Gravitational waves of two neutron stars

Gravitational waves are disturbances in the curvature (fabric) of spacetime, generated by accelerated masses, that propagate as waves outward from their source at the speed of light. They were proposed by Henri Poincaré in 1905 and subsequently predicted in 1916 by Albert Einstein on the basis of his general theory of relativity. Gravitational waves transport energy as gravitational radiation, a form of radiant energy similar to electromagnetic radiation. Newton's law of universal gravitation, part of classical mechanics, does not provide for their existence, since that law is predicated on the assumption that physical interactions propagate instantaneously (at infinite speed)—showing one of the ways the methods of classical physics are unable to explain phenomena associated with relativity.

Gravitational-wave astronomy is a branch of observational astronomy that uses gravitational waves to collect observational data about sources of detectable gravitational waves such as binary star systems composed of white dwarfs, neutron stars, and black holes; and events such as supernovae, and the formation of the early universe shortly after the Big Bang.

In 1993, Russell A. Hulse and Joseph H. Taylor, Jr. received the Nobel Prize in Physics for the discovery and observation of the Hulse-Taylor binary pulsar, which offered the first indirect evidence of the existence of gravitational waves.

On 11 February 2016, the LIGO (Laser Interferometer Gravitational-Wave Observatory) and Virgo Scientific Collaboration announced they had made the first direct observation of gravitational waves. The observation was made five months earlier, on 14 September 2015, using the Advanced LIGO detectors. The gravitational waves originated from a pair of merging black holes. After the initial announcement the LIGO instruments detected two more confirmed, and one potential, gravitational wave events. In August 2017, the two LIGO instruments and the Virgo instrument observed a fourth gravitational wave from merging black holes, and a fifth gravitational wave from a binary neutron star merger. Several other gravitational wave detectors are planned or under construction.

In 2017, the Nobel Prize in Physics was awarded to Rainer Weiss, Kip Thorne and Barry Barish for their role in the direct detection of gravitational waves.

History

The possibility of gravitational waves was discussed in 1893 by Oliver Heaviside using the analogy between the inverse-square law in gravitation and electricity. In 1905, Henri Poincaré proposed gravitational waves, emanating from a body and propagating at the speed of light, as being required by the Lorentz transformations and suggested that, in analogy to an accelerating electrical charge producing electromagnetic waves, accelerated masses in a relativistic field theory of gravity should produce gravitational waves. When Einstein published his general theory of relativity in 1915, he was skeptical of Poincaré's idea since the theory implied there were no "gravitational dipoles". Nonetheless, he still pursued the idea and based on various approximations came to the conclusion there must, in fact, be three types of gravitational waves (dubbed longitudinal-longitudinal, transverse-longitudinal, and transverse-transverse by Hermann Weyl).

However, the nature of Einstein's approximations led many (including Einstein himself) to doubt the result. In 1922, Arthur Eddington showed that two of Einstein's types of waves were artifacts of the coordinate system he used, and could be made to propagate at any speed by choosing appropriate coordinates, leading Eddington to jest that they "propagate at the speed of thought". This also cast doubt on the physicality of the third (transverse-transverse) type that Eddington showed always propagate at the speed of light regardless of coordinate system. In 1936, Einstein and Nathan Rosen submitted a paper to Physical Review in which they claimed gravitational waves could not exist in the full general theory of relativity because any such solution of the field equations would have a singularity. The journal sent their manuscript to be reviewed by Howard P. Robertson, who anonymously reported that the singularities in question were simply the harmless coordinate singularities of the employed cylindrical coordinates. Einstein, who was unfamiliar with the concept of peer review, angrily withdrew the manuscript, never to publish in Physical Review again. Nonetheless, his assistant Leopold Infeld, who had been in contact with Robertson, convinced Einstein that the criticism was correct, and the paper was rewritten with the opposite conclusion and published elsewhere.

In 1956, Felix Pirani remedied the confusion caused by the use of various coordinate systems by rephrasing the gravitational waves in terms of the manifestly observable Riemann curvature tensor. At the time this work was mostly ignored because the community was focused on a different question: whether gravitational waves could transmit energy. This matter was settled by a thought experiment proposed by Richard Feynman during the first "GR" conference at Chapel Hill in 1957. In short, his argument known as the "sticky bead argument" notes that if one takes a rod with beads then the effect of a passing gravitational wave would be to move the beads along the rod; friction would then produce heat, implying that the passing wave had done work. Shortly after, Hermann Bondi, a former gravitational wave skeptic, published a detailed version of the "sticky bead argument".

After the Chapel Hill conference, Joseph Weber started designing and building the first gravitational wave detectors now known as Weber bars. In 1969, Weber claimed to have detected the first gravitational waves, and by 1970 he was "detecting" signals regularly from the Galactic Center; however, the frequency of detection soon raised doubts on the validity of his observations as the implied rate of energy loss of the Milky Way would drain our galaxy of energy on a timescale much shorter than its inferred age. These doubts were strengthened when, by the mid-1970s, repeated experiments from other groups building their own Weber bars across the globe failed to find any signals, and by the late 1970s general consensus was that Weber's results were spurious.

In the same period, the first indirect evidence for the existence of gravitational waves was discovered. In 1974, Russell Alan Hulse and Joseph Hooton Taylor, Jr. discovered the first binary pulsar, a discovery that earned them the 1993 Nobel Prize in Physics. Pulsar timing observations over the next decade showed a gradual decay of the orbital period of the Hulse-Taylor pulsar that matched the loss of energy and angular momentum in gravitational radiation predicted by general relativity.

This indirect detection of gravitational waves motivated further searches despite Weber's discredited result. Some groups continued to improve Weber's original concept, while others pursued the detection of gravitational waves using laser interferometers. The idea of using a laser interferometer to detect gravitational waves seems to have been floated by various people independently, including M. E. Gertsenshtein and V. I. Pustovoit in 1962, and Vladimir B. Braginskiĭ in 1966. The first prototypes were developed in the 1970s by Robert L. Forward and Rainer Weiss. In the decades that followed, ever more sensitive instruments were constructed, culminating in the construction of GEO600, LIGO, and Virgo.

After years of producing null results improved detectors became operational in 2015 - LIGO made the first direct detection of gravitational waves on 14 September 2015. It was inferred that the signal, dubbed GW150914, originated from the merger of two black holes with masses 36 M⊙ and 29 M⊙, resulting in a 62 M⊙ black hole. This suggested that the gravitational wave signal carried the energy of roughly three solar masses, or about 5x10⁴⁷ joules.

A year earlier it appeared LIGO might have been beaten to the punch when the BICEP2 claimed that they had detected the imprint of gravitational waves in the cosmic microwave background. However, they were later forced to retract their result.

Gravitational waves are constantly passing Earth; however, even the strongest have a minuscule effect and their sources are generally at a great distance. For example, the waves given off by the cataclysmic final merger of GW150914 reached Earth after travelling over a billion light-years, as a ripple in spacetime that changed the length of a 4-km LIGO arm by a thousandth of the width of a proton, proportionally equivalent to changing the distance to the nearest star outside the Solar System by one hair's width. This tiny effect from even extreme gravitational waves makes them observable on Earth only with the most sophisticated detectors.

The effects of a passing gravitational wave, in an extremely exaggerated form, can be visualized by imagining a perfectly flat region of spacetime with a group of motionless test particles lying in a plane, e.g. the surface of a computer screen. As a gravitational wave passes through the particles along a line perpendicular to the plane of the particles, i.e. following the observer's line of vision into the screen, the particles will follow the distortion in spacetime, oscillating in a "cruciform" manner, as shown in the animations. The area enclosed by the test particles does not change and there is no motion along the direction of propagation.

The oscillations depicted in the animation are exaggerated for the purpose of discussion — in reality a gravitational wave has a very small amplitude (as formulated in linearized gravity). However, they help illustrate the kind of oscillations associated with gravitational waves as produced by a pair of masses in a circular orbit. In this case the amplitude of the gravitational wave is constant, but its plane of polarization changes or rotates at twice the orbital rate, so the time-varying gravitational wave size, or 'periodic spacetime strain', exhibits a variation as shown in the animation. If the orbit of the masses is elliptical then the gravitational wave's amplitude also varies with time according to Einstein's quadrupole formula.

As with other waves, there are a number of characteristics used to describe a gravitational wave:

• Amplitude: Usually denoted h, this is the size of the wave — the fraction of stretching or squeezing in the animation. The amplitude shown here is roughly h = 0.5 (or 50%). Gravitational waves passing through the Earth are many sextillion times weaker than this — h ≈ 10⁻²⁰.
  
• Frequency: Usually denoted f, this is the frequency with which the wave oscillates (1 divided by the amount of time between two successive maximum stretches or squeezes)
  
• Wavelength: Usually denoted λ, this is the distance along the wave between points of maximum stretch or squeeze.
  
• Speed: This is the speed at which a point on the wave (for example, a point of maximum stretch or squeeze) travels. For gravitational waves with small amplitudes, this wave speed is equal to the speed of light (c).
  

The speed, wavelength, and frequency of a gravitational wave are related by the equation c = λf, just like the equation for a light wave. For example, the animations shown here oscillate roughly once every two seconds. This would correspond to a frequency of 0.5 Hz, and a wavelength of about 600 000 km, or 47 times the diameter of the Earth.

In the above example, it is assumed that the wave is linearly polarized with a "plus" polarization, written h₊. Polarization of a gravitational wave is just like polarization of a light wave except that the polarizations of a gravitational wave are 45 degrees apart, as opposed to 90 degrees. In particular, in a "cross"-polarized gravitational wave, h_×, the effect on the test particles would be basically the same, but rotated by 45 degrees, as shown in the second animation. Just as with light polarization, the polarizations of gravitational waves may also be expressed in terms of circularly polarized waves. Gravitational waves are polarized because of the nature of their source.

Neutron star merger

A neutron star merger is a type of stellar collision. It occurs in a fashion similar to the rare brand of type Ia supernovae resulting from merging white dwarfs. When two neutron stars orbit each other closely, they spiral inward as time passes due to gravitational radiation. When the two neutron stars meet, their merger leads to the formation of either a more massive neutron star, or a black hole (depending on whether the mass of the remnant exceeds the currently poorly known Tolman–Oppenheimer–Volkoff limit). The merger can also create a magnetic field that is trillions of times stronger than that of Earth in a matter of one or two milliseconds. These events are believed to create short gamma-ray bursts. The mergers are also believed to produce kilonovae, which are transient sources of fairly isotropic longer wave electromagnetic radiation due to the radioactive decay of heavy r-process nuclei that are produced and ejected during the merger process.

In October 2018, astronomers reported that GRB 150101B, a gamma-ray burst event detected in 2015, may be directly related to the historic GW170817, a gravitational wave event detected in 2017, and associated with the merger of two neutron stars. The similarities between the two events, in terms of gamma ray, optical and x-ray emissions, as well as to the nature of the associated host galaxies, are "striking", suggesting the two separate events may both be the result of the merger of neutron stars, and both may be a kilonova, which may be more common in the universe than previously understood, according to the researchers.

Also in October 2018, scientists presented a new third way (two earlier methods, one based on redshifts and another on the cosmic distance ladder, gave results that do not agree), using information from gravitational wave events (especially those involving the merger of neutron stars, like GW170817), of determining the Hubble Constant, essential in establishing the rate of expansion of the universe.

On 17 August 2017, LIGO/Virgo collaboration detected a pulse of gravitational waves, named GW170817, associated with the merger of two neutron stars in NGC 4993, an elliptical galaxy in the constellation Hydra. GW170817 also seemed related to a short (~ 2 second long) gamma-ray burst, GRB 170817A, first detected 1.7 seconds after the GW merger signal, and a visible light observational event first observed 11 hours afterwards, SSS17a.

The association of GW170817 with GRB 170817A in both space and time is strong evidence that neutron star mergers do create short gamma-ray bursts. The subsequent detection of an SSS17a in the area in which GW170817 and GRB 170817A were known to have occurred and its having the expected characteristics for a kilonova is strong evidence that neutron star mergers do produce kilonovae.

A stellar sign

The gravitational signal, named GW170817, was first detected on Aug. 17 at 8:41 a.m. Eastern Daylight Time; the detection was made by the two identical LIGO detectors, located in Hanford, Washington, and Livingston, Louisiana. The information provided by the third detector, Virgo, situated near Pisa, Italy, enabled an improvement in localizing the cosmic event. At the time, LIGO was nearing the end of its second observing run since being upgraded in a program called Advanced LIGO, while Virgo had begun its first run after recently completing an upgrade known as Advanced Virgo.

The NSF-funded LIGO observatories were conceived, constructed, and operated by Caltech and MIT. Virgo is funded by the Istituto Nazionale di Fisica Nucleare (INFN) in Italy and the Centre National de la Recherche Scientifique (CNRS) in France, and operated by the European Gravitational Observatory. Some 1,500 scientists in the LIGO Scientific Collaboration and the Virgo Collaboration work together to operate the detectors and to process and understand the gravitational-wave data they capture.

Each observatory consists of two long tunnels arranged in an L shape, at the joint of which a laser beam is split in two. Light is sent down the length of each tunnel, then reflected back in the direction it came from by a suspended mirror. In the absence of gravitational waves, the laser light in each tunnel should return to the location where the beams were split at precisely the same time. If a gravitational wave passes through the observatory, it will alter each laser beam’s arrival time, creating an almost imperceptible change in the observatory’s output signal.

On Aug. 17, LIGO’s real-time data analysis software caught a strong signal of gravitational waves from space in one of the two LIGO detectors. At nearly the same time, the Gamma-ray Burst Monitor on NASA’s Fermi space telescope had detected a burst of gamma rays. LIGO-Virgo analysis software put the two signals together and saw it was highly unlikely to be a chance coincidence, and another automated LIGO analysis indicated that there was a coincident gravitational wave signal in the other LIGO detector. Rapid gravitational-wave detection by the LIGO-Virgo team, coupled with Fermi’s gamma-ray detection, enabled the launch of follow-up by telescopes around the world.

The LIGO data indicated that two astrophysical objects located at the relatively close distance of about 130 million light-years from Earth had been spiraling in toward each other. It appeared that the objects were not as massive as binary black holes — objects that LIGO and Virgo have previously detected. Instead, the inspiraling objects were estimated to be in a range from around 1.1 to 1.6 times the mass of the sun, in the mass range of neutron stars. A neutron star is about 20 kilometers, or 12 miles, in diameter and is so dense that a teaspoon of neutron star material has a mass of about a billion tons.

While binary black holes produce “chirps” lasting a fraction of a second in the LIGO detector’s sensitive band, the Aug. 17 chirp lasted approximately 100 seconds and was seen through the entire frequency range of LIGO — about the same range as common musical instruments. Scientists could identify the chirp source as objects that were much less massive than the black holes seen to date.

Theorists have predicted that when neutron stars collide, they should give off gravitational waves and gamma rays, along with powerful jets that emit light across the electromagnetic spectrum. The gamma-ray burst detected by Fermi, and soon thereafter confirmed by the European Space Agency’s gamma-ray observatory INTEGRAL, is what’s called a short gamma-ray burst; the new observations confirm that at least some short gamma-ray bursts are generated by the merging of neutron stars — something that was only theorized before.

That exciting event was GW170817, which was the merger of two neutron stars. One of the many really exciting aspects of that merger was that there were detectable electromagnetic signatures across the spectrum – radio, optical, and X-rays. Astronomers were ready to pounce on this with every available facility and telescope, and that's exactly what happened.

“For decades we’ve suspected short gamma-ray bursts were powered by neutron star mergers,” says Fermi Project Scientist Julie McEnery of NASA’s Goddard Space Flight Center. “Now, with the incredible data from LIGO and Virgo for this event, we have the answer. The gravitational waves tell 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 a collision of black holes is not expected to give off light."

But while one mystery appears to be solved, new mysteries have emerged. The observed short gamma-ray burst was one of the closest to Earth seen so far, yet it was surprisingly weak for its distance. Scientists are beginning to propose models for why this might be, McEnery says, adding that new insights are likely to arise for years to come.

Each electromagnetic observatory will be releasing its own detailed observations of the astrophysical event. In the meantime, a general picture is emerging among all observatories involved that further confirms that the initial gravitational-wave signal indeed came from a pair of inspiraling neutron stars.

Approximately 130 million years ago, the two neutron stars were in their final moments of orbiting each other, separated only by about 300 kilometers, or 200 miles, and gathering speed while closing the distance between them. As the stars spiraled faster and closer together, they stretched and distorted the surrounding space-time, giving off energy in the form of powerful gravitational waves, before smashing into each other.

At the moment of collision, the bulk of the two neutron stars merged into one ultradense object, emitting a “fireball” of gamma rays. The initial gamma-ray measurements, combined with the gravitational-wave detection, also provide confirmation for Einstein’s general theory of relativity, which predicts that gravitational waves should travel at the speed of light.

Theorists have predicted that what follows the initial fireball is a “kilonova” — a phenomenon by which the material that is left over from the neutron star collision, which glows with light, is blown out of the immediate region and far out into space. The new light-based observations show that heavy elements, such as lead and gold, are created in these collisions and subsequently distributed throughout the universe.

In the weeks and months ahead, telescopes around the world will continue to observe the afterglow of the neutron star merger and gather further evidence about various stages of the merger, its interaction with its surroundings, and the processes that produce the heaviest elements in the universe.

LIGO is funded by the NSF, and operated by Caltech and MIT, which conceived of LIGO and led the Initial and Advanced LIGO projects. Financial support for the Advanced LIGO project was led by the NSF with Germany (Max Planck Society), the U.K. (Science and Technology Facilities Council) and Australia (Australian Research Council) making significant commitments and contributions to the project.

More than 1,200 scientists and some 100 institutions from around the world participate in the effort through the LIGO Scientific Collaboration, which includes the GEO Collaboration and the Australian collaboration OzGrav. Additional partners are listed at http://ligo.org/partners.php

The Virgo collaboration consists of more than 280 physicists and engineers belonging to 20 different European research groups: six from Centre National de la Recherche Scientifique (CNRS) in France; eight from the Istituto Nazionale di Fisica Nucleare (INFN) in Italy; two in the Netherlands with Nikhef; the MTA Wigner RCP in Hungary; the POLGRAW group in Poland; Spain with the University of Valencia; and the European Gravitational Observatory, EGO, the laboratory hosting the Virgo detector near Pisa in Italy, funded by CNRS, INFN, and Nikhef.

WHAT GRAVITATIONAL WAVES CAN TELL US ABOUT COLLIDING STARS AND BLACK HOLES

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