The closest ten or so white dwarf binaries have had their orbits determined very precisely using electromagnetic observations of the stars’ motions. As a result, we can predict the gravitational wave signal they emit almost exactly using general relativity. These are called “verification sources,” because LISA had better detect them clearly and unambiguously, otherwise there is something wrong with LISA or with general relativity. LISA may also be able to identify up to 25,000 additional binaries, especially at higher frequencies. But there may be so many binaries in the galaxy that they will produce a background of “noise” that is actually louder than the intrinsic noise within the instruments.
This is familiar to anybody who has been in a sports stadium. If you close your eyes and listen, you will hear many voices talking, laughing, yelling at the same time. It is hard to pick up any one voice from the combination. You can perhaps pick out the closest and loudest ones, but that’s only a few in a sea of noise. With galactic binaries, we will still be able to pick out a few of the waves that stand out in this background, but in general, the wealth of sources will contribute to a form of noise.
New sources of gravitational waves mean new tests of general gelativity. Probably the strongest advantage of these new sources is that they are so loud that they can be heard even when their distance to Earth is truly cosmologically large. Certain modifications of Einstein’s theory, such as the idea that gravitational waves might travel at a speed different from that of light, or that the particle associated with gravity (the graviton) might not be massless, have effects that build up with the distance traveled. Therefore, LISA observations of supermassive black holes will lead to tests of such deviations that could be a million times more powerful than what has been achieved by the ground-based interferometers (see pages 168 and 176).
In an extreme mass-ratio inspiral, the small black hole acts as a tracer of the warped spacetime geometry around the spinning hole: now very close, now very far away, now on the equatorial plane, now over one of the poles, mapping space and time the way a cartographer documents every bump and every valley on the Earth’s surface. These inspirals can trace the gravitational field outside of a black hole similar to the way GRACE traces the gravitational field of Earth (see Chapter 4). The gravitational waves emitted encode all of this information, and the detection and analysis of the waves then allows us to determine whether the geometry of a supermassive black hole is truly described by Einstein’s equations or not.
And there is one more surprise that LISA has up its sleeve: it allows for multi-wavelength observations. Imagine that LISA observes the gravitational waves emitted by a binary composed of black holes, each with a mass of roughly 30 solar masses. For LISA to achieve this, the binary has to be relatively close to Earth, say 1.4 billion light years away. In addition, the orbital separation of the binary has to be large enough that it is emitting gravitational waves at a sufficiently low frequency that LISA can hear them. Such a source would be in LISA’s sensitivity band for many months, with its frequency slowly increasing and the black holes slowly spiraling into each other. Eventually, the waves’ frequency will increase beyond the detector’s sensitivity band. This is similar to listening to a sound whose frequency is slowly getting higher and higher, until eventually you can’t hear it anymore because our ears cannot detect sound above a certain frequency.
Such a signal would then disappear from LISA’s band, but a few months later the same signal, now at a frequency of 10 hertz, would reappear in the ground-based detectors! We call such an observation, first by LISA and then by ground-based instruments, a multi-wavelength event because the same signal is observed at very different frequencies by different instruments.
The potential of such a multi-wavelength event is truly breathtaking. The LISA observation would make it possible to predict when in the future the same event would be detectable by ground-based instruments. Moreover, LISA would be able to localize the source in the sky, thus allowing telescopes on Earth and in orbit to point to this box in the sky to watch the fireworks (if there are any) as they occur. And for tests of general relativity, such an event would also be fantastic, since it would allow us to measure very precisely the rate at which the frequency of a binary changes over many, many orders of magnitude. This rate of change is very precisely predicted in general relativity, so any deviation from these predictions would be catastrophic for Einstein’s theory.
There is a final advantage of LISA for testing Einstein’s theory. Many of the sources that LISA will see will be observable for many months, and even years, in contrast to the short chirps of minutes to fractions of a second that LIGO–Virgo detected. During this time the LISA triangle will be in orbit around the Sun, with both the orientation and the plane of the triangle rotating around during the orbit. In this way, LISA will behave like the multiple interferometers on Earth, allowing us to extract the different polarizations of the signal, even though we only have a single instrument. Therefore, LISA can test Einstein’s prediction that gravitational waves only have two polarizations, the “plus” and the “cross” modes shown in Figure 7.3. This is a strong statement because many modified theories predict additional polarizations. If we can verify that gravitational waves truly only possess two polarizations, it would be a fatal blow to many modified gravity theories.
So far we have discussed in detail the many different instruments we can build to detect gravitational waves, but there is a natural detector that is provided to us by nature; it involves pulsars (see Chapter 5 for an account of the discovery and characteristics of pulsars). The pulses emitted by some of these objects, particularly the old, recycled pulsars, are incredibly stable over long times, arriving at the detector with essentially the same pulse period week after week, year after year. Most of these special pulsars have rotational periods of milliseconds, so the neutron stars that produce the radio beacons are spinning faster than the blades in a professional kitchen blender. Their periods are typically stable to better than a microsecond over a year, making them competitive with some of the best atomic clocks on Earth. But if a gravitational wave goes through spacetime between the pulsar and Earth, their measured periods will be altered by the passing gravitational waves. One can think about it crudely as the wave alternately stretching and shrinking the distance between the Earth and the pulsar, thus inducing an increasing and decreasing Doppler shift in the apparent frequency of the pulses. Therefore, a sufficiently precise measurement of the pulse frequencies could in principle be used to detect gravitational waves.
One problem is that although millisecond pulsars are stable over long times, they are not so stable over short times, say of the order of tens of milliseconds. This is because of the intrinsic variability in the pulse frequency, but also because the speed of the light pulses varies as the radio signals propagate through the clumpy ionized gas, called the interstellar medium, that lies between us and the pulsar. Avoiding such speed variations in the light signals is why LIGO–Virgo had to have ultra-high vacuum tubes. So the observed pulses need to be averaged over long periods, of the order of a year, in order to averge out any intrinsic or propagation-induced variability. This is similar to the fact that, over ten billion flips of a perfect coin, the outcome will be fifty–fifty heads vs. tails to one part in 100,000, while over ten flips you could easily get four heads in a row, followed by three tails and then two more heads. The result of such averaging is a set of pulses with the remarkably stable period described above. On the other hand, when a given gravitational wave from a very distant source passes through the Milky Way, it affects the measured variations in pulse period from a given pulsar in a very predictable way that depends only on the direction to the pulsar relative to the direction of the source of the waves, and on the distance between the Earth and the pulsar. Therefore, if one can observe pulses simultaneously from an array of pulsars, say fifteen or twenty, distributed all around the Milky Way, then it is possible to do a better job of averaging out the short-term fluctuations in pu
lse periods that are specific to each pulsar and are more or less random, revealing the common gravitational wave signal.
This effort, known as pulsar timing arrays (PTAs), is being carried out by teams of radio astronomers around the world. There is the Parkes Pulsar Timing Array (PPTA) based at the Parkes radio telescope in Australia, the European Pulsar Timing Array (EPTA) that uses the four largest radio telescopes in Europe, and the North American Nanohertz Observatory for Gravitational Waves (NANOGRAV) that uses the Arecibo and Green Bank, West Virginia telescopes. An international organization (IPTA, what else?) oversees and coordinates the various teams.
What kind of gravitational waves can we detect with such PTAs? Since we have to average the pulses over a year, then we can only detect waves that vary over longer times. Since a year is about 0.03 billion seconds, we are thus looking for waves with frequencies of around 30 billionths of a hertz or 30 nanohertz. At these frequencies, the loudest sources of gravitational waves are orbiting supermassive black holes in the centers of galaxies, but long before they are close enough to each other to merge. There could be thousands to millions of potential sources in the sky at nanohertz frequencies. So many sources cannot necessarily be separated in the data, but instead they lead to a noise background, similar to the white dwarf binary background for LISA. But this “noise” has very specific characteristics that can be used to distinguish it from other noise sources, such as intrinsic pulsar jitter and propagation effects. By focusing on this characteristic (called a correlation), we can learn about the black hole binary population that produced the waves.
A background of gravitational waves from binary massive black holes has not yet been detected by the PTA method, but detections may be imminent. Once this is achieved, we will be able to learn not just about the gravitational wave background itself, but also about other astrophysical effects that may be causing the supermassive black holes that produced the waves to inspiral toward each other. And when this is taken into account, one can also in principle place constraints on modified theories of gravity that predict the existence of other gravitational wave polarizations, because the “correlation” we mentioned depends on the number of polarizations in the waves.
As we have seen, gravitational waves have provided a soundtrack to the universe, and the sophisticated headphones we have constructed to hear it will only improve in the coming decades with third-generation ground-based detectors, LISA, and PTAs. Einstein’s gravitational wave playlist encompasses many keys and genres, from the high-pitched, staccato chirps of the stellar mass inspirals to the hiss of the white dwarf binary noise to the motorcycle vroom of EMRIs. All we have to do is listen.
CHAPTER 10
A Dialogue
Nico Cliff, you’ve been working in general relativity since like a million years before I was even born. You must have had some pretty exciting moments during your career. What was number one?
Cliff It has to be learning that gravitational waves had been detected by LIGO. We were all pretty confident that the advanced interferometers would eventually detect waves, but we had no idea when. As you know, during the fall of 2015 there were many rumors going around that LIGO had something, but since I was not part of the LIGO–Virgo collaboration, I had no inside knowledge. Finally, in late January 2016, about two weeks before the actual announcement, various science journalists started calling me to ask if I knew anything. All I could say was that I had heard the same rumors as everybody else. Finally, I emailed some colleagues in my department at the University of Florida, who were members of the collaboration, if I should begin thinking about preparing some remarks for journalists. One of them answered “you should always be prepared for whatever life sends your way.” This was not very helpful! But a few days later, another colleague came into my office, closed the door and made me swear not to reveal what he was going to show me, which was the draft of the discovery paper. Needless to say I was blown away! I’m normally a very calm person, but when I saw my wife that evening, she immediately said, “What’s wrong?” I had to tell her! (I knew she could keep the secret.) A week later came the big press conference. In many ways, my career began in 1969 with Weber’s flawed claims of detection of gravitational waves, so I’d been waiting almost fifty years for that moment.
I have a feeling that your most exciting moment might be the same, but how did you learn about it and what was your reaction?
Nico I was in the same boat as you. Back when I was a graduate student at Penn State, I was a member of the LIGO collaboration. But then, after graduate school, I decided I was more interested in theoretical physics, so I stepped away, although my research has always remained very close to the science that one could do with LIGO observations. By the fall of 2015 I was already at Montana State, and although colleagues of mine were members of the collaboration, I wasn’t, so I was not privy to any “secret” information. But I was hearing the same rumors as everybody else. By the time of the announcement, everybody in our institute essentially knew what was happening, so we gathered in the conference room and bought a cake to celebrate when those five magical words were uttered: “We have detected gravitational waves.”
I was a bit surprised when I heard that one of my colleagues told his ten-year-old son about the discovery essentially the day it was made, back in September 2015. But the boy kept the secret! Now, we get alerts on our mobile phones. I’m happy we are finally done with the secrecy. I’ll bet this is nothing like what the field was like back when you were young, you know, back in the hippie era.
Cliff Indeed, my hair was appropriately long, particularly compared to today. That reminds me of another exciting moment from “back in the day.” In the fall of 1974 I was a brand new assistant professor at Stanford University, working with the astrophysicist Robert V. Wagoner. In late September, Bob burst into my office waving an “IAU telegram.”
Nico A telegram! Really?
Cliff In those pre-internet days, new discoveries in astronomy were announced by a service of the International Astronomical Union, which would send a telegram to observatories and universities worldwide outlining the basic facts of the discovery. Bob, who is one of the most enthusiastic physicists I know, shouted “Cliff, they’ve just discovered a pulsar in a binary system! Whatever you are working on, drop it. We have to get to work on this new system.” Of course, this was the Hulse–Taylor binary pulsar, which we discussed in Chapter 5. Within a few weeks, Bob wrote a key paper on how it would be possible to measure the change in the orbital period of the binary and thus prove the existence of gravitational waves, and I wrote a paper on the implications of measuring the advance of the pericenter of the orbit. For the next eight or so years, the science related to the binary pulsar occupied almost half of my research life. And when Joe Taylor announced at the 1978 Texas Symposium his team’s measurement of the inspiral of the orbit in agreement with Einstein’s prediction for gravitational wave energy loss (page 128), it was a fantastic moment. Of course, the icing on the cake came in October 1993, when I received a fat envelope from the Nobel Foundation containing an invitation for me and my wife to attend the Nobel Prize ceremonies in Stockholm honoring Joe and Russell Hulse.
Nico Wow! Obviously, there have been many moments during your career. Another big moment for me was when Frans Pretorius completed the first computer simulation of the merger of two black holes in full general relativity. When my physics life started at Washington University in Saint Louis, in your gravity group, if you recall, nobody could simulate such a collision. It was really hard even to use a computer to simulate a single black hole just sitting there doing nothing (even though we had the Schwarzschild solution, which you can write down in one line on a piece of paper). One of the problems was the apparent singularity at the event horizon of the black hole. Even though some mathematical functions become infinite there, we know how to handle that and we know that nothing physically bad happens there.
Cliff Indeed, we discussed this in Chapter 6. But while our minds can
fathom infinity and even make peace with it, computers can’t; they simply stop and emit an error message whenever they encounter a number divided by zero. And this was only one problem with computer solutions of Einstein’s equations.
Nico But it all changed in 2005. I was a graduate student at Penn State at the time, and I recall being in my office, because I was too young to attend a conference in Banff, Canada, that more senior students were attending to present their work. Suddenly, a graduate student or postdoc, I can’t remember, barged into my office and excitedly told me about the computer simulation that Frans Pretorius had presented in Banff. My jaw dropped! He had done it! It would now be possible to predict what the gravitational waves produced in the final part of a black hole merger looked like. It was the biggest breakthrough I had ever experienced in relativity, and I was super excited. Soon, many other groups around the world were able to merge black holes on the computer, using techniques quite different from Frans’, but getting the same result. The black hole merger problem was basically solved.
Cliff That breakthrough came at just the right time, because LIGO was laying the groundwork for advanced LIGO, and this gave confidence that we would have good theoretical predictions for the waves by the time real waves were detected.
Nico Without that 2005 breakthrough we would not have been able to interpret the signals shown in Figure 8.2 so clearly and confidently as coming from a binary black hole merger, and we would not have been able to measure the masses and the distance so accurately.
Is Einstein Still Right? Page 31