It was September 14, 2015, 1.50 a.m. at Hanford in Washington state, US, and 3.50 a.m. at Livingstone in Louisiana state. It was 3:20 p.m. in India. None of us knew that the earth shook. Yes, the earth shook. But it was not an earthquake; it was the ripples in spacetime itself, i.e. gravitational waves, caused by the merger of two black holes some 1.3 billion light years away.

We could not feel the tremor, but thankfully two instruments made for this purpose detected the events. Scientists working with those instruments came to know this, and analysed the data for a few months to learn more about the cause of this ripple. They finally announced the results at a press conference in Washington DC on February 11. Scientists and science enthusiasts all over the world watched the live broadcast over the Internet.

The next day, all media were flooded with the excitement caused by the press conference. What was it all about? Why did this detection cause such a worldwide furore? For that we need to understand the background to the event.

The phenomenon of gravitation is at the heart of this. Simply put, it is what causes the moon to rotate around the earth, and the earth (and other planets) to rotate around the sun. In 1687, Isaac Newton explained these motions with his concept of gravitation. His law of universal gravitation states that any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

This law enabled Newton and his successors to explain lots of natural phenomena. Scientists were happy almost always but there were some unexplained problems. The most famous example is the orbit of Mercury. The elliptical orbit of the planet seemed to rotate (precess) in its plane more than that could be explained by Newtonian laws of gravitation.

In 1861, James Clerk Maxwell unified electricity and magnetism and interpreted light as an electromagnetic wave. Scientists proposed the existence of an invisible medium called the aether to explain the propagation of light as an electromagnetic wave. But experimentalists failed to prove the existence of the aether. The definitive solution came in 1905, when Albert Einstein unified space and time and gave us the concept of four-dimensional spacetime (three dimensions of space, length, width, and height; and one dimension of time) in his theory of “Special Relativity”.

This unification seems to be a natural consequence of two basic postulates; first, the laws of physics are identical in all non-accelerating frames; and the second is that the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or the observer. Special relativity does not need aether for the propagation of light, so one problem was solved. But still the problem with the extra precession of Mercury’s orbit remained. Again, Einstein provided the solution within a decade. In 1915, he proposed the “General Theory of Relativity”. According to this theory, spacetime has a specific geometry. The minimum distance between two points in space at a specific time might not necessarily be a straight line. This implies that spacetime is curved.

Gravitation is just a manifestation of this curvature of spacetime. Any object changes the curvature of spacetime around it, and the more massive it is, the greater the curvature. When an object moves, it just follows the curvature of spacetime. This motion again affects the curvature of spacetime! It is like a loop.

---

The interaction of matter with spacetime is specified by Einstein’s field equation. This general theory of relativity explains the extra precession of the orbit of Mercury. It can also reduce to Newton’s picture when gravitation is very weak and objects move slowly (in comparison with the speed of light). An interesting aspect of this theory (one of many) is that after some algebra, Einstein’s field equation looks like the wave equation. What is this wave? This is the gravitational wave, the topic of almost all scientific discussion since early February.

Now if the object moves or rotates, this curvature also starts changing, i.e., spacetime is disturbed. This results in ripples in spacetime, just as a disturbance in the sea causes a wave. This is the gravitational wave. Like any other wave the gravitational wave carries energy and angular momentum.

Let us now try to understand this gravitational wave from a physical point of view. We have already mentioned that an object changes the curvature of spacetime around it. The spacetime most adjacent to the object is most curved and as we go further from the object, the curvature decreases and eventually vanishes (flat spacetime implies no gravitational effect of the object).

Now if the object moves or rotates, this curvature also starts changing, i.e., spacetime is disturbed. This results in ripples in spacetime, just as a disturbance in the sea causes a wave. This is the gravitational wave. Like any other wave the gravitational wave carries energy and angular momentum.

You might be curious at this point whether every non-static mass distribution creates a gravitational wave. The answer is no. A perfectly spherical object will not create gravitational waves. The mass distribution of the object should be at least quadrupolar and the quadrupole moment (or any higher moment) should have an accelerated time dependence. In simple words, there should be some asymmetry in the mass configuration and some time dependence.

An arm of the LIGO antenna at the observatory in Hanford, Washington.  Photo: Caltech/M.I.T/LIGO Lab

Interestingly, when a spherical object rotates, it does not remain spherical, it becomes oblate because of the centrifugal force. This makes the object emit gravitational waves. When two gravitationally bound objects move around each other, they also emit gravitational waves (this configuration is not spherically symmetric even if each of the objects were perfect spheres).

We know that gravitational waves carry energy. Here this energy would come from the kinetic energy of the binary system resulting in a shrinking of the orbit. As a result, the two objects will come closer and closer, and eventually merge.

The above logic tells us that the earth emits gravitational waves because of its rotation around its own axis (the earth is oblate, right), as well as because of its rotation around the sun. But the amplitude of these gravitational waves is so small that we can simply forget about them.

Now, the question is, what type of objects emit significant quantities of gravitational waves. The answer is gravitationally dense objects like black holes and neutron stars. These two classes are the most and the second-most compact (and strongly gravitating) objects in the universe. What are these objects?

---

Many of us have heard about black holes, and know that a black hole is a region in space at the boundary of which the gravitation (curvature) is so strong that nothing including light is able to escape. There are mainly three types of black holes: (i) mini black holes of masses in the range 10₁₄ kg to 10₂₃ kg and radii in the ranges of 3x10_-11 cm to 3x10_-2 cm. These are believed to have been created in the early universe, so called primordial black holes. Although there is no observational evidence for such tiny black holes, based on theoretical predictions, some scientists believe they do exist and might be part of the mysterious dark matter of the universe.

The second type is a stellar mass black hole, formed by the gravitational collapse of a massive star (more than 25 times the mass of the Sun) after it consumes all its nuclear fuel. These black holes have masses ranging from about five to several tens of solar masses (the mass of the Sun is 10₃₀ kg) and radii ranging from 15 km to around 100 km. In fact, if a black hole is n (n can be any number) times heavier than the Sun, then its radius becomes 3xn km while the radius of the Sun is 7x10₅ km. This relation is valid for black holes of any masses, even for mini black holes for which n is much less than 1.

We know of the existence of several stellar mass black holes, because each of those observed is gravitationally bound to a regular star. The extreme gravitational effect of the black hole is forcing matter from the companion star into the black hole. As the matter moves towards the black hole it heats up to temperatures of several hundred million degrees and radiates X-rays which can be detected by X-ray telescopes.

The third category is super-massive black holes, with masses in the order of 10₆ to 10₉ solar masses. They are found in the centre of almost all massive galaxies (including our Milky Way). The origin of super-massive black holes is not well understood, but there are many theoretical models and lots of research is going on. But the existence of such black holes is well established. Their great mass means a tremendous curvature of space-time around them. It is so great that nearby stars and other massive objects (like stellar-mass black holes, etc) just fall into them as a result.

Again, near the black hole, these objects heat up and start emitting electromagnetic radiations. We call such systems quasars (or under some special circumstances “blazars”).
You have possibly noticed that there is a huge gap between the mass ranges of stellar mass black holes and super-massive black holes. We do not know whether black holes of intermediate masses exist. But some scientists believe they do.

Now let us turn to another significant source of gravitational waves, the neutron star. They are formed by the gravitational collapse of moderately massive stars (having masses approximately in the range of ten to 25 times of the mass of the Sun; stars of lower masses collapse to white dwarfs). When such a massive star consumes all its nuclear fuel (the cause of star-shine), it undergoes a supernova explosion and most of the matter is expelled. Only the central part (the “core”) of the star collapses into a neutron star of mass in the range of 1.1–2 solar masses. During the collapse, atoms of the progenitor stars break down into subatomic particles, become free and then positively charged protons convert to charge- neutral neutrons (in addition to already existing neutrons) by absorbing negatively charged electrons.

---

Neutron stars are very dense objects. Their density can be as high as 10₁₄ gm per cubic centimetre. They are also highly magnetised, their magnetic fields are usually in the range of 10₈ to 10₁₆ Gauss (the strength of refrigerator magnets is around 50 Gauss). Neutron stars spin very fast, rotating up to a few hundred times in a second. Unlike normal visible stars like the sun, there is no nuclear fusion inside neutron stars. Still, they sometimes emit faint electromagnetic radiations because of the residual heat. The significant emission comes from their magnetic fields, combined with the rotation. A neutron star emits collimated electromagnetic beams (like the light from a torch) from its magnetic poles along the magnetic axis.

There is no reason for the magnetic axis to be aligned with the spin axis (even for Earth these two axes are not aligned). Due to the misalignment between these two axes, when a neutron star rotates, the magnetic axis with the electromagnetic beam also rotates around the spin axis. It may happen that once during the rotation, the beam falls on to Earth making it visible for us. This phenomenon is similar to the way you see the light from a lighthouse once in every rotation. That is the reason neutron stars seem to be pulsating and why they are called pulsars.

On the other hand, if the beam never falls to earth, we will not even know about its existence unless the faint emission of the residual heat is detectable. Due to the specific properties of the magnetic field, the wavelength of the electromagnetic emission is generally in the radio wavelength and so we call them “radio pulsars”. Neutron stars can be isolated or in binary (or even in a triple) systems. If the companion of the neutron star is large enough (giant star), then the neutron star can accrete matter from the companion. This accreted matter heats up, causing X-ray emissions when it falls on to the neutron star. Such neutron stars are known as “X-ray pulsars”. When the companion of the neutron star is not a giant (no accretion of matter), the neutron star can still behave as a radio pulsar binary, i.e., a binary radio pulsar.

Based on their rotational properties, pulsars can be classified either as “normal” (or “slow”) pulsars and “millisecond” pulsars (MSPs). Most normal pulsars have periods of between 0.1 and 5 seconds, whereas MSPs have much shorter periods, generally between 2 and 50 milliseconds. It is believed that once upon a time, MSPs were normal pulsars in binaries, and then their companions got bloated during the course of evolution and those pulsars accreted matter (behaved like X-ray pulsars for sometime).

This accretion made those pulsars rotate fast, with periods in the ranges of milliseconds, and when the episode of accretion is over, they still continue to rotate rapidly, this time as radio pulsars. MSPs are very stable. If you record the arrival times of a few pulses from an MSP, you can predict when the next million pulses will arrive. The companion of a binary radio pulsar could be a sun-like normal star, a white dwarf, another neutron star, or even a black hole (although no neutron star-black hole binary is known yet). We already know that a binary system emits gravitational waves, so binary neutron stars as well as binary black holes emit gravitational waves in significant amounts. Now, the question is whether these gravitational waves are detectable, and how.

Interestingly, the first discovered (in 1974) radio pulsar in a binary has another neutron star as a companion. This pulsar is known as the Hulse-Taylor pulsar after the surnames of the discoverers Russel Hulse and Joseph Taylor. When Hulse and Taylor were studying the properties of this pulsar, they found that the orbit was shrinking with time. This could be caused only by the emission of gravitational waves from the binary, as the emitted gravitational waves would carry the orbital energy. Indeed, they found that the observed rate of shrinkage of the orbit matched exactly with the theoretical predictions of the general theory of relativity. So, this proves that gravitational waves exist. Because of this discovery, Hulse and Taylor received the Nobel prize in physics in 1993.
Later, orbital shrinkage due to the emission of gravitational waves have been observed for many other binary radio pulsars. But such detection of gravitational waves is not direct detection. We have to prove that gravitational waves emitted from the binary hit something on Earth.

It is like the optical detection of a new comet (or a star) where light from the comet hits the telescope. So, scientists kept trying to detect gravitational waves in a more direct manner. There is another reason for the insistence upon direct detection. It can tell us many more things about the properties of the source than the information we get through indirect detection (as in the case of binary pulsars), which is somewhat limited.

---

To detect gravitational waves directly, scientists came with a variety of ideas, to build detectors on Earth, to build them in space, to use pulsars as detectors, etc. Every idea is equally important, because different types of detectors are suitable for gravitational waves of different frequencies, and gravitational waves of different frequencies are emitted by different types of sources.

The frequency of gravitational waves is inversely proportional to the linear size of the source, that is, the length of the major axis in case of a binary. The orbit of a binary comprising two super-massive black holes is much larger than the orbit of a binary comprising two stellar mass black holes. Hence gravitational waves will be of much lower frequency in the first case than in the second. The lower the frequency, the larger the wavelength, and to detect a wave of larger wavelength, you need a detector of larger size. But due to technological constraints and the earth’s finite size, it is not possible to build a detector as large as you wish. Hence people thought of space detectors and other alternative approaches.

Our present understanding of the physics tells us that the highest frequency (100 Hz) gravitational waves can be detected by the laser interferometers on Earth and they are the ones that detected the gravitational waves that reached the earth on September 14, 2015.

A laser interferometer consists of two perpendicular “arms” of equal length along which a laser beam, split into two, travels and is reflected by mirrors at each end (to make it travel through the arms multiple times). A passing gravitational wave would cause the mirrors to vibrate, making the arms alternately longer and shorter, one getting longer while the other gets shorter and then vice versa. This change is very small, around 1/10,000th the width of a proton. But because of this change laser beams travelling through the arms travel different distances and they do not remain in phase and create an interference pattern. A scientist’s job is to look for this interference pattern.

As gravitational waves of different strength and frequency would create different interference patterns, one can tell the properties of the source by analysing this interference pattern. There are a few such laser interferometers on Earth, the Laser Interferometer Gravitational-Wave Observatory’ aka LIGO (two separate interferometers in the US), Virgo (Italy), etc. The typical arm length of these detectors is three to four kilometres, as they are aimed at detecting the highest frequency gravitational waves, around 100 Hz. One would need much longer arms to detect gravitational waves of lower frequencies.

The LIGO detectors initially came into operation in 2002 and the Virgo in 2000. None of them detected any signature of gravitational waves in their first few years of operations. So the scientists decided to upgrade them to increase their sensitivities. Virgo is still undergoing upgrades, but is expected to start operations within the next few months. The upgrades to the two LIGO detectors were finished last year, and advanced LIGO detectors then became operational.

One of the two LIGO detectors in the US is at Hanford in Washington and the other at Livingstone in Louisiana. These detectors recorded the same interference pattern on September 14, 2015, proving that gravitational waves passed through Earth that day. Analysing the interference pattern, scientists understood that the source of this wave was the late stage of inspiral and merger of two black holes. One of them was almost 29 times the mass of the Sun and the other was 36 times more massive.

These two black holes merged to give one single black hole of a mass 62 times that of the Sun. Notice that the mass of the final black hole is less than we get if we simply add the masses of the two black holes. Where did this extra mass equivalent to three suns go? It was converted into gravitational energy, exactly obeying Einstein’s now immortal equation E=mc₂. This energy was carried away by gravitational waves. The data also led scientists to conclude that the final, merged black hole is rotating with a moderately high spin.

The data also told them that the site of this merger is 1.3 billion light years away. One light year is the distance traveled by light in one year, i.e., almost 10₁₃ km. This also means that the gravitational waves which passed the earth on September 14, 2015, started their journey from the source 1.3 billion years ago (as gravitational waves also travel at the speed of light).

---

In summary, this discovery is exciting in many aspects, but we need to get rid of some common misconceptions. It is not the first proof of the general theory of relativity. It has been proved right already by many experiments, although this discovery agrees with the predictions of the general theory of relativity. Moreover, this discovery is not the first proof of the existence of gravitational waves, their existence having been proved by the shrinkage of the orbits of binary pulsars.

Nevertheless, this discovery is of tremendous significance. It is the first direct detection of gravitational waves, the first evidence of a binary containing two stellar mass black holes, the first evidence of a merger of two black holes, and the first evidence of stellar mass black holes greater than 20 solar masses. It is also the first observed case of a “Kerr black hole” (a rotating black hole). At a human level it is proof of technology that can measure infinitesimal changes in length with laser interferometry. So the excitement is justified.

Ligo Hafors laser equipment.  Photo: Caltech/M.I.T/LIGO Lab

Although the event was recorded on September 14, 2015, scientists took a few months to analyse the data. The final results were declared at a huge press conference in Washington DC on 11th February, 2016. This discovery is also an excellent example of how difficult problems in science should be approached; experimentalists and theorists should join hands beyond any barrier of countries or continents. Scientists from every corner of the globe were involved in this project, more than a thousand people from 15 countries (the US, Brazil, Germany, Netherlands, Poland, France, Germany, Italy, Russia, Spain, Japan, China, Korea, Australia, India). The participation of women scientists in this project was noticeable. The Indian contribution is also worth noting. Some 37 Indian scientists were (and still are) involved in this project. Also, there is a plan to construct another similar interferometer in India. Increased number of detectors (and improved technology over time) will enable people to discover more events of gravitational waves and shed more light into the properties of gravitational wave emitting sources.

Now even if we are all excited about the first direct detection of gravitational waves by the laser interferometers constructed on the Earth, we should not forget the fact that this is not the only way to detect gravitational waves directly (look at the figure again). Any binary system with the total mass in the range of 10₆ to 10₉ solar masses (e.g. a binary comprising a supermassive and a stellar mass black hole) will emit gravitational waves of frequencies around 10_-4 Hz, and to detect that one will need much longer interferometer arms. It is impossible to build such a long interferometer not only due to technological issues, but also because of the finite size of earth.

So scientists came up with the idea of a space interferometer, called LISA (Laser Interferometer Space Antenna) or recently modified eLISA (Evolved Laser Interferometer Space Antenna). eLISA will be a collection of three spacecraft, arranged in an equilateral triangle of 1 million kilometre long arms (original LISA design was for 5 million km long arms). These spacecraft will be placed in an orbit around the sun and the specific configuration will be maintained and scientists will look for interference patterns bearing the signature of any passing gravitational waves.

We routinely launch satellites in earth orbit, but here we need to put spacecraft orbiting the Sun as well as maintain the equilateral triangle configuration. A small test mission called “LISA Pathfinder” was launched on December 3, 2015, to test some of the basic technological aspects needed for eLISA which has a launch date of 2034.

Supermassive black holes in binaries emit gravitational waves of frequencies around 10-8 Hz. The existence of some super-massive black holes in binaries is known. One example is PKS 1302102 which is located in the Virgo constellation around 3.5 billion light years away.

---

The best way to detect gravitational waves in this frequency range is to use pulsars. As we have seen, millisecond pulsars (MSPs) are extremely stable. If we measure arrival times of hundred pulses from a particular pulsar, we can predict the arrival of the next thousands of pulses. But if you see that the pulses are not arriving at the expected times what would you suspect? One obvious cause might be the passing of gravitational waves, changing the distance between Earth and the pulsar, causing the signal to take more or less time to reach Earth.

But you cannot be sure. It is possible that over such a long period of time, the properties of the pulsar have changed a bit, so it is emitting at slightly different times. But if you have a number of pulsars and you see all of them showing deviations from the expected pulse arrival times? It is too unlikely that the properties of all of them have changed concurrently. So there would be reason to blame the passage of gravitational waves for the phenomenon.

Moreover, scientists know from theoretical calculations how these deviations from expected pulse arrival times for one pulsar would differ from another because of a passing gravitational wave if we know the separation between the pulsars in the sky. You can detect gravitational waves by monitoring a number of pulsars; this is the concept of pulsar timing array. You have an array of pulsars and you are timing them, i.e. recording pulses over time with the aim to find correlated deviations from expected pulse arrival times, hence the name. The sensitivity of this method would increase with the increase of the number of pulsars you monitor, as well as a wide range of angular separation between them. But different celestial objects are visible from different locations on Earth. So you need international collaboration to increase the sensitivity of the pulsar timing array.

At present there are three groups of scientists hunting for gravitational waves using the concept of pulsar timing array. The first is the Australian group “Parkes Pulsar Timing Array” (PPTA), named after the radio telescope (Parkes) they are using. The second is the European Pulsar Timing Array (EPTA), and the third is the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). These three groups together are called the ‘International Pulsar Timing Array’ (IPTA), as they work in harmony, discussing together, sharing data, etc. Very recently, a few Indian scientists have also started to monitor a few pulsars with the same goal, which we can recognise as a first step to the “Indian Pulsar Timing Array” (InPTA), and it might become a part of IPTA very soon. If IPTA works out, it will improve our knowledge not only of gravitational waves in this frequency range, but also the astrophysics of the sources causing such gravitational waves.

The lowest frequency (around 10_-16 Hz) “primordial” gravitational waves, which bear the signature of very early universe aged even less than 10_-32 seconds can be detected through the polarisation map of the cosmic microwave background. Cosmic microwave background (CMB) is an almost uniform thermal energy coming from all parts of the sky, and it is actually the leftover heat from the quantum fluctuation (“inflation”) of the very early universe. In 2014, it was claimed that an experiment called “BICEP2” had detected such primordial gravitational waves. But later it was found that there was some mistake in interpreting the data, that the experiment actually did not detect any gravitational waves. But we should not lose hope, improved experiments in this area are ongoing and we can hope that one day, scientists will be able to see the signature of the primordial gravitational waves. This will improve our understanding of the early evolutionary history of the universe.

The September 15, 2015 event is just the tip of the iceberg, so to speak. A new generation of detectors, as well as other approaches like the pulsar timing array will lead to discoveries of more gravitational wave emitting events, and will improve our understanding of the numbers and properties of such sources in the universe, especially because there are many objects or systems which cannot be seen in the electromagnetic waves but can be “seen” in the gravitational waves (examples include the binary comprising two stellar mass black holes).

In the case of mergers of two neutron stars, the stars get disrupted just before the merger. The properties of this disruption event depend on the internal structure of the neutron star. As the emitted gravitational waves bear the signature of this disruption, it eventually reveals information about the internal structure of the neutron star. Electromagnetic waves (pulsar beams) do not provide such internal information (although indirect and complicated studies reveal some amount of information). Moreover, the detection of primordial gravitational waves would lead to refined knowledge about the early stage of our universe. It is an area of research that has an extremely bright future. The work indeed is just beginning.