Gravitational waves

Ripples from the past

Print edition : March 18, 2016

Two black holes merge into one. The collision of two black holes holes is seen in this computer simulation. LIGO detected gravitational waves, or ripples in space and time generated as the black holes spiralled in toward each other, collided, and merged 1.3 billion years ago. This simulation shows how the merger would appear to our eyes if we could somehow travel in a spaceship for a closer look. Photo: The SXS project (http://www.black-holes.org)

Figure 1: How our Sun and Earth warp space-time is represented here with a green grid. According to Albert Einstein's General Theory of relativity, the gravity of massive bodies warps the fabric of space-time and those bodies move along paths determined by this geometry. Photo: T. Pyle/Caltech/MIT/LIGO Lab

A map of the sky, from the earth's perspective, showing the probable locations of the binary black hole merger. Photo: Shane Larson, Northwestern University

Figure 2: These plots show the signals of gravitational waves detected by the twin LIGO observatories at Livingston and Hanford.

Figure 3: Comparison of the reconstructed wave strain with the predictions of the best-matching waveform computed numerically from general relativity over the three stages of the event: in-spiral, merger and ringdown. Also shown are the separation (in units of about 200 km, the Schwarzschild Radius of the binary system) and velocity of the black holes (in units of c, the velocity of light.) The plot shows the black holes were within a few hundred km before merging and were moving towards each other at significant fractions of the velocity of light.

Fig. 3. A schematic depiction of LIGO's interferometric gravitational wave detector. Light from a laser is split in two by a beam splitter; one half travels down the vertical arm of the interferometer, the other half travels down the horizontal arm. The detector is designed so that in the absence of gravitational waves (top left) the light takes the same time to travel back and forth along the two arms and interferes destructively at the photodetector, producing no signal. As the wave passes the travel times for the lasers change, and a signal appears in the photodetector. (The actual distortions are extremely small, but are exaggerated here for easier viewing.) Inset: The elongations in a ring of particles show the effects of a gravitational wave on spacetime. Photo: Alan Stonebraker/American Physical Society

The first detection of the sounds of the cosmos may be the harbinger of more such signals, which may tell us new things about the universe.

WHAT appears as a serene, calm and awe-inspiring sky to a stargazer should be extremely noisy with a cacophony of vibrations arising from violent and cataclysmic events occurring every now and then in different parts of the cosmos. This is what the equations of Albert Einstein’s general theory of relativity (GTR), which governs the way objects in the universe interact and move under the force of gravitation, tell us. The universe appears silent because we cannot hear these “noises”. Craig Hogan wrote in American Scientist in 2006: “The universe is a musical that we have been watching all this time as a silent movie.”

The movie of the universe entered the “sound era” on September 14, 2015, when the effect of the violent vibrations from the collision and merging of two massive black holes about 1.3 billion years ago arrived on the earth as a faint “chirp”, lasting a mere 200 milliseconds, and the signal was successfully picked up by the large and the most precise instruments in the world. This marked the triumph of decades of scientific and technological efforts to listen to these sounds of the cosmos whose existence Einstein had predicted exactly 100 years ago.

According to Einstein’s special theory of relativity (STR), which he formulated in 1905, space and time form a four-dimensional continuum, and no signal can travel faster than the speed of light. Ten years later he formulated the GTR, which viewed gravitation as nothing but the geometry of space-time itself, and this geometry is determined by the configuration of objects and the manner in which they move about on this space-time structure. This perspective of space, time, and the universe is far removed from the earlier Newtonian concept of gravitation as a force acting instantaneously over large distances in a background of stationary, and separate, space and time domains.

The presence of a mass, according to the GTR, warps the fabric of space-time in its neighbourhood just as a ball does when placed on a canvas—the larger the mass, the greater the warp (Figure 1). The curvature of the warp determines its gravitational force, and other objects under its influence move along paths determined by this warped space-time geometry. So when large masses move about, or rapidly accelerate, the disturbance causes distortions in this warped space-time.

Within a few months of arriving at the equations of the GTR, Einstein had realised that the equations implied the existence of gravitational waves (GWs). Just as Maxwell’s equations of electromagnetism imply that moving electric charges will generate electromagnetic waves, the equations of the GTR predicted the existence of gravitational waves when massive bodies move through space and time.

Unlike electromagnetic waves (light), GWs do not travel through space; the fabric of space-time itself is oscillating in response to the disturbances caused by moving masses. The slight distortion in one region distorts nearby regions, and so on. Thus, in Einstein’s theory, space-time is a dynamic entity and GWs are ripples in space-time, much like the ripples of water created in the  wake of a moving boat. But these are travelling distortions of space-time geometry itself, which propagate outward from the sources of disturbances at the speed of light carrying with them information about their sources and clues about the nature of gravity itself. It is the finiteness of the speed of any signal that is intimately connected with the existence of GWs. In Newton’s theory, therefore, there are no GWs.

Quest for evidence

Although Einstein began to have doubts about the existence of these waves 20 years after he had formulated the theory, and even wrote a paper with Nathan Rosen arguing for their non-existence (which is an interesting episode in itself), the analogy with the electromagnetic field was so compelling that other scientists strongly believed that these waves must exist. And, for the last five decades, since Joseph Weber’s first experiments in the 1960s, scientists have been looking for the evidence of GWs.

Indirect evidence for these has been around since Russel Hulse and Joseph Taylor found that in a binary pulsar, a twin pulsating neutron star system where the two neutron stars orbit a common centre of mass, they discovered in 1974, the orbital period decreased progressively over time.

Einstein’s equations predicted that such a tightly paired system of massive stars would emit GWs and, owing to the loss of orbital energy carried away by GWs, their orbits would progressively shrink. The observations of the orbital period of the Hulse-Taylor binary pulsar (called PSR 1913+16) over nearly a decade perfectly matched the results from Einstein’s equations. Hulse and Taylor won the 1993 Nobel Prize for the discovery of the first binary pulsar and its analysis. Binary pulsars like the Hulse-Taylor system are today one of the major testing grounds for the GTR.

But direct detection of GWs had proved extremely difficult as the gravitational force is inherently weak, so waves generated by the movement of planets and sun-like stars, and even the movement of huge masses on the earth itself, would be too feeble to be detected. It requires rapid acceleration of extremely large masses on the cosmic scale ending in powerful cataclysmic events, such as supernova explosions and collisions of compact gravitational systems such as coalescing binary neutron stars or black holes, which spew out enormous amounts of gravitational energy, to produce waves that one can expect to detect on the earth.

Even then, since most such systems are very distant, while the space-time in the vicinity of the event would experience violent shaking, GWs from that would become extremely faint by the time they reach the earth. Detection of these required enormous advances in precision technology to achieve instrument sensitivity enough to detect space-time distortions on the earth as tiny as 10 -18 m (billionth of a billionth of a metre), which is a thousandth of proton diameter, and less.

The September 14 event marks the first direct detection of these elusive waves, a remarkable achievement indeed. It should truly rank as the discovery of the century and eminently qualifies for a Nobel Prize. Beginning with the classical tests that Einstein himself suggested, such as deflection of light by the sun, precession of the perihelion of Mercury and gravitational red shift of light, there have been several other tests of the GTR like gravitational lensing and decaying orbital period of binary pulsars. Einstein has come out with flying colours in all these tests. Direct detection of GWs was one prediction of the GTR that remained unverified for 100 years. With its detection now, Einstein has been proved right yet again. The great physicist Max Born had described the GTR as “the greatest feat of human thinking about nature”.

Gravitational waves were detected by the upgraded version of the Laser Interferometer Gravitational-wave Observatory (LIGO), U.S. LIGO, operated by Caltech and the Massachusetts Institute of Technology (MIT), is a system of two laser Michelson interferometers (see article by Stanley Whitcomb), located at Hanford, Washington, and Livingston, Louisiana. From a careful analysis of the nature of the waves, scientists have concluded that the gravitational-wave signal of September 14, 2015, now christened GW150914, was generated by the violent merging of the two massive black holes in a binary system 1.3 billion years ago somewhere along the direction of the Magellanic Cloud galaxy in the southern hemisphere.

The two black holes, weighing respectively 36 and 29 times the solar mass and compacted in a region of about 150 kilometres, moved towards each other picking up speed perhaps over millions of years as their orbits continuously shrank and, towards the end of this runaway in-spiralling, they were moving at nearly half the speed of light, before they finally coalesced to end up as a single massive black hole of 62 solar masses. The end moments of the merger and settling down of the final black hole  occurred in just 0.2 seconds, with the missing three solar masses being radiated away as GWs.

That is an enormous amount of energy to be radiated away within less than the twinkle of an eye. It has been estimated that the total power radiated as gravitational waves was 10 49 watts (1 followed by 49 zeroes), which is about 50 times the combined light power from all the stars and galaxies in the observable universe (see article by P. Ajith and K.G. Arun). And yet, by the time it arrived on the earth, it was the faintest of whispers. The amount of strain (length change/original length) that this whisper caused the kilometre-long LIGO interferometer was a puny 10 -21. The remarkable achievement is that advances in science (to which Indian scientists have contributed significantly) and technology has enabled this minutest of displacements to be picked up and measured.

Two breakthroughs

There are actually two breakthroughs in the current discovery, both verifying predictions of Einstein’s GTR: one, the direct detection of GWs itself, and two, the first ever observation of a collision and merger of a binary black hole system. The first, in fact, opens up an entirely new window to the universe—gravitational astronomy—that will provide instances to test the GTR more stringently under extreme conditions of strong gravitation. As regards the second, Karl Schwarzschild showed in 1916 that Einstein’s equations predicted the existence of black holes—strange objects that are so dense that even light, trapped by their intense gravitational fields, cannot escape from them.

Theoretical studies suggested that black holes are stable and that they could be indirectly observed. Indeed, while black holes cannot be observed directly, their existence has been inferred from their various effects on their immediate vicinity. One of the earliest studies in this direction was that by the Indian physicist C.V. Visveshwara (see article by P. Ajith and K.G. Arun) who, in 1970, showed that when GWs scatter off a black hole, the tail of the scattered wave would have a characteristic pattern. Theoretical modelling of binary black hole systems and computer simulations of their in-spiralling and merging based on Einstein’s equations have enabled scientists to construct precise waveforms of the GWs emitted by merging black holes, including the tail, called ringdown, as the final black hole settles down, which is quite like what Visveshwara had predicted. Matching the waveform in this direct observation of GW150914 had the unambiguous mark of a binary black hole merger as the GTR would have it, thus proving Einstein in this detailed aspect as well.

While guarded rumours had begun to float over the Internet about this historic moment in November 2015 itself, the 1,000-odd scientists from 16 countries associated with the discovery, called the LIGO Scientific Collaboration (LSC), kept it under wraps until February 11 when David Reitze, the LIGO Executive Director, made the earth-shaking announcement in Washington: “We did it. We have detected gravitational waves.” The finding has been published in the journal, Physical Review Letters, and the authorship includes 35 scientists from Indian institutions who are part of the LSC.

It took five months for LSC scientists to pore over the data to ensure that what they detected was: (1) a true signal that significantly stood out from the background instrumental and environmental noise with a good signal-to-noise ratio; and (2) indeed a gravitational wave and not an artefact due to some local seismic vibration or some spurious signal mimicking a gravitational wave. If it was a gravitational wave from an astrophysical event, what kind was it? That required correlating the signal (using the “matched-filtering” technique developed by Sanjeev Dhurandhar, B.S. Sathyaprakash and others at the Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune, with hundreds of waveform templates that have been constructed in the last couple of decades for typical astrophysical events that can produce detectable GWs, like compact binary systems (to which Bala Iyer’s team at the Raman Research Institute, Bengaluru, has contributed). Once the nature of the source is identified, it had to be localised in the sky. Lastly, the source and the event had to be characterised in terms of physical parameters (to which P. Ajith, K.G. Arun and others have contributed).

How does LIGO detect GWs? LIGO is the world’s largest GW observatory and the most sensitive instrument ever built. It comprises two identical but differently oriented giant L-shaped laser interferometers located about 3,000 km apart, one in Hanford, Washington, and the other at Livingston, Louisiana. Detection of a clear signal above the background at both the instruments, with the calculated time delay of the time taken by light (or gravitational wave) to travel that distance, ensures that the detected signal by the two detectors is the same, and not an artefact.

Each of the arms of the L of the interferometers is a 4-km tube in which laser beams bounce back and forth between two highly sensitive suspended mirrors to improve its sensitivity several orders of magnitude over the simple Michelson interferometer that one learns about in college (see article by Stanley Whitcomb). The laser beams are tuned to be perfectly 180 o out of step (in opposite phase) so that there is total interference—hence the name interferometer—when the beams arrive at the intersection of the arms, and no light passes through the beam splitter at the intersection into the photodetector behind. But, when a GW passes through the detector, the space-time gets distorted in the directions perpendicular to its direction of propagation, oscillating between the two states of being compressed in along one arm and elongated in the other, and vice versa, much like a squeezed ball. So the effect of this oscillatory compression and elongation of the arms is that there is no longer total interference of laser beams at the intersection of the arms, and a net signal gets through the beam splitter to the photodetector (Figure 4).

LIGO was completed in early 2000 and the twin interferometers began taking data in 2002 in joint observations with other detectors—TAMA300 in Japan, GEO600 in Germany and Virgo in Italy. However, between 2002 and 2011, LIGO did not detect any signal indicating a GW. After major upgrades to improve its sensitivity by a factor of 10, and thus enabling it to measure as tiny a stretch as 10 -18 m in its kilometre-long arms, Advanced LIGO (a-LIGO) began operating in September 2015. The first scientific run with a-LIGO was scheduled to begin on September 18, 2015, but days before that, on September 14, 2015, even as the interferometers were being put through final tests and the instrument was only three to five times better than the initial LIGO, it could pick up GWs.

The instrument could still detect the signal because it was much stronger than what scientists had anticipated in a-LIGO’s initial scientific runs. Also, the instrumental noise, which depends on the frequency, happens to be the lowest around the frequency range of a few hundred hertz, exactly where frequencies of GWs from compact binary systems lie. But more significantly, scientists were hoping to see a binary neutron star system rather than a binary black hole. While this undoubtedly indicates a fortuitous occurrence, it also suggests that binary black hole systems may be lurking in greater numbers than estimates.

On September 14, 2015, at 09:50:45 UTC, both the Hanford and Livingston interferometers detected a signal that was identical, and with a significant signal-to-noise ratio of about 24, but relatively shifted by seven milliseconds corresponding precisely to the calculated time delay between the two stations (Figure 2). As Gabriela Gonzalez, the chief spokesperson of the LIGO at Livingston, said at the February 11 announcement, “The coincidence is remarkable.” The total signal lasted for about 0.2 second.

The signal was identified by what is called low-latency search, which analyses the signal data promptly and looks for GW-like pattern but without modelling the precise details of the waveform. In fact, according to the LSC team, this method picked the candidate event within three minutes of receiving the signal at the detectors. The waveform of the detected wave was then compared with the huge bank of theoretically predicted patterns of GWs from possible astrophysical sources—the “matched-filtering” technique mentioned earlier—to find which waveform matched the data best.

Details of the analysis

Figure 3 shows the details of this analysis, which unmistakably point to GW150914 having been produced by a binary black hole merger. There is remarkable agreement between the waveform computed by methods of numerical relativity and the actual signal detected by the Hanford interferometer.

The frequency of the waveform rapidly increases at different stages of the coalescence—the black holes approaching each other (the “in-spiral”), the black holes joining together (the “merger”), and the newly formed black hole finally settling down after brief oscillation (the “ringdown”). The frequency of the received signal increased sharply from about 35 Hz to 150 Hz in a matter of 0.2 second. But how do we know that these objects are indeed black holes? While waveform simulations point to the objects being black holes, even empirically speaking, their physical parameters imply that they must be black holes.

The estimates of the pre-merger and post-merger masses as well as their enormous velocity and separation of just a few hundred kilometres before they merged (Figure 3, bottom panel), and the frequency of the GW at the time of merging, are all strongly suggestive of a binary black hole merger. According to theory, only black holes can get so close to each other without merging and also neutron star binary or neutron star-black hole binary would produce a wave of a frequency lower than 150 Hz at the time of merging.

The specific physical characteristics of the binary black hole system that produced GW150914 were also estimated from the wave data. As mentioned before, the pre-merger stage involved two black holes with 36 and 29 solar masses and the post-merger single black hole was 62 times more massive than the sun. This implies that three times the mass of the sun (6 x 10 30 kg or six million trillion trillion kilograms) was converted into GWs, most of which being emitted within a fraction of a second. In comparison, the sun burns just two billionths of one trillionth of its mass into electromagnetic radiation every second. Furthermore, all the black holes were rotating black holes, known as Kerr black holes after the mathematician Roy Kerr, who in 1963 predicted their existence, with the final black hole achieving about two-thirds of the spin value that Einstein’s theory maximally allows (see article by P. Ajith and K.G. Arun).

Also, the event did not produce any accompanying electromagnetic waves as follow-up observations by several observational astronomy groups across the world, who are part of the LSC, did not see any electromagnetic signal from the inferred direction of the source, which would be the case only with black hole merger events.

Finally, to be sure that GW150914 was indeed a real GW event, the LSC team carried out a detailed statistical analysis with 16 days of stable, high-quality detector strain data from the month following the event. GW150914 was found to be much stronger than any stray signal that the detector’s random strain data showed. The detailed analysis of the data from both the Hanford and Livingston detectors gave a false alarm rate—how often a random noise fluctuation could mimic GW150914—of less than 2 x 10 -7 (less than a one-in-20 million chance). That is, such a false alarm would be extremely rare, occurring once in 203,000 years of such data. This translates in technical parlance to a statistical significance of 5.1 sigma; a significance of more than 5 sigma is regarded as a real event, and not a chance event.

Pinpointing the source

Another important astronomical issue to resolve is the source of GW150914. With just two instruments in Washington and Louisiana, the source could be pinpointed only to within a large patch of about 600 square degrees in the southern hemisphere; a crescent-like region of about 60 degrees x 10 degrees across. The moon subtends an angle of 0.5 o on the earth, that is, a 0.25 square degree region in the sky. So, the uncertainty in the localisation was a region as wide as about 2,500 moons stacked together, an area as large as many stellar surveys cover. For astronomical identification of the source, that is indeed a very large uncertainty and astronomers would like to do better by at least an order of magnitude.

Localisation of a source is done by the technique of triangulation using a network of detectors. The technique uses the time delay in the arrival of a signal at the two ends of a baseline formed by any two detectors in the network, and the accuracy of this technique increases with more baselines as well as longer baselines between any two instruments in the network. With only one baseline between Hanford and Louisiana, with just a 7-10 milliseconds delay in the arrival of a signal with the velocity of light, the level of uncertainty is clearly huge.

According to Tarun Souradeep of the IUCAA, the spokesperson for the Indian Initiative in Gravitational-wave Observations (IndIGO) Consortium, if the interferometer Virgo at Pisa had been operational on Septem ber 14, 2015, the time delay would have been about 22 ms, and the localisation accuracy would have improved to a smaller 200 square degree window. More interestingly, if an operational LIGO-India existed, the time delay between LIGO and India would have been much greater, about 36-39 ms, which would have narrowed down the localisation to a small 5-10 square degree patch in the sky, which is nearly a factor of hundred better.

Therein lies the importance of a LIGO-like instrument in this part of the world, and a proposal by the IndIGO Consortium for constructing a replica of Advanced LIGO in India has been awaiting the government’s approval since 2011. But the detection of GW150914 had the salutary effect of prompting Prime Minister Narendra Modi to tweet his approval for an advanced Indian interferometer and the Union Cabinet giving an in-principle nod for setting up LIGO-India (see articles by Abhay Ashtekar and by Bala Iyer & Tarun Souradeep).

Hopefully, the approval by the Cabinet is quickly followed up by financial sanction and other clearances so that the instrument becomes operational by 2022 as planned and becomes part of the global network of detectors as envisaged by the Gravitational Wave International Committee (GWIC).

This becomes all the more important with an entirely new paradigm of doing astronomy with GWs opening up. The discovery itself has already thrown up interesting questions.

Firstly, as mentioned earlier, the cosmos may be harbouring a greater number of black hole binaries than thought earlier. Further, it is rather unusual that black holes of about 30-35 and even 60 solar masses exist. From a stellar evolution perspective, you would expect black holes to be only a few to about 10-15 solar masses.

What are the kinds of stars that leave behind “stellar black holes” with tens of solar masses? Will more such objects show up as GW astronomy evolves? Quite likely. After GW150914, the estimate for the rate of detection of such objects has increased to one a year. Already, another signal received around the same time is currently being investigated by the LSC team.

More such objects, and others that are entirely unexpected, may reveal themselves through their gravitational wave emissions, telling us new things about the universe. The discovery has thus now tuned our ears to an entirely new and unfamiliar symphony of the universe.

In fact, GWs from compact binary systems span the audible frequency range, and one can actually hear the “chirp” or “hoot” merger and “ringdown” in GW150914 if the waveform is converted into sound waves and played through a speaker. With the new window of GW astronomy opening up, we can expect to hear more chirps and hoots from the seemingly calm heavens above.

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