Is Einstein Still Right?

by Clifford M. Will

  The Faller–Bender concept drifted around the community of researchers for a number of years. An alternative version involving spacecraft orbiting the Earth was put forward by Ronald Hellings of the Jet Propulsion Laboratory. Another person interested in a space detector was Karsten Danzmann of the Max Planck Institute in Garching, Germany, who was engaged in building the GEO-600 ground-based interferometer. In 1992, it all came to a head.

  That year, the thirteenth International Conference of General Relativity and Gravitation (the conferences that began with GR0 in Bern in 1955) was held in Huerta Grande, Argentina, a picturesque little town in the middle of the country in the province of Cordoba. The conference venue was one of the many “summer holiday camps” built for the families of workers in labor unions around Argentina’s countryside by Juan Domingo Perón during his presidency between 1946 and 1955. At that meeting, there was considerable discussion among Bender, Hellings, Danzmann and other proponents of a space detector, and an agreement was reached to submit a proposal to the European Space Agency, which had put out a call for proposals for new space missions. There is a legend that as the conference came to an end and participants began heading back home to the United States, Europe and Asia, a luggage strike at the airports took place. This caused delays and cancelations of flights, forcing a large group of relativists to be stranded in the middle of Argentina. It was during this forced delay, recall some, that the agreements to make a pitch to ESA were forged. Needless to say, with the passage of time, the memories of the key people have become fuzzy on this point, so we will leave it there as a legend.

  By 1997, following numerous assessment studies by both ESA and NASA, a “baseline” mission for LISA was developed (we will describe it shortly). The science of the proposed mission was impeccable, the technical challenges would be great, and the mission would be expensive, with costs likely to be measured in billions of US dollars. But unforseen events and circumstances arose that kept pushing LISA farther into the future. For example, the discovery of extrasolar planets in 1997, and the discovery in 1998 that the expansion of the universe was accelerating rather than decelerating, brought forth numerous proposals for space telescopes to find more planets and to solve this cosmic riddle. And beginning around 2005, NASA’s James Webb Space Telescope, being built as the successor to the Hubble Space Telescope, began to experience substantial cost overruns and delays, eating into the funds available for all new projects, such as LISA. By 2010 it was clear that the top priority, billion dollar astrophysics mission that NASA would mount after the Webb telescope would be a mission called the Wide Field Infrared Survey Telescope (WFIRST), designed to probe the acceleration of the universe in more depth and to look for more exoplanets. LISA was third on the list, behind a suite of small missions, known in NASA jargon as “Explorer” class.

  Meanwhile, ESA was planning its long-term strategy for large space missions, and convened a meeting in Paris in 2011 to organize the queue. Three large projects were competing to be the first in a proposed sequence of launches, at roughly eight-year intervals, beginning in the early 2020s. They were the Jupiter Icy Moon Explorer (JUICE), the Advanced Telescope for High Energy Astrophysics (ATHENA), and LISA. The presentation made by the LISA team received a standing ovation, but rumors coming out of Washington DC forced ESA to defer ranking the missions.

  The year before, the Republican Party had won a majority of seats in the US Congress, and they refused to raise the country’s debt ceiling without a negotiation over deficit reduction. On 31 July 2011 the Congress agreed to raise the debt ceiling in exchange for severe spending cuts in the future. These cuts, together with the James Webb telescope overruns, hit NASA hard, forcing it to freeze development of almost all future missions, including joint projects with ESA, such as JUICE, ATHENA and LISA.

  With NASA out of the picture, ESA came up with a compromise: they would go it alone, but the design of each mission would have to be descoped to save money. For two of the missions, descoping was somewhat straightforward. In JUICE, the spacecraft could visit just one of Jupiter’s moons, say Ganymede, instead of also visiting Europa. For ATHENA, you could simply remove one of the secondary X-ray telescopes from the satellite. But by this time, the LISA design was for a triangle-shaped interferometer, with three satellites separated by five million kilometers each and with two laser links along each arm of the triangle, very similar in concept to the triangular design of ET shown in Figure 9.3. Descoping this design was not so simple. Decreasing the arm lengths from five to one million kilometers saved money in focusing requirements for the telescopes directing the laser beams, and in the fuel needed to situate the three spacecraft properly, but not enough. So the LISA team also proposed eliminating one of LISA’s arms, returning to a V-shaped arrangement, very much like the original LISA proposals of the 1980s, thus dramatically simplifying two of the three spacecraft.

  But ESA still had to decide on the ordering of the launches of each descoped mission, so it called for another “shoot-out” in 2013. This time the LISA proposal ranked first! Everything was set for the construction and launch of the mission, except for one condition: the LISA team had to demonstrate that the technology required for LISA was possible in reality. This forced them to design, construct and launch an entirely separate mission, to be called LISA Pathfinder. Such a requirement is not unprecedented. We recall from Chapter 4 that Gravity Probe-B planned a technology demonstration mission, but the Challenger disaster caused it to be scrubbed. In retrospect, such a “GP-B Pathfinder” might have discovered the “patch effect” problems that caused that project such grief. Ironically, the LISA proponents had proposed a Pathfinder-type mission back in 1998, but it had never been accepted by the agencies.

  The idea of LISA Pathfinder was to test the most challenging aspects of LISA, the ability of the optical sensors to make extremely precise measurement of the location of the floating “test” masses, the drag-free control system, and the micronewton thrusters. The experiment consisted of a satellite with two test masses separated by 38 centimeters that represented a miniaturized version of one of the LISA arms. There is no need for large separations because light propagates the same no matter how far it travels. The test masses were made of gold and platinum, machined as perfect cubes of 4.6 centimeters (about 2 inches) on a side and weighing about 2 kilograms. When the satellite was launched, and while it was en route to its final orbital configuration, the test masses were secured inside their chambers to prevent them from bouncing around. But once the satellite reached its final orbital configuration, roughly 74 days after launch, the test masses were released and allowed to float freely as the spacecraft orbited around the Sun. The satellite had accurate sensors to constantly measure the position of each test mass relative to the walls of its chamber. Two different micronewton thrusters were tested, one a device that emits a minuscule stream of cold gas, the other a device that uses electric fields to accelerate a stream of a few ions (recall the flea on the dog’s tail).

  The eighteen-month mission was launched on 3 December 2015, with the idea of coming close enough to the performance requirements of the full LISA mission that the agency could feel confident that the final goals could be met with subsequent development. Pathfinder succeeded far beyond anybody’s expectations. The sensors were able to measure the relative position and orientation of the test masses to better than a billionth of a centimeter, and the thrusters were able to keep the test masses isolated to this accuracy. LISA Pathfinder actually beat many of the performance goals.

  In fact, Pathfinder’s extraordinary performance was clear within a few months of the launch. Meanwhile, on day 70 of the mission, LIGO announced the first detection of gravitational waves, making gravitational wave astronomy a reality. These two facts led to a dramatic turnaround for LISA’s fortunes. In June 2016, a NASA committee recommended ways that the agency could rejoin LISA as a junior partner with ESA. In August, an assessment of US priorities for all of astronomy and astrophysics recommended that NASA
restore support for LISA, and a month later a NASA official announced to a symposium of LISA scientists that the agency was ready to return. Finally, in June 2017, ESA announced approval of LISA, with the third arm restored, for launch around 2034.

  Figure 9.5 shows what the “final” version of LISA will look like. Three independent spacecraft will orbit the Sun once per year on orbits very similar to the Earth’s orbit. If the initial orbits are chosen in a clever manner and there are no disturbances to the orbit, then a miraculous thing happens: the three spacecraft orbit the Sun in formation, maintaining the rigid triangular arrangement with equal separations, without the need to fire their thrusters. The secret is to start the orbits on a plane that is tilted by 60 degrees relative to the Earth’s orbital plane.

  Figure 9.5 Three LISA spacecraft orbit the Sun in a triangular formation. The plane of the triangle is tilted by 60° relative to the plane of the Earth’s orbit. Laser beams travel in both directions between the spacecraft, separated by about three million kilometers. The array trails the Earth by about 20°.

  To get an idea of how this would work, let’s assume that the Earth’s orbit is perfectly circular (it isn’t quite, but that is a detail that can be added later). At the beginning of the orbit, one spacecraft is below the Earth’s orbital plane, and closer to the Sun (it is at perihelion), while the other two are above the plane, and farther from the Sun. When the three reach the opposite side of the Sun, the orientation is reversed. The spacecraft that was below and inside is now above and outside (it is now at aphelion), while the two that were above and outside are now below and inside (recall the elliptical orbit displayed in Figure 3.1). But they will have exactly the same separation as they had at the start. Figure 9.6 shows that, as the trio orbits the Sun counterclockwise as seen from above, the triangle rotates clockwise within the 60 degree tilted plane, retaining its equilateral triangular shape at all times. No thrusters are needed to achieved this beautiful formation flying. Newton’s theory of gravity (which is a good enough approximation here) does all the work. Probably only a physicist would call such a solution of Newton’s equations “cute,” but we assure you, it is extremely cute.

  Figure 9.6 As the LISA configuration orbits the Sun, the plane of the triangle rotates, and the three spacecraft perform a cartwheel within the plane. This special orbital solution keeps the distance between the spacecraft approximately constant.

  The approved LISA design calls for arms three million kilometers long. In Figure 9.5 we have blown up the triangle by a factor of about forty-five; in reality it would be the size of a tiny speck on that figure (the Sun and the planets are also blown up way out of proportion). On the other hand, the arms will be about eight times the Earth–Moon distance. The array will follow the Earth in its orbit, lagging behind by about 20 degrees. There is nothing magic about that number. It is determined by requiring that the array be far enough from the Earth–Moon system that the gravitational tug of those bodies doesn’t distort the triangle too much, but still close enough that the data can be easily transmitted to Earth. Each spacecraft will have two of everything: two cubic test masses, two lasers and two telescopes. Two laser beams will propagate continuously along each arm, one in each direction. As each beam arrives at each spacecraft, its “timestamp” or phase will be recorded, and these six streams of data will be sent to Earth to be analyzed in search of tiny variations induced by a gravitational wave passing through the array.

  Once LISA launches, it will open our ears to a whole new genre of cosmic music. The ground-based interferometers are sensitive to frequencies between about 10 and 1,000 hertz, or wavelengths between 30,000 and 300 kilometers. Because of the seismic noise wall, lower-frequency waves are inaudible to those devices. By contrast, LISA will be able to hear waves between ten millionths of a hertz and a few tenths of a hertz, or wavelengths between 200 astronomical units (the Earth–Sun distance is one astronomical unit) and a few million kilometers. The spacetime ripples detectable by LISA will undulate with periods ranging from 10 seconds to a day. Just as the transition from astronomy using visible light to astronomy using light in the radio band transformed our view of the universe, so too will the low-frequency gravitational wave band reveal a whole new world of exotic sources.

  What kinds of sources would they be? The prototypical example is the merger of two supermassive black holes. We learned in Chapter 6 that most massive galaxies, including our own, contain a massive black hole in their center. Their masses range from a million to ten billion solar masses. It is also well known that galaxies can collide with each other and merge. This is not a very common occurrence in the present universe, although it is known that our Milky Way and the nearby Andromeda galaxy are speeding toward each other at over 100 kilometers per second. Whether they will actually collide and merge or pass each other by in more of a “strangers in the night” encounter is a subject of current debate. However, earlier in cosmic history galaxies were much closer together, more likely to tug at each other via their mutual gravitational attraction, in spite of the overall universal expansion, and more likely to merge, and this is borne out by observations.

  If each galaxy has a supermassive black hole in its core, then the two black holes, being much more massive than stars, will settle toward the core of the merged galaxy and begin to orbit each other. In fact, astronomers have found a few examples of galaxies that show all the signs of being the product of a merger, and that also have two very small and very bright spots in their cores, each presumably a supermassive black hole with its accompanying accretion disk of hot gas. When the two black holes finally begin their fatal inspiral dance, they will emit spectacularly loud gravitational wave chirps.

  LISA’s “ears” will hear the waves far above the instrument’s intrinsic noise, quite unlike the chirps detected from black hole inspirals by LIGO–Virgo, which required sophisticated filtering of the background noise (see Figure 8.2). LISA will be able to detect these sources from the farthest reaches of the universe, and because gravitational waves travel at the same speed as light, this means that LISA will detect massive mergers from the very early universe. LISA will be able to answer questions such as: did supermassive black holes form at the same time as the earliest galaxies, or did they form much later? To astronomers who study the formation and evolution of galaxies this is a burning question, and conventional astronomical telescopes cannot “see” far enough to answer it.

  Another audible gravitational wave signal is produced when a small black hole or a neutron star falls into a supermassive one. This typically occurs in the dense core of a galaxy when an unfortunate small black hole or neutron star has a close encounter with another body such as a star, and suffers a gravitational “slingshot” that sends it hurtling toward the massive black hole lurking at the center. It would take an incredibly lucky (or unlucky) aim for the body to go straight across the event horizon of the black hole, simply because the black hole is an incredibly small target. The more likely outcome is that the body will come close to the black hole, whirl around it at maybe half the speed of light, zoom outward to a large distance, then fall back toward the hole and whirl around it again and so on. But instead of moving on a nice elliptical orbit, as depicted in Figure 3.1, the body will undergo a very complicated gyrating motion, induced by the strong general relativistic warpage of spacetime near the black hole. Figure 9.7 gives an example of what such a “zoom–whirl” orbit might look like. All the while the orbit will slowly shrink, because of the orbital energy being lost to the gravitational waves being emitted. Because the ratio of the mass of the small black hole or neutron star to that of the supermassive black hole is extremely small, this is called an EMRI, or extreme mass-ratio inspiral. EMRIs produce gravitational waves that are very rich in frequency structure. Close to the black hole, the body’s motion is changing very rapidly, so the waves emitted have high frequencies, while far from the hole, the motion is changing slowly, so the waves have low frequency. If we played these gravitational wave sound
s on a speaker, they would sound like a throttling motorcycle, with the bumps and peaks associated with the many frequencies present in the EMRI orbit.

  Figure 9.7 Zoom–whirl orbit of an extreme mass-ratio inspiral around a spinning black hole. Because of the large pericenter advance and the strong dragging of inertial frames, the orientation of the elliptical orbit undergoes wild gyrations, while at the same time shrinking because of gravitational radiation emission. Credit: Maarten van der Meent.

  A third source of gravitational waves that will become audible with LISA are called “galactic binaries.” These are binary systems of two white dwarf stars, objects that sometimes result from a supernova and are supported from gravitational collapse by a special type of quantum mechanical pressure (see Chapter 2). Recall that these objects have masses that are typically between a tenth and one and a half times the mass of the Sun, but they are much smaller than the Sun in size, with radii of several thousand kilometers. White dwarves in a binary system are still far away from each other, so that the gravitational wave signal is very weak and the inspiral is negligible. This implies that the frequency of the waves stays constant over long periods of time. But for many of them the frequency of the gravitational waves is in the millihertz band, right where LISA is most sensitive.

  Because the waves are weak, we can essentially hear only those white dwarf binaries within our own Milky Way galaxy. About ten such binaries are known from electromagnetic observations, but because white dwarfs are intrinsically dim, these are all in the immediate solar neighborhood. It is not known how many there are altogether in the galaxy but there could be millions (the galaxy contains a trillion stars in total). In addition, there could be neutron star and black hole binaries in wide orbits, emitting no electromagnetic radiation, but sending out detectable gravitational waves. Learning about these populations could teach us a lot about how stars evolve, age and end their lives as one of these compact objects.