s this new mirror was incorporated into the design for the future Advanced-LIGO interferometers. Strain and others used semiclassical (not fully quantum) theory to deduce the shot noise and radiation pressure noise in these advanced-LIGO interferometers. This was worrisome because Advanced LIGO was expected to operate very near its standard quantum limit, SQL, where the semiclassical analysis might be flawed. So theory postdoc Alessandra Buonanno and graduate student Yanbei Chen carried out a full quantum mechanical analysis of the noise.

  • The noise predictions of the semi-classical theory were wrong, so planning for Advanced LIGO would have to be modified, though not greatly.
  • The interferometer's signal recycling mirror triggers the beam's light pressure in each arm to act as a frequency-dependent spring pushing against the mirrors, and so gives rise to an oscillatory, opto-mechanical behavior.
  • The signal recycling mirror also creates quantum correlations between the shot noise and radiation-pressure noise. These correlations make it no longer viable to talk separately about shot noise and radiation pressure noise instead, one must focus on a single, unified quantum noise.
  • These correlations also enable the Advanced LIGO interferometer to beat Caves’ SQL by as much as a factor 2 over a bandwidth of order the gravitational-wave frequency.

Quantum Fluctuations, Quantum Nondemolition, and Squeezed Vacuum

According to quantum theory everything fluctuates randomly, at least a little bit.

A half century ago, the Russian physicist Vladimir Braginsky argued (in effect) that in gravitational wave detectors, when monitoring an object on which the waves act, one might have to measure motions so small that they could get hidden by quantum fluctuations of the object. 38 Later, in the mid-1970s, 39 Braginsky realized that it should be possible to create quantum nondemolition (QND) technology to circumvent these quantum fluctuations.

In 1980, Caves recognized that, although he derived his standard quantum limit [Equation 1] for an interferometer's sensitivity by analyzing its interaction with light, this SQL actually has a deeper origin: it is associated with the quantum fluctuations of the centers of mass of the interferometer's mirrors. The challenge, then, was to devise QND technology to circumvent those fluctuations and thereby beat their SQL.

Since the SQL is enforced by the electromagnetic vacuum fluctuations that enter the output port, Caves realized that a key QND tool might be to modify those vacuum fluctuations — and thereby, through their radiation-pressure influence on the mirrors, modify the mirrors’ own quantum fluctuations.

More precisely, Caves 36 proposed to reduce the electromagnetic vacuum fluctuations in one quadrature of each fluctuational frequency (e.g., the cos ωt quadrature) at the price of increasing the vacuum fluctuations in the other quadrature (e.g., sin ωt). (The uncertainty principle dictates that the product of the fluctuation strengths for the two quadratures cannot be reduced, so if one is reduced, the other must increase.)

One quadrature is responsible for shot noise, and the other for radiation pressure noise, Caves had shown so by squeezing the vacuum in this way, one can reduce the shot noise at the price of increasing the radiation pressure noise—which is the same thing as one achieves by increasing the laser light intensity. (This use of squeezed vacuum has since become very important: The original plan for bringing Advanced LIGO to its design sensitivity entailed pushing up to 800 kW the light power bouncing back and forth between mirrors in each interferometer arm. However, such high light power produces exceedingly unpleasant side effects the mirrors have trouble handling it. Therefore, the new plan today, being implemented for LIGO's next observing run in late 2018, entails injecting squeezed vacuum into the output port in precisely the manner Caves envisioned, instead of a corresponding increase in light power.)

In Advanced LIGO, shot noise dominates at high gravitational-wave frequencies (well above 200 Hz), radiation pressure noise dominates at lower frequencies (well below 200 Hz). Therefore, it is advantageous to inject vacuum that is squeezed at a frequency-dependent quadrature cos[ωt – φ(ω)], which produces a shot-noise reduction (φ = 0) at high frequencies, and a radiation-pressure reduction at low frequencies (φ = π/2). At intermediate frequencies an amazing thing happens — as was discovered by Bill Unruh 40 in 1981: the two noises, shot and radiation-pressure, partially cancel each other out! (See Figure 21.) As a result, the interferometer beats the SQL (it achieves quantum nondemolition), and with sufficient squeezing, it can do so by an arbitrarily large amount — in principle, but not in practice.

Although we have known this QND technique since 1983, in the 1980s and 1990s no practical method was known for producing the required frequency-dependent squeeze phase φ(ω).

In 1999, I discussed this problem in depth with my colleague Jeff Kimble (Caltech's leading experimenter in squeezing and other quantum-information-related techniques), and he devised a solution: Squeeze the vacuum at a frequency-independent phase, then send the squeezed vacuum through one or two carefully tuned Fabry-Perot cavities (“optical filters”) before injecting it into the interferometer's output port. 41

Among many different QND techniques that have been devised for LIGO interferometers, 42 this frequency-dependent squeezing, using Kimble filter cavities, is the one that currently looks most promising for future generations of gravitational interferometers: LIGO A+, Voyager, Cosmic Explorer, and Einstein Telescope (see Barish's Part II of this lecture). A small amount of QND will be required in LIGO A+, and a substantial amount in all subsequent interferometers.


Astronomers See Light Show Associated With Gravitational Waves

Marking the beginning of a new era in astrophysics, scientists have detected gravitational waves and electromagnetic radiation, or light, from the same event for the first time. This historic discovery reveals the merger of two neutron stars, the dense cores of dead stars, and resolves the debate about how the heaviest elements such as platinum and gold were created in the Universe.

To achieve this remarkable result, thousands of scientists around the world have worked feverishly using data from telescopes on the ground and in space. Researchers at the Harvard-Smithsonian Center for Astrophysics (CfA) in Cambridge, Mass., have played a pivotal role. A series of eight papers led by CfA astronomers and their colleagues detail the complete story of the aftermath of this event and examine clues about its origin.

"It's hard to describe our sense of excitement and historical purpose over the past couple of months," said the leader of the team, CfA's Edo Berger. "This is a once in a career moment -- we have fulfilled a dream of scientists that has existed for decades."

Gravitational waves are ripples in space-time caused by the accelerated motion of massive celestial objects. They were first predicted by Einstein’s General Theory of Relativity. The Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) made the first direct detection of gravitational waves in September 2015, when the merger of two stellar-mass black holes was discovered.

On 8:41 am EDT August 17, 2017, LIGO detected a new gravitational wave source, dubbed GW170817 to mark its discovery date. Just two seconds later NASA's Fermi satellite detected a weak pulse of gamma rays from the same location of the sky. Later that morning, LIGO scientists announced that two merging neutron stars produced the gravitational waves from GW170817.

"Imagine that gravitational waves are like thunder. We've heard this thunder before, but this is the first time we’ve also been able to see the lightning that goes with it," said Philip Cowperthwaite of the CfA. "The difference is that in this cosmic thunderstorm, we hear the thunder first and then get the light show afterwards."

A few hours after the announcement, as night set in Chile, Berger's team used the powerful Dark Energy Camera on the Blanco telescope to search the region of sky from which the gravitational waves emanated. In less than an hour they located a new source of visible light in the galaxy NGC 4993 at a distance of about 130 million light years.

"One of the first giant galaxies we looked at had an obvious new source of light popping right out at us, and this was an incredible moment," said Matt Nicholl of the CfA. “We thought it would take days to locate the source but this was like X marks the spot."

The CfA team and collaborators then launched a series of observations that spanned the electromagnetic spectrum from X-rays to radio waves to study the aftermath of the neutron star merger.

In their set of papers, the CfA scientists report their studies of the brightness and spectrum of the optical and infrared light and how it changed over time. They show that the light is caused by the radioactive glow when heavy elements in the material ejected by the neutron star merger are produced in a process called a kilonova.

"We've shown that the heaviest elements in the periodic table, whose origin was shrouded in mystery until today are made in the mergers of neutron stars,” said Edo Berger. "Each merger can produce more than an Earth’s mass of precious metals like gold and platinum and many of the rare elements found in our cellphones."

The material observed in the kilonova is moving at high speeds, suggesting that it was expelled during the head-on collision of two neutron stars. This information, independent of the gravitational wave signature, suggests that two neutron stars were involved in GW170817, rather than a black hole and a neutron star.

Radio observations with the Very Large Array in New Mexico helped confirm that the merger of the two neutron stars triggered a short gamma ray burst (GRB), a brief burst of gamma rays in a jet of high-energy particles. The properties match those predicted by theoretical models of a short GRB that was viewed with the jet initially pointing at a large angle away from Earth. Combining the radio data with observations from NASA’s Chandra X-ray Observatory shows that the jet pointed about 30 degrees away from us.

"This object looks far more like the theories than we had any right to expect," said the CfA's Kate Alexander who led the teams' VLA observations. "We will continue to track the radio emission for years to come as the material ejected from the collision slams into the surrounding medium," she continued.

An analysis of the host galaxy, NGC 4993, and the environment of the cataclysmic merger shows that the neutron star binary most likely formed more than 11 billion years ago.

"The two neutron stars formed in supernova explosions when the universe was only two billion years old, and have spent the rest of cosmic history getting closer and closer to each other until they finally smashed together," said Peter Blanchard of the CfA.

A long list of observatories were used to study the kilonova, including the SOAR and Magellan telescopes, the Hubble Space Telescope, the Dark Energy Camera on the Blanco, and the Gemini-South telescope.

The series of eight papers describing these results appeared in the Astrophysical Journal Letters on October 16th. The four papers with first authors from CfA are led by Philip Cowperthwaite about the changes with time of light from the kilonova, one led by Matt Nicholl about the changes with time of the kilonova's spectrum, another led by Kate Alexander about the VLA observations, and another led by Peter Blanchard about how long the merger took to unfold and the properties of the host galaxy.

Completing the series of eight papers, Marcelle Soares-Santos from Brandeis University in Waltham MA led a paper about the discovery of the optical counterpart Ryan Chornock from Ohio University in Athens, OH, led a paper about the kilonova's infrared spectra, Raffaella Margutti from Northwestern University in Evanston, IL, led a paper about the Chandra observations of the jet, and Wen-fai Fong also from Northwestern led a paper about the comparison between GW170817 and previous short GRBs.

Graphics and other additional information on this result can be found at http://www.kilonova.org.

Headquartered in Cambridge, Mass., the Harvard-Smithsonian Center for Astrophysics (CfA) is a collaboration between the Smithsonian Astrophysical Observatory and the Harvard College Observatory. CfA scientists, organized into six research divisions, study the origin, evolution and ultimate fate of the universe.


Images and movies: gravitational waves

The state parliament of North Rhine-Westphalia has unanimously pledged its support for the groundbreaking international science project Einstein Telescope (ET).

Einstein Telescope proposal submitted to ESFRI roadmap

The proposal to include the Einstein Telescope, a pioneering third-generation gravitational-wave (GW) observatory, in the 2021 update of the European Strategic Forum for Research Infrastructures (ESFRI) roadmap has been submitted.

The Federal Ministry of Education and Research supports the development of the Einstein Telescope

For the next generation of gravitational-wave detectors on Earth: Laser development and squeezed-light research in Hannover

A signal like none before

LIGO and Virgo detectors catch first gravitational wave from binary black hole merger with unequal masses

Continued discoveries from public data

International team led by Max Planck researchers finds promising new candidates for gravitational waves from binary black hole mergers in public LIGO/Virgo data

Squeezed light success at Virgo

The gravitational-wave observatory near Pisa listens deeper into the cosmos with technology from Hanover

Discovering exoplanets with gravitational waves

Researchers from the AEI in Potsdam and from the CEA in Saclay, Paris suggest how the planned space-based gravitational-wave observatory LISA can detect exoplanets orbiting white dwarf binaries everywhere in our Milky Way and in the nearby Magellanic Clouds.

LIGO and Virgo detect more neutron star coalescences

The gravitational-wave candidates were likely produced by mergers of a neutron star-black hole binary and a binary neutron star

LIGO and Virgo announce four new gravitational-wave detections

The observatories are also releasing their first catalog of gravitational-wave events

First open gravitational-wave catalog of binary mergers

AEI researchers publish first open catalog of compact binary merger gravitational-wave signals in LIGO's O1 data

Gravitational waveforms with higher modes from merging black holes

The first higher-multipole model of spinning and coalescing black-hole binaries improves accuracy of waveforms and measurement of astrophysical parameters

Cutting-edge technology from Hannover for the Virgo gravitational-wave detector in Italy

Squeezed-light source developed at the Albert Einstein Institute to make Virgo even more sensitive to gravitational waves


Would LIGO Detect Head-On Collision? - Astronomy

Feb. 12 — For the first time, scientists have observed ripples in the fabric of spacetime called gravitational waves, arriving at the earth from a cataclysmic event in the distant universe. This confirms a major prediction of Albert Einstein’s 1915 general theory of relativity and opens an unprecedented new window onto the cosmos.

Gravitational waves carry information about their dramatic origins and about the nature of gravity that cannot otherwise be obtained. Physicists have concluded that the detected gravitational waves were produced during the final fraction of a second of the merger of two black holes to produce a single, more massive spinning black hole. This collision of two black holes had been predicted but never observed.

The gravitational waves were detected on Sept. 14, 2015, at 5:51 a.m. Eastern Daylight Time (9:51 UTC) by both of the twin Laser Interferometer Gravitational-wave Observatory (LIGO) detectors, located in Livingston, La., and Hanford, Wash. The LIGO Observatories are funded by the National Science Foundation, and were conceived, built, and are operated by Caltech and Massachusetts Institute of Technology. The discovery, accepted for publication in the journal Physical Review Letters, was made by the LIGO Scientific Collaboration (which includes the GEO Collaboration and the Australian Consortium for Interferometric Gravitational Astronomy) and the Virgo Collaboration using data from the two LIGO detectors.

NCSA’s Role in the Discovery

Thirty years ago, the National Center for Supercomputing Applications (NCSA) was founded at the University of Illinois at Urbana-Champaign by Larry Smarr based on the premise that numerically modeling scientific problems, such as the colliding of black holes, required high-performance computing to make progress. Smarr’s doctoral thesis had itself been on the modeling of the head-on collision of two black holes. In 2014, Smarr was honored with the Golden Goose award to highlight the impact that his black hole research had on creating NCSA and the NSF supercomputing centers program which led to the public Internet revolution via the creation of the NCSA Mosaic web browser, the first browser to have visual features like icons, bookmarks, and pictures, and was easy to use.

At NCSA, Smarr formed a numerical group, led by Edward Seidel—the current NCSA director. The group quickly became a leader in applying supercomputers to black hole and gravitational wave problems. For example, in 1994 the very first 3-dimension simulation of two colliding black holes providing computed gravitational waveforms was carried out at NCSA by this group in collaboration with colleagues at Washington University.

NCSA as a center has continued to support the most complex problems in numerical relativity and relativistic astrophysics, including working with several groups addressing models of gravitational waves sources seen by LIGO in this discovery. Even more complex simulations will be needed for anticipated future discoveries such as colliding neutron stars and black holes or supernovae explosions.

NCSA has also played a role in developing the tools needed for simulating relativistic systems. The work of Seidel’s NCSA group led to the development of the Cactus Framework, a modular and collaborative framework for parallel computing which since 1997 has supported numerical relativists as well as other disciplines developing applications to run on supercomputers at NCSA and elsewhere. Built on the Cactus Framework, the NSF-supported Einstein Toolkit developed at Georgia Tech, RIT, LSU, AEI, Perimeter Institute and elsewhere now supports many numerical relativity groups modeling sources important for LIGO on the NCSA Blue Waters supercomputer.

“This historic announcement is very special for me. My career has centered on understanding the nature of black hole systems, from my research work in numerical relativity, to building collaborative teams and technologies for scientific research, and then also having the honor to be involved in LIGO during my role as NSF Assistant Director of Mathematics and Physical Sciences. I could not be more excited that the field is advancing to a new phase,” said Seidel, who is also Founder Professor of Physics and professor of astronomy at Illinois.

Gabrielle Allen, professor of astronomy at Illinois and NCSA associate director, previously led the development of the Cactus Framework and the Einstein Toolkit. “NCSA was a critical part of inspiring and supporting the development of Cactus for astrophysics. We held our first Cactus workshop at NCSA and the staff’s involvement in our projects was fundamental to being able to demonstrate not just new science but new computing technologies and approaches,” said Allen.

Eliu Huerta, member of the LIGO Scientific Collaboration since 2011 and current leader of the relativity group at NCSA, is a co-author of the paper to be published in Physical Review Letters. Huerta works at the interface of analytical and numerical relativity, specializing in the development of modeled waveforms for the detection and interpretation of gravitational wave signals. Huerta uses these models to infer the astrophysical properties of compact binary systems, and shed light on the environments in which they form and coalesce.

“The first direct observation of gravitational waves from a binary black hole system officially inaugurates the field of gravitational wave astronomy. There can be no better way to celebrate the first centenary of Einstein’s prediction of gravitational waves. We can gladly say that Einstein is right, and that the beautiful mathematical framework he developed to describe gravity is valid even in the most extreme environments. A new era has begun, and we will be glad to discover astrophysical objects we have never dreamt of,” said Huerta.

Stuart Shapiro, a professor of physics and astronomy at Illinois, was appointed an NCSA research scientist by Smarr two decades ago. A leading expert in the theory that underpinned the search for gravitational waves, he has developed software tools that can simulate on NCSA supercomputers like Blue Waters the very binary black hole merger and gravitational waves now detected by LIGO. Shapiro said he is thrilled by the discovery.

“This presents the strongest confirmation yet of Einstein’s theory of general relativity and the cleanest evidence to date of the existence of black holes. The gravitational waves that LIGO measures can only be generated by merging black holes—exotic relativistic objects from which nothing, including light, can escape from their interior,” said Shapiro.

“Work at NCSA helps open windows into the universe,” said Peter Schiffer, vice chancellor for research at the University of Illinois at Urbana-Champaign. “This is a wonderful fundamental discovery, and it’s exciting that the high performance computing capabilities that we developed to address challenges like this one are also being used to solve other significant societal problems.”

Black holes are formed when massive stars undergo a catastrophic gravitational collapse. The gravitational field of these ultra compact objects is so strong that not even light can escape from them.

Gravitational waves are generated when ultra compact objects—black holes, neutron stars or white dwarfs—are accelerated to velocities that are a significant fraction of the speed of light. Gravitational waves couple weakly to matter, which means that they can travel unimpeded throughout the Universe and that only extremely sensitive detectors such as LIGO can detect them.

LIGO research is carried out by the LIGO Scientific Collaboration, a group of more than 1,000 scientists from universities around the United States and in 14 other countries. More than 90 universities and research institutes in the collaboration develop detector technology and analyze data approximately 250 students are strong contributing members of the collaboration.

The LIGO Scientific Collaboration’s detector network includes the LIGO interferometers and the GEO600 detector. The GEO team includes scientists at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute, AEI), Leibniz Universität Hannover, along with partners at the University of Glasgow, Cardiff University, the University of Birmingham, other universities in the United Kingdom, and the University of the Balearic Islands in Spain.

LIGO was originally proposed as a means of detecting these gravitational waves in the 1980s by Rainer Weiss, professor of physics, emeritus, from MIT Kip Thorne, Caltech’s Richard P. Feynman Professor of Theoretical Physics, emeritus and Ronald Drever, professor of physics, emeritus, also from Caltech.

Virgo research is carried out by the Virgo Collaboration, consisting of more than 250 physicists and engineers belonging to 19 different European research groups: six from Centre National de la Recherche Scientifique (CNRS) in France eight from the Istituto Nazionale di Fisica Nucleare (INFN) in Italy two in the Netherlands with Nikhef the Wigner RCP in Hungary the POLGRAW group in Poland and the European Gravitational Observatory (EGO), the laboratory hosting the Virgo detector near Pisa in Italy.

The discovery was made possible by the enhanced capabilities of Advanced LIGO, a major upgrade that increases the sensitivity of the instruments compared to the first generation LIGO detectors, enabling a large increase in the volume of the universe probed—and the discovery of gravitational waves during its first observation run.

The U.S. National Science Foundation leads in financial support for Advanced LIGO. Funding organizations in Germany (Max Planck Society), the U.K. (Science and Technology Facilities Council, STFC) and Australia (Australian Research Council) also have made significant commitments to the project. Several of the key technologies that made Advanced LIGO so much more sensitive have been developed and tested by the German UK GEO collaboration.

Significant computer resources have been contributed by the AEI Hannover Atlas Cluster, the LIGO Laboratory, Syracuse University, and the University of Wisconsin-Milwaukee. Several universities designed, built, and tested key components for Advanced LIGO: The Australian National University, the University of Adelaide, the University of Florida, Stanford University, Columbia University in the City of New York and Louisiana State University.


References

  • Gertsenshtein and Pustovoit (1962) M. E. Gertsenshtein and V. I. Pustovoit, Sov. Phys. – JETP 16 , 433 (1962).
  • Weiss (1972) R. Weiss, in Quarterly report of the Research Laboratory for Electronics, MIT (1972).
  • Drever (1983) R. W. P. Drever, in Gravitational Radiation, edited by N. Deruelle and T. Piran (North-Holland, Amsterdam, 1983) p. 321.
  • Abramovici et al. (1992) A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, W. S. E., and Z. M. E., Science 256 , 325 (1992).
  • Virgo Collaboration (1990) Virgo Collaboration, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 289 , 518 (1990).
  • Grote et al. (2005) H. Grote, B. Allen, P. Aufmuth, C. Aulbert, S. Babak, R. Balasubramanian, B. W. Barr, S. Berukoff, A. Bunkowski, G. Cagnoli, C. A. Cantley, M. M. Casey, S. Chelkowski, D. Churches, T. Cokelaer, C. N. Colacino, D. R. M. Crooks, C. Cutler, K. Danzmann, R. Davies, R. J. Dupuis, E. Elliffe, C. Fallnich, A. Franzen, A. Freise, S. Goßler, A. Grant, S. Grunewald, J. Harms, G. Heinzel, I. S. Heng, A. Hepstonstall, M. Heurs, M. Hewitson, S. Hild, J. Hough, Y. Itoh, R. Jones, S. H. Huttner, K. Kawabe, C. Killow, K. Kötter, B. Krishnan, V. Leonhardt, H. Lück, B. Machenschalk, M. Malec, R. A. Mercer, C. Messenger, S. Mohanty, K. Mossavi, S. Mukherjee, P. Murray, S. Nagano, G. P. Newton, M. A. Papa, M. Perreur-Lloyd, M. Pitkin, M. V. Plissi, V. Quetschke, V. Re, S. Reid, L. Ribichini, D. I. Robertson, N. A. Robertson, J. D. Romano, S. Rowan, A. Rüdiger, B. S. Sathyaprakash, R. Schilling, R. Schnabel, B. F. Schutz, F. Seifert, A. M. Sintes, J. R. Smith, P. H. Sneddon, K. A. Strain, I. Taylor, R. Taylor, A. Thüring, C. Ungarelli, H. Vahlbruch, A. Vecchio, J. Veitch, H. Ward, U. Weiland, H. Welling, P. Williams, B. Willke, W. Winkler, G. Woan, and I. Zawischa, Classical and Quantum Gravity 22 , 193 (2005).
  • Riles (2013) K. Riles, Progress in Particle and Nuclear Physics 68 , 1 (2013).
  • LIGO Scientific Collaboration (2009a) LIGO Scientific Collaboration, Reports on Progress in Physics 72 , 076901 (2009a).
  • The LIGO Scientific Collaboration and The Virgo Collaboration (2014a) The LIGO Scientific Collaboration and The Virgo Collaboration, Phys. Rev. Lett. 113 , 231101 (2014a).
  • The LIGO Scientific Collaboration and The Virgo Collaboration (2014b) The LIGO Scientific Collaboration and The Virgo Collaboration, Astrophys. J. 785 , 119 (2014b), arXiv:1309.4027 [astro-ph.HE] .
  • The LIGO Scientific Collaboration and The Virgo Collaboration (2013) The LIGO Scientific Collaboration and The Virgo Collaboration (LIGO-Virgo Scientific Collaboration), Phys. Rev. D 88 , 062001 (2013).
  • The LIGO Scientific Collaboration and The Virgo Collaboration (2012) The LIGO Scientific Collaboration and The Virgo Collaboration, Phys. Rev. D 85 , 122007 (2012).
  • Fritschel (2003) P. Fritschel, in Gravitational-Wave Detection, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 4856, edited by M. Cruise and P. Saulson (2003) pp. 282–291, gr-qc/0308090 .
  • The LIGO Scientific Collaboration and The Virgo Collaboration (2016a) The LIGO Scientific Collaboration and The Virgo Collaboration, Phys. Rev. Lett. 116 , 061102 (2016a).
  • The LIGO Scientific Collaboration and The Virgo Collaboration (2016b) The LIGO Scientific Collaboration and The Virgo Collaboration, submitted to PRD (2016b).
  • Kwee et al. (2012) P. Kwee, C. Bogan, K. Danzmann, M. Frede, H. Kim, P. King, J. Pöld, O. Puncken, R. L. Savage, F. Seifert, P. Wessels, L. Winkelmann, and B. Willke, Opt. Express 20 , 10617 (2012).
  • Mueller (2014) C. Mueller, Techniques for Resonant Optical Interferometry with Applications to the Advanced LIGO Gravitational Wave Detectors, Ph.D. thesis, University of Florida (2014).
  • Mueller et al. (2016) C. L. Mueller, M. A. Arain, G. Ciani, R. T. DeRosa, A. Effler, D. Feldbaum, V. V. Frolov, P. Fulda, J. Gleason, M. Heintze, K. Kawabe, E. J. King, K. Kokeyama, W. Z. Korth, R. M. Martin, A. Mullavey, J. Peold, V. Quetschke, D. H. Reitze, D. B. Tanner, C. Vorvick, L. F. Williams, and G. Mueller, Review of Scientific Instruments 87 , 014502 (2016), http://dx.doi.org/10.1063/1.4936974.
  • Ajith et al. (2011) P. Ajith, M. Hannam, S. Husa, Y. Chen, B. Brügmann, N. Dorband, D. Müller, F. Ohme, D. Pollney, C. Reisswig, L. Santamaría, and J. Seiler, Phys. Rev. Lett. 106 , 241101 (2011).
  • Matichard et al. (2015a) F. Matichard, B. Lantz, R. Mittleman, K. Mason, J. Kissel, B. Abbott, S. Biscans, J. McIver, R. Abbott, S. Abbott, E. Allwine, S. Barnum, J. Birch, C. Celerier, D. Clark, D. Coyne, D. DeBra, R. DeRosa, M. Evans, S. Foley, P. Fritschel, J. A. Giaime, C. Gray, G. Grabeel, J. Hanson, C. Hardham, M. Hillard, W. Hua, C. Kucharczyk, M. Landry, A. L. Roux, V. Lhuillier, D. Macleod, M. Macinnis, R. Mitchell, B. O’Reilly, D. Ottaway, H. Paris, A. Pele, M. Puma, H. Radkins, C. Ramet, M. Robinson, L. Ruet, P. Sarin, D. Shoemaker, A. Stein, J. Thomas, M. Vargas, K. Venkateswara, J. Warner, and S. Wen, Classical and Quantum Gravity 32 , 185003 (2015a).
  • The LIGO Scientific Collaboration (2015) The LIGO Scientific Collaboration, Classical and Quantum Gravity 32 , 074001 (2015).
  • Aston et al. (2012) S. M. Aston, M. A. Barton, A. S. Bell, N. Beveridge, B. Bland, A. J. Brummitt, G. Cagnoli, C. A. Cantley, L. Carbone, A. V. Cumming, L. Cunningham, R. M. Cutler, R. J. S. Greenhalgh, G. D. Hammond, K. Haughian, T. M. Hayler, A. Heptonstall, J. Heefner, D. Hoyland, J. Hough, R. Jones, J. S. Kissel, R. Kumar, N. A. Lockerbie, D. Lodhia, I. W. Martin, P. G. Murray, J. O’Dell, M. V. Plissi, S. Reid, J. Romie, N. A. Robertson, S. Rowan, B. Shapiro, C. C. Speake, K. A. Strain, K. V. Tokmakov, C. Torrie, A. A. van Veggel, A. Vecchio, and I. Wilmut, Classical and Quantum Gravity 29 , 235004 (2012).
  • Carbone et al. (2012) L. Carbone, S. M. Aston, R. M. Cutler, A. Freise, J. Greenhalgh, J. Heefner, D. Hoyland, N. A. Lockerbie, D. Lodhia, N. A. Robertson, C. C. Speake, K. A. Strain, and A. Vecchio, Classical and Quantum Gravity 29 , 115005 (2012).
  • Rosa et al. (2010) R. D. Rosa, F. Garufi, L. Milano, S. Mosca, and G. Persichetti, Journal of Physics: Conference Series 228 , 012018 (2010).
  • Arain and Mueller (2008) M. A. Arain and G. Mueller, Optics Express 16 , 10018 (2008).
  • Hild et al. (2007) S. Hild, H. Grote, M. Hewtison, H. Lück, J. R. Smith, K. A. Strain, B. Willke, and K. Danzmann, Classical and Quantum Gravity 24 , 1513 (2007).
  • Staley et al. (2014) A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, Classical and Quantum Gravity 31 , 245010 (2014).
  • Drever et al. (1983) R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Applied Physics B: Lasers and Optics 31 , 97 (1983).
  • Schnupp (1988) L. Schnupp, “Talk at a european collaboration meeting on interferometric detection of gravitational waves, sorrento,” (1988).
  • Fricke et al. (2012) T. T. Fricke, N. D. Smith-Lefebvre, R. Abbott, R. Adhikari, K. L. Dooley, M. Evans, P. Fritschel, V. V. Frolov, K. Kawabe, J. S. Kissel, B. J. J. Slagmolen, and S. J. Waldman, Classical and Quantum Gravity 29 , 065005 (2012).
  • Arai et al. (2013) K. Arai, S. Barnum, P. Fritschel, J. Lewis, and S. Waldman, Output Mode Cleaner Design, Tech. Rep. (Caltech, 2013).
  • Barsotti et al. (2010) L. Barsotti, M. Evans, and P. Fritschel, Classical and Quantum Gravity 27 , 084026 (2010).
  • Mavalvala et al. (1998) N. Mavalvala, D. Sigg, and D. Shoemaker, Appl. Opt. 37 , 7743 (1998).
  • LIGO Scientific Collaboration (2010) LIGO Scientific Collaboration, Nuclear Instruments and Methods 624 , 223 (2010).
  • Goetz et al. (2009) E. Goetz, P. Kalmus, S. Erickson, R. L. S. Jr, G. Gonzalez, K. Kawabe, M. Landry, S. Marka, B. O’Reilly, K. Riles, D. Sigg, and P. Willems, Classical and Quantum Gravity 26 , 245011 (2009).
  • The LIGO Collaboration (2016) The LIGO Collaboration, Physical Review D (2016).
  • Adhikari (2004) R. Adhikari, Sensitivity and Noise Analysis of 4 km Laser Interferometric Gravitational Wave Antennae, Ph.D. thesis, MIT (2004).
  • LIGO Scientific Collaboration (2009b) LIGO Scientific Collaboration, Reports on Progress in Physics 72 , 076901 (2009b).
  • Matichard et al. (2015b) F. Matichard, B. Lantz, K. Mason, R. Mittleman, B. Abbott, S. Abbott, E. Allwine, S. Barnum, J. Birch, S. Biscans, D. Clark, D. Coyne, D. DeBra, R. DeRosa, S. Foley, P. Fritschel, J. Giaime, C. Gray, G. Grabeel, J. Hanson, M. Hillard, J. Kissel, C. Kucharczyk, A. L. Roux, V. Lhuillier, M. Macinnis, B. O’Reilly, D. Ottaway, H. Paris, M. Puma, H. Radkins, C. Ramet, M. Robinson, L. Ruet, P. Sareen, D. Shoemaker, A. Stein, J. Thomas, M. Vargas, and J. Warner, Precision Engineering 40 , 273 (2015b).
  • Matichard et al. (2015c) F. Matichard, B. Lantz, K. Mason, R. Mittleman, B. Abbott, S. Abbott, E. Allwine, S. Barnum, J. Birch, S. Biscans, D. Clark, D. Coyne, D. DeBra, R. DeRosa, S. Foley, P. Fritschel, J. Giaime, C. Gray, G. Grabeel, J. Hanson, M. Hillard, J. Kissel, C. Kucharczyk, A. L. Roux, V. Lhuillier, M. Macinnis, B. O’Reilly, D. Ottaway, H. Paris, M. Puma, H. Radkins, C. Ramet, M. Robinson, L. Ruet, P. Sareen, D. Shoemaker, A. Stein, J. Thomas, M. Vargas, and J. Warner, Precision Engineering 40 , 287 (2015c).
  • Driggers et al. (2012) J. Driggers, J. Harms, and R. Adhikari, Phys. Rev. D 86 (2012).
  • Yamamoto (2000) K. Yamamoto, Study of the thermal noise caused by inhomogeneously distributed loss, Ph.D. thesis, U Tokyo (2000).
  • Crooks et al. (2006) D. R. M. Crooks, G. Cagnoli, M. M. Fejer, G. Harry, J. Hough, B. T. Khuri-Yakub, S. Penn, R. Route, S. Rowan, P. H. Sneddon, I. O. Wygant, and G. G. Yaralioglu, Classical and Quantum Gravity 23 , 4953 (2006).
  • Harry et al. (2007) G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, Classical and Quantum Gravity 24 , 405 (2007).
  • Harry et al. (2002) G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, Classical and Quantum Gravity 19 , 897 (2002).
  • Harry et al. (2012) G. Harry, T. P. Bodiya, and R. DeSalvo, eds., Optical coatings and thermal noise in precision measurement (Cambridge University Press, 2012).
  • Agresti et al. (2006) J. Agresti, G. Castaldi, R. DeSalvo, V. Galdi, and I. Pierro, V Pinto, in SPIE Proceedings, Advances in Thin-Film Coatings for Optical Applications III, Vol. 6286 (2006).
  • Villar et al. (2010) A. E. Villar, E. D. Black, R. DeSalvo, K. G. Libbrecht, C. Michel, N. Morgado, L. Pinard, I. M. Pinto, V. Pierro, V. Galdi, M. Principe, and I. Taurasi, Phys. Rev. D 81 , 122001 (2010).
  • Braginsky et al. (1999) V. Braginsky, M. Gorodetsky, and S. Vyatchanin, Phys. Lett. A 264 , 1 (1999).
  • Liu and Thorne (2000) Y. Liu and K. Thorne, Phys. Rev. D 62 (2000).
  • Levin (1998) Y. Levin, Phys. Rev. D 57 (1998).
  • Caves (1980) C. M. Caves, Phys. Rev. Lett. 45 , 75 (1980).
  • Caves (1981) C. M. Caves, Phys. Rev. D 23 , 1693 (1981).
  • Braginsky et al. (1992) V. B. Braginsky, F. Y. Khalili, and K. S. Thorne, Quantum Measurement (Cambridge University Press (CUP), 1992).
  • Buonanno and Chen (2001) A. Buonanno and Y. Chen, Phys. Rev. D 64 , 042006 (2001).
  • Corbitt (2008) T. Corbitt, Quantum Noise and Radiation Pressure Effects in High Power Optical Interferometers, Ph.D. thesis, MIT (2008).
  • The LIGO Scientific Collaboration (2013) The LIGO Scientific Collaboration, Nature Photonics 7 , 613 (2013).
  • Suijlen et al. (2009) M. Suijlen, J. Koning, M. van Gils, and H. Beijerinck, Sensors and Actuators A: Physical 156 , 171 (2009).
  • Cavalleri et al. (2010) A. Cavalleri, G. Ciani, R. Dolesi, M. Hueller, D. Nicolodi, D. Tombolato, S. Vitale, P. Wass, and W. Weber, Physics Letters A 374 , 3365 (2010).
  • Dolesi et al. (2011) R. Dolesi, M. Hueller, D. Nicolodi, D. Tombolato, S. Vitale, P. J. Wass, W. J. Weber, M. Evans, P. Fritschel, R. Weiss, J. H. Gundlach, C. A. Hagedorn, S. Schlamminger, G. Ciani, and A. Cavalleri, Phys. Rev. D 84 , 063007 (2011).
  • Zucker and Whitcomb (1996) M. Zucker and S. Whitcomb, in Proceedings of the Seventh Marcel Grossman Meeting on recent developments in theoretical and experimental general relativity, gravitation, and relativistic field theories (1996) pp. 1434–1436.
  • Hewitson et al. (2007) M. Hewitson, K. Danzmann, H. Grote, S. Hild, H. Luck, J. R. Smith, B. Willke, J. Hough, S. Rowan, and K. A. Strain, Class. Quant. Grav. 24 , 6379 (2007).
  • Billingsley and Phelps (2010) G. Billingsley and M. Phelps, Advantages of cleaning optics with Red First Contact, Tech. Rep. (Caltech, 2010).
  • Ugolini et al. (2014) D. Ugolini, C. Fitzgerald, I. Rothbarth, and J. Wang, Review of Scientific Instruments 85 , 034502 (2014).
  • Campsie et al. (2011) P. Campsie, L. Cunningham, M. Hendry, J. Hough, S. Reid, S. Rowan, and G. D. Hammond, Classical and Quantum Gravity 28 , 215016 (2011).
  • Zhao et al. (2006) C. Zhao, J. Degallaix, L. Ju, Y. Fan, D. G. Blair, B. J. J. Slagmolen, M. B. Gray, C. M. M. Lowry, D. E. McClelland, D. J. Hosken, D. Mudge, A. Brooks, J. Munch, P. J. Veitch, M. A. Barton, and G. Billingsley, Physical Review Letters 96 , 231101 (2006), gr-qc/0602096 .
  • Sigg (1997) D. Sigg, Frequency response of the LIGO interferometer, Tech. Rep. LIGO-T970084 (LIGO Hanford Observatory, 1997).
  • Izumi and Sigg (2015) K. Izumi and D. Sigg, Frequency response of the aLIGO interferometer, part 1, Tech. Rep. LIGO-T1500325-v2 (LIGO Hanford Observatory, 2015).
  • Fritschel and Zucker (2010) P. Fritschel and M. E. Zucker, Wide-angle scatter from LIGO arm cavities, Tech. Rep. LIGO-T070089 (MIT, 2010).
  • Stover (2012) J. Stover, Optical Scattering: Measurement and Analysis, Second Edition (Spie Press Book, 2012).
  • Flanagan and Thorne (1994) E. Flanagan and K. S. Thorne, Noise due to backscatter off baffles, the nearby wall and objects at the far end of the beam tube and recommended actions, Tech. Rep. LIGO-T940063-00 (Caltech, 1994).
  • Ottaway et al. (2012) D. J. Ottaway, P. Fritschel, and S. J. Waldman, Optics Express 20 , 8329 (2012).
  • Fritschel and Yamamoto (2013) P. Fritschel and H. Yamamoto, Scattered light noise due to the ETM coating ripple, Tech. Rep. LIGO-T1300354 (MIT, 2013).
  • Effler et al. (2015) A. Effler, R. M. S. Schofield, V. V. Frolov, G. González, K. Kawabe, J. R. Smith, J. Birch, and R. McCarthy, Classical and Quantum Gravity 32 , 035017 (2015).
  • Canuel et al. (2013) B. Canuel, E. Genin, G. Vajente, and J. Marque, Opt. Express 21 , 10546 (2013).
  • Martynov (2015) D. Martynov, Lock Acquisition and Sensitivity Analysis of Advanced LIGO Interferometers, Ph.D. thesis, Caltech (2015).
  • Nuttall et al. (2015) L. Nuttall, T. J. Massinger, J. Areeda, J. Betzwieser, S. Dwyer, A. Effler, R. P. Fisher, P. Fritschel, J. S. Kissel, A. P. Lundgren, D. M. Macleod, D. Martynov, J. McIver, A. Mullavey, D. Sigg, J. R. Smith, G. Vajente, A. R. Williamson, and C. C. Wipf, Classical and Quantum Gravity 32 , 245005 (2015).
  • The LIGO Scientific Collaboration (2016) The LIGO Scientific Collaboration, submitted to CQG (2016).
  • Grote et al. (2013) H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, Phys. Rev. Lett. 110 , 181101 (2013).
  • LIGO Scientific Collaboration (2011) LIGO Scientific Collaboration, Nature Physics 7 , 962 (2011).
  • Evans et al. (2015) M. Evans, S. Gras, P. Fritschel, J. Miller, L. Barsotti, D. Martynov, A. Brooks, D. Coyne, R. Abbott, R. X. Adhikari, K. Arai, R. Bork, B. Kells, J. Rollins, N. Smith-Lefebvre, G. Vajente, H. Yamamoto, C. Adams, S. Aston, J. Betzweiser, V. Frolov, A. Mullavey, A. Pele, J. Romie, M. Thomas, K. Thorne, S. Dwyer, K. Izumi, K. Kawabe, D. Sigg, R. Derosa, A. Effler, K. Kokeyama, S. Ballmer, T. J. Massinger, A. Staley, M. Heinze, C. Mueller, H. Grote, R. Ward, E. King, D. Blair, L. Ju, and C. Zhao, Physical Review Letters 114 (2015).
  • Hirose et al. (2010) E. Hirose, K. Kawabe, D. Sigg, R. Adhikari, and P. R. Saulson, Appl. Opt. 49 , 3474 (2010).

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