CHAPTER 8
What Do Gravitational Waves Tell Us?
T minus 2 hours: At the LIGO Hanford observatory in Washington State it is 12:50 a.m., and the last two scientists depart to get a well-deserved night’s sleep after a long day of engineering tests, leaving only the night-duty operator on site. The detectors had been turned on a few months before to calibrate the instruments in preparation for the first science run of the “Advanced LIGO” detectors, which is scheduled to begin in four days.
Two billion kilometers away, about one and a half times the distance to Saturn, a packet of spacetime ripples approaches the solar system at the speed of light (Figure 8.1).
Figure 8.1 A packet of gravitational waves approaches the solar system on 14 September 2015. The waves come from below, about 15° from the “south pole” of the solar system. Shown are the positions of the Earth, Mars, Jupiter and Saturn at that time. The waves from this source may have been passing through the solar system for millions of years; we only show the final burst of strong waves, the ones detected by the LIGO instruments.
T minus 15 minutes: In Livingston, Louisiana it is 4:35 a.m. and two technicians at the LIGO Livingston observatory are about to run one last test before finishing their shift. The “bump test” consists of driving a car at 5 or 10 miles per hour over speed bumps right outside the LIGO building, GPS unit in hand, to check whether the motion of the car over the speed bumps creates ground vibrations strong enough to be detected by the interferometer. Right before starting the test, they realize their GPS unit is malfunctioning and needs to be recalibrated, so instead of running the test they call it a night and go home.
The packet of spacetime ripples is now 270 million kilometers, or 1.5 astronomical units, away.
T minus 0 minutes: The packet of spacetime ripples passes through the LIGO Livingston detector, and 7 milliseconds later it passes through the LIGO Hanford detector. For about a fifth of a second the mirrors at opposite ends of the interferometers move back and forth a few times by a tiny amount and the interference patterns of the laser beams inside the instruments change a bit, generating electrical signals that record the passage of the spacetime ripples. The signals are recorded automatically, but nobody notices. Not just yet.
T plus 10 minutes: It is noon in Hannover, Germany, close to lunch time. Postdoctoral researcher Marco Drago at the Albert Einstein Institute notices that an automated computer program has pinged, announcing the presence of something strange in the LIGO data. He is curious and so he checks the logs to see if there was a scheduled injection, a test to make the mirrors in the instrument vibrate artificially just as if a wave had gone through. But the logs show no scheduled injection.
Marco goes next door to the office of his friend, Andrew Lundgren, also a postdoctoral researcher. He tells Andrew about the ping and together they investigate it further. Could it have been an injection that was not logged? No, there was truly nothing scheduled. Could it have been a bump test? No, there was nobody testing the interferometers. Could it have been a micro-earthquake or some atmospheric effect? No, the data quality monitors were all showing perfect conditions.
T plus 54 minutes: Marco sends an email to the entire LIGO scientific collaboration, over 1,000 researchers spread around the world. He describes the event that was recorded and he ends the email asking for confirmation that this was not an artificial injection. A flurry of emails ensues. Within hours, there is confirmation from the LIGO leadership that this event was not an injection or test of any kind.
T plus 10 hours: The LIGO executive committee gathers via telephone conference call. They discuss the event and make a decision: maintain the instruments in their current state and continue taking data. The software is locked. The hardware is locked. Cabinets housing the electronics are physically locked. For the next two weeks, nobody is to touch either of the two instruments or alter a setting, so that more data can continue to accumulate to be able to compare the event to data that presumably contains only random noise.
The event prompts an “all hands on deck” response by the thousand-member team to verify or refute the idea that this was a gravitational wave detection. Several independent computer analyses of the data reveal the same signal in each detector. One simple analysis applies a technique that is similar to that used in high-end headphones and hearing aids to cancel part of the background noise so that you can hear the music or dialogue you are interested in, even in a noisy airplane or restaurant. Known as a “band-pass filter,” it suppresses noise in the frequency range above and below the frequency range where the signal resides, between about thirty and a few hundred hertz, while not altering anything in that critical frequency range. What emerges when that simple filter is applied to the data from each detector is shown in the two panels of Figure 8.2.
Figure 8.2 Data from the Hanford and Livingston detectors during the crucial 0.2 seconds, after being run through a band-pass filter, and after certain noise effects associated with well-understood vibrations in the instrument have been removed. Credit: Gravitational Wave Open Science Center.
Each panel shows a stretch of filtered output lasting about two tenths of a second, occurring at the same time in each detector. The clocks at the detectors are all set to Greenwich Mean Time in order to avoid any possible confusion with time zones or daylight savings time. From about 0.25 seconds to about 0.34 seconds the outputs look very spiky and do not resemble each other at all. This is the random, independent noise present in each detector. From 0.34 seconds to about 0.38 seconds we see three peaks and valleys that roughly match each other in each detector, but with some spiky noise superimposed. Those three peaks represent two complete cycles of the wave, over a time of 0.04 seconds, corresponding to about 50 cycles per second or 50 hertz. These are followed by four more peaks and valleys that are significantly higher than the first three, but also are more closely spaced than the previous peaks. Those three full cycles span only about 0.025 seconds, corresponding to a frequency of about 120 hertz. This implies that not only is the strength of the signal increasing with time, but its frequency is also increasing with time. But the last of these four peaks in each detector is already lower than its predecessor. After this, the output looks once again like independent random noise in each detector.
Even if you had no idea what this signal represented, you would be tempted to think that this was a candidate gravitational wave signal. First, the signal is almost exactly the same in the two detectors. To be sure, it is conceivable that some event, such as a tree falling near the Livingston detector (the surrounding forest there happens to undergo active logging) could, by some fluke, produce exactly the right vibrations of the ground to produce the signal seen in the bottom panel of the figure. But those ground vibrations in Louisiana could not possibly affect the Hanford detector, 3,000 kilometers away in Washington State. And the chance of some unrelated event at Hanford (which is surrounded by almost treeless high desert) producing exactly the same response at exactly the same time is astronomically small (we will quote a number later). This is one of the positive legacies of Joseph Weber’s failed attempt to detect gravitational waves, the principle that for a claimed detection of gravitational waves to be credible, the same signal must be sensed in independent, widely separated detectors. The fact that the two signals are not exactly the same reflects the everyday fact that two people listening to a third person in a very noisy room might not hear exactly the same thing, but will still get the gist of what is being said.
Another feature of the two signals is important. While the peaks and valleys in the two panels seem to line up in time, the features in the Hanford detector are consistently about 7 milliseconds (0.007 seconds) later than those in the Livingston detector (the difference is too small to show up on the figures, but it is easily measured from the data). Now, if the gravitational waves were propagating from somewhere in the sky exactly perpendicular to the line joining the Livingston and Hanford detectors (the baseline), they would arrive at the two detectors at exactly the same time (see Figure 8.3). If they were traveling exactly parallel to the baseline, then they would arrive at one detector 10 milliseconds before the other. This is the time it would take a signal traveling at the speed of light to traverse the 3,000 kilometers between the two detectors. The actual time difference of 7 milliseconds was comfortably between these two limits, indicating that the signal actually arrived from a direction about 45 degrees from the baseline (right panel of Figure 8.3). On the other hand, if the time difference had been greater that 10 milliseconds, this would not have been accepted as a candidate gravitational wave.
Figure 8.3 Left: Waves approaching the Hanford and Livingston detectors from any direction perpendicular to the line joining them will reach the detectors at the same time. Middle: Waves approaching parallel to the line joining the detectors will reach one detector 10 milliseconds before the other, because of the 3,000 kilometers separating them. Right: Waves approaching from a direction approximately 45 degrees relative to the baseline will reach the Livingston detector about 7 milliseconds before the Hanford detector. The measured time differences give important information about the location of the source on the sky.
The researchers at the LIGO scientific collaboration actually had a very good idea of what the signals in Figure 8.2 represented: the “chirp” signal from the final inward spiral and merger of two bodies such as black holes or neutron stars. We will describe the history and physics of this idea later in this chapter, but the bottom line is this: as the two bodies orbit each other they emit gravitational waves, thus losing energy, getting closer to each other and orbiting faster (recall the binary pulsars from Chapter 5). This “inspiral” phase leads to waves of increasing strength or amplitude and increasing frequency, as shown in Figure 8.4. This part of the signal is called a chirp because of the similarity between a sound with these characteristics and the songs of some birds. The two bodies then merge, forming a black hole, a process that leads to a brief burst of strong waves (the “merger” part of Figure 8.4). The newly formed black hole is very distorted and it oscillates or “rings” a few times, emitting “ringdown” waves and quickly settling down to a stationary black hole that ceases to emit gravitational waves. The wave shown in Figure 8.4, calculated using an approximate solution from general relativity, displays all the features shown in the two panels of Figure 8.2.
Figure 8.4 A chirp signal from two black holes calculated using general relativity, showing the inspiral part, when the two black holes are orbiting each other with increasing speed, the merger part, when the two holes merge to form one very distorted black hole, and the ringdown part, when the distorted black hole emits gravitational waves and settles down to a final stationary black hole.
One can imagine the level of euphoria that occurred within the collaboration. But with this euphoria came an accompanying sense of paranoia. What if somebody maliciously inserted an artificial signal just to fool us? Surely this is unlikely. Hackers are not typically interested in astronomical data sets, and it would be unfathomable for a collaboration member to be so malicious.
More worrisome was the possibility that some bizarre noise artifact, erroneous instrumental setting or faulty line of computer code was making them believe they had detected a gravitational wave, when in reality they had not. It would not be the first time in the history of physics that an erroneous claim had been made. After all, physics is done by people, and people make mistakes. The important fact about physics is that it is self-correcting, and errors are eventually fixed and the record is set straight. But nobody wants to be known for the mistake rather than the discovery.
Luckily, examples of such errors are rare in physics. But when they occur, they generally make headlines and cause much embarrassment.
In 1989, electrochemists Stanley Pons and Martin Fleischmann announced they had observed “cold fusion” in their lab. Nuclear fusion occurs regularly inside the Sun, converting hydrogen into helium, releasing energy sufficient to warm and illuminate the Earth (the same process occurs in thermonuclear bombs). But this process requires extremely high temperatures. Achieving fusion at room temperature would have been revolutionary, as it would provide an effectively limitless energy source. Many scientists tried immediately to replicate their experiment but most failed, and in time the flaws in the original experiment that had led Pons and Fleischmann to the wrong conclusion were identified. Apart from the effect on the careers of the two scientists, the episode was a major embarrassment for the University of Utah, which had exploited the discovery for maximum publicity.
In 2011, an experiment with the acronym OPERA made a dramatic announcement. The instrument was designed to study subatomic particles called neutrinos emitted in the CERN accelerator in Geneva, Switzerland and directed toward detectors 730 kilometers away, inside the Gran Sasso mountain in Italy. In September of that year, the OPERA collaboration announced they had measured an anomaly that might be a sign of neutrinos traveling faster than the speed of light. Such a discovery, if correct, would have been revolutionary, as it would have contradicted Einstein’s special theory of relativity, and consequently, his general theory. But a few months later, the OPERA team reported two flaws in their equipment: one related to a fiber optic cable that was not connected properly and another related to a clock that ran fast. These flaws, they concluded, were responsible for the anomaly. After correcting the problems, they found that neutrinos indeed travel at the speed of light, up to measurement uncertainty. But in the end, OPERA is remembered more for the mistake than for the final valid result.
And finally, there is the internal history of gravitational wave science. As we described in Chapter 7, an announcement of the discovery of gravitational waves had already been made in the late 1960s by Weber. Immediately after this announcement experimentalists set out to replicate Weber’s results, but they failed. Eventually, a consensus arose that Weber’s result had to be wrong, so when the LIGO detectors were built, the collaboration wanted to be particularly careful to not make the same mistake again. Many checks and counter-checks were established and tested to ensure that a detection was real prior to any announcement of a discovery.
This system of checks was so rigorous that it led to what is now known as the infamous “Big Dog” event. On 16 September 2010, an initial, less sensitive version of the LIGO detectors was in science mode, collecting data in the (admittedly unlikely) event that a sufficiently loud gravitational wave would pass through the Earth. And on that day, the alarms went off. A candidate event was identified, and it seemed to be coming from somewhere near the direction of Sirius, the Dog Star. In a fit of creativity, the event was named the “Big Dog.” Eight minutes after the event was detected, roughly twenty-five people in the collaboration were notified to follow up on it and see whether it was worthy of further study. These twenty-five people concluded that this was the case, and the collaboration sent a circular to a group of collaborating astronomers to tell them that a candidate event had been detected, while they continued to analyze the data.
Everybody involved was sworn to secrecy because the Big Dog could have been a false alarm, either from a rare simultaneous disturbance at both detectors, or from a “blind injection.” A blind injection is an internal test carried out routinely by the collaboration in which a tiny group of pre-selected technical people in the collaboration inject a fake signal in the data without telling anybody else, except an even tinier group of pre-selected VIPs in the collaboration. The purpose of this test is to see if the automated data analysis tools they have created can catch the blind injection and if the collaboration can identify it properly. For several months, the collaboration carried out all the tests and checks on the Big Dog, verified that the signal represented a gravitational wave, and wrote a draft of the discovery paper. On 14 March 2011, the “envelope was opened” and (drum roll) the LIGO leadership announced to the team that the Big Dog had been a blind injection after all. The good news was that the collaboration had caught it and so the data analysis tools were working as expected. Well, not exactly: some of the inferred parameters, like the location of the source in the sky, were not the same as those of the injected signal. This led to the discovery and correction of a line of computer code with a wrong sign. The bad news was that they hadn’t detected a real signal.
You might now understand why, in September 2015, when the data analysis tools signaled that a candidate event had just been detected, the collaboration was extremely cautious and secretive. Not satisfied with the simple filter that revealed the signals shown in Figure 8.2, they analyzed the data using sophisticated computer code and managed to extract a beautiful chirp using a sum of short waves of fixed frequency. This was an important test because it was agnostic to the true theory of gravity, using almost no information about Einstein’s theory. Simultaneously, the collaboration also compared the data to an array of detailed general relativity predictions of the gravitational wave signal emitted by merging black holes, finding agreement with their initial conclusions based on cruder analyses. Those comparisons also allowed them to measure such quantities as the masses of the two black holes, and to test Einstein’s theory. We will describe what was learned in a moment.
The collaboration also calculated the probability that this was a fluke, a pair of random events at each detector that happened to jiggle the mirrors just so. After ten million computer simulations, they found that such an accident would happen less often than once every 200,000 years. So this was not a fluke, and it was not an injection of any kind. In fact, right after the detection, LIGO management had revealed that there was no “Big Dog”-style blind injection. This event was the real thing.
This extraordinary degree of caution, secrecy and obsessively detailed analysis explains why it took five months from the initial “ping” that caught Marco Drago’s eye to David Reitze’s announcement at the National Press Club in February 2016.
As we have said, the first detection was of waves from the final few inspiraling orbits and the merger of two black holes. This seems like a ridiculously special, once-in-a-lifetime event. Although we knew that binary neutron stars exist (see Chapter 5), there was no observational evidence that binary black holes exist. Surely a much more plausible possibility for the first detection would have been a supernova, examples of which had been observed by humans for millenia. These were the sources that Joe Weber was after when he built his resonant bar detectors.
But in fact, theorists had been thinking about black hole or neutron star inspirals and mergers for some time, and by the time the LIGO detectors were being considered by the NSF for major funding, gravitational waves from inspirals and mergers already formed the centerpiece of the science case that LIGO advocates were making.
Strangely enough, the idea was first proposed in 1963 by physicist Freeman Dyson while he was studying how advanced extraterrestrial civilizations could sustain their energy needs. Born in England in 1923, Dyson moved to the US in 1947 to study for a Ph.D. at Cornell (although he never actually received the degree). Over his seventy-year career (he is a professor emeritus at the Institute for Advanced Studies in Princeton) he made important contributions to an eclectic array of scientific subjects, including pure mathematics, quantum field theory (in 1947 he proved that the seemingly discordant theories for quantum electrodynamics that had been devised by Richard Feynman and by Julian Schwinger were actually different versions of the same theory, today called QED), biology and space exploration, as well as topics in the public interest, such as nuclear warfare and climate change. In 1955 he met Joe Weber during Weber’s sabbatical with John Wheeler, and became intrigued with the idea of detecting gravitational radiation.
However, in 1963 he was interested in whether there was a better source of energy to sustain an advanced extraterrestrial civilization than the light and heat from its host star. In an article entitled “Gravitational Machines” he imagined a civilization stationing its home planet or base station not too far from a binary star system. If the civilization sends a probe toward one of the stars, allowing it to make a close flyby of the star at a time when the star is approaching the base station, then the probe would return to the base station with more kinetic energy than it had when it departed. That energy could then be extracted and used to sustain the civilization. The effect he was employing in his model is called the “gravitational slingshot,” well known to planetary scientists as a way to boost the speed of spacecraft to higher levels than they could ever acquire from rockets; it is routinely exploited to get spacecraft to Jupiter and Saturn and beyond, for example. The problem with Dyson’s idea is that binary stars typically move so slowly in their orbits that the energy obtained from the slinghot effect is trivial compared to the conventional energy from the light of the stars. A binary system of white dwarfs would be better because, being a hundred to a thousand times smaller than a solar-type star, they can orbit more closely to each other and thus achieve much higher velocities. This would be more promising for the civilization, particularly since white dwarfs are too dim to provide sufficient light and heat.
But then, Dyson reasoned, even better would be a binary system of neutron stars. These bodies are so small compared to their masses—roughly 20 kilometers in diameter—that they can orbit each other in very close proximity and with speeds that are a significant fraction of the speed of light, and thus the energy available to the civilization on each slingshot is even larger. This was quite a radical idea in 1963, since, as we saw in Chapter 5, neutron stars were at the time little more than a figment of Baade’s and Zwicky’s imaginations, and the first neutron star, in the form of a pulsar, would not be detected until four years later. Of course, there was also no evidence of extra-solar planets at the time, let alone other civilizations. In any event, Dyson immediately realized that this idea would not work. Such a close neutron star binary would emit copious amounts of gravitational radiation, and would then inspiral and merge so quickly that the civilization would soon lose its source of energy. On the other hand, he noted, the gravitational wave signal itself might be of interest, prophesying that “[it] would seem worthwhile to maintain a watch for events of this kind, using Weber’s equipment or some suitable modification of it.”
But because Dyson’s paper appeared in a book on extraterrestrial life, nobody working in general relativity noticed it or followed up on it. It was the discovery of the binary pulsar in 1974 that made the idea of binary inspiral respectable (see Chapter 5). The binary pulsar was proof that binary neutron stars exist, and the measurement of its decreasing orbital period proved that such systems spiral inward because of the emission of gravitational waves. As Taylor and his collaborators found, the rate of inspiral is absolutely tiny, only 76 microseconds per year in its orbital period, or 4 meters per year in separation. But the measured rate agreed with the prediction of general relativity. The theory goes on to predict that as the orbit shrinks, the stars speed up, thereby emitting stronger gravitational waves, which thus accelerates the inspiral, leading to even stronger waves, and so on, culminating in a runaway rush toward a final merger. For the Hulse–Taylor system, the formula predicted that the merger would occur in a few hundred million years, while for the double pulsar, it would occur in 85 million years. These are ridiculously long times—don’t bother to mark your calendars—but they are only a few percent of the thirteen-billion-year age of the Milky Way galaxy. So one could easily imagine counterparts to these binary pulsars starting their evolutions a few hundred million years ago and merging today, thus fulfilling Dyson’s prophesy.
As planning for large-scale laser interferometers moved forward, the idea that neutron star inspirals might be a leading potential source of gravitational waves began to take hold. The discovery of a few more binary pulsars in our galaxy similar to the Hulse–Taylor system made it possible to estimate, albeit very crudely, that the rate of final inspirals of such systems in our galaxy could be of the order of one every 100,000 years. Obviously this is not a rate of occurrence on which to build a thriving career in gravitational wave detection. And indeed this fact was the Achilles heel for Joe Weber’s attempts to detect gravitational waves. His detectors might have been capable of sensing waves from a nearby binary neutron star inspiral in our galaxy, but the rate of such events was far too small.
However, the strength of the gravitational wave signal received on Earth is inversely proportional to the distance of the source. If the waves from a source at a given distance have a certain strength, then waves from an equivalent source twice as far away are half as strong; waves from such a source ten times farther way are one tenth as strong, and so on. So if one could build an interferometer sensitive enough to detect waves from such a distance that a sphere surrounding the Earth of that radius contained about a million galaxies, then all of a sudden the rate of detectable neutron star inspirals could be a few (maybe up to ten) per year. A graduate student could even get a Ph.D. out of detections that frequent.
It is important to remember that a laser interferometer differs from a normal telescope in a crucial respect. A telescope can see light coming from only a very narrow range of directions and therefore has to be pointed toward a potential source. It is blind to all other directions. By contrast, a laser interferometer can hear gravitational waves coming from essentially every direction. There are only four source directions to which the interferometer is “deaf.” If the wave approaches the interferometer traveling parallel to the ground at the site, but making an angle of 45 degrees with respect to the arms, the interference pattern when the laser beams recombine will not change at all (see Figure 8.5). But if the wave is approaching at just 7 degrees off from those special directions, the interferometer will hear the signal with 25 percent efficiency. At 15 degrees, the efficiency is up to 50 percent. Only a tiny number of signals unlucky enough to arrive from the vicinity of those four special directions would be missed. So if the designers and builders of LIGO and Virgo could reach the required sensitivity to hear inspirals from the nearest million galaxies (roughly a million times more sensitive than Weber’s resonant bars), then one could imagine a decent rate of detections.
Figure 8.5 An interferometer is deaf to any gravitational waves approaching it parallel to the ground at an angle of 45 degrees relative to the arms.
Another reason that the neutron star inspiral took hold as the most popular potential source is that the gravitational wave signal could be calculated very accurately from Einstein’s theory. General relativity is a notoriously difficult and complicated mathematical theory, but fortunately the problem of two very small bodies orbiting each other was one that could be attacked by a number of methods. In one method, the equations of the theory could be replaced by an approximate set of equations which could be solved for the orbital motion and the gravitational waves emitted. This approximation could then be systematically improved in a step-by-step procedure. The results of these calculations were enormously long formulae that would typically span two or three pages of paper. But using these formulae and a simple laptop computer or tablet, one could generate a very accurate prediction for thousands of cycles of the inspiral part of the gravitational signal in a tiny fraction of a second. The last few cycles of a characteristic inspiral signal are displayed in Figure 8.4. In another method, the exact equations of the theory were formulated in a way that they could be solved numerically using large computers. This method was particularly important for accurately predicting the merger part of the signal, also shown in Figure 8.4. By the early 1990s, as inspirals were being recognized as the leading potential source for detection by the interferometers, Kip Thorne realized the importance of having accurate predictions of the waves in advance, and he urged theorists to begin the arduous task of developing these methods for predicting the wave shapes. Progress was slow at first, but by the time LIGO began its advanced run in September 2015, the tools for making accurate predictions were in place.
Why did this matter? The answer is a version of the child’s puzzle that requires spotting a character named Waldo in the middle of a page of hundreds of cartoon characters; this version is called “Where’s Nico?”. If you were asked to spot a certain Nico in a teeming crowd of random people, knowing that Nico is a man would not be very helpful. But knowing that he is wearing a purple shirt with a black vest and a white gaucho hat would be very useful in finding him. The more you know about a signal, the easier it is to find it, even if it is buried in a lot of noise. In the same way, one could compare a library of predicted wave shapes (similar to the wave shown in Figure 8.4) to the output of the detector to see if there was a match. This would be done, not by eye, which is notoriously unreliable, but using sophisticated and extremely fast data analysis algorithms. Also, since the wave shape depends on things like the masses of the two bodies, that wave from the library that gives the best match to the data provides information about the system that produced the gravitational wave in the first place.
The neutron star inspiral idea was so popular that if you had asked anybody in the field just prior to the start of the Advanced LIGO run in 2015 what would be the most likely first detection, a large majority would have predicted a binary neutron star merger. The authors of this book certainly would have predicted that, though neither of us felt strongly enough to put serious money or seriously expensive wine on the table. But according to a Danish proverb (also attributed to Danish physicist Niels Bohr), prediction is difficult, especially about the future. Our predictions were wrong.
Not only was the first signal detected that of a binary black hole inspiral and merger, but the masses of the two black holes were completely unexpected. Until then, all the observational evidence and theoretical modeling on black holes pointed to two basic classes of black holes. The first was the class of stellar mass black holes, with masses between 6 and 15 solar masses, the classic example being the 10 solar mass black hole in Cygnus X-1. The second was the class of massive black holes, with masses between a hundred thousand and several billion solar masses, residing in the centers of galaxies, such as Sgr A* or the black hole in M87. We encountered these black holes in Chapter 6. A third class of intermediate mass black holes, between 100 and 100,000 solar masses, has been proposed, but the evidence is still not very solid.
Suffice it to say that black holes with masses of 36 and 30 solar masses were not expected. This was the set of values that gave the best fit between the theoretical wave shapes and the observed wave shapes during the inspiral phase. From that portion of the signal (the left-hand part of Figure 8.2), we can infer that the black holes were separated by roughly 700 kilometers, each revolving around the other at about one fifth of the speed of light, emitting waves at a frequency of about 50 hertz. By the time they collided and merged, each was moving at roughly a quarter of the speed of light. Using those masses and the equations of general relativity, and recalling that the overall strength of the waves decreases inversely with distance, one can then calculate how far the source would have to be so that the overall size of the wave agreed with the measured size shown in Figure 8.2. The answer turned out to be 1.4 billion light years. The final waves were emitted 1.4 billion years ago, around the time when the first green algae were forming in the oceans of the primitive Earth. Even though the two black holes were extremely far away, their larger than expected masses made the waves still “loud” enough at Earth for LIGO to detect them in 2015.
When two black holes merge they form a single black hole in a process that pictorially is similar to the way two soap bubbles merge into one big soap bubble. The main difference is that the “surface” of each black hole, known as the event horizon (see Chapter 6), is not made of any material such as soap, but is a surface where the warpage of spacetime has specific characteristics (such as allowing you to go in but never come back out). But just as the newly formed soap bubble may initially have a convoluted shape, the black hole remnant is a highly distorted beast, unlike the simple pictures you might see that represent black holes as dark spherical objects. The spacetime surrounding it also has bumps and distortions that vibrate and generate additional gravitational waves as the distorted black hole rotates. The frequency of the waves is related to the mass of the black hole, just as a bell whacked by a hammer emits sound of a specific tone. Eventually, friction within the metal of the bell reduces the vibrations and the bell goes quiet. But for the black hole “bell,” these waves, called “ringdown” waves, carry the energy of the vibrations away so effectively (some waves go into the hole as well) that the black hole goes quiet after only a few cycles.
Unfortunately, the gravitational waves detected in 2015 were not loud enough during this ringdown phase to extract the ringdown frequency and decay time directly from the data, but something else could be done. The LIGO collaboration was able to extract the masses of the black holes from the earlier part of the signal, as we described earlier. Using this, together with numerical simulations of the Einstein equations, scientists were then able to predict that the mass of the final black hole was 63 solar masses, which is roughly consistent with the frequency of the ringdown part of the signal shown in Figure 8.2. Incidentally, those final cycles of radiation also provided evidence that the final object is a black hole. Other stellar objects, such as neutron stars, white dwarfs or ordinary stars, also vibrate at specific frequencies (the Sun has its own set of modes of oscillation), but their frequencies and decay rates are nowhere near the values inferred for the remnant of GW150914.
If you noticed a discrepancy between the initial total mass (66 solar masses) and the final mass (63 solar masses), you are correct. Three solar masses were converted into the energy of the outward-flowing gravitational waves, and most of this happened during the two tenths of a second of the signal detected by LIGO (see Figure 8.2). At its peak this represented a rate of energy output that is larger than that of all the stars in the observable universe combined! The energy emitted was the equivalent of a decillion (i.e. a million billion billion billion, or 1033) 1 megaton hydrogen bombs. Interestingly, while stars and hydrogen bombs convert one form of matter into another (mainly hydrogen into helium), with the mass difference being converted into energy, here there is no matter. Whatever matter was involved in forming the black holes is inside their event horizons and can no longer affect the outside world. Instead, the conversion is from the mass imprinted on the spacetime curvature surrounding each hole into the energy of the spacetime ripples propagating outward.
In fact, using the characteristics of the detected wave and the distance to the source, one can estimate the total energy carried by the waves in all directions (some of which might conceivably have been detected by a LIGO in a galaxy on the far side of the universe). That energy turns out to agree reasonably well with Einstein’s famous formula E = mc2, where m is the 3 solar mass difference between the initial and final masses of the source, and c is the speed of light. That iconic formula, so well verified in the laboratory, also holds on cosmic scales!
You can think about this loss of mass–energy in another way. We saw in Chapter 5 that the orbital period of binary pulsars decreased as gravitational waves took energy away from the system. In that case, the rate of change of orbital period was minuscule, roughly 70 microseconds per year. But for the LIGO observations, the period change was so fast that one could see it in the 0.2 second data stream by eye (Figure 8.2)! Using the same formula that relates energy loss to period change for the binary pulsar, one could show that the the amount of energy lost during the inspiral in order to cause the observed period change was perfectly consistent with the 3 solar mass difference.
Everything about the event GW150914 supported key predictions of general relativity: gravitational waves exist, and carry energy away from the source. We knew this indirectly already from binary pulsars, but a direct detection and confirmation was essential. Binary black holes exist. There was already abundant observational evidence for black holes using electromagnetic radiation from material swirling or stars orbiting around them (see Chapter 6), but this was the first evidence using gravitational signals alone. Until then there was no observational evidence for binary black holes. This was the first, but it would not be the last. Newly formed, distorted black holes settle down by emitting “ringdown” gravitational radiation. This was confirmed.
GW150914 provided another important test of general relativity. The theory predicts that gravitational waves travel at exactly the speed of light, and, as with light traveling in vacuum, the speed is independent of the frequency of the waves. But during the inspiral, the frequency of the emitted waves changes dramatically, yet Einstein’s theory predicts the waves always travel at the speed of light. In some modified theories of gravity, however, this is not the case.
One example is a class of theories developed in an effort to explain the fact that the universe appears to be expanding faster with time rather than slowing down with time, as standard general relativity predicts (see page 8). In these theories the “particle” associated with gravitational waves is given a small mass. Just as light can be thought of both as a manifestation of Maxwell’s electromagnetic waves and as a quantum mechanical particle called the photon, vibrations in gravity can also be thought of as a manifestation of Einstein’s gravitational waves or as a quantum mechanical particle called the graviton. But while the particle aspect of light has been abundantly demonstrated and even finds practical applications in things like solar panels, gravity is so weak that we will never be able to measure the particle aspect of gravity directly. If gravitons had a mass, then they would travel more slowly than light, with their velocity dependent on the wavelength of the waves associated with them. In particular, waves of long wavelength would travel slower than waves of short wavelength. Figure 8.6 illustrates what happens: waves emitted in the final part of the inspiral and merger travel a bit faster than waves emitted in the early inspiral. This then allows the merger waves to “catch up” with the inspiral waves in their long, long journey from the source to the Earth. The waves received by a detector would therefore be compressed or squashed a bit in time, compared to the wave that was emitted. But the signature of such a distortion was not seen at all in the LIGO observations, once again confirming Einstein’s predictions in a spectacular way. The LIGO observation places a bound on how large the mass of the graviton could be, as otherwise, if it were any larger, they would have been able to detect its effects. The bound says that the mass of the graviton must be smaller than one part in ten octodecillion kilograms, in other words one divided by ten followed by fifty-seven zeroes! General relativity predicts that its mass is exactly zero, in agreement with the measured bound.
Figure 8.6 If short-wavelength gravitational waves travel more quickly than long-wavelength waves, then the later “merger” waves will catch up with the earlier inspiral waves, so that the wave received by the interferometer is slightly squashed in time compared to the emitted wave. No such effect was detected in the data, placing a very tight upper limit on the mass of a hypothetical “graviton.”
Despite the string of experimental successes for general relativity that we have been describing in the first part of this book, experimental verifications like these matter. The reason is that Einstein’s theory had not yet been seriously tested in extreme gravity situations, where gravity is very strong and rapidly changing. At the same time, observations of the universe as a whole have revealed apparent anomalies such as the accelerating expansion of the universe. The combination of these two facts has led theorists to propose that some of these anomalies could be resolved by modifying general relativity. And the potential outcome of these tests could be dramatic: any measurement that demonstrates and confirms a deviation from Einstein’s predictions could direct us toward a resolution of observational anomalies, potentially leading to a theory of gravity that is “beyond Einstein.”
The “discovery” event GW150914 was not the only one recorded during that first observing run, called O1 by the LIGO collaboration, which ran from mid September 2015 until 19 January 2016. The second event came on 12 October, but it was so weak that the statistical probability that it was a fluke was just once every three years, much larger than the probability of less than once every 200,000 years for the discovery event. Because of this, the LIGO collaboration decided not to announce this event as a proper detection, but rather as a “candidate” event which could not be confidently confirmed as an actual gravitational wave. A later reanalysis would promote this to a reasonably confident detection of a 23 and 14 solar mass black hole merger. The third signal was detected in the early hours of 26 December 2015, Greenwich time, although it was still Christmas day in the US. It was called the “Boxing Day event,” after a tradition in England and Commonwealth countries of giving tradesmen, postal workers or staff a box containing cash or a small gift on the day after Christmas. This event was quite similar to the first one in that it was produced in the merger of black holes, located roughly the same distance from Earth, but with smaller masses (14 and 7 solar masses). Consequently, this event was not as loud as the first one, but still loud enough to be statistically significant.
The events we just described are the only ones LIGO detected during its first observing run. Following some improvements in the sensitivity of the detectors, the second observing session, O2, ran from November 2016 to the end of August 2017, and the haul of detections was impressive. A high-mass binary black hole inspiral (31 and 20 solar masses) was detected on 4 January 2017, and a moderate-mass inspiral (11 and 8 solar masses) was found on 8 June. Four more black hole inspirals were detected by LIGO during O2 between late July and the end of August, including an event with two huge black holes, weighing in at 50 and 34 solar masses, producing a final monster hole of 80 solar masses. This source was also the most distant by far, at nine billion light years. The other three detections were quite similar to the discovery event GW150914 in mass, distance and other characteristics.
Ironically, these four detections made during the summer of 2017 were not announced until December 2018, because of what occurred during the fateful week of 13 August 2017. Two detections made three days apart during that week were so exciting that everything else was pushed aside in order to focus on these finds.
As we discussed in Chapter 7, the Virgo gravitational wave detector in Italy was about a year behind LIGO in the various stages of construction, commissioning and upgrading. But on 1 August it joined LIGO in a three-way session, scheduled to last for three weeks, until the end of O2. And on Monday 14 August 2017, the three instruments heard the gravitational waves emitted by another binary black hole merger, with masses in the 25 to 30 solar mass range. But the triple detection allowed for something new: pinpointing the location of the source in the sky.
How can these detectors determine where the waves came from? Just as in navigation using GPS, discussed in Chapter 2, the answer is triangulation, exploiting the arrival time of a signal. In GPS, it is the arrival time at the user of signals from multiple GPS satellites that allows the user to determine her location. In gravitational wave triangulation, it is the arrival of the signal from a single source at different detectors. For two LIGO detectors, we saw in Figure 8.3 how measuring the difference in arrival times at the two sites allows you to determine that the source lies somewhere on a circle on the sky (except for the special case where the source lies precisely along the line joining the two detectors). But if there is a third detector, such as Virgo, then in exactly the same manner, the difference in arrival time between Virgo and, say LIGO-Livingston, gives a second circle on the sky (the time difference between Virgo and LIGO-Hanford gives redundant information).
There are three possibilities for these two circles. The first is that they do not intersect at all, in which case the event would have to be rejected as a candidate gravitational wave. This is analogous to the case where the time difference between the arrival at two sites is larger than the light travel time between the sites. The second possibility is that they intersect in two places, as illustrated in Figure 8.7. In this case, since the source must reside somewhere on both circles, it must therefore be at one of the two intersection points, either A or B. The third is a very special and lucky case in which the circles just touch each other at a single point, giving a single location for the source on the sky. In reality, these circles are really bands of some width, reflecting the uncertainties that are inevitable in noisy and imperfect data. And exploiting additional details of the response of the detectors to an impinging wave, it is possible to exclude parts of each circle as being less likely to correspond to the source’s location. Thus, while data on the prior LIGO-only detections could confine the sources at best to large elongated banana-shaped regions on the sky, the data on the LIGO–Virgo source GW170814 confined it to an oval region in the southern sky about the size of a major league baseball held at arm’s length.
Figure 8.7 The arrival-time delay between two detectors fixes the source to lie on a circle in the sky. The delay between one of those and a third detector fixes the source on another circle. If the circles intersect, the source must lie at one or other intersection point (A or B).
Three days later, on 17 August, another signal passed the Earth, reaching Virgo first, then LIGO-Livingston 22 milliseconds later, and LIGO-Hanford 3 milliseconds after that. This signal was quite different from all the black hole inspiral signals detected to that point. Instead of a very short, rapidly changing chirp–merger–ringdown signal, as shown in Figure 8.2, the signal was detected for a whopping 100 seconds, and appeared pretty boring, something like the signal shown schematically in Figure 8.8. In fact, Figure 8.8 illustrates only about the final quarter of a second of the signal (to picture the whole signal you have to imagine it continuing about 200 page widths to the left). The signal was a regular undulating wave, suggesting that the source is a binary system. Its frequency was roughly the same as for the black hole mergers, around 100 hertz, suggesting that the bodies are revolving around each other very fast. But compared to the black hole signals, where the changes in size and frequency of the wave could be seen over a few orbits, here the orbit-by-orbit changes are minuscule, suggesting that the rate of leakage of energy into gravitational waves is tiny. This indicates that the masses of the two bodies are much smaller than the masses in the black hole inspirals. All of this pointed to an inspiral of two neutron stars. The event was denoted GW170817.
Figure 8.8 Gravitational wave of a neutron star binary inspiral. Only the last quarter of a second of the wave is displayed. The observed wave GW170817 lasted 100 seconds.
In addition, while the signal was detected in both LIGO instruments, it was barely detected by Virgo. While it was possible that the Virgo detector was somehow malfunctioning at that particular moment (which would have been strange, since it worked perfectly three days earlier), the more likely explanation was that the source was at a location in the sky close to one of the four directions for which Virgo is “deaf” (see Figure 8.5). Because of that unlucky alignment, the Virgo interferometer did not respond as strongly to the signal as it might otherwise have. This useful information, combined with the circle in the sky inferred from the arrival times at the two LIGO detectors, gave a decent sky location for this source.
Meanwhile, orbiting 534 kilometers above the Earth, detectors on board the Fermi Gamma-ray Space Telescope detected a burst of gamma rays in its routine sweep of the sky. The gamma rays arrived 1.74 seconds after the end of the gravitational wave signal. Fourteen seconds later, even before the automated software at LIGO and Virgo had fully registered what they had detected, Fermi issued an automated alert to astronomers worldwide (including the LIGO–Virgo team) so that follow-up observations could begin. This detection was denoted GRB170817 (for gamma ray burst). Forty minutes later, LIGO–Virgo issued its own worldwide alert, noting the near coincidence in time between the gravitational wave signal and the gamma ray burst. Five hours after the gravitational wave event, they had localized the source to be in a region of the sky about 30 square degrees in angular size, and at a distance of 130 million light years, good to about 20 percent. These observations meant that the source was somewhere within a three-dimensional cube in space containing about 49 galaxies. The Fermi observation was consistent with this, but was not accurate enough to pinpoint the specific galaxy from which the gamma rays had originated. About 12 hours after the initial detections, a team using the Swope Telescope at Las Campanas Observatory in Chile detected a counterpart signal in the visible band, and identified the host galaxy as NGC 4993.
The galaxy NGC 4993 is not particularly interesting. Discovered in 1789 by astronomer Wilhelm Herschel, it is an elliptical galaxy in the constellation of Hydra. Unlike the Milky Way or the Andromeda galaxies, which are rotating galaxies with spiral arms and a dense core, an elliptical galaxy is more egg shaped, with stars that orbit almost randomly around its center. NGC 4993 is about the size of the Milky Way, and like most galaxies it hosts a supermassive black hole at its center, which in this case has a mass of roughly 80 to 100 million solar masses. It also shows evidence that it merged with another galaxy about 400 million years ago. So, apart from hosting humanity’s first ever detected neutron star inspiral and merger, NGC 4993 is a fairly run-of-the-mill galaxy.
Ironically, while all this was happening that August morning, Nico was hosting a workshop at the eXtreme Gravity Institute at Montana State University in Bozeman, called “eXtreme Gravity meets eXtreme Matter.” The main purpose of this workshop was to bring experts together to discuss the science one would be able to extract once LIGO–Virgo detected gravitational waves from the merger of two neutron stars. This made it extremely difficult for half the attendees (who belonged to the LIGO–Virgo collaboration and had seen both alerts) to participate in the workshop discussions, as they had to abide by LIGO secrecy rules. How they managed to hold their excitement at bay and not spill the beans is a mystery. Those constraints would be lifted only months later, after the event was confirmed as a true detection.
What followed the LIGO–Virgo and Fermi alerts was one of the most extraordinary observational campaigns in the history of astronomy. Over the next thirty days, follow-up observations were made in every band of the electromagnetic spectrum, using telescopes on the ground and in space. Thirteen separate teams made gamma ray and X-ray observations. The Hubble Space Telescope made observations in the ultraviolet, visible and infrared. Thirty-eight teams observed in the visible band, while twelve worked in the infrared band. Fifteen teams made observations in the radio band. Three teams even looked for signals of neutrinos (not surprisingly, given the distance of the source, they saw none). On 20 October 2017, Astrophysical Journal Letters published a summary of what all the observations had yielded during those first two months in what was being dubbed “multi-messenger” astronomy. The paper had 3,500 authors, of whom 1,100 were in the LIGO–Virgo collaboration and the rest were associated with astronomical projects. Virtually every astronomy department or center in the world was represented in the 953 listed institutes. A year after the detection of GW170817 and GRB170817, observations of the electromagnetic radiation from the source continued in many wavelength bands, and almost a hundred papers had been published in a range of astronomy journals, along with around fifty in physics journals.
We might be forgiven for pointing out a certain irony in all this. In the early 1990s, when the US government was trying to decide whether to give the go-ahead for major funding to begin the construction of LIGO, many prominent American astronomers lobbied vigorously against it. The astronomers’ arguments roughly boiled down to some combination of: it won’t work; it will only detect gravitational waves, which we already know exist (see Chapter 5); it’s just a physics experiment with nothing to do with astronomy; and it is too expensive. One astronomer, J. Anthony (Tony) Tyson, reported that an informal poll he conducted in early 1991 of seventy astronomers ran four to one against LIGO. In March 1991, Cliff testified in favor of LIGO before a US House of Representatives Science subcommittee, alongside Tyson who, while supportive of LIGO in general, testified against construction funding at that time. What a difference a detection makes!
What did we learn from this multi-messenger source? Detailed analysis of the gravitational wave signal indicated that the masses, around 1.5 and 1.3 solar masses, were quite consistent with those of known neutron stars. The gamma ray burst showed that it could not have been two black holes, because you need hot matter to get such high-energy radiation, and black holes are pure spacetime. A “mixed merger” of a neutron star and a black hole could not be definitively excluded, although it was hard to imagine where such a low-mass black hole would come from.
The association of a neutron star merger with a burst of gamma rays resolved a long-standing mystery. Gamma ray bursts have been observed and studied since the 1960s, when the US Vela satellites accidentally detected the first bursts. These satellites had been deployed in the middle of the Cold War by the US military to investigate whether the Soviet Union was testing nuclear weapons in space. Gamma rays are a byproduct of such nuclear explosions, and indeed the Vela satellites detected many bursts of gamma rays. But the bursts did not have the characteristics of those emitted by nuclear bombs, and appeared to be coming from far outside the solar system.
Within a few years, the study of these mysterious gamma ray bursts exploded. In 1991, the Compton Gamma Ray Observatory (CGRO) was launched, and over the next nine years it observed and localized around 2,700 gamma ray bursts (almost one per day), finding that they were not coming from any preferred direction, and thus suggesting an extragalactic origin. Moreover, astronomers deduced that the bursts came in two rough classes based on their duration: “short” bursts had an average duration of about 0.3 seconds, while “long” bursts lasted 30 seconds on average. Although the short bursts comprise only about 30 percent of all observed gamma ray bursts, they were particularly interesting. Astronomers realized that there was no correlation between these short bursts and supernovae, ruling out the latter as possible progenitors. They also realized that most of the short bursts came from elliptical galaxies where there is an underabundance of massive stars, which are needed for supernovae.
Theoretical arguments made the short bursts even more intriguing. Imagine that the source that produces these short bursts of gamma rays is a ball or blob of matter of some size. Imagine that the burst is caused by an explosion of the blob, producing a flash of light that is directed toward us. The duration of the burst must be related to the finite extent of the source: we first see the light emitted from the region of the source closest to us, and later we see radiation emitted from other regions farther away from us. Since the entire duration of the burst is about 0.3 seconds, and since gamma rays travel at the speed of light, we conclude that the emitting region must be of the order of the time duration multiplied by the speed of light, which comes out to roughly 100,000 kilometers, or eight times Earth’s diameter. And because of the tremendous energy produced in these bursts, there had to be an enormous amount of matter contained in such a small region of space. Whatever produced these short bursts had to involve dense compact objects such as neutron stars, as Russian physicist Sergei Blinnikov and collaborators had theoretically predicted back in 1984.
By 2005, astrophysicists began to suggest that the short bursts were the result of either neutron stars merging with each other or of a neutron star merging with a small black hole. But there was no way to prove this, since no light would be detected from the merging pair before the short gamma ray burst started. The LIGO–Virgo observations provided the missing piece of the puzzle, unequivocally proving that at least one of the possible progenitors of short gamma ray bursts is the merger of neutron stars. This observation also validated other ingredients of the model, such as the fact that the bursts are emitted in a very narrow cone, which we detect on Earth only if the cone happens to be pointing in the right direction. This, in turn, suggests that many more short gamma ray bursts must be occurring in the universe, but with their emissions beamed in cones that do not point toward Earth. Gravitational wave observations will be able to determine precisely how many such events occur in the universe, since gravitational waves are not emitted narrowly in a cone, but rather more or less equally in all directions.
These short gamma ray burst models also claimed to answer a question asked by anybody who has ever bought a wedding ring or examined the insides of a cell phone: where does gold come from? Today we have a very good idea of the origin of the key elements in nature. About three minutes after the big bang, around 20 percent of the primordial hydrogen was converted via nuclear fusion to helium, along with a sprinkling of lithium, a process known as big bang nucleosynthesis. Stars continue the process, converting more of their hydrogen into helium, but also extending the fusion process to elements such as carbon, nitrogen and oxygen, so crucial for the life forms that inhabit Earth. Very massive stars also produce those elements, but when they explode as supernovae, they produce elements up to the so-called “iron group” (iron, manganese, cobalt, nickel) and spew them into interstellar space, later to be incorporated into planets such as Earth. Unfortunately it is not so easy to produce elements heavier than iron. Many elements above iron in the periodic table are unstable, decaying to other elements by various radioactive processes, and they all have many more neutrons than protons in their nuclei. Nuclear physicists had developed a set of chain reactions, known as “r-process nucleosynthesis” (“r” meaning rapid, not the most imaginative of names), that could in principle produce heavier elements in the right proportions, but they all required that the processes take place in an extremely neutron-rich environment. Normal stars and supernovae utterly failed to produce the right environment. But neutron stars are almost completely made of neutrons (with a small contamination of protons and electrons), and so proponents of the neutron star merger model for short gamma ray bursts argued that this would be the right environment for the r-process.
One class of models for what happens after two neutron stars merge came to be called “kilonova models.” This is a variant of the word “supernova,” but it has nothing to do with the explosion of a massive star. According to these models, when neutron stars merge, they will spew a few hundredths of a solar mass of material into space at about a few tenths the speed of light. Some of this material will fall back onto the remnant, maybe forming a disk of material that is slowly swallowed or “accreted” by the remnant. But some of the ejected material will have enough of an initial velocity after the collision that it will escape altogether, creating a cloud of very hot and very neutron-rich material. As the cloud expands and cools, the r-process produces elements like gold, platinum and silver, as well as heavier elements in the lanthanide part of the periodic table (elements that are crucial for computers, cell phones and batteries).
And this is precisely what optical and infrared telescopes observed when following up the gravitational wave detection. In fact, the electromagnetic radiation detected from the radioactive decay of material in the hot cloud expanding from the merger site suggests that about fifty times the mass of the Earth was produced in silver, a hundred times the mass of the Earth in gold and five hundred times the mass of the Earth in platinum, a mere second after the merger.
Astronomer and science TV host Carl Sagan once said that we are made of star dust. He was referring to the elements forged through nuclear fusion in stars and supernovae. But now we know that we are not just that. A little part of us also contains neutron star dust (not too much, as that would be toxic). What’s more, neutron star dust (in the form of gold, platinum and silver) is forged into jewelry that routinely adorns our bodies. We even sometimes bind ourselves to each other through rings of neutron star dust.
We close this chapter with an extroardinary test of Einstein’s theory provided by GW170817 and GRB170817. We already learned from the black hole inspirals that the speed of gravitational waves is independent of wavelength, in accord with general relativity, but we learned nothing about the actual value of that speed. That is because only gravitational waves were received from those inspiral events, and since we do not know exactly when the signals were emitted, there is no way to calculate the speed of the waves. General relativity predicts that the speed of gravitational waves is exactly the same as the speed of light. The nearly simultaneous arrival of the gravitational waves and the gamma ray burst proved that they are the same to incredible precision. The argument goes like this.
The LIGO–Virgo collaboration compared the time at which the peak of the gravitational waves arrived at the detectors to the time at which gamma rays arrived at the Fermi satellite. After correcting for the altitude and location of the satellite and for the radius of the Earth, the scientists concluded that the gamma rays arrived about 1.7 seconds after the peak of the gravitational wave train. This delay is presumably caused by the fact that the gamma ray emission did not start when the neutron stars first touched each other, which does coincide with the peak of the gravitational wave signal, but instead the gamma ray emission originated in whatever violent explosion followed the merger. The details of that explosion are still an area of active research, but different models suggest a delay between 1 and 10 seconds.
Let us assume that the gamma rays were emitted at exactly the same time as the peak of the gravitational waves, that is, roughly at the time the neutron stars first touched. If so, then we would attribute the delay in the gamma ray arrival entirely to gravitational waves moving more quickly than the gamma rays. How much more quickly would they have traveled? The travel time of the gravitational waves is simply the distance traveled divided by their velocity, and similarly the travel time of the gamma rays is the same distance divided by the speed of light. Remember that the distance over which this little race occurred is 130 million light years. The difference in these travel times must equal the 1.7 second time delay measured, which then allows us to estimate that the gravitational waves were faster than the gamma rays by at most about three quarters of a millimeter per hour. Alternatively, let us assume that the gamma rays were emitted 10 seconds after the gravitational waves. In this case the faster gamma rays would have narrowed the gravitational waves’ head start to 1.7 seconds, requiring them to be faster by about 3 millimeters per hour. Comparing these two estimates to the speed of light, a million billion millimeters per hour, one sees that the permitted speed difference is truly minuscule: smaller than parts in 1015! As we discussed earlier, many of the latest attempts to account for the accelerated expansion of the universe and the effects attributed to dark energy by invoking an alternative gravitational theory require that the speed of gravitational waves be different from that of light. The single observation from GW170817 and GRB170817 that this is not the case forced theorists to throw a large heap of such theories immediately into the trash. Conversely, if we assume that general relativity is correct, and thus that the two speeds are identical, then the 1.7 second delay between the arrival of the two signals corresponds precisely to the delay between the emission of the two signals, a fact that is already proving very important in sorting through the many complex models for how the gamma rays were generated.
In the end, most of us were wrong in our predictions that neutron star mergers would be the first events detected by LIGO–Virgo. But hey, ninth place isn’t so bad! Those unexpectedly massive black hole inspirals were loud, and the rate of such events is obviously higher than people expected. The third observing run of LIGO–Virgo began on 1 April 2019 at even better sensitivity, with the expectation of more detections of black hole mergers, neutron star mergers, and maybe even mixed mergers of a black hole and a neutron star. As we end this chapter we don’t want you to get the impression that this is it. The ground-based interferometers will also be searching for other sources of gravitational waves, and completely different kinds of detectors are in operation or under development, including one destined to go into space. The future is loud for gravitational wave detection, and we can look forward to hearing many more movements in the symphony of the universe.