LIGO detection of Gravitational waves

 Listening to the Sound of Light and the Sound of Gravitational waves with Laser

        S. N. Thakur, Ex-Professor of Physics, Banaras Hindu University, India

1. Introduction

I was in California when the 2017  Nobel Prize in Physics was announced and I could access through the internet a number of video discussions and specialized lectures in addition to scientific articles by the leading scientists directly involved in the Laser Interferometer Gravitational-wave Observatory (LIGO) that revealed the gravitational waves, originating from the collision and merging together of two black holes located at 1.3 billion light years from Earth. This experimental observation aroused the same kind of thoughts in my mind as I had experienced six decades ago when I came to know about gravity and the solar system. I had learnt that in 1589 Galileo had carried out experiments on objects of different masses falling at the same rate from the leaning tower of Pisa and had later seen the planets of the solar system with his telescope. I had also learnt that Newton had discovered  gravity when he saw a falling apple while thinking about the motion of the moon around the earth and those of planets of the solar system around the Sun (Fig.1). 

Fig.1 Illustrations of Galileo with the leaning tower of Pisa and with his telescope (in the middle) and the story of Newton’s falling apple revelation. 

Left:  ourplnt.com/wp-content/uploads/2015/07/Galileo-Pisa-Experiment-Luigi-Catani.jpg

i.pinimg.com/736x/ed/b6/17/edb6173603958fd45db2a5844cf0e9ae--high-school-google-images.jpg  Right: http://4rsolutions.net/wp-content/uploads/2015/05/SirIsaacNewton.jpg 

Newton formulated the law of universal gravitation but did not explain the origin of gravity which pervades the universe. Although the word  ‘gravity’ was used in a qualitative sense before Newton, he was the first to recognize the force of gravity and gave it a quantitative meaning through his law of universal gravitation. Gravitational   force is extremely small compared to electric or magnetic forces. Thus the gravitational force between the electron and proton in a hydrogen atom is 10-40 times smaller than the electrical force between them. One of the major problems with Newtonian theory was the instantaneous gravitational interaction between two astronomical objects separated by vast space. Special Relativity requires that no signal can propagate in space faster than light and, in 1916 Albert Einstein came up with a geometrical origin for the gravitational force in his  general theory of relativity. In this description what we perceive as force of gravity, in fact arises from the curvature of spacetime. In a layman’s language, matter tells space to curve according to its mass, and curved space tells matter how to move in the curved space.      

Spacetime is a mathematical model that joins space and time into a single idea of a four dimensional continuum called Minkowski space. Many people attribute spacetime to Einstein, who proposed Special Relativity in 1905 but it was his teacher Hermann Minkowski, who suggested spacetime in 1908 [1]. Minkowski spacetime is only accurate in describing the constant velocity of moving systems and it was Einstein who generalized  spacetime to include the effects of acceleration. Using his theory of General Relativity, Einstein found that the curvature of the 4-dimensional spacetime representation was actually the cause of gravity [2]. It was found that wherever matter exists, it bends the geometry of spacetime and this curved shape of spacetime gives rise to gravity. The geometrical trap thus created in the spacetime  fabric by the very large mass of Sun traps, in its gravitational field,  relatively lighter-mass planets to form the solar system. An artist's concept of this geometrical distortion, in the space-time fabric, caused by the earth is shown in Fig.2(a) trapping a satellite  or moon around it. This geometrical description brings to my mind Fig. 2(b) of floods in river Ganga, the like of which in 1948 had submerged  fields around my village creating whirlpools and causing  deaths of many livestock trapped in it. As we will see later in this article, gravitational waves are caused by violent events in space where the gravity associated with two black holes or two neutron neutron stars coming together, creates havoc of the same kind in the universe as the flood in Ganga does in the flat fields of north India

 (a)    (b)

Fig. 2 (a) Artist’s depiction of earth's gravitational field by distortion of the space-time fabric and (b) Image of whirlpool made by the flooded river Ganga.

Gravitational waves are created by formation of massive black holes in violent astronomical events (see Figs. 3a and 3b) but they are very weak and Einstein, himself, didn't believe that they could be detected on  Earth. During one of the discussion sessions, in the World Science Festival, when Professor Rainer Weiss was asked about his reaction to the LIGO detection of 14 September 2015, he said, “It was too good to believe.” He further elaborated that the gravitational waveform signal was so strong and matched so closely with the theoretical prediction that it raised some doubts and it took a period of 4 months, to check thousands of ports in the huge LIGO machine before it was established that no error was involved. It is important to note that LIGO’s two L-shaped interferometers (one at Hanford, and the other at Livingston) are aligned ‘back to back’ pointing away from each other to enhance the sensitivity, and exactly same waveforms were detected at the two sites separated by 3000 kilometers as shown in Fig.4 [3]. Professor Weiss, who has been working on LIGO since 1972, said that they were looking for signals from neutron stars and it was a pleasant surprise that the very first signal they received was from a pair of colliding black holes. It is remarkable that the gravitational waves were travelling for 1.3 billion light years and happened to pass through the earth just when the advanced LIGO, 10 times more sensitive than the initial LIGO, was made operational after enhancement in its detection sensitivity. In this discovery, the contribution of theoreticians is immense, who perfected the technique of simulating gravitational interaction between two approaching black holes. In the present case one of the colliding black holes was 36 times as massive as the sun, the other 29 and the newly formed black hole was of 62 solar mass. Thus 3 solar masses were converted into gravitational radiation giving rise to the gravity wave detected by LIGO 1.3 billion years after their creation.

                                                         

  (a)

  (b)

Fig. 3(a) Theoretical models of black holes and 3(b) Scenes from floods in river Ganga  

Fig.4 Gravitational wave induced strain signal in LIGO at Hanford (top left) and that detected 6.9 ms earlier at Livingston (top right). The second row exhibits noise free waveform of the corresponding signals and the last row represents noise. Variation in the amplitude and frequency during the period of observation (0.2 sec) is shown at the bottom which can be converted into a chirping sound. 

Professor Weiss also said that the LIGO group had carried out calculations for a variety of binary neutron systems in anticipation of detecting gravitational waves emanating from their merger, in addition to that for closely moving black holes. The waveform templates of gravitational waves from these calculations were used in the analysis of the observed signals. Although there was no prior knowledge of gravitational waves originating from the merger of two black holes, the 1993 Nobel prize in physics was awarded for indirect evidence about them. Hulse and Taylor discovered  a binary system of a pulsar and a neutron star, and found that the distance between them was shrinking over a period of time, which was interpreted as release of energy in the form of gravitational waves [4]. This was a very convincing example of emission of gravitational radiation as indicated in Fig.5

                                                                         

Fig.5 Artist’s concept of a binary neutron star system where each star is spiralling closer to its companion (left) and decrease in the orbital period, in agreement with Einstein’s theory of general relativity. of the pulsar in the binary system observed by Taylor and his colleagues over a period of 30 years.[ Fig. credit Ref.4]

As gravitational radiation carries energy away from the binary system, the orbit loses energy and the stars spiral in towards each other. This has resulted in progressive decrease in the pulsar’s period of revolution around its orbit, as meticulously and very accurately measured for three decades (Fig.5). The dots are measurements of how early the pulsar is in its orbit while the curve represents the theoretical scenario of gravitational waves carrying energy away from the system at the rate predicted by Einstein's theory of General Relativity. The excellent agreement between observation and theory represents the first and one of  the strongest prior evidence that gravity waves exist. According to Professor Weiss, this indirect evidence of gravitational waves provided a great impetus for him and his team to carry out extremely complicated and difficult tasks of LIGO experiments.

I have worked in the field of laser spectroscopy and I do not have any expertise in General Relativity, but I got very interested in LIGO work because of two facts. At the bottom of Fig. 4 is shown the ‘audio signal’ from the colliding black holes which has been converted into audible sound by appropriate software. This reminds me of the emergence of Photoacoustic spectroscopy after almost a century of its discovery by Graham Bell, with the availability of tunable lasers (see Fig.6). This technique is now widely used in the investigation of all kinds of matter, solid, liquid, or gas, including biological matter literally by listening to the interaction between electromagnetic radiation and molecules [5]. In the LIGO experiment laser is being used in listening to the response of spacetime fabric, as in the photoacoustic spectroscopy experiment laser is used to listen to the response of molecules. This comparison has prompted me to name the title of this article which is basically about the history and analysis of LIGO results. Professor Weiss said that there is no sound generation but the computer-conversion of the gravitational wave LIGO signal into  the chirp can be reproduced by running one’s fingernails across the keys of a piano from low end to middle C.

 The second reason of my interest in this marvellous discovery was LIGO’s similarity with the Michelson- Morley experiment of 1887, which was as difficult to perform in those days as LIGO is now. There were many criticisms of the negative result of Michelson-Morley experiment and it was Einstein’s theory of special relativity that eventually put it on the high pedestal with the award of 1907 Nobel Prize in Physics to Albert Michelson. It is thus a rare coincidence that LIGO has validated the predictions of the theory of General Relativity with the award of 2017 Nobel Prize in Physics. In the following sections I would endeavour to present my own understanding of LIGO, Neutron stars, Black holes and the Gravitational waves.

       

Fig. 6 Graham Bell and his Spectrophone for listening to the spectra of atoms and molecules

2.  The Laser Interferometer Gravitational-wave Observatory (LIGO)

The L-shaped LIGO detector has two arms, like a Michelson interferometer, with highly reflecting mirrors at the ends of both arms to reflect light [6]. A beam-splitter (half silvered mirror) is mounted at the junction of the two arms as shown in Fig.7. The laser light source is placed close to the beam-splitter such that 50% of the incident light is transmitted to one of the end mirrors and 50% reflected along the other L-shaped arm. The two mirrors are set with their surfaces perpendicular to their respective arms, so that the incident light beams are reflected back to the beam-splitter. The detector is placed close to the beam-splitter and in-line with the L-shaped arm that is normal to the arm aligned with the source. When the optical paths of the two beams, from the beam-splitter to the respective mirrors and back to the beam-splitter, are made equal, there is destructive interference between the two beams and no light falls on the detector. If one of the mirrors is moved slowly, alternate dark and bright fringes appear at the centre of the field of view.

         

Fig. 7 Diagram of Michelson interferometer with a laser source set for the equal optical paths

        

Fig. 8a. Professor Michelson and mirror arrangement of d, d1, e and e1 at the four corners of a square base to increase  effective path for each of the interferometer arms from 1.5 meter to 11 meters. The beam splitter is ‘b’ and ‘c’ is an identical compensating glass plate. Incident light is from ‘a’ to ‘b’ and the fringe pattern for white light is shown on the bottom right. (Figure credit Wikipedia)

                                 

Fig.8b Results of Michelson-Morley experiment with the upper solid line showing measurements at noon and the lower one that in the evening. The dotted curve represents one-eighth of the theoretical displacements.(Figure credit Wikipedia)

Professor Michelson did not have the advantage of using a highly monochromatic light source and Yellow sodium light was used for initial settings but white light was used for actual measurements. It had been estimated that an ether-drift would produce a fringe displacement of 0.4 of a fringe. The experiment revealed a maximum displacement of 0.02 of a fringe and the average much less than 0.01 (see Figs. 8a and 8b). The experimental measurements were carried out at different orientations by rotating the Interferometer base about a vertical axis several times a day. It was expected that during each complete rotation of the Interferometer each of its arms will be parallel to the ether wind twice ( facing into the wind and away from it) giving identical readings and perpendicular to the wind twice. A plot of the experimental fringe shift was expected to yield a sine curve with two peaks and two troughs per rotation. The negative result of detecting Earth’s motion through ether is graphically shown in Fig. 8b.

In the LIGO experiment, the distance of the horizontal end mirror from the beam-splitter is Lx and that of the vertical end mirror Ly in Fig. 7, defines the differential arm length as:

                                       L   =  Lx -  Ly                                                                (1)

The photodetector of Fig.7 produces an optical signal proportional to S such that

  S = P0cos2 (kL)         = P0cos2(2L/)                                                       (2)

where P0 is the laser power, k the wavevector and is the laser wavelength

It is seen from the variation of interferometer signal S, at the detector in Fig.9, that power changes periodically between the input power P0 and zero with a period L/=0.5. The interferometer in LIGO operates at or near the condition of the dark fringe. It may seem to indicate that the macroscopic arm lengths Lx and Ly are not important in fringe formation but the situation shown in Fig. 9 corresponds to an ideal laser beam with infinite coherence length. In LIGO experiments the macroscopic arm-length difference is an important design parameter and it is kept small to reduce coupling of laser noise into the output at the detector.

 

    

Fig. 9  Power at the Detector in Michelson interferometer shown in Fig.7 as a function of the arm length difference L. No light reaches the Detector when the interferometer is set to satisfy the condition of the dark fringe at L/=0.25. 

 

   

Fig. 10 Schematic representation of the laser beam (red), the associated noise (black) and the signal (blue) generated by differential motions (dL) of the end mirrors in the interferometer (a) and the phase relationship between the laser light, the noise and the signal at Detector (b)

The best sensitivity for Michelson interferometer can be achieved when it is operated in a quasi stationary mode such that the light power inside the interferometer and at the detector remain nearly constant. The LIGO experiment measures a very small differential change in the length of one arm versus the other. The detection of very small amplitudes of gravitational waves or the equivalent small differential change in the arm lengths requires very high sensitivity. The quasi stationary mode of the interferometer is described by using a steady state model where laser noise can be represented by a sinusoidal modulation with a small amplitude at a single frequency, say 50 Hz. The phase noise of the laser can be then described by a pair of sidebands superposed on the main carrier light field entering the interferometer. Similarly the change of an interferometer arm represents a phase modulation of the light reflected back from the end mirrors and the resulting optical signal can be represented by a pair of phase modulation sidebands. The insertion of  the noise and signal sidebands along with the laser is schematically shown in Fig.10a. The plot of the sideband amplitude at the detector as a function of the differential arm length of the interferometer is shown in Fig.10b. A tuning of the differential arm length corresponding to a phase angle of 90 degree results in a dark fringe at the detector. The plot of Fig.10b shows that corresponding to the dark fringe, the signal sidebands at the detector are maximised while the noise is minimised. In the case of gravitational wave detection, however, the signal sidebands are many orders of magnitude smaller than the amplitude of the carrier laser and its detection requires a beat between the signal sideband and another field, called the local oscillator, to generate a strong electronic signal proportional to the amplitude of the signal sidebands. When the Michelson interferometer is set close to, but not exactly on, the dark fringe, the carrier laser leaking into the Detector can thus be used as the local oscillator. This scheme preserves the advantage of the dark fringe but requires a very good power stability of the carrier laser light.

2.1 Gravitational Waves & Design of LIGO

According to General Relativity, when two material particles rotate about each other, they constitute a quadrupole emission source and generate transverse gravitational waves  that travel at the speed of light. In contrast to electromagnetic waves, the gravitational waves (GW) have two polarization states denoted by plus (+) and cross (x) as illustrated at the top of Fig.11. If we assume that a (+) polarized GW, travelling from left to right  hits a circular ring of material particles perpendicular to its plane, the ring will be distorted as shown at the bottom in Fig. 11. The vertical plane of the ring would get distorted into a vertical ellipse, then back into a circle, then distorted into a horizontal ellipse and back to circle again. It is thus clear that gravitational waves are basically distortions in spacetime that can be detected by measuring the distance between test masses as shown in Fig.11. A Michelson interferometer is an ideal detector of geometry since it is designed to measure length changes of two perpendicular directions as shown in Fig.7. The end mirrors of the Michelson interferometer represent the test masses and any change in the relative distance under the influence of gravitational waves depends on L, the length of interferometer arm. 

                         

                          

Fig. 11 Comparison between dipole emission of Electromagnetic waves and quadrupole emission of Gravitational waves (top). Distortion of a circular ring of particles oriented perpendicular to the direction of propagation of the gravitational wave which will be periodically distorted as shown at the top of the waveform (bottom)

Since the gravitational wavelength is much larger than the size of the detector we get the following relation:

                                                   L   =       sL                                                          (3)

where  ‘L’ is the length of each of the two arms of the interferometer and ‘s’ is the strain amplitude of the gravitational wave.The interferometer configuration with two perpendicular arms benefits from the differential effect induced by a gravitational wave in the plane transverse to its direction of propagation (see Fig.11). When the length of L changes by L, the perpendicular optical path of same length changes by -L(same magnitude but opposite sign). Since the interference at the output port (at photodetector) depends on the difference of length between the two arms, the measured effect is amplified by a factor of 2. The task of signal detection becomes very challenging because of the extremely small effects produced by the gravitational waves. The strain amplitude, produced by the first gravitational wave detected in September 2015, was 10-21 and this signal could not have been measured with a simple Michelson interferometer. The performance of an interferometer detection is limited by its various noise sources including the inherent quantum fluctuations of the laser beam used to generate the output signal. The amplitude spectral sensitivity of a Michelson Interferometer is limited by the shot noise:

                                 Noise =   (h/πP)½[c/L].                                                          (4)

Where 'h’ is Planck's constant , 'c’ the velocity of light, ‘L’ is length of Interferometer arm, and '’ is the angular frequency of laser light of power 'P’.

Thus, for a laser wavelength of 1064 nm, and 4 km Interferometer arm, to reach a sensitivity of better than 10-22 to overcome the noise the required power is:

                             P  >  (h/10-44)[c/L]2    =        70kW                                          (5)

Transmitting a laser beam of kilowatt power through the Interferometer would cause undesirable and significant thermal deformations of the beam-splitter and the mirrors. This requires alternate means of enhancing laser power and decreasing noise.

2.1.1 Sources of Noise in LIGO Detection

The initial LIGO of 2002,  had typical bandwidth from 40 Hz to 6kHz for detection of gravitational waves from astrophysical  sources. The noise spectrum across this detection bandwidth is not flat and can be divided into three distinct regions: 

(1) The dominant noise source below 50 Hz comes from Seismic noise, due to motion on the earth surface as well as the fluctuations underground.

 (2) In the range 50- 150 Hz the dominant noise is thermal, due to Brownian motion in the optics and the suspensions. 

(3) At frequencies above 150 Hz, the dominant cause of noise is the shot noise.

Seismic Noise: 

Vibrations coming from seismic activity, man made objects such as trains or cars and the waves crashing into the continents, will limit the sensitivity of interferometers at lower frequencies. A system of complicated isolation is used to suspend the mirrors within the interferometer  to reduce the effects of seismic noise. Multi-stage pendulums are good filters for reducing motion above their natural frequency,  and these are  located on isolation platforms for suspending the mirrors’

Thermal Noise: 

In the region of a few hundred Hz, the interferometers are most sensitive to noise due to vibrations of the mirrors or suspensions due to Brownian motion. This noise can be reduced by keeping the resonant frequency of the suspension systems and mirrors, far away from this region, on the order of a few Hz for the suspensions and several kHz for the mirrors. By using material with a high quality factor the noise can be reduced by confining it to a narrow bandwidth around the resonant frequency, which allows interferometers to operate at room temperature. Thermal noise could also be reduced by employing cryogenic cooling which will be employed by the Japanese KAGRA detector.

Shot Noise:

The noise is caused by the random arrival time of the photons within the laser beam, which causes fluctuations in the intensity of the light detected, and it will dominate above a few hundred Hz. Use of a high power laser which increases the number of photons helps reduce this source of noise. Shot noise can also be reduced by power cycling techniques which increase the amount of power within the Interferometer.

Radiation Pressure Noise: 

Increasing the power of the laser causes the momentum transferred to the mirrors, as photons are reflected by them, to increase. Therefore there must be a trade-off between this radiation pressure noise and shot noise. To do this the quadrature sum of the two is minimised which occurs when the two noise sources are of equal amplitude at some target frequency.

Gravity Gradient Noise: 

This form of noise will limit the sensitivity of the detectors with a frequency limit of around 1 Hz and below. A possible option to eliminate this effect is to put detectors in space such as the proposed eLISA space mission. To reduce this effect on Earth, the detector can be built underground where most of the gravitational field effects will be reduced as they mostly occur at the surface. The Japanese KAGRA detector is currently being built in the Kamioka mine.

2.1.2 Location Details of Twin LIGO Detectors

There are two identical gravitational wave observatories separated by a distance of 3002 kilometers, one located in Hanford  in Washington State (in the north-west) and the other in Livingston in Louisiana State (in south) as shown in Fig.12. LIGO’s two L-shaped interferometers are aligned ‘back to back,’ pointing away from each other to enhance the sensitivity of the pair for waves coming from some direction in space. One of the arms of the interferometer in Hanford points in the North-West direction ( at about 37 degree West of North) an identical arm of the interferometer in Livingston points in the South-East direction (at 18 degree East of South). Thus they are almost parallel but back to back.  The two sites, for the interferometers, are located on flat landscape, to minimize external noise, these are away from heavy traffic of vehicles and other manmade movements on Earth. Each of these interferometers has L-shaped arms 4 km long from the beam splitter and freely-hung mirrors of 40 kg mass suspended as in a pendulum with thin silicone wires at the two ends. The site at Hanford also had a middle station with another set of suspended heavy mirrors 2 km from the beam-splitter sharing the same vacuum system. The optimum interferometer arm length is one quarter of the gravitational wavelength. However this is not practically achievable on the earth's surface because, for a gravitational wave of 100 Hz the interferometer arm length comes out  to be about 700 km. Even in setting up 4 km  long arms of LIGO interferometers, a change of about 1 meter in height from the surface was encountered because of Earth’s curvature. This required the most precise concrete pouring and levelling imaginable to counteract the Earth’s curvature and to ensure that LIGO’s 4 km long evacuated tubes were flat and level. In the absence of such a high degree of precision in the construction work LIGO’s lasers would hit the end of each arm 1 meter above the end mirrors. Advanced LIGO interferometers are designed to detect gravitational waves from distant astrophysical sources in the frequency range from 10 Hz to 10 kHz.

Fig. 12  An aerial view of the twin LIGO interferometers located at Hanford (bottom left) and at Livingston (bottom right) Locations of of the two sites are shown on the map of USA (top left) and a view at the junction of the two interferometer arms inside the observatory is shown on the top right. (Adopted from www.ligo.caltech.edu/image/ligo20150731f and www.ligo.caltech.edu/image/ligo20150731a )

It is required to maintain ultra-high vacuum with pressure of 10-9 torr inside the two arms of the interferometer. This pressure is one-trillionth that of atmospheric air pressure at sea level. To remove 10,000 cubic meter of air and all other residual gases, from each of the interferometer tubular arms, needed 40 days and 1100 hours of evacuation using extremely efficient vacuum pumps. Each vacuum chamber encloses a volume equivalent of 11 Boeing 747-400 commercial airliners. The air that was removed from each of the interferometer arms could be used to inflate 1.8 million soccer balls and LIGO’s evacuated volume is surpassed only by the Large Hadron Collider in Switzerland. It is important to note that 155 million kg of air press down on each 4 km long vacuum tube, and the steel tubes that sustain this heavy weight, are only 3 mm thick.

2.1.3 The Fabry-Perot Cavities

                

Fig. 13 Schematic representation of the modification of the basic Michelson interferometer of Fabry-Perot cavities by use of additional mirrors (ITM) between the beam-splitter and the end mirrors (ETM). The FP cavity is formed between each  ITM and the ETM pair. Most of the laser light intensity is trapped inside the FP cavity, and only a tiny fraction leaks out towards the beam-splitter because the transmission of each ITM is only 1.4%.

The basic LIGO’s Michelson interferometer, schematically shown in Fig.7, is the largest ever built and its 4 kilometer long arms are 360 times larger than that used in the Michelson-Morley experiment which had 11 meter effective arm length. But as discussed before and shown in Eq.3, the gravitational waves produce a differential length change of 10-21 only and the sensitivity of even 4 km long arms of Michelson Interferometer is not good enough to detect it.

The idea of basic design for a Michelson Interferometer with very long arms was originally put forward by Prof. Rainer Weiss of MIT in 1972. When it was found in mid 1980s, that the detection sensitivity of even the largest Interferometer was insufficient for measurements of theoretically estimated length changes, 1000 times smaller than diameter of Atomic nucleus (10-18 meter), late Prof. Ronald Drever of Glasgow University  came up with the idea of FP cavity [7]. Since the end mirrors of Michelson interferometer move under the effects of gravitational waves they are termed as end test mass (ETM). Prof. Drever introduced a highly reflecting mirror close to the beam-splitter in each arm of the interferometer and named it as input test mass (ITM). Thus, a Fabry Perot cavity is created in each arm as shown in Fig.13, and a major part of each laser beam is reflected back and forth within each 4 km long arm about 280 times before they are merged together again. All mirrors inside the LIGO interferometer use the multi-pendulum suspension system for noise reduction as illustrated in Fig.14.

      

Fig. 14 Prof. Rainer Weiss, Prof. Ronald Drever and on extreme right is the pendulum suspension system for the interferometer mirrors. Main mirrors are suspended at the bottom of 4 pendulums. Each mass absorbs vibrations from the mass above it until nothing reaches the lowest hanging mass of the mirror.

The use of F-P cavity in LIGO’s interferometer arms increases their effective length to 1120 kilometers. and makes them 102,000 times bigger than Michelson’s original interferometer and now this instrument is capable of measuring mirror movements 1000 times smaller than the atomic nucleus. This modification can be compared with the sensitivity to vibrations in a telescope, which is disturbing, when viewing a distant object through the telescope. By increasing the focal length of a telescope, not only do we increase the magnification of any given eyepiece, but it also magnifies the tiniest vibrations of the telescope-mount and makes image flicker in the eyepiece. The longer the telescope focal length, the smaller are the vibrations that can be seen in the eyepiece. These vibrations are very annoying in  telescope viewing but LIGO has been designed to sense the tiniest of vibrations produced by gravity waves. Thus the interferometer arm length is akin to telescope focal length and with an effective arm length of 1120 km LIGO can readily magnify the smallest conceivable vibrations enough that they become measurable.

2.1.4 Stable Laser & Power Boosting

The high level of precision required for interferometric measurements of gravitational waves needs frequency stabilisation of the laser because all lasers exhibit some degree of frequency wander. Drever perfected a method, now called Pound-Drever-Hall (PDH) stabilisation, that was used for the laser source in LIGO experiments [8]. The principle of PDH technique is illustrated in Fig.15 and it provides a tool to control and decrease the laser linewidth using an optical cavity that is more stable than the laser source. This method responds to the frequency of laser emission independently of intensity instabilities.

         

Fig. 15 Schematic of a servo loop to lock the frequency of the laser (top left) to a Fabry Perot optical cavity (top right) [Figure credit PDH technique, wikipedia]

        

Laser power is one of the most important parameters for enhancing the detection capability of LIGO as has been earlier illustrated in Eqs. 2 and 5. While increasing the interferometer arm’s length increases LIGO’s sensitivity, the increase of laser power increases its resolution. With higher power, larger the number of photons that merge at the beam-splitter, sharper is the resulting fringe pattern, and thus it becomes easier to recognize the gravitational wave signal from the noise. This capability is achieved by introducing a partially transmitting mirror (PRM) between the laser source and the beam splitter as shown in Fig.16. The interferometer is illuminated with a 1064 nm wavelength Nd:YAG laser, stabilised in amplitude, frequency and beam geometry [9,10]. The stability of the laser source maximizes the gravitational wave induced strain to optical signal, by minimizing the impact of photon shot noise. Thermal noise is minimized by using end mirrors (ETM) of 40 kg fused silica substrates with low loss dielectric optical coatings. The mirrors are suspended with fused silica fibers from the stage above.

               

Fig. 16. Schematics of the Michelson interferometer coupled to  Fabry-Perot (FP) cavities and the power recycling mirror (PRM) [ Figure credit LIGO Caltech]

              

With the interferometer set for the condition of a dark fringe at the photodetector, all of the laser light returning to the beam-splitter, from the two end mirrors, is directed back to the laser source. The power recycling mirror PRM, with only 3% transmission, sends back this returning light into the FP cavities. The interferometer is aligned so well that almost all the light reflected from the two end mirrors (ETM), follows a path to the recycling mirror PRM, rather than to the photodetector. Thus, laser light coming from the ends of the two arms is returned back into the interferometer where these photons add to those just coming from the laser source. This process greatly boosts the laser power trapped in FP cavities of the two arms such that, a stabilized input power of 125 W from the laser source grows up to 750 kW. Calculations show that the detector sensitivity scales as: 1/(LP1/2) where L is the arm length and P the laser power on the beam splitter [11]. This helps to enhance LIGO sensitivity, to be better than 10-22, required for the strain of 10-21  to be detectable.

The principle of reducing noise due to vibrations in the mirrors has already been illustrated in Fig. 14 but the actual process of damping the vibrations is much more complicated and is a very important part of LIGO Technology. In effect, the end mirrors remain perfectly still and the only vibration they suffer is when the gravitational waves pass through the interferometer and compress or extend the two interferometer arms.

2.1.5 Theoretical Modelling of Gravitational Waveforms

The detection of gravitational waves requires their precise theoretical modelling to allow for the construction of waveform templates with which to filter the noise data from the signal. This is a very complex and difficult process involving numerical relativity and other mathematical techniques for solving the equations of General Relativity (GR). Einstein’s theory of GR predicts that accelerating massive bodies will produce vibrations in the fabric of spacetime. The analytical modelling of the emitted gravitational waves from a binary system of massive astronomical objects has to be done at several stages of their motion- such as during the inspiral and merger of compact objects like black holes or neutron stars. 

                              

Fig. 17. A typical waveform template of two compact masses in spiralling and merging to form a heavier black hole or a neutron star

The modelling requires the solution to the Einstein equations analytically via mathematical series techniques. When the compact objects have small velocities, relative to the speed of light, during their inspiral motion, the techniques to be employed are post- Minkowskian and post- Newtonian to solve the Einstein equations. When the remnant compact object settles down to its final stationary state, after the merger, black hole perturbation theory is employed to solve the field equations. These solutions make it possible to predict the observable gravitational waves from which template filters are constructed.

                      

Fig. 18  Professor Kip Thorne, when he was younger and Professor Barry Barish                            

  

In the forward to the book “Black Holes & Time Warps” by Kip Thorne, published in 1994, Stephen Hawking says, “It is a history of the scientific discovery in the making written by one of the participants, rather like The Double Helix by James Watson about the discovery of DNA, which led to the understanding of the genetic code. But unlike the case of DNA, there were no experimental results to guide the investigators. Instead the theory of black holes was developed before there was any indication from observations that they actually existed.” Prof. Kip Thorne has a lifelong interest in Black holes and Neutron stars and he has been one of the main pillars of theoretical modelling of waveforms for detection of gravitational waves emanating from far away galaxies [12]. He was responsible for bringing Prof Drever from Glasgow to Caltech for his contributions in enhancing the detection sensitivity of the giant Michelson interferometer by addition of the Fabry Perot cavity and stabilizing the optical power of the laser source by using PDH technology. His Caltech colleague Prof. Barry Barish, under whose direction LIGO was built, played a very important role in the successful operation of LIGO. When Prof. Barish became leader of the LIGO project in 1994 he took the crucial decision to increase the power and sensitivity of the detectors. He expanded the group from 40 researchers to more than 1000 from all over the world (see Fig.18). He inducted experts specializing in gravity, black holes, vacuum systems, lasers, statistics and in every other area that was involved in the task of measuring tiny contractions in 4 km long arms of LIGO interferometer. As the LIGO director, in 1997, Prof. Barish formed LIGO Scientific Collaboration (LSC) involving international physics institutes and research groups dedicated to the search of gravitational waves in addition to the members of LIGO laboratory. The LSC members have access to the US based Advanced LIGO detector and also have access to data from the Virgo detector in Pisa, Italy.

2.2 Commissioning of LIGO &  Detection of Gravitational Waves

In the very beginning of the LIGO project it was decided to develop the system with new generation detectors of increased sensitivity to detect gravitational waves. The instruments with which the first ever detection was made, on 14 September 2015, belong to the second generation of development and it has been named Advanced LIGO. Commissioning of LIGO after any modification is a very laborious task. It can be described as the process of tuning and improving the detector after its subsystems have been installed and before the full system is operational. The time involved may be several years because the interferometer couples all the subsystems in an unique and complex manner. During the process of commissioning, the interferometer is assembled in increments leading to its full recycled configuration. It is crucial to have a very accurate model of the interferometer functioning to assess the component of noise from unavoidable corners. Thus, measurements of mirror surfaces are taken prior to installation and used in the simulation to model the expected distortion of the laser beams within the real interferometer. During the commissioning, if it is found that the experimental measurements are different from that expected on the basis of the model, then the possible causes are investigated, and more measurements made to tune the parameters of the model to create the observed behaviour

The first generation of LIGO detectors were constructed in late 1990s and were operated at their designed sensitivity in a continuous data-taking mode from November 2005 to September 2007 [13]. The interferometers and the laser sources were upgraded to improve the sensitivity and this enhanced LIGO was used to collect data from July 2009 to October 2010 [14]. There were no gravitational wave signals detected either with the initial LIGO or its enhanced version but they produced several results of great interest in astrophysics [15]. The Advanced LIGO was designed with a 10 times increase in its strain sensitivity and the lower limit of its band width was extended down to 10 Hz from initial value of 40 Hz. The second generation LIGO instruments are capable of investigating a volume of the universe 103 times larger than that possible for its initial version as  illustrated in Fig 19.

 Fig. 19 The relative volumes of universe accessible by Advance and Initial LIGO  

 2.2.1  Gravitational Waves from Binary Black Holes

Professors Weis, Thorne and Barish, who were awarded the 2017 Physics Nobel Prize  (see Fig.20), were unanimous in lauding the roles and the contributions of over a thousand scientists spread over many countries for the success of the LIGO project. GEO600 gravitational-wave detector located near Hannover in Germany is a   technologically sophisticated Michelson Interferometer with 600 meter arm length. It is handled by scientists from Max Planck Gravitational Physics Institute (Albert Einstein Institute) and from Leibniz University of Hannover. This group of scientists have access to data from LIGO and Virgo under the LSC umbrella. When the gravitational wave signal was detected by LIGO in the USA on 14 September 2015, it was 3 in the morning at Hanford and 5 in the morning at Livingston. Fortunately it was noon in Germany and scientists in Hannover were the first to see the signal on their computer screens. It was this group that had supplied the most stable laser source, ever built, for the Advanced LIGO interferometers and there was reason for them to be delighted because laser noise was one of the major stumbling blocks in the precision measurement. The LSC group, at Glasgow University- Institute for Gravitational Research, also received the signal in daytime at 9:51 UTC on 14 September. They had been responsible for developing the all fused silica suspension system for the mirrors which increased the sensitivity of detection by a factor 10. It was a rare coincidence that this very strong gravitational wave signal was detected within 2 days of the Advanced LIGO having been made operational and it was operating in engineering mode. The event has been named GW150914 based on the Year, Month and Date of detection, in that order I recall the title of a popular lecture at SUNY Binghamton in 1973, “Lucky Accidents Prepared Mind and Great Inventions.” The success of GW150914 falls in that category.

            

Fig. 20  Professors:  Barry C. Barish (Caltech), Kip S. Thorne (Caltech), Rainer Weiss (MIT)

The Atlas Computing Cluster (ACC) is the world’s largest and most powerful resource dedicated to gravitational wave searches and data analysis. It contributes roughly half of the entire computer power available within the LIGO Scientific Collaboration (LSC). It was clear to the theorists that the LIGO signal originated by merger of a binary system of two very compact objects but it was unexpectedly too strong a signal. Scientists got busy to simulate the masses of the two colliding objects and their distance from Earth. The simulated signals are shown in Figs. 3 and 21.

 

                      

Fig.21. Computed gravitational-wave strain amplitude from GW150914 superposed on the waveform H1, but without filtering used in Fig.3. The coalescing black hole separation is in units of Schwarzschild radius (Rs) and the effective relative velocity is in post-Newtonian parameter v/c. Gravitational wave frequency ‘f’ has been computed for total mass ‘M’ of about 70 solar masses.[Adapted from Ref.17]

                                     

Fig. 22. Approximate location of the GW150914 event in the sky map of the southern hemisphere is marked by the blue-green patch. The purple and yellow contours define the target region with confidence levels of 90% and 10% respectively. Fuzzy blobs under the marked area reveal the Large and Small Magellanic clouds. [Image credit LIGO/Axel Mellinger]     

                 

The strength and appearance of GW150914 was such that the experts in the field immediately realized the signal to have arisen from the merger of two black holes orbiting each other. Approximately 0.2 second long waveform shown in Fig.21 corresponds to two black holes orbiting each other about 20 times per second in the beginning (left). As the black holes come closer they orbit faster about 75 times per second before they merge to form a single heavy black hole of mass greater than 70 solar masses. The gravitational strain signal of Fig.21 increases  in frequency from 35 to 75 Hz and its amplitude rises to the maximum value in 8 cycles over a period of 0.2 second before the final black hole ringdown [16]. More refined simulations led to the fact that the two colliding black holes were of 36 and 29 solar masses respectively at a distance of 1.3 billion light years from Earth. The heavy black hole created after the merger was of 62 solar masses and 3 solar masses equivalent of energy emitted in the form of gravitational radiation carried away by the waves resulting in a peak luminosity of 3.6 x 1049 Watt.

Researchers were able to locate the origin of the source of gravitational waves on the basis of LIGO data from Livingston and Hanford. The gravitational waves arrived at Livingston 7 milliseconds before arriving at Hanford. This time delay indicated a ring in the sky from where the signal must have originated. After taking into account the strength of signals from both detectors the blue-green patch was estimated to be the more probable region of binary black hole collision as shown in Fig. 22. It was found that the signals at the two LIGO sites were related by a minus sign which is consistent with the relative back to back orientation of the two detectors. The 7 milliseconds difference in arrival time of gravitational waves at the two locations separated by 3000 Km also support the GR result that their propagation speed is that of light.

2.2.2 Gravitational waves from a 22-Solar mass Binary Black hole Merger

A gravitational-wave event GW151226 was identified within 70 seconds during an online matched-filter search on 26 December 2015. The gravitational wave signal had arrived at LIGO in Livingston around 3.30 in the morning of 26 December and about 1.1 milliseconds later at LIGO in Hanford. This signal was genuine in view of the probability of finding a false signal of this type being 1 per 1000 year. The gravitational wave signal had passed through LIGO’s sensitive band in 1 second with its amplitude increasing with frequency, from 35 Hz to reach the maximum at 450 Hz,  over about 55 cycles as shown in Fig.23. In this case the signal to noise ratio (SNR) accumulates equally during the first 45 cycles from 35 to 100 Hz (inspiral) and during the last 10 cycles from 100 Hz to 450 Hz (merger). In this respect GW151226 is different from the more massive GW150914 binary where only the last 10 cycles, comprising inspiral and merger, dominated the signal to noise ratio (SNR). 

    

Fig. 23.  1st row shows filtering with 30 -600 Hz bandpass to remove strong instrumental spectral lines. The 2nd row is the accumulated peak to noise ratio for the best matched template for  gravitational waves of 30 Hz up to its merger time. The 3rd row is the SNR time series obtained by time shifting the best-match template waveform  and computing the integrated SNR at each point of time, its peaks indicating merger. The 4th row is time frequency representation but the signal is not easily visible as in GW150914. [ Adapted from Ref. 17]

The gravitational wave signal of 26 December corresponds to Coordinated Universal Time (UTC) at 3:38:53 and its waveforms at the two detectors are shown in Fig. 24. From the analysis of GW151226 LIGO data, the black hole binary was estimated to have members of mass 14.3 and 7.5 solar masses orbiting around each other at a distance of 1.4 billion light years from Earth.. When the binary merged into a black hole of 20.8 solar mass, radiation equivalent to 1 solar mass was carried away by the gravitational waves with a peak intensity of 3.3x1049 Watt [17].  The luminosity distance of binary coalescence distance can be determined from the amplitude of the signal, if the orientation of the orbital plane is known. Whether the orbital plane is face-on or end-on is extracted from the two polarizations of the gravitational wave. However, the twin LIGO interferometers are coaligned and the source is likely to be located close to the maxima of the directional responses of both, but polarization content cannot be determined.

Fig. 24 Observed strain signal for GW151226, beginning 1 second prior to merger (Top) The computed waveforms are shown in the middle. The change of gravitational wave frequency and velocity during the merger is shown at the bottom.[Adapted from Ref.17]

2.2.3 GW170104: A 50-Solar-Mass Binary Black Hole Coalescence

                          

Fig.25. The signals of GW170104 measured at Hanford and Livingston (in gray). The waveforms reconstructed from the morphology-independent wavelet analysis is shown in orange and that from binary black hole (BBH) models from both waveform families (in blue) [Adapted from Ref. 18]

GW170104 was first identified by inspection of low-latency triggers from Livingston data. After it was manually determined that the calibration of both detectors was in a nominal state, an alert with an initial source localization was distributed to collaborating astronomers for the purpose of searching for transient counterparts. Two independently designed matched filter analysis used 5.5 days of coincident data from January 4 to 22, 2017. Candidate events must  be found in both detectors by the same template within 15 milliseconds, which is determined by the 10 millisecond propagation time plus an allowance for uncertainty in identified signal arrival times for weak signals. GW170104 was detected with a network matched-filter signal-to-noise of 13 with the probability of 1 in 70,000 years of coincident observing time (see Fig. 25).

Analysis of the data revealed that the gravitational wave signal first arrived at Hanford detector around 10 in the morning of 4 January, and 3 millisecond later it reached Livingston. The gravitational wave frequency at peak value of the strain was from 160 to 199 Hz. The pair of black holes with 32 and 19 times the solar mass were located at a distance of about 3 billion light years from Earth [18]. The mass of the black hole after merger was estimated to be 49 solar masses and radiation equivalent of 2 solar masses was carried away by the gravitational waves with a peak intensity of 3.1x1049 Watt. The analysis of data showed that the graviton Compton wavelength is at least 1.6 light years (1.5x1016m) corresponding to a graviton mass of no more than 7.7x10-23 eV/c2 if it has any mass at all. Compton wavelength is about 9x109 times greater than the gravitational wavelength of GW170104.

2.2.4 GW170814:Three Detectors Observation of a Binary Black Hole Merger 

     

Fig.26 Aerial view of Virgo showing the 3 kilometer-long west arm and the beginning of the north arm. Virgo member countries shown on the right.[Credit The Virgo collaboration/CCO]

Virgo is a scientific collaboration of laboratories from six countries, Italy and France started the project which was joined by the Netherlands, Poland, Hungary and Spain. Virgo detector is a giant Michelson interferometer made of two orthogonal arms each 3 kilometer long [Fig.26]. Located near Pisa in Italy the interferometer is named after the Virgo Cluster of 1500 galaxies in the Virgo constellation about 50 million light years from Earth. It has the same kind of highly advanced detection systems as the twin LIGO interferometers in the US. A collision between two binary black holes was detected in all three interferometers on 14 August, 2017 at 10:30:43 a.m. Coordinated Universal Time (UTC). The detection by the LIGO Scientific Collaboration (LSC) and the Virgo collaboration is the first confirmed gravitational wave signal recorded by the Virgo detector designated as GW170814.

Advanced Virgo detector joined the Advanced LIGO second run (O2) which ran from 30 November 2016 until 25 August 2017. On 14 August at 10:30:43 UTC, a transient gravitational wave signal was detected by automated software analyzing the data recorded by the twin LIGO detectors. This signal was found to be consistent with the final moments of the merger of two stellar mass black holes. Subsequent analysis using all the information from all three detectors showed clear evidence of the signal in the Virgo detector. 

The identification of a new transient event follows several steps. The first one after data acquisition relies on low-latency pipelines which use matched-filtering techniques to look for coincident candidate signals in the two LIGO interferometers. GW170814 was observed by LIGO at high statistical significance within 30 seconds of its arrival and an alert was sent out to the various telescope partners of the LIGO-Virgo Collaboration. Later, the significance was computed more accurately, using about six days of LIGO data that found the false alarm rate to be lower than 1 in 2700 years. Virgo also saw this gravitational wave event, as demonstrated by two independent analyses. Two different unmodeled reconstructions were compared for GW170814- one using only the two LIGO detectors and the other based on the three detector network. Using only two detectors, the computed false-alarm rate was 1 in 300 years while the use of a full network reduced it to lower than 1 in 5700 years. Thus, the three detector case is clearly favoured over the two detector hypothesis. Three different modes of looking at the recorded data is shown in Fig.27.

Researchers found from the analysis of data, from the three interferometers, that the members of the binary black hole were of 31 and 25 solar masses, located at 1.8 billion light years from Earth, and after merger the new black hole is of 53-Solar mass. Thus 3 solar-mass was converted into gravitational radiation and carried away by the waves with the peak luminosity of 3.7x1049 W [19].

A network of three detectors improves the sky localization of the source, reducing the area from 1160 degree2 using only the two LIGO detectors to 60 degree2 using all three detectors. Also, it has been possible for the first time to test the nature of  gravitational wave polarization from the antenna response of the LIGO-Virgo network. For the purpose of position reconstruction, the LIGO-Virgo GW detector network can be thought of as a phased array of antennas. A single detector provides only minimal position information, its slowly varying antenna pattern favours two broad regions perpendicular to the plane of the interferometer arms. A network of detectors enables the sky position to be inferred by triangulation employing the amplitude ratios, phase differences and the time differences on arrival of the wave at the sites. In the present case a rapid localization was performed by coherent triangulation of the matched-filter estimates of the times, phases, and amplitudes on arrival. GW170814 source is localized in an 1160 degree2 area on the sky from the twin LIGO data but inclusion of Virgo data brings down this area to 100 degree2. The full parameter Bayesian estimation further constrains the source to an area of 60 degree2 as shown in Fig.28.

         

Fig. 27. Top row: The peaks occur at different times in three detectors, because gravitational waves propagate with speed of light, first Livingston, 8 ms later at Hanford, 6 ms after that in Virgo. Middle row: Frequency-time representation of strain data. The brighter a given pixel in any of 2D maps, the larger the signal at the particular time and frequency with respect to noise. Bottom row: Strain time series with the best waveforms selected by the matched filtering (black curves) and unmodeled search methods (gray bands) superposed. [Adapted from LSC-Virgo collaboration]

    

                             A                                                                             B 

Fig. 28  (A): Sky localization of GW170814 source using LIGO-Virgo network. (B): Relative regions of localization of sources of GW using only two and in the present case three detectors spread over two continents.[Adapted from LSC-Virgo collaboration]

General Relativity predicts transverse gravitational waves which stretch and squeeze spacetime in the plane perpendicular to their direction of propagation. The allowed distortions are of only two types: (+) ‘plus’ (Fig.29a) and (x) ‘cross’ (Fig.29b). The ‘metric’ theory of gravitation predicts six different polarizations including the two allowed by GR. Any additional polarization would distort spacetime in a different way. This difference in polarization behaviour can be detected by comparing the signals from two non parallel interferometers. The twin LIGO interferometers are aligned almost parallel to each other but the Virgo interferometer is not. GW170814 provided the first opportunity to test the polarization behaviour of gravitational waves. A full parameter estimation analysis was carried out by assuming those gravitational wave polarizations that are forbidden by GR. It was found that the alternative polarization combinations (c, d, e and f in Fig.29) were disfavoured by the analysis. This proves that GW170814 data are consistent with Einstein’s GR theory.

                                        

Fig. 29  Representation of the six polarizations permitted in general ‘metric’ theories of gravity. Only two transverse polarizations permitted by GR are denoted by ‘+’ (a) and ‘x’ (b). Although ( c) also represents a transverse polarization, it is not permitted by GR. In plane- distortions shown by (d), (e), and (f) occur when the gravitational wave travels in the direction indicated by the arrows. [Credit: Clifford Will, Living Reviews in Relativity)

LIGO’s two L shaped Interferometers are aligned ‘back to back,’ pointing away from each other. This arrangement enhances the sensitivity of the pair for waves coming from some direction but prevents a direct test of polarization. The different orientation of the VIRGO interferometer allowed the scientists to study polarization and show that the data strongly favour a pure tensor waveform over a pure vector or a pure scalar form. In one of the panel discussions in September 2017, Deirdre Shoemaker, Logo team member from Georgia Institute of Technology, Atlanta said, “This is the first direct test of the polarization of gravitational waves, future tests will try to set limits on the proportion of scalar and vector waves in the gravitational radiation. But a complete analysis of the polarization would require detectors set at five different orientations.”

3. Physics of Star Formation

The LIGO discoveries have marked the beginning of a new era in astronomy. Not only has it opened a new field of astrophysics, it is opening ‘a new window’ to the universe. In a popular sense, if every observatory and telescope has allowed people to ‘see’ the universe, LIGO is now allowing them to ‘hear’ it. No one has ever ‘heard’ the universe in this manner before. This new mode of knowing the universe has the ability to detect an entirely different kind of information about the nebula, the star and the galaxy. So far our source of information about these heavenly bodies was the detection and analysis of electromagnetic waves emanating from them. Light comes in many forms in addition to that visible to the human eye. It turns out that the human body produces infrared light which is detected by its heat generating effects. Similarly stars emit electromagnetic radiation in different wavelength regions depending on their physical state and chemical composition. A spectrometer attached to an optical telescope may reveal data in the UV, Visible and IR regions and the radio telescopes provide information in the microwave and radio frequency regions. There are now space-borne highly powerful telescopes that cover astronomical objects located  billions of light years away to provide data in the X-ray and gamma ray regions in addition to those in the optical region. There is a fairly good understanding of the process of star formation and their life cycle but the information that a pair of  colliding neutron stars created elements heavier than iron (Fe) and nickel (Ni) could be obtained only when the LIGO-Virgo collaboration provided exact location of the event [20]. In the following sections I would try to summarize the life-cycle of a star. 

Like people, stars are born, they grow old and they die. Their birthplaces are huge, cold clouds of gas and dust known as nebulas. Magellanic clouds, named after the Portuguese navigator (Magellan in 1609), are visible to the unaided eye from the southern sky in the form of nebulous patches. These are two dwarf galaxies, the larger one called Large Magellanic Cloud (LMC) is about 160,000 light years away from Earth and the small one called SMC is 200,000 light years away. In February of 1987, the death of a star was observed in LMC, in a supernova explosion shown in  Fig.30. This event was named 1987A and it was the first supernova visible without a telescope since 1604, the star gradually brightened over the next few months before fading out. 

Among the star clusters of Small Magellanic Cloud (SMC) and nebula NGC 346, is a star-forming region of large clouds, about 200 light years wide shown in Fig.31. Within the SMS, stellar nurseries like NGC 346 also are thought to be similar to those found in the early universe. The large clouds start to shrink under their own gravity and as they get smaller, they break into clumps. Each clump eventually becomes so hot and dense that nuclear reactions begin in their interior and with temperature reaching  10 million Celsius, the clump becomes a new star.

Fig. 30. Supernova 1987A in LMC photographed by Hubble space telescope in 1995

                                    

Fig.31. Hubble Space Telescope image of a region of SMS and NGC 346 exhibiting young stars covered by clouds of their birth so that they look reddened.[Image Credit NASA, ESA, A. Nota]

After their birth, most young stars lie at the center of a flat disc of gas and dust and most of this material is eventually blown away by the star’s radiation. However, before this stage is reached planets may form around the central star, from material of  the flat disc. Infrared observations are able to detect heat coming from invisible stars that are forming inside such clouds. One of the most powerful infrared instruments is the Herschel Space Observatory, launched in May 2009.

3.1 The Mystery of the White Dwarf

   

Fig. 32 Relative size of Sirius A and Sirius B in visible and X-ray light and their relative orbital motion around each other

                      

Sirius is the brightest star in our sky at a distance of about 8.6 light years from Earth. Sirius A has a tiny tiny companion, called Sirius B, orbiting around it once in 50 years. The mass and circumference of Sirius B has been estimated by astronomers, from telescopic observations, to be 1.05 solar mass and 31,000 kilometers respectively. This leads to a mean density of Sirius B to be 4 million grams per cubic centimeter (see Fig.32). Although these values were not as accurately known in 1925 as today, even then the density was so high that the leading British Astronomer Arthur Eddington did not believe it. In his book ‘The Internal Constitution of the Stars’, Eddington had proposed that the internal structure of a star, such as the Sun or Sirius B, is governed by the balance of outward internal pressure created by heating and inward squeeze due to its gravity. As the star cools by emitting radiation into outer space, the random motion of its atoms slows down, so that its outward internal pressure will go down and the weight of the star's outer shell will squeeze it to a smaller volume. The resulting compression would heat up the star raising its internal pressure so that a new balance between squeeze and pressure will be established for the star of size slightly smaller than before. According to this model, as Sirius B continues gradually to cool by radiating heat into interstellar space, it must gradually shrink in size. The most obvious (but wrong) result of this gradual shrinkage was that the star will shrink until it is so small that it becomes a black hole. Eddington did not believe in black holes.

As a 20 year old Indian scholar, Subrahmanyan Chandrasekhar who was to join his graduate studies at Cambridge University, was very impressed with the theoretical work of Prof. R.H. Fowler on ‘Dense Matter’. He was quick to realize that for a high density, tiny star like a white dwarf one has to take recourse to quantum mechanics where motion of electrons, rather than atoms, would come into play. Thus, the pressure, inside Sirius B and other  white dwarfs, would not be due to heat as in a normal star, but due to a quantum mechanical phenomenon called the ‘degenerate motions of electrons’ or ‘electron degeneracy’. This is a consequence of wave / particle duality when matter is compressed to high densities, and each electron inside the matter gets confined to an extremely small cell. An electron squeezed up in a tiny cell against neighbouring electron cells begins to behave in part like a wave but its wavelength cannot be larger than the cell. Therefore an electron inside very dense matter, with its short wavelength and accompanying high energy, would fly around rapidly within its cell. These electrons are called ‘degenerate’ and the pressure that their high speed random motions produce, is called ‘electron degeneracy pressure’. The dwarf star would get stability as a result of the electron degeneracy pressure balancing the inward compression of the star's gravity. The compression of the gravity is proportional to the mass of the star, and for very massive stars the random velocity of degenerate electrons could become comparable to the speed of light. Since an electron's speed cannot exceed the speed of light, Chandrasekhar tried using Special Relativity in conjunction with Quantum Mechanics to account for the additional energy of degenerate electrons that would enable them to balance the squeezing effect of a massive star’s gravity. He came up with the result that the additional energy appears as inertia of the electron and makes it behave as though it had become a bit heavier. In this process of explaining the structure of white dwarfs, he came to the conclusion that no white dwarf can ever be heavier than 1.4 times solar mass [21,22]. This is the well known ‘Chandrasekhar limit’.

Chandrasekhar’s diagram, of the star’s mass versus its circumference, implies that there is only one set of masses and circumferences for which gravity can be counterbalanced by nonthermal pressure (the degenerate electron pressure that remains after star turns cold) of the white dwarfs (see Fig.33). There are two regions clearly separated by the curve, the area with hatched lines and the clear white area beyond the curve. In the hatched region, the star’s nonthermal degeneracy pressure completely overwhelms gravity and it will drive any star in this region to explode. On the other hand for stars of larger circumference to the right of the curve, gravity completely overwhelms the star’s degeneracy pressure and any ‘cold’ star in this region will immediately implode under gravity’s squeeze. The Sun can live in the unhatched region only because it is now very hot and its thermal pressure manages to counterbalance its gravity. When the Sun ultimately cools down, its thermal pressure will disappear and it will no longer be able to remain stable. Gravity will force it to shrink smaller and smaller, squeezing the Sun’s electrons into smaller and smaller cells until enough degeneracy pressure is generated to halt the shrinkage. During this process of shrinkage (or death), The Sun's mass will remain nearly constant, but its circumference will decrease, so it will move leftward on a horizontal line till it stops on the white dwarf curve (its grave) as shown in Fig.33. As a white dwarf, the Sun will continue to reside forever, gradually cooling and becoming a black dwarf- a cold, dark, solid object about the size of the Earth but million times heavier and denser. 

Fig.33 The Chandrasekhar Limit: No white dwarf can ever be heavier than 1.4 times the mass of the Sun. When the Sun cools its shrinkage will stop when it reaches the white-dwarf curve and it will become a white dwarf. Sirius, more than twice heavier than Sun will never hit the white dwarf curve and it will continue shrinking under its gravity as it cools by emitting radiation.

Sirius A  with 2.3 times the mass of the Sun would never die the gentle death that awaits the Sun. When the radiation it emits into outer space has carried away enough heat for the star to begin to cool, its thermal pressure will decline, and gravity’s squeeze will make it shrink smaller and smaller. Because of its very large mass, the shrinkage of Sirius A cannot be halted by nonthermal degeneracy pressure, It is clear from Fig. 33 that Sirius A path during the shrinkage cannot be intercepted by the white dwarf curve. 

Eddington opposed Chandrasekhar in a meeting of the Royal Astronomical Society in London saying, “The star has to go on radiating and radiating and contracting and contracting, until, I suppose, it gets down to a few kilometers radius, when gravity becomes strong enough to hold in the radiation, and the star can at last find peace.” His description matches with the description of the 1990s in the formation of a black hole. Eddington was wrong, but because of his opposition, it took the next 40 years for Chandrasekhar to be recognized for his enormous contribution as a 23 year old in 1935.

3.2 Internal Structure of a Pre-Supernova Star

One of the central problems facing the physicists of the first half of the 20th century was: Why are stars composed mostly of hydrogen and helium? How are all the elements of the Periodic Table formed?. They wanted to know the reasons for elements, such as uranium and gold being rare in nature but others, such as iron and oxygen found in great abundance. Although there had been several suggestions that helium was formed at the center of the Sun, it was Hans Bethe, in a remarkable paper in 1939, who discussed two possible energy-producing paths in which hydrogen could convert to helium [23]. Yet Bethe’s theory fell short of demonstrating how carbon or nitrogen formed in the universe in the first place. In the fall of 1944 Fred Hoyle, from Cambridge, visited the Mount Wilson Observatory in California and learned how enormously dense and hot the cores of massive stars can become during the late stages in their lives. In nuclear statistical equilibrium, while nuclear reactions continue to occur, each reaction and its inverse occur at the same rate, so that there is no further overall net change in the abundances of the elements. 

To actually perform calculations based on statistical mechanics, to estimate the relative abundances of various chemical elements Hoyle needed masses of all the nuclei involved. When tables of nuclear masses became available from Otto Frisch in 1945, Hoyle published an epoch-making paper delineating the framework of a theory for the formation of the elements from carbon and higher in stellar interiors [24]. Hoyle realized the great importance of the synthesis of 12C and also the fact that if a carbon nucleus happened to have an energy level that perfectly matched the energy equivalent of the combined masses of a beryllium nucleus and an alpha particle,  the rate of fusion would increase significantly. He calculated precisely this resonant state of 12C at about 7.68 MeV above the ground state of the carbon nucleus. It was January of 1953 and Hoyle was spending a few months at Caltech. He persuaded Willy Fowler at Kellogg Laboratory to experimentally verify his predicted resonant state of carbon nucleus. Within a couple of weeks the experimental group did find a resonance in carbon at 7.68 MeV with a possible error of 0.03 MeV, in incredible agreement with Hole’s prediction. Hoyle, in a 1954 paper, established the foundation for the theory of nucleosynthesis in stars: the concept that most chemical elements and their isotopes were synthesized from Hydrogen and helium by nuclear reactions within massive stars [25]. Hoyle explained how the abundances of heavy elements today are the direct products of stellar evolution.

  

                       

Fig.34 Products of nucleosynthesis in the core of a very heavy star before supernova explosion

      Stars spend their lives in a continuous battle against gravity. In the absence of an opposing force, gravity would cause any star to collapse to its center. By 'igniting’ nuclear reactions in their cores, stars create extremely high temperatures, and the associated high pressures support the stars against their own weight. In a star's core, first, hydrogen is fused into helium, then helium into carbon, then carbon into oxygen and so on. Hoyle described how after each central fuel is consumed, gravitational contraction causes the temperature in the core to increase until the 'ignition’ of the next nuclear reaction. In this manner, new elements are synthesized, all the way up to iron, in each successive core-burning episode. Since each burning core is smaller than the preceding one, the star develops an onion skin-like structure in which each layer is composed of the main product- 'ashes’, of the preceding nuclear reaction as shown in Fig.34. Since iron is the most stable nucleus, once an iron core forms, no more nuclear energy is available from fusion of nuclei into heavier ones. Without a source of internal heat to combat gravity, the stellar core collapses, triggering a dramatic explosion. This is called supernova explosion and it powerfully ejects all the forged elements into interstellar space, where they enrich the gas from which later generations of stars and planets form. The temperatures attained during the explosion are so high that elements heavier than iron are formed by neutrons bombarding the stellar material.

When the hydrogen, in the core of a medium size star, is exhausted the core contracts under star’s gravity till the inside temperature reaches the ignition point for the conversion of helium into carbon and oxygen, while the outer hydrogen-rich shell  expands due to the radiation pressure from the core and this enormous looking star is called a red giant. Our Sun is a good example of this kind of process which comes for stars that are about 10 billion years old. The life of a red giant lasts for about one billion year compared to 10 billion years for its parent star. The core of the red giant star, however, remains intact to form a ‘white dwarf’ surrounded by an expanding cloud of gas and dust. This cloud-like structure, with white dwarf at its center, is called a planetary nebula and marks the star’s transition from a red giant to a white dwarf in about 100 thousand years. The white dwarf continues to slowly shine for the next 10 billion years before turning into a black hole.  At 8.6 light years away from Earth, Sirius B is the nearest known white dwarf star. In 1844 astronomer Friedrich Bessel observed Sirius A, the brightest star in the sky, to move around an unseen object and eventually in 1863 this mysterious object was found to be Sirius B and the orbital period of this binary system was estimated to be 50 years (see Fig.32).  Very massive stars turn into a neutron star or a black hole as described in the next section.

3.3 The Neutron Star and the Black Hole

A neutron star is the collapsed core of a large star of 10 to 20 times the solar mass. Its diameter is 10 to 20 kilometers and a mass 2 to 3 times that of the Sun. When a massive star evolves away from the main sequence, subsequent nuclear burning produces an iron-rich core. Further deposits of mass from shell burning cause the core to exceed Chandrasekhar limit and electron degeneracy pressure is overcome by the gravitational collapse. The contraction of the core generates temperatures in excess of 5x109 K. As the temperature rises even higher, electrons and protons combine to form neutrons, via the process of electron capture, releasing a flood of neutrinos. When the density of the core reaches the nuclear density of 4x1017 kg/m3, neutron degeneracy pressure halts the core contraction in a similar manner as the electron degeneracy pressure halts the shrinking in a white dwarf.. The infalling outer envelope of the star is halted and it is flung outwards by the flux of neutrinos produced by neutron formation, creating a supernova and the remnant left is a neutron star. If the remnant has a mass greater than 3 times the solar mass, it collapses further to become a black hole.

When they are formed, neutron stars rotate in space and as they compress and shrink, the speed of spinning increases to conserve the angular momentum during the process of neutron star formation. The collapsing force of gravity is counterbalanced by the outward force due to neutron degeneracy pressure. The observed neutron stars are very hot with surface temperature around 600,000 K. The magnetic field on a neutron star's surface is about 2x1011 times that on Earth. Some neutron stars emit beams of electromagnetic radiation that make them detectable as pulsars. The radiation from a pulsar is thought to be emitted from regions close to its magnetic poles. When the magnetic poles do not coincide with the rotational axis of the neutron star, the emission beam will  sweep the sky (see Fig.35), and if the observer happens to be in the path of this beam, it will appear as pulses of radiation coming from a fixed point in space. 

     

Fig.35 Artist concept of a Neutron Star with its rotational axis perpendicular to the magnetic axis (in the center). Jocelyn Bell (on the left) and S. Chandrasekhar (on the right) who made path breaking contributions to Astrophysics when they were in their early twenties.(Adopted from www.aps.org/publications/apsnews/200602/history.cfm      and news/day/dayitems/item/14886-subrahmanyan-chandrasekhar)

The existence of neutron stars was established by the discovery of radio pulsars in 1967 by Jocelyn Bell Burnell as part of her Ph D  investigations [26]. However, she was not part of the Nobel prize in Physics, shared by her thesis supervisor Antony Hewish with astronomer Martin Ryle, despite having been the first to observe and precisely analyse pulsars. The fastest-spinning neutron star,  known till date, rotates at the rate of 716 times per second giving a linear speed to its surface of about one quarter the speed of light. The number of neutron stars in the Milky Way Galaxy is estimated to be around 100 million based on the stars that have undergone supernova explosions. The speed of a neutron star’s rotation decreases with age and it is almost impossible to detect slow rotating or cold neutron stars. X-ray pulsars result from neutron stars in binary systems that undergo accretion which produces X-rays with matter from the companion star falling into the neutron star during the orbital rotation. The companion star may eventually become a white dwarf or a neutron star. The merger of binary neutron stars may be the source of short duration gamma ray bursts and are likely strong sources of gravitational waves. The equation of state of a neutron star is still not known. It is assumed that it differs significantly from that of a white dwarf, whose equation of state is that of a degenerate electron gas that can be descrin।में।।।ñn nnnnnñnnnnnnnnn   न ननीनननbed in close agreement with special Relativity. However, with a neutron star the increased effects of general Relativity can no longer be ignored. The origins of high magnetic fields are not very clear. One hypothesis is that of 'flux freezing’ or conservation of the original magnetic flux during the formation of the neutron star.

                                          

Fig. 36  Artist’s illustration of a spinning neutron star emitting radio waves along its magnetic axis (top) and a binary system with a pair of neutron stars rotating around each other (bottom)

PSR 1913+16 was the first binary pulsar to be discovered by Russell A. Hulse and Joseph H. Taylor, Jr., in 1974 by using the Arecibo 305 meter antenna to detect pulsed radio emission [27]. The source was identified as a rapidly rotating and highly magnetized neutron star that rotates on its axis 17 times per second and has a radio pulse period of 59 milliseconds. When the system had been observed for a prolonged period of time, it was found to have a systematic variation in the arrival time of the pulses. Sometimes the pulses would arrive a little earlier than expected and sometimes a little later than expected. These variations were repetitive with a period of 7.75 hours. It was soon realized that the pulsar was in a binary orbit as shown in Fig. 36. The second member of the binary pair was also identified as a neutron star but the pulses from this companion neutron star have not been detected, perhaps due to an unfavourable viewing angle. [4]. As stated earlier, the findings of this Hulse-Taylor binary was one of the greatest incentives for the LIGO project.

3.4  Merger of two Neutron Stars and the ‘Kilonova’

Gamma-ray Burst Monitor (GBM) aboard Fermi Space Telescope detected a gamma ray burst on 17 August 2017 at 12:41:06 UTC, which was designated as GRB170817A. About 6 minutes later the analysis of data from LIGO at Hanford, was found to be consistent with a binary neutron star (BNS) coalescence with merger time 12:41:04 designated GW170817 which happened about 2 seconds before GRB170817A. A rapid re-analysis of the data from the twin LIGO detectors and the Virgo detector confirmed a highly significant gravitational wave event consistent with a BNS coalescence associated with the time of GRB170817A in the galaxy NGC4993 located about 130 million light years from Earth (see Fig. 37).

     

Fig. 37 Detection of short gamma-ray bursts (GRB170817A) and gravitational waves (GW170817)  from a  Binary Neutron Star merger in galaxy NGC4993 located 130 million light years from Earth. Gamma ray signals in the first two rows were detected by Fermi Space telescope and that in the third row by International Gamma Ray Astrophysics Laboratory (INTEGRAL). [Adapted from Ref. 28]

Theoretical models for the merger of two Neutron stars predict a chirping gravitational wave signal as the stars spiral closer and closer. The end of chirp from merging neutron stars should coincide with a short gamma-ray burst. This is a powerful storm of gamma rays produced as the two finally collide and it is unlike the merger of two black holes where no emission of electromagnetic waves occurs. The emission of gravitational waves and gamma rays is followed by a kilonova, which is a transient visible source with emission in the infrared as well as in the ultraviolet. This optical emission arises from radioactive decay of heavy elements formed in the collision. This source slowly decays over a time scale of weeks (see Fig.38). It is also predicted that the merger could create a powerful jet of high energy particles which could emit X-rays and radio wavelengths. 

                       

Fig. 38. (1):Artist's impression of two inspiraling neutron stars of a binary system. (2) The production of a gamma-ray jet and gravitational waves at the point of merger. (3): A small fraction of their ejected mass radiating as a kilonova, and finally (4): A massive neutron star or black hole remains after the event. [Adapted from NASA, ESA, and A. Field (STScl)]

The operation of a three detector network was very significant in precise sky localization of the Binary Neutron Star merger event GW170817. The three-detector skymap was localized within 30 square degrees. And has been the most precise sky localization of all detected gravitational waves so far as shown in Fig.39. The relatively small sky area and distance of GW170817, the detected gamma ray emission and the expectation for other electromagnetic signals led to a worldwide alert to be issued. Coordinated efforts were immediately started by ground-based as well as space-based observatories to detect signals over the entire electromagnetic spectrum. Less than 11 hours after the BNS merger a bright optical transient  SSS17a was discovered in the galaxy NGC 4993 [29].

                       

Fig. 39. Localization of the source of GW170817 from gravitational waves, gamma ray and optical signals. On the left image: light green (LIGO), dark green (LIGO-Virgo), light blue (IPN Fermi / INTEGRAL, dark blue (Fermi-GBM). Right inset: host galaxy NGC4993 on the day of BNS merger (top) and 20.5 days before the event. [Adapted from Ref.28] i0.wp.com/public.virgo-gw.eu/wp-content/uploads/2017/10/GW170817_MMA_Skymap.png

Within hours of detecting SSS17a, multiple ground and space based telescopes were utilized to trace the photometric evolution of the transient in the ultraviolet (UV), visible and infrared (IR) regions. The light emission rapidly declined in brightness and changed from being bluish to becoming reddish with the transition of the spectral peak from UV to the IR. The spectrum evolved from an initial featureless blackbody shape peaking in the UV one day after the merger, to an IR dominated spectrum , with broad absorption features only a few days later. Thus, spectra were found to closely resemble predictions for a ‘Kilonova’ powered by radioactive decay of heavy nuclei and isotopes synthesized through the r-process in the merger ejecta. The rapid neutron capture process (r-process) is a set of reactions in nuclear astrophysics that are responsible for the nucleosynthesis of almost half the atomic nuclei heavier than iron. The process involves a succession of rapid neutron capture by a heavy nucleus, such as 56Fe, and the capture should be so rapid that the nucleus does not have time to undergo radioactive decay before another neutron arrives to be captured. The r-process occurs in environments where there is a high density of free neutrons, such as material ejected from a core-collapse supernova or matter thrown off a kilonova from a binary neutron star merger. SSS17a is the first clear demonstration that r-process nucleosynthesis occurs in BNS merger near NGC4993 in the constellation of Hydra as shown in Fig. 40. There is no evidence of the SSS17a kilonova in an image of galaxy NGC4993 taken many days before the event and it is clearly seen after the binary neutron-star coalescence (BNC)

 

Fig. 40. Images of galaxy NGC4993 enlarged with SSS17a (left), before the BNC (middle) and after the BNC (right), by a team of four Carnegie astronomers [Image credit: Carnegie,Tony Piro]

It is to be noted that the emission in UV/ Visible/ IR is dominated by radioactive decay of r-process matter; the emission of short gamma ray bursts is indicative of relativistic ejecta. In the case of GW170817, the gamma ray energy is about five orders of magnitude lower than detected for cosmological short GRBs, which may be due to an off axis viewing angle. This view is consistent with the detection of X-ray by Chandra Space Telescope during two week of observations after the GW170817 event.  In the first observation on 19 August no X-ray were detected at the location of SSS17a as marked by the cirule in the inset of Fig. 41A. On 26 August, X-ray were seen for the first time and the level of X-ray brightness remained almost the same on September 1 and 2. These observations match with that predicted by theoretical models of a short GRB. A burst of X-ray and gamma ray is generated by a narrow jet of high energy particles produced by the merger of two neutron stars. Thus, initial non-detection by Chandra, followed by its detection indicates that X-ray emission is consistent with the afterglow from a GRB viewed off axis- that is the jet not pointing towards Earth.

This is the first time astronomers have ever detected an off axis short GRB. It is believed that initially the jet was narrow, with Chandra viewing it from the side, but as time passed the material in the jet slowed down and widened as it hit the surrounding material causing the X-ray emission to increase as the widened jet came into direct view of Chandra. The Chandra data has allowed the researchers to estimate the angle between the jet and the line of sight to be between 20 and 60 degrees (see Fig. 41B). The detection of this off axis short GRB helps explain the weakness of the gamma ray signal detected with Fermi Space telescope for a burst that is so close by. Because the telescopes are not looking straight down the barrel of the jet as they have for other short GRB, the gamma ray signal is much fainter. By detecting an off axis short GRB at the location of the radioactive glow, the Chandra observations provide the missing observational link between short GRBs and gravitational waves from neutron star merger.

                                                 

                         A                                                                           B

Fig. 41 (A) Region of NGC4993 recorded by Hubble and that by Chandra in the inset. The location of SSS17a is marked by the black and white circles. (B) Model of GRB and energetic particle jet oriented with respect to the line of sight. [Image Credit: NASA/ Chandra]

The optical and infrared light is likely  caused by the radioactive glow from heavy elements such as gold and platinum in the material ejected by the neutron star merger. This glow had been predicted to occur after neutron stars merged.This is the first time astronomers have all of the necessary pieces of information of neutron stars merger- from the production of gravitational waves followed by signals in gamma rays, X-rays, optical and infrared light that all agree with predictions for a short GRB viewed off axis. These observations localized the GW170817 event at a distance about 130 million light years from Earth in an area of 28 degree2 in galaxy NGC4993. The counterpart radio emission from the source was detected 16 days after GW170817, which has allowed the diagnosis of the energetics and environment of the merger. The observed radio emission can be explained by either a collimated ultra-relativistic jet viewed off-axis, or a cocoon of mildly relativistic ejecta from the neutron star merger. It is expected that the observations of radio light curves, within 100 days of the merger, will distinguish between the two models and a very long baseline interferometry will have the capability of directly measuring the angular velocity and geometry of the debris.

4.  Science from Merger of Black Holes and of Neutron Stars

The only method of detecting a black hole, before September 2015, was based on the observations of X-ray  emission from material falling from a star into its invisible companion of enormous gravity. This mass of the invisible companion 'black hole’ was estimated in terms of the Solar mass, on the basis of its gravitational field and other indirect astronomical parameters. All this changed on September 14, 2015 when a pair of black holes with combined mass of 65 solar masses was detected in a black hole merger event by LIGO. It was a very big surprise and 5 more such pairs of black holes have been detected during a span of two years, making  scientists in the field greatly interested to find explanations for the origins and existence of the black hole binaries (see Fig.42).

  

Fig. 42  Masses distribution as function of detection-date of the black holes, detected in 5 separate mergers, by LIGO collaboration till November 2017 (Image credit LIGO)

       

Fig. 43. Massive black holes detected by LIGO (blue) and those of smaller mass detected by X-rays(purple). Neutron stars (yellow) in the cosmos detected by LIGO-Virgo (at the center) and  others detected by electromagnetic waves in the bottom row of lowest masses.

The pair of black holes detected by LIGO in June 2017 during the merger event GW170608 involve members with masses 7 times and 12 times the solar mass. The merger created a black hole 18 times the mass of the Sun with about one solar mass radiated out as gravitational waves. This is the lightest combined mass black hole detected so far with that in the merger event GW151226 being slightly heavier at 21 times the solar mass.The GW170608 event has masses consistent with black holes previously detected through X-ray observations as shown in Fig.43. We are beginning to have a population of black holes that establishes a link between the population of black holes detected by electromagnetic waves alone and that by  only through gravitational waves . It is interesting to note that gravitational wave detections have led to binary black holes whereas electromagnetic detections have led to single black holes. 

It is speculated that the pair of binary black holes results either from  a massive binary star system formed alone or that formed in dense clusters bustling with stars. It is known that stars born in dense environments get knocked around much more than stars formed in isolation. It is hoped that with enough LIGO-Virgo data on binary black holes, it may be possible to determine the ratio of black holes formed in isolation to those formed in crowded environments. The task of LIGO scientists is now akin to biologists studying a rare species in the wild. They have now to establish links  between the characteristics of the individuals and those of the entire population.

The observations of gravitational-wave, short gamma-ray burst and electromagnetic radiation spanning over UV, Visible, IR and Radio-wave regions leaves little doubt that GW170817 event is anything but a binary neutron star merger (see center image of bottom row Fig.43). The analysis of experimental data from the merger of two inspiral black holes (e.g. GW150714) is quite different from that due to the merger of two inspiral neutron stars.  Black holes are just made of warped spacetime and the merger creates a new warped spacetime which is described by its mass and spin. Neutron stars, on the other hand, are made of nuclear matter, which can be distorted during the inspiral due to tides raised on one by the gravity of the other. These processes extract energy from the orbit and accelerate the inspiral. The tidal deformability of the Neutron stars depends on their compactness. The fluffier a neutron star is, the bigger the impact of tides; the more compact, the smaller the impact. Unfortunately not enough is known about neutron star material to take into account the tidal effects due to the star’s gravity.

GW170817 signal was measured several thousand cycles from the inspiral and it is the loudest gravitational signal yet found beating even GW150914 with a signal to noise ratio of 32 while for GW150914 it was just 24.  From the gravity wave signal the source distance has been estimated to be about 130 million years which corresponds to the Late Jurassic period on Earth. The gamma ray burst arrived at Earth 1.7 seconds after the merger. It is not expected that gamma-rays would be emitted at exactly the moment of merger, but taking into account a sensible range of emission times, one can bound the difference between the speed of gravity and the speed of light, which should be the same in General Relativity and the difference should be no more than 3 parts in 1015.

The gravitational wave distance can be combined with the redshift of galaxy NGC4993 to measure the Hubble constant, the rate of expansion of the Universe. The best estimates for the Hubble constant, from the cosmic microwave background and from supernova observations are inconsistent with each other. It is hoped that gravitational wave observations should have different sources of error and it would help to resolve the difference.

In the merger of two compact objects of a binary system to produce gravitational wave the Chirp mass is given by

            M=  (m1m2)⅗ /  (m1+m2)⅕                                                                      (6)

From the measurement of a large number of cycles during inspiral, the chirp mass of the merger is easily obtained but the determination of individual neutron star masses is complicated because the ratio of two masses is degenerate with the spins of the neutron stars. Once the determination of mass and spin becomes possible, one could explore how electromagnetic signals, from the merger of two neutron stars, are affected by their mass and spin.

  Researchers have performed radiative transfer simulations of the kilonova to derive properties of ejected material from the neutron star merger using the optical and near infrared emissions powered by radioactive decay of r-process nuclei synthesized in the merger. It has been observed that near-IR emission lasting more than 10 days is explained by 0.03 Solar mass of ejecta containing lanthanide elements. However, in the observed optical emission, the proportion of blue light requires an ejecta component with a relatively high electron fraction. Thus, theoretical models need to be developed to explain the emission characteristics of light at the two ends of the visible spectrum.

The analysis of gravitational waves from GW170817 tells us that the merging objects had masses consistent with neutron stars, and the flash of gamma rays tells us that the objects are unlikely to be black holes since this kind of collision is not expected to emit light. However, the observed gamma ray burst was one of the closest to Earth, yet it was surprisingly weak for its distance, and models need to be developed to explain this anomaly.

The gravitational wave signal from a merger is a ‘Standard Siren’ which means that all merger sources have the same loudness. Thus, the strength of the signal can be used to calculate the distance, from Earth, of the merger containing the galaxy. Such measurements can also be used to determine the Hubble constant, which describes the expansion of the Universe [30]. Since neutron star mergers last for a longer time than black hole mergers, they can be used as more sensitive indicators for deviations from General Relativity.

5. Conclusion

Nearly 400 years ago when Galileo carried out his experiment by dropping unequal masses from the leaning tower of Pisa, he put an end to the 1900 years old perception of the Greek philosopher, Aristotle, that  objects were  attracted by Earth in accordance with  their masses. Galileo not only showed that the force of gravity induces the same acceleration in all objects irrespective of their masses, he was also the first to use the optical telescope to study the motions of the planets and their satellites in the Solar system. About 50 years later Newton came up with the law of Universal Gravitation, according to which the force of attraction between any two objects was directly proportional to the product of their masses and inversely to the square of the distance between them. Inherent in Newton's law of Gravitation was the concept of ‘action at a distance’ which implies that the force of attraction at a distant object was instantaneous. Einstein did not agree with Newton’s theory of gravitation, and in 1916 he used the theory of General Relativity to show that gravity was associated with the geometry of spacetime. His theory also predicted the emission of gravitational waves from an accelerated material particle, in a manner similar to that of electromagnetic waves emitted by an accelerated electrically charged particle. Einstein, himself, did not believe that it would be possible to detect the gravitational waves using the technology available in the first half of the 20th century. 

Indian astrophysicist  Chandrasekhar came up with the theory of ‘white dwarf’ star formation in 1935,  showing that stars more massive than 1.4 times the Sun’s mass, would shrink to become even smaller and more massive than a white dwarf. It was not until the observation of the first pulsar in 1967, that astronomers and astrophysicists started believing in the ‘Chandrasekhar limit’ and the existence of neutron stars and of black holes. The first observation of a pulsar from a binary neutron star system in 1974 led to indirect evidence of the existence of gravitational waves. It was observed that the orbital motion of the pulsar around its companion neutron star was slowing with passage of time and the rate of this decrease was in agreement with General Relativity, which predicted emission of gravitational waves from such a binary system. It was about this time that Prof. Rainer Weiss of MIT started doing experiments with large-arm Michelson interferometer as a possible detector of the gravitational waves and Prof. Kip Thorne, from Caltech, collaborated with him with his efforts of modelling the pattern of gravitational waves when two neutron stars or two black holes collided to form a heavier massive object. The continued efforts of the two led to establish the Light Interferometer Gravitational-wave Observatory (LIGO), and the association of Prof. Barry Barish, from Caltech, as the director in 1997 gave the project the momentum necessary for building the twin LIGO interferometers, one in Hanford (Washington state) and the other in Livingston (Louisiana) each with 4 km long arms.

The highly sophisticated Advanced LIGO interferometers are capable of detecting change in length of 10-18 meter in the 4 km long arms. More than a thousand member team of scientists and engineers belonging to the LIGO Scientific Collaboration (LSC) worked for more than a decade to achieve unprecedented accuracy and precision in measurements of length strains smaller than 10-22, and calculated thousands of waveform templates of stellar mass objects in various stages of spiral motion around each other till they merged to form a heavier object. With great advancements in technology breathtaking telescope images of the far-away cosmos have been made possible using photon messengers of different varieties from X-ray, through visible and infrared to radio waves. This all changed with the LIGO detection of gravitational waves from the merger of a pair of black holes in September 2015, an achievement that was recognized with the 2017 Nobel Prize in Physics. The Virgo interferometer joined LIGO in detection of gravitational waves in August 2017 and the joint effort resulted in the observation of a merger of two black holes and a merger of two neutron stars, in addition to five black hole merger events detected by LIGO alone.

The detection of neutron star merger signal GW170817 by three detectors, the twin LIGO detectors separated by 3000 km in the US and Virgo in Italy, is of great importance. The gamma ray burst from the merger was detected by Fermi space telescope 1.7 seconds after its gravitational wave detection and subsequently the merger was detected worldwide from X-ray to Radio waves using ground based as well as space based telescopes. Since the process of merger lasted for about 100 seconds, the analysis of data indicated that the colliding objects were between 1 and 2 solar masses, which is consistent with known neutron star masses. GW170817 source was only 130 million light years from Earth compared to the first black hole merger GW150914 a billion light years away, and hence it was much stronger than the latter. The scientists were able to localize the neutron star merger event to a 28 degree2 patch of sky using the LIGO-Virgo combination, which is about 20 times smaller than the localization of LIGO’s first detection. Radio astronomy surveys have indicated that there are about two dozen binary neutron systems within the Milky Way Galaxy, but none of them are likely to merge for millions of years. But there are neutron binaries outside our Galaxy and indirect evidence of the merger of such extragalactic neutron stars exist in the form of short gamma ray bursts. These intense flashes of gamma rays last for about a second but the energy emission during the process is as much as our Sun would emit in a trillion years. It is expected that with further enhancement of the ground based interferometric detection facilities, it would be possible to detect the gravitational waves associated with the violent events that give rise to intense flashes of gamma ray.

The chirp-like signal, caused by a travelling ripple through spacetime, has given us a new way to sense the Universe, like being able to hear, when before we could only see. It is like advancing from watching the Universe in a silent movie to that accompanied by a gravitational-wave cacophony. We are entering the new era of ‘multi messenger’ astronomy [31], in which we can observe a source through both gravitational waves and photons. In the history of astronomy, the emergence of a new observational tool has often witnessed the discovery of phenomena we never imagined. So there may be many surprises in store for us with the detection of gravitational waves as a new astronomical tool.

Acknowledgements

It was my good fortune to have watched the Physics Nobel Prize webcasts on October 3, 2017 from MIT, where Prof. Rainer Weiss talked briefly about the interferometer and the audible frequencies associated with the the gravitational wave signal, and that from Caltech, where Prof. Kip Thorne explained how it was more probable to detect collision of two black holes from a distant part of the Universe. I was greatly enthused by watching Youtube videos of these two great scientists and the clarity of their explaining the complex processes induced me further to look into the vast literature that was rapidly coming out on the details of the momentous discovery. I have tried to summarize the basic features of the LIGO experiments, a glimpse of the complex computation and results, with some historical instances that helped my layman understanding of this wonderful discovery. I am greatly indebted to the vast number of authors, whose papers I could get freely on the internet to prepare this article. Prof. A. N. Mantri spent many hours of his valuable time to make me understand the basics of General Relativity and its application to gravity and I owe him more than my grateful thanks for his help. I am thankful to Dr Rama S. Singh who not only introduced me to the book, ‘Brilliant Blunders’, but also took me to an excellent lecture on ‘Gravitational Waves’ by Brian Lantz under the auspices of Photonic Society at Santa Clara, both of which greatly improved my level of comprehension. I was also benefited by interactions with many people while working as a volunteer in the ‘Destination Universe’ and ‘Touch the Sun’ sections of the Chabot Space and Science Center. Sudheer and Sangeeta helped me with writing this article and Michelle took care of most of my needs during my stay in California. Punam and Vineeta keep a constant vigil on my health, which has helped me to remain alert. This article is a token of my affection to my grandchildren Leo and Mia who kept me refreshed and happy with their childhood antics.

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