Binary star

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Artist's impression of the evolution of a hot high-mass binary star.

 

Hubble image of the Sirius binary system, in which Sirius B can be clearly distinguished (lower left)

A binary star is a star system consisting of two stars orbiting around their common barycenter. Systems of two or more stars are called multiple star systems. These systems, especially when more distant, often appear to the unaided eye as a single point of light, and are then revealed as multiple by other means. Research over the last two centuries suggests that half or more of visible stars are part of multiple star systems.

The term double star is often used synonymously with binary star; however, double star can also mean optical double star. Optical doubles are so called because the two stars appear close together in the sky as seen from the Earth; they are almost on the same line of sight. Nevertheless, their "doubleness" depends only on this optical effect; the stars themselves are distant from one another and share no physical connection. A double star can be revealed as optical by means of differences in their parallax measurements, proper motions, or radial velocities. Most known double stars have not been studied sufficiently closely to determine whether they are optical doubles or they are doubles physically bound through gravitation into a multiple star system.

Binary star systems are very important in astrophysics because calculations of their orbits allow the masses of their component stars to be directly determined, which in turn allows other stellar parameters, such as radius and density, to be indirectly estimated. This also determines an empirical mass-luminosity relationship (MLR) from which the masses of single stars can be estimated.

Binary stars are often detected optically, in which case they are called visual binaries. Many visual binaries have long orbital periods of several centuries or millennia and therefore have orbits which are uncertain or poorly known. They may also be detected by indirect techniques, such as spectroscopy (spectroscopic binaries) or astrometry (astrometric binaries). If a binary star happens to orbit in a plane along our line of sight, its components will eclipse and transit each other; these pairs are called eclipsing binaries, or, as they are detected by their changes in brightness during eclipses and transits, photometric binaries.

If components in binary star systems are close enough they can gravitationally distort their mutual outer stellar atmospheres. In some cases, these close binary systems can exchange mass, which may bring their evolution to stages that single stars cannot attain. Examples of binaries are Sirius, and Cygnus X-1 (Cygnus X-1 being a well-known black hole). Binary stars are also common as the nuclei of many planetary nebulae, and are the progenitors of both novae and type Ia supernovae.

Discovery

The term binary was first used in this context by Sir William Herschel in 1802, when he wrote:

If, on the contrary, two stars should really be situated very near each other, and at the same time so far insulated as not to be materially affected by the attractions of neighbouring stars, they will then compose a separate system, and remain united by the bond of their own mutual gravitation towards each other. This should be called a real double star; and any two stars that are thus mutually connected, form the binary sidereal system which we are now to consider.

By the modern definition, the term binary star is generally restricted to pairs of stars which revolve around a common center of mass. Binary stars which can be resolved with a telescope or interferometric methods are known as visual binaries. For most of the known visual binary stars one whole revolution has not been observed yet, they are observed to have travelled along a curved path or a partial arc.

This figure shows a system with two stars

The more general term double star is used for pairs of stars which are seen to be close together in the sky. This distinction is rarely made in languages other than English. Double stars may be binary systems or may be merely two stars that appear to be close together in the sky but have vastly different true distances from the Sun. The latter are termed optical doubles or optical pairs.

Since the invention of the telescope, many pairs of double stars have been found. Early examples include Mizar and Acrux. Mizar, in the Big Dipper (Ursa Major), was observed to be double by Giovanni Battista Riccioli in 1650 (and probably earlier by Benedetto Castelli and Galileo). The bright southern star Acrux, in the Southern Cross, was discovered to be double by Father Fontenay in 1685.

John Michell was the first to suggest that double stars might be physically attached to each other when he argued in 1767 that the probability that a double star was due to a chance alignment was small. William Herschel began observing double stars in 1779 and soon thereafter published catalogs of about 700 double stars. By 1803, he had observed changes in the relative positions in a number of double stars over the course of 25 years, and concluded that they must be binary systems; the first orbit of a binary star, however, was not computed until 1827, when Félix Savary computed the orbit of Xi Ursae Majoris. Since this time, many more double stars have been catalogued and measured. The Washington Double Star Catalog, a database of visual double stars compiled by the United States Naval Observatory, contains over 100,000 pairs of double stars, including optical doubles as well as binary stars. Orbits are known for only a few thousand of these double stars, and most have not been ascertained to be either true binaries or optical double stars. This can be determined by observing the relative motion of the pairs. If the motion is part of an orbit, or if the stars have similar radial velocities and the difference in their proper motions is small compared to their common proper motion, the pair is probably physical. One of the tasks that remains for visual observers of double stars is to obtain sufficient observations to prove or disprove gravitational connection.

Classifications

Edge-on disc of gas and dust present around the binary star system HD 106906.

Methods of observation

Binary stars are classified into four types according to the way in which they are observed: visually, by observation; spectroscopically, by periodic changes in spectral lines; photometrically, by changes in brightness caused by an eclipse; or astrometrically, by measuring a deviation in a star's position caused by an unseen companion. Any binary star can belong to several of these classes; for example, several spectroscopic binaries are also eclipsing binaries.

Visual binaries

A visual binary star is a binary star for which the angular separation between the two components is great enough to permit them to be observed as a double star in a telescope, or even high-powered binoculars. The angular resolution of the telescope is an important factor in the detection of visual binaries, and as better angular resolutions are applied to binary star observations, an increasing number of visual binaries will be detected. The relative brightness of the two stars is also an important factor, as glare from a bright star may make it difficult to detect the presence of a fainter component.

The brighter star of a visual binary is the primary star, and the dimmer is considered the secondary. In some publications (especially older ones), a faint secondary is called the comes (plural comites; companion). If the stars are the same brightness, the discoverer designation for the primary is customarily accepted.

The position angle of the secondary with respect to the primary is measured, together with the angular distance between the two stars. The time of observation is also recorded. After a sufficient number of observations are recorded over a period of time, they are plotted in polar coordinates with the primary star at the origin, and the most probable ellipse is drawn through these points such that the Keplerian law of areas is satisfied. This ellipse is known as the apparent ellipse, and is the projection of the actual elliptical orbit of the secondary with respect to the primary on the plane of the sky. From this projected ellipse the complete elements of the orbit may be computed, where the semi-major axis can only be expressed in angular units unless the stellar parallax, and hence the distance, of the system is known.

Spectroscopic binaries

Sometimes, the only evidence of a binary star comes from the Doppler effect on its emitted light. In these cases, the binary consists of a pair of stars where the spectral lines in the light emitted from each star shifts first towards the blue, then towards the red, as each moves first towards us, and then away from us, during its motion about their common center of mass, with the period of their common orbit.

In these systems, the separation between the stars is usually very small, and the orbital velocity very high. Unless the plane of the orbit happens to be perpendicular to the line of sight, the orbital velocities will have components in the line of sight and the observed radial velocity of the system will vary periodically. Since radial velocity can be measured with a spectrometer by observing the Doppler shift of the stars' spectral lines, the binaries detected in this manner are known as spectroscopic binaries. Most of these cannot be resolved as a visual binary, even with telescopes of the highest existing resolving power.

In some spectroscopic binaries, spectral lines from both stars are visible and the lines are alternately double and single. Such a system is known as a double-lined spectroscopic binary (often denoted "SB2"). In other systems, the spectrum of only one of the stars is seen and the lines in the spectrum shift periodically towards the blue, then towards red and back again. Such stars are known as single-lined spectroscopic binaries ("SB1").

The orbit of a spectroscopic binary is determined by making a long series of observations of the radial velocity of one or both components of the system. The observations are plotted against time, and from the resulting curve a period is determined. If the orbit is circular then the curve will be a sine curve. If the orbit is elliptical, the shape of the curve will depend on the eccentricity of the ellipse and the orientation of the major axis with reference to the line of sight.

It is impossible to determine individually the semi-major axis a and the inclination of the orbit plane i. However, the product of the semi-major axis and the sine of the inclination (i.e. a sin i) may be determined directly in linear units (e.g. kilometres). If either a or i can be determined by other means, as in the case of eclipsing binaries, a complete solution for the orbit can be found.

Binary stars that are both visual and spectroscopic binaries are rare, and are a valuable source of information when found. About 40 are known. Visual binary stars often have large true separations, with periods measured in decades to centuries; consequently, they usually have orbital speeds too small to be measured spectroscopically. Conversely, spectroscopic binary stars move fast in their orbits because they are close together, usually too close to be detected as visual binaries. Binaries that are found to be both visual and spectroscopic thus must be relatively close to Earth.

Eclipsing binaries

Algol B orbits Algol A. This animation was assembled from 55 images of the CHARA interferometer in the near-infrared H-band, sorted according to orbital phase.

An eclipsing binary star is a binary star system in which the orbit plane of the two stars lies so nearly in the line of sight of the observer that the components undergo mutual eclipses. In the case where the binary is also a spectroscopic binary and the parallax of the system is known, the binary is quite valuable for stellar analysis. Algol, a triple star system in the constellation Perseus, contains the best-known example of an eclipsing binary.

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This video shows an artist's impression of an eclipsing binary star system. As the two stars orbit each other they pass in front of one another and their combined brightness, seen from a distance, decreases.

Eclipsing binaries are variable stars, not because the light of the individual components vary but because of the eclipses. The light curve of an eclipsing binary is characterized by periods of practically constant light, with periodic drops in intensity when one star passes in front of the other. The brightness may drop twice during the orbit, once when the secondary passes in front of the primary and once when the primary passes in front of the secondary. The deeper of the two eclipses is called the primary regardless of which star is being occulted, and if a shallow second eclipse also occurs it is called the secondary eclipse. The size of the brightness drops depends on the relative brightness of the two stars, the proportion of the occulted star that is hidden, and the surface brightness (ie. effective temperature) of the stars. Typically the occultation of the hotter star causes the primary eclipse.

An eclipsing binaries' period of orbit may be determined from a study of its light curve, and the relative sizes of the individual stars can be determined in terms of the radius of the orbit, by observing how quickly the brightness changes as the disc of the nearest star slides over the disc of the other star. If it is also a spectroscopic binary, the orbital elements can also be determined, and the mass of the stars can be determined relatively easily, which means that the relative densities of the stars can be determined in this case.

Since about 1995, measurement of extragalactic eclipsing binaries' fundamental parameters has become possible with 8-meter class telescopes. This makes it feasible to use them to directly measure the distances to external galaxies, a process that is more accurate than using standard candles. By 2006, they had been used to give direct distance estimates to the LMC, SMC, Andromeda Galaxy, and Triangulum Galaxy. Eclipsing binaries offer a direct method to gauge the distance to galaxies to an improved 5% level of accuracy.

Non-eclipsing binaries that can be detected through photometry

Nearby non-eclipsing binaries can also be photometrically detected by observing how the stars affect each other in three ways. The first is by observing extra light which the stars reflect from their companion. Second is by observing ellipsoidal light variations which are caused by deformation of the star's shape by their companions. The third method is by looking at how relativistic beaming affects the apparent magnitude of the stars. Detecting binaries with these methods requires accurate photometry.

Astrometric binaries

Astronomers have discovered some stars that seemingly orbit around an empty space. Astrometric binaries are relatively nearby stars which can be seen to wobble around a point in space, with no visible companion. The same mathematics used for ordinary binaries can be applied to infer the mass of the missing companion. The companion could be very dim, so that it is currently undetectable or masked by the glare of its primary, or it could be an object that emits little or no electromagnetic radiation, for example a neutron star.

The visible star's position is carefully measured and detected to vary, due to the gravitational influence from its counterpart. The position of the star is repeatedly measured relative to more distant stars, and then checked for periodic shifts in position. Typically this type of measurement can only be performed on nearby stars, such as those within 10 parsecs. Nearby stars often have a relatively high proper motion, so astrometric binaries will appear to follow a wobbly path across the sky.

If the companion is sufficiently massive to cause an observable shift in position of the star, then its presence can be deduced. From precise astrometric measurements of the movement of the visible star over a sufficiently long period of time, information about the mass of the companion and its orbital period can be determined. Even though the companion is not visible, the characteristics of the system can be determined from the observations using Kepler's laws.

This method of detecting binaries is also used to locate extrasolar planets orbiting a star. However, the requirements to perform this measurement are very exacting, due to the great difference in the mass ratio, and the typically long period of the planet's orbit. Detection of position shifts of a star is a very exacting science, and it is difficult to achieve the necessary precision. Space telescopes can avoid the blurring effect of Earth's atmosphere, resulting in more precise resolution.

Configuration of the system

Detached

Semidetached

Contact

 

Configurations of a binary star system with a mass ratio of 3. The black lines represent the inner critical Roche equipotentials, the Roche lobes.

Another classification is based on the distance between the stars, relative to their sizes:

Detached binaries are binary stars where each component is within its Roche lobe, i.e. the area where the gravitational pull of the star itself is larger than that of the other component. The stars have no major effect on each other, and essentially evolve separately. Most binaries belong to this class.

Semidetached binary stars are binary stars where one of the components fills the binary star's Roche lobe and the other does not. Gas from the surface of the Roche-lobe-filling component (donor) is transferred to the other, accreting star. The mass transfer dominates the evolution of the system. In many cases, the inflowing gas forms an accretion disc around the accretor.

A contact binary is a type of binary star in which both components of the binary fill their Roche lobes. The uppermost part of the stellar atmospheres forms a common envelope that surrounds both stars. As the friction of the envelope brakes the orbital motion, the stars may eventually merge. W Ursae Majoris is an example.

Cataclysmic variables and X-ray binaries

Artist's conception of a cataclysmic variable system

When a binary system contains a compact object such as a white dwarf, neutron star or black hole, gas from the other (donor) star can accrete onto the compact object. This releases gravitational potential energy, causing the gas to become hotter and emit radiation. Cataclysmic variable stars, where the compact object is a white dwarf, are examples of such systems. In X-ray binaries, the compact object can be either a neutron star or a black hole. These binaries are classified as low-mass or high-mass according to the mass of the donor star. High-mass X-ray binaries contain a young, early-type, high-mass donor star which transfers mass by its stellar wind, while low-mass X-ray binaries are semidetached binaries in which gas from a late-type donor star or a white dwarf overflows the Roche lobe and falls towards the neutron star or black hole. Probably the best known example of an X-ray binary is the high-mass X-ray binary Cygnus X-1. In Cygnus X-1, the mass of the unseen companion is estimated to be about nine times that of the Sun, far exceeding the Tolman–Oppenheimer–Volkoff limit for the maximum theoretical mass of a neutron star. It is therefore believed to be a black hole; it was the first object for which this was widely believed.

Orbital period

Orbital periods can be less than an hour (for AM CVn stars), or a few days (components of Beta Lyrae), but also hundreds of thousands of years (Proxima Centauri around Alpha Centauri AB).

Variations in period

The Applegate mechanism explains long term orbital period variations seen in certain eclipsing binaries. As a main-sequence star goes through an activity cycle, the outer layers of the star are subject to a magnetic torque changing the distribution of angular momentum, resulting in a change in the star's oblateness. The orbit of the stars in the binary pair is gravitationally coupled to their shape changes, so that the period shows modulations (typically on the order of ∆P/P ∼ 10⁻⁵) on the same time scale as the activity cycles (typically on the order of decades).

Another phenomenon observed in some Algol binaries has been monotonic period increases. This is quite distinct from the far more common observations of alternating period increases and decreases explained by the Applegate mechanism. Monotonic period increases have been attributed to mass transfer, usually (but not always) from the less massive to the more massive star.

Designations

A and B

Artist’s impression of the binary star system AR Scorpii.

The components of binary stars are denoted by the suffixes A and B appended to the system's designation, A denoting the primary and B the secondary. The suffix AB may be used to denote the pair (for example, the binary star α Centauri AB consists of the stars α Centauri A and α Centauri B.) Additional letters, such as C, D, etc., may be used for systems with more than two stars. In cases where the binary star has a Bayer designation and is widely separated, it is possible that the members of the pair will be designated with superscripts; an example is Zeta Reticuli, whose components are ζ¹ Reticuli and ζ² Reticuli.

Discoverer designations

Double stars are also designated by an abbreviation giving the discoverer together with an index number. α Centauri, for example, was found to be double by Father Richaud in 1689, and so is designated RHD 1. These discoverer codes can be found in the Washington Double Star Catalog.

Hot and cold

The components of a binary star system may be designated by their relative temperatures as the hot companion and cool companion.
Examples:

• Antares (Alpha Scorpii) is a red supergiant star in a binary system with a hotter blue main-sequence star Antares B. Antares B can therefore be termed a hot companion of the cool supergiant.
• Symbiotic stars are binary star systems composed of a late-type giant star and a hotter companion object. Since the nature of the companion is not well-established in all cases, it may be termed a "hot companion".
• The luminous blue variable Eta Carinae has recently been determined to be a binary star system. The secondary appears to have a higher temperature than the primary and has therefore been described as being the "hot companion" star. It may be a Wolf–Rayet star.
• R Aquarii shows a spectrum which simultaneously displays both a cool and hot signature. This combination is the result of a cool red supergiant accompanied by a smaller, hotter companion. Matter flows from the supergiant to the smaller, denser companion.
• NASA's Kepler mission has discovered examples of eclipsing binary stars where the secondary is the hotter component. KOI-74b is a 12,000 K white dwarf companion of KOI-74 (KIC 6889235), a 9,400 K early A-type main-sequence star. KOI-81b is a 13,000 K white dwarf companion of KOI-81 (KIC 8823868), a 10,000 K late B-type main-sequence star.

Evolution

Formation

While it is not impossible that some binaries might be created through gravitational capture between two single stars, given the very low likelihood of such an event (three objects being actually required, as conservation of energy rules out a single gravitating body capturing another) and the high number of binaries currently in existence, this cannot be the primary formation process. The observation of binaries consisting of stars not yet on the main sequence supports the theory that binaries develop during star formation. Fragmentation of the molecular cloud during the formation of protostars is an acceptable explanation for the formation of a binary or multiple star system.

The outcome of the three-body problem, in which the three stars are of comparable mass, is that eventually one of the three stars will be ejected from the system and, assuming no significant further perturbations, the remaining two will form a stable binary system.

Mass transfer and accretion

As a main-sequence star increases in size during its evolution, it may at some point exceed its Roche lobe, meaning that some of its matter ventures into a region where the gravitational pull of its companion star is larger than its own. The result is that matter will transfer from one star to another through a process known as Roche lobe overflow (RLOF), either being absorbed by direct impact or through an accretion disc. The mathematical point through which this transfer happens is called the first Lagrangian point. It is not uncommon that the accretion disc is the brightest (and thus sometimes the only visible) element of a binary star.

If a star grows outside of its Roche lobe too fast for all abundant matter to be transferred to the other component, it is also possible that matter will leave the system through other Lagrange points or as stellar wind, thus being effectively lost to both components. Since the evolution of a star is determined by its mass, the process influences the evolution of both companions, and creates stages that cannot be attained by single stars.

Studies of the eclipsing ternary Algol led to the Algol paradox in the theory of stellar evolution: although components of a binary star form at the same time, and massive stars evolve much faster than the less massive ones, it was observed that the more massive component Algol A is still in the main sequence, while the less massive Algol B is a subgiant at a later evolutionary stage. The paradox can be solved by mass transfer: when the more massive star became a subgiant, it filled its Roche lobe, and most of the mass was transferred to the other star, which is still in the main sequence. In some binaries similar to Algol, a gas flow can actually be seen.

Runaways and novae

Artist rendering of plasma ejections from V Hydrae

It is also possible for widely separated binaries to lose gravitational contact with each other during their lifetime, as a result of external perturbations. The components will then move on to evolve as single stars. A close encounter between two binary systems can also result in the gravitational disruption of both systems, with some of the stars being ejected at high velocities, leading to runaway stars.

If a white dwarf has a close companion star that overflows its Roche lobe, the white dwarf will steadily accrete gases from the star's outer atmosphere. These are compacted on the white dwarf's surface by its intense gravity, compressed and heated to very high temperatures as additional material is drawn in. The white dwarf consists of degenerate matter and so is largely unresponsive to heat, while the accreted hydrogen is not. Hydrogen fusion can occur in a stable manner on the surface through the CNO cycle, causing the enormous amount of energy liberated by this process to blow the remaining gases away from the white dwarf's surface. The result is an extremely bright outburst of light, known as a nova.

In extreme cases this event can cause the white dwarf to exceed the Chandrasekhar limit and trigger a supernova that destroys the entire star, another possible cause for runaways. An example of such an event is the supernova SN 1572, which was observed by Tycho Brahe. The Hubble Space Telescope recently took a picture of the remnants of this event.

Astrophysics

Binaries provide the best method for astronomers to determine the mass of a distant star. The gravitational pull between them causes them to orbit around their common center of mass. From the orbital pattern of a visual binary, or the time variation of the spectrum of a spectroscopic binary, the mass of its stars can be determined, for example with the binary mass function. In this way, the relation between a star's appearance (temperature and radius) and its mass can be found, which allows for the determination of the mass of non-binaries.

Because a large proportion of stars exist in binary systems, binaries are particularly important to our understanding of the processes by which stars form. In particular, the period and masses of the binary tell us about the amount of angular momentum in the system. Because this is a conserved quantity in physics, binaries give us important clues about the conditions under which the stars were formed.

Calculating the center of mass in binary stars

In a simple binary case, r₁, the distance from the center of the first star to the center of mass or barycenter, is given by:

${\displaystyle r_{1}=a\cdot {\frac {m_{2}}{m_{1}+m_{2}}}={\frac {a}{1+{\frac {m_{1}}{m_{2}}}}}}$

where:

a is the distance between the two stellar centers and

m₁ and m₂ are the masses of the two stars.

If a is taken to be the semi-major axis of the orbit of one body around the other, then r₁ will be the semimajor axis of the first body's orbit around the center of mass or barycenter, and r₂ = a – r₁ will be the semimajor axis of the second body's orbit. When the center of mass is located within the more massive body, that body will appear to wobble rather than following a discernible orbit.

Research findings

It is estimated that approximately one third of the star systems in the Milky Way are binary or multiple, with the remaining two thirds being single stars. The overall multiplicity frequency of ordinary stars is a monotonically increasing function of stellar mass. That is, the likelihood of being in a binary or a multi-star system steadily increases as the mass of the components increase.

There is a direct correlation between the period of revolution of a binary star and the eccentricity of its orbit, with systems of short period having smaller eccentricity. Binary stars may be found with any conceivable separation, from pairs orbiting so closely that they are practically in contact with each other, to pairs so distantly separated that their connection is indicated only by their common proper motion through space. Among gravitationally bound binary star systems, there exists a so-called log normal distribution of periods, with the majority of these systems orbiting with a period of about 100 years. This is supporting evidence for the theory that binary systems are formed during star formation.

In pairs where the two stars are of equal brightness, they are also of the same spectral type. In systems where the brightnesses are different, the fainter star is bluer if the brighter star is a giant star, and redder if the brighter star belongs to the main sequence.

Artist's impression of the sight from a (hypothetical) moon of planet HD 188753 Ab (upper left), which orbits a triple star system. The brightest companion is just below the horizon.

The mass of a star can be directly determined only from its gravitational attraction. Apart from the Sun and stars which act as gravitational lenses, this can be done only in binary and multiple star systems, making the binary stars an important class of stars. In the case of a visual binary star, after the orbit and the stellar parallax of the system has been determined, the combined mass of the two stars may be obtained by a direct application of the Keplerian harmonic law.

Unfortunately, it is impossible to obtain the complete orbit of a spectroscopic binary unless it is also a visual or an eclipsing binary, so from these objects only a determination of the joint product of mass and the sine of the angle of inclination relative to the line of sight is possible. In the case of eclipsing binaries which are also spectroscopic binaries, it is possible to find a complete solution for the specifications (mass, density, size, luminosity, and approximate shape) of both members of the system.

Planets

Schematic of a binary star system with one planet on an S-type orbit and one on a P-type orbit.

While a number of binary star systems have been found to harbor extrasolar planets, such systems are comparatively rare compared to single star systems. Observations by the Kepler space telescope have shown that most single stars of the same type as the Sun have plenty of planets, but only one-third of binary stars do. According to theoretical simulations, even widely separated binary stars often disrupt the discs of rocky grains from which protoplanets form. On the other hand, other simulations suggest that the presence of a binary companion can actually improve the rate of planet formation within stable orbital zones by "stirring up" the protoplanetary disk, increasing the accretion rate of the protoplanets within.

Detecting planets in multiple star systems introduces additional technical difficulties, which may be why they are only rarely found. Examples include the white dwarf-pulsar binary PSR B1620-26, the subgiant-red dwarf binary Gamma Cephei, and the white dwarf-red dwarf binary NN Serpentis; among others.

A study of fourteen previously known planetary systems found three of these systems to be binary systems. All planets were found to be in S-type orbits around the primary star. In these three cases the secondary star was much dimmer than the primary and so was not previously detected. This discovery resulted in a recalculation of parameters for both the planet and the primary star.

Science fiction has often featured planets of binary or ternary stars as a setting, for example George Lucas' Tatooine from Star Wars, and one notable story, "Nightfall", even takes this to a six-star system. In reality, some orbital ranges are impossible for dynamical reasons (the planet would be expelled from its orbit relatively quickly, being either ejected from the system altogether or transferred to a more inner or outer orbital range), whilst other orbits present serious challenges for eventual biospheres because of likely extreme variations in surface temperature during different parts of the orbit. Planets that orbit just one star in a binary system are said to have "S-type" orbits, whereas those that orbit around both stars have "P-type" or "circumbinary" orbits. It is estimated that 50–60% of binary systems are capable of supporting habitable terrestrial planets within stable orbital ranges.

Examples

The two visibly distinguishable components of Albireo.

The large distance between the components, as well as their difference in color, make Albireo one of the easiest observable visual binaries. The brightest member, which is the third-brightest star in the constellation Cygnus, is actually a close binary itself. Also in the Cygnus constellation is Cygnus X-1, an X-ray source considered to be a black hole. It is a high-mass X-ray binary, with the optical counterpart being a variable star. Sirius is another binary and the brightest star in the night time sky, with a visual apparent magnitude of −1.46. It is located in the constellation Canis Major. In 1844 Friedrich Bessel deduced that Sirius was a binary. In 1862 Alvan Graham Clark discovered the companion (Sirius B; the visible star is Sirius A). In 1915 astronomers at the Mount Wilson Observatory determined that Sirius B was a white dwarf, the first to be discovered. In 2005, using the Hubble Space Telescope, astronomers determined Sirius B to be 12,000 km (7,456 mi) in diameter, with a mass that is 98% of the Sun.

Luhman 16, the third closest star system, contains two brown dwarfs.

An example of an eclipsing binary is Epsilon Aurigae in the constellation Auriga. The visible component belongs to the spectral class F0, the other (eclipsing) component is not visible. The last such eclipse occurred from 2009–2011, and it is hoped that the extensive observations that will likely be carried out may yield further insights into the nature of this system. Another eclipsing binary is Beta Lyrae, which is a semidetached binary star system in the constellation of Lyra.

Other interesting binaries include 61 Cygni (a binary in the constellation Cygnus, composed of two K class (orange) main-sequence stars, 61 Cygni A and 61 Cygni B, which is known for its large proper motion), Procyon (the brightest star in the constellation Canis Minor and the eighth-brightest star in the night time sky, which is a binary consisting of the main star with a faint white dwarf companion), SS Lacertae (an eclipsing binary which stopped eclipsing), V907 Sco (an eclipsing binary which stopped, restarted, then stopped again) and BG Geminorum (an eclipsing binary which is thought to contain a black hole with a K0 star in orbit around it).

Multiple star examples

Systems with more than two stars are termed multiple stars. Algol is the most noted ternary (long thought to be a binary), located in the constellation Perseus. Two components of the system eclipse each other, the variation in the intensity of Algol first being recorded in 1670 by Geminiano Montanari. The name Algol means "demon star" (from Arabic: الغول‎ al-ghūl), which was probably given due to its peculiar behavior. Another visible ternary is Alpha Centauri, in the southern constellation of Centaurus, which contains the fourth-brightest star in the night sky, with an apparent visual magnitude of −0.01. This system also underscores the fact that binaries need not be discounted in the search for habitable planets. Alpha Centauri A and B have an 11 AU distance at closest approach, and both should have stable habitable zones.

There are also examples of systems beyond ternaries: Castor is a sextuple star system, which is the second-brightest star in the constellation Gemini and one of the brightest stars in the nighttime sky. Astronomically, Castor was discovered to be a visual binary in 1719. Each of the components of Castor is itself a spectroscopic binary. Castor also has a faint and widely separated companion, which is also a spectroscopic binary. The Alcor–Mizar visual binary in Ursa Majoris also consists of six stars, four comprising Mizar and two comprising Alcor.

First observation of gravitational waves

From Wikipedia, the free encyclopedia

GW150914

LIGO measurement of the gravitational waves at the Livingston (right) and Hanford (left) detectors, compared with the theoretical predicted values
Other designations	GW150914
Event type	Gravitational wave event
Date	14 September 2015
Duration	0.2 second
Instrument	LIGO
Distance	410+160 −180 Mpc
Redshift	0.093+0.030 −0.036
Total energy output	3.0+0.5 −0.5 M☉ × c2
Followed by	GW151226

The first direct observation of gravitational waves was made on 14 September 2015 and was announced by the LIGO and Virgo collaborations on 11 February 2016. Previously, gravitational waves had only been inferred indirectly, via their effect on the timing of pulsars in binary star systems. The waveform, detected by both LIGO observatories, matched the predictions of general relativity for a gravitational wave emanating from the inward spiral and merger of a pair of black holes of around 36 and 29 solar masses and the subsequent "ringdown" of the single resulting black hole. The signal was named GW150914 (from "Gravitational Wave" and the date of observation 2015-09-14). It was also the first observation of a binary black hole merger, demonstrating both the existence of binary stellar-mass black hole systems and the fact that such mergers could occur within the current age of the universe.

This first direct observation was reported around the world as a remarkable accomplishment for many reasons. Efforts to directly prove the existence of such waves had been ongoing for over fifty years, and the waves are so minuscule that Albert Einstein himself doubted that they could ever be detected. The waves given off by the cataclysmic merger of GW150914 reached Earth 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. The energy released by the binary as it spiralled together and merged was immense, with the energy of 3.0+0.5
−0.5 c² solar masses (5.3+0.9
−0.8×10⁴⁷ joules or 5300+900
−800 foes) in total radiated as gravitational waves, reaching a peak emission rate in its final few milliseconds of about 3.6+0.5
−0.4×10⁴⁹ watts – a level greater than the combined power of all light radiated by all the stars in the observable universe.

The observation confirms the last remaining directly undetected prediction of general relativity and corroborates its predictions of space-time distortion in the context of large scale cosmic events (known as strong field tests). It was also heralded as inaugurating a new era of gravitational-wave astronomy, which will enable observations of violent astrophysical events that were not previously possible and potentially allow the direct observation of the very earliest history of the universe. The second observation of gravitational waves was made on 26 December 2015 and announced on 15 June 2016. Four more observations were made in 2017, including GW170817, the first observed merger of binary neutron stars, which was also observed in electromagnetic radiation.

Gravitational waves

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Video simulation showing the warping of space-time and gravitational waves produced, during the final inspiral, merge, and ringdown of black hole binary system GW150914.

 

Albert Einstein originally predicted the existence of gravitational waves in 1916, on the basis of his theory of general relativity. General relativity interprets gravity as a consequence of distortions in space-time, caused by mass. Therefore, Einstein also predicted that events in the cosmos would cause "ripples" in space-time – distortions of space-time itself – which would spread outward, although they would be so minuscule that they would be nearly impossible to detect by any technology foreseen at that time. It was also predicted that objects moving in an orbit would lose energy for this reason (a consequence of the law of conservation of energy), as some energy would be given off as gravitational waves, although this would be insignificantly small in all but the most extreme cases.

One case where gravitational waves would be strongest is during the final moments of the merger of two compact objects such as neutron stars or black holes. Over a span of millions of years, binary neutron stars, and binary black holes lose energy, largely through gravitational waves, and as a result, they spiral in towards each other. At the very end of this process, the two objects will reach extreme velocities, and in the final fraction of a second of their merger a substantial amount of their mass would theoretically be converted into gravitational energy, and travel outward as gravitational waves, allowing a greater than usual chance for detection. However, since little was known about the number of compact binaries in the universe and reaching that final stage can be very slow, there was little certainty as to how often such events might happen.

Observation

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Slow motion computer simulation of the black hole binary system GW150914 as seen by a nearby observer, during 0.33 s of its final inspiral, merge, and ringdown. The star field behind the black holes is being heavily distorted and appears to rotate and move, due to extreme gravitational lensing, as space-time itself is distorted and dragged around by the rotating black holes.

 

Gravitational waves can be detected indirectly – by observing celestial phenomena caused by gravitational waves – or more directly by means of instruments such as the Earth-based LIGO or the planned space-based LISA instrument.

Indirect observation

Evidence of gravitational waves was first deduced in 1974 through the motion of the double neutron star system PSR B1913+16, in which one of the stars is a pulsar that emits electro-magnetic pulses at radio frequencies at precise, regular intervals as it rotates. Russell Hulse and Joseph Taylor, who discovered the stars, also showed that over time, the frequency of pulses shortened, and that the stars were gradually spiralling towards each other with an energy loss that agreed closely with the predicted energy that would be radiated by gravitational waves. For this work, Hulse and Taylor were awarded the Nobel Prize in Physics in 1993. Further observations of this pulsar and others in multiple systems (such as the double pulsar system PSR J0737-3039) also agree with General Relativity to high precision.

Direct observation

Northern arm of the LIGO Hanford Gravitational-wave observatory.

Direct observation of gravitational waves was not possible for the many decades after they were predicted due to the minuscule effect that would need to be detected and separated from the background of vibrations present everywhere on Earth. A technique called interferometry was suggested in the 1960s and eventually technology developed sufficiently for this technique to become feasible.

In the present approach used by LIGO, a laser beam is split and the two halves are recombined after travelling different paths. Changes to the length of the paths or the time taken for the two split beams, caused by the effect of passing gravitational waves, to reach the point where they recombine are revealed as "beats". Such a technique is extremely sensitive to tiny changes in the distance or time taken to traverse the two paths. In theory, an interferometer with arms about 4 km long would be capable of revealing the change of space-time – a tiny fraction of the size of a single proton – as a gravitational wave of sufficient strength passed through Earth from elsewhere. This effect would be perceptible only to other interferometers of a similar size, such as the Virgo, GEO 600 and planned KAGRA and INDIGO detectors. In practice at least two interferometers would be needed, because any gravitational wave would be detected at both of these but other kinds of disturbance would generally not be present at both, allowing the sought-after signal to be distinguished from noise. This project was eventually founded in 1992 as the Laser Interferometer Gravitational-Wave Observatory (LIGO). The original instruments were upgraded between 2010 and 2015 (to Advanced LIGO), giving an increase of around 10 times their original sensitivity.

LIGO operates two gravitational-wave observatories in unison, located 3,002 km (1,865 mi) apart: the LIGO Livingston Observatory (30°33′46.42″N 90°46′27.27″W) in Livingston, Louisiana, and the LIGO Hanford Observatory, on the DOE Hanford Site (46°27′18.52″N 119°24′27.56″W) near Richland, Washington. The tiny shifts in the length of their arms are continually compared and significant patterns which appear to arise synchronously are followed up to determine whether a gravitational wave may have been detected or if some other cause was responsible.

Initial LIGO operations between 2002 and 2010 did not detect any statistically significant events that could be confirmed as gravitational waves. This was followed by a multi-year shut-down while the detectors were replaced by much improved "Advanced LIGO" versions.  In February 2015, the two advanced detectors were brought into engineering mode, in which the instruments are operating fully for the purpose of testing and confirming they are functioning correctly before being used for research, with formal science observations due to begin on 18 September 2015.

Throughout the development and initial observations by LIGO, several "blind injections" of fake gravitational wave signals were introduced to test the ability of the researchers to identify such signals. To protect the efficacy of blind injections, only four LIGO scientists knew when such injections occurred, and that information was revealed only after a signal had been thoroughly analyzed by researchers. On 14 September 2015, while LIGO was running in engineering mode but without any blind data injections, the instrument reported a possible gravitational wave detection. The detected event was given the name GW150914.

GW150914 event

Event detection

GW150914 was detected by the LIGO detectors in Hanford, Washington state, and Livingston, Louisiana, USA, at 09:50:45 UTC on 14 September 2015. The LIGO detectors were operating in "engineering mode", meaning that they were operating fully but had not yet begun a formal "research" phase (which was due to commence three days later on 18 September), so initially there was a question as to whether the signals had been real detections or simulated data for testing purposes before it was ascertained that they were not tests.

The chirp signal lasted over 0.2 seconds, and increased in frequency and amplitude in about 8 cycles from 35 Hz to 250 Hz. The signal is in the audible range and has been described as resembling the "chirp" of a bird; astrophysicists and other interested parties the world over excitedly responded by imitating the signal on social media upon the announcement of the discovery. (The frequency increases because each orbit is noticeably faster than the one before during the final moments before merging.)

The trigger that indicated a possible detection was reported within three minutes of acquisition of the signal, using rapid ('online') search methods that provide a quick, initial analysis of the data from the detectors. After the initial automatic alert at 09:54 UTC, a sequence of internal emails confirmed that no scheduled or unscheduled injections had been made, and that the data looked clean. After this, the rest of the collaborating team was quickly made aware of the tentative detection and its parameters.

More detailed statistical analysis of the signal, and of 16 days of surrounding data from 12 September to 20 October 2015, identified GW150914 as a real event, with an estimated significance of at least 5.1 sigma or a confidence level of 99.99994%. Corresponding wave peaks were seen at Livingston seven milliseconds before they arrived at Hanford. Gravitational waves propagate at the speed of light, and the disparity is consistent with the light travel time between the two sites. The waves had traveled at the speed of light for more than a billion years.

At the time of the event, the Virgo gravitational wave detector (near Pisa, Italy) was offline and undergoing an upgrade; had it been online it would likely have been sensitive enough to also detect the signal, which would have greatly improved the positioning of the event. GEO600 (near Hannover, Germany) was not sensitive enough to detect the signal. Consequently, neither of those detectors was able to confirm the signal measured by the LIGO detectors.

Astrophysical origin

Simulation of merging black holes radiating gravitational waves

The event happened at a luminosity distance of 440+160
−180 megaparsecs (determined by the amplitude of the signal), or 1.4±0.6 billion light years, corresponding to a cosmological redshift of 0.093+0.030
−0.036 (90% credible intervals). Analysis of the signal along with the inferred redshift suggested that it was produced by the merger of two black holes with masses of 35+5
−3 times and 30+3
−4 times the mass of the Sun (in the source frame), resulting in a post-merger black hole of 62+4
−3 solar masses. The mass–energy of the missing 3.0±0.5 solar masses was radiated away in the form of gravitational waves.

During the final 20 milliseconds of the merger, the power of the radiated gravitational waves peaked at about 3.6×10⁴⁹ watts or 526 dBm – 50 times greater than the combined power of all light radiated by all the stars in the observable universe.

Across the 0.2-second duration of the detectable signal, the relative tangential (orbiting) velocity of the black holes increased from 30% to 60% of the speed of light. The orbital frequency of 75 Hz (half the gravitational wave frequency) means that the objects were orbiting each other at a distance of only 350 km by the time they merged. The phase changes to the signal's polarization allowed calculation of the objects' orbital frequency, and taken together with the amplitude and pattern of the signal, allowed calculation of their masses and therefore their extreme final velocities and orbital separation (distance apart) when they merged. That information showed that the objects had to be black holes, as any other kind of known objects with these masses would have been physically larger and therefore merged before that point, or would not have reached such velocities in such a small orbit. The highest observed neutron star mass is two solar masses, with a conservative upper limit for the mass of a stable neutron star of three solar masses, so that a pair of neutron stars would not have had sufficient mass to account for the merger (unless exotic alternatives exist, for example, boson stars), while a black hole-neutron star pair would have merged sooner, resulting in a final orbital frequency that was not so high.

The decay of the waveform after it peaked was consistent with the damped oscillations of a black hole as it relaxed to a final merged configuration. Although the inspiral motion of compact binaries can be described well from post-Newtonian calculations, the strong gravitational field merger stage can only be solved in full generality by large-scale numerical relativity simulations.

In the improved model and analysis, the post-merger object is found to be a rotating Kerr black hole with a spin parameter of 0.68+0.05
−0.06, i.e. one with 2/3 of the maximum possible angular momentum for its mass.

The two stars which formed the two black holes were likely formed about 2 billion years after the Big Bang with masses of between 40 and 100 times the mass of the Sun.

Location in the sky

Gravitational wave instruments are whole-sky monitors with little ability to resolve signals spatially. A network of such instruments is needed to locate the source in the sky through triangulation. With only the two LIGO instruments in observational mode, GW150914's source location could only be confined to an arc on the sky. This was done via analysis of the 6.9+0.5
−0.4 ms time-delay, along with amplitude and phase consistency across both detectors. This analysis produced a credible region of 150 deg² with a probability of 50% or 610 deg² with a probability of 90% located mainly in the Southern Celestial Hemisphere, in the rough direction of (but much farther than) the Magellanic Clouds.

For comparison, the area of the constellation Orion is 594 deg².

Coincident gamma-ray observation

The Fermi Gamma-ray Space Telescope reported that its Gamma-Ray Burst Monitor (GBM) instrument detected a weak gamma-ray burst above 50 keV, starting 0.4 seconds after the LIGO event and with a positional uncertainty region overlapping that of the LIGO observation. The Fermi team calculated the odds of such an event being the result of a coincidence or noise at 0.22%. However a gamma ray burst would not have been expected, and observations from the INTEGRAL telescope's all-sky SPI-ACS instrument indicated that any energy emission in gamma-rays and hard X-rays from the event was less than one millionth of the energy emitted as gravitational waves, which "excludes the possibility that the event is associated with substantial gamma-ray radiation, directed towards the observer." If the signal observed by the Fermi GBM was genuinely astrophysical, INTEGRAL would have indicated a clear detection at a significance of 15 sigma above background radiation. The AGILE space telescope also did not detect a gamma-ray counterpart of the event.

A follow-up analysis by an independent group, released in June 2016, developed a different statistical approach to estimate the spectrum of the gamma-ray transient. It concluded that Fermi GBM's data did not show evidence of a gamma ray burst, and was either background radiation or an Earth albedo transient on a 1-second timescale. A rebuttal of this follow-up analysis, however, pointed out that the independent group misrepresented the analysis of the original Fermi GBM Team paper and therefore misconstrued the results of the original analysis. The rebuttal reaffirmed that the false coincidence probability is calculated empirically and is not refuted by the independent analysis.

Black hole mergers of the type thought to have produced the gravitational wave event are not expected to produce gamma-ray bursts, as stellar-mass black hole binaries are not expected to have large amounts of orbiting matter. Avi Loeb has theorised that if a massive star is rapidly rotating, the centrifugal force produced during its collapse will lead to the formation of a rotating bar that breaks into two dense clumps of matter with a dumbbell configuration that becomes a black hole binary, and at the end of the star's collapse it triggers a gamma-ray burst. Loeb suggests that the 0.4 second delay is the time it took the gamma-ray burst to cross the star, relative to the gravitational waves.

Other follow-up observations

The reconstructed source area was targeted by follow-up observations covering radio, optical, near infra-red, X-ray, and gamma-ray wavelengths along with searches for coincident neutrinos. However, because LIGO had not yet started its science run, notice to other telescopes was delayed.

The ANTARES telescope detected no neutrino candidates within ±500 seconds of GW150914. The IceCube Neutrino Observatory detected three neutrino candidates within ±500 seconds of GW150914. One event was found in the southern sky and two in the northern sky. This was consistent with the expectation of background detection levels. None of the candidates were compatible with the 90% confidence area of the merger event. Although no neutrinos were detected, the lack of such observations provided a limit on neutrino emission from this type of gravitational wave event.

Observations by the Swift Gamma-Ray Burst Mission of nearby galaxies in the region of the detection, two days after the event, did not detect any new X-ray, optical or ultraviolet sources.

Announcement

GW150914 announcement paper – click to access

The announcement of the detection was made on 11 February 2016 at a news conference in Washington, D.C. by David Reitze, the executive director of LIGO, with a panel comprising Gabriela González, Rainer Weiss and Kip Thorne, of LIGO, and France A. Córdova, the director of NSF. Barry Barish delivered the first presentation on this discovery to a scientific audience simultaneously with the public announcement.

The initial announcement paper was published during the news conference in Physical Review Letters, with further papers either published shortly afterwards or immediately available in preprint form.

Awards and recognition

In May 2016, the full collaboration, and in particular Ronald Drever, Kip Thorne, and Rainer Weiss, received the Special Breakthrough Prize in Fundamental Physics for the observation of gravitational waves. Drever, Thorne, Weiss, and the LIGO discovery team also received the Gruber Prize in Cosmology. Drever, Thorne, and Weiss were also awarded the 2016 Shaw Prize in Astronomy and the 2016 Kavli Prize in Astrophysics. Barish was awarded the 2016 Enrico Fermi Prize from the Italian Physical Society (Società Italiana di Fisica). In January 2017, LIGO spokesperson Gabriela González and the LIGO team were awarded the 2017 Bruno Rossi Prize.

The 2017 Nobel Prize in Physics was awarded to Rainer Weiss, Barry Barish and Kip Thorne "for decisive contributions to the LIGO detector and the observation of gravitational waves".

Implications

The observation was heralded as inaugurating a revolutionary era of gravitational-wave astronomy. Prior to this detection, astrophysicists and cosmologists were able to make observations based upon electromagnetic radiation (including visible light, X-rays, microwave, radio waves, gamma rays) and particle-like entities (cosmic rays, stellar winds, neutrinos, and so on). These have significant limitations - light and other radiation may not be emitted by many kinds of objects, and can also be obscured or hidden behind other objects. Objects such as galaxies and nebulae can also absorb, re-emit, or modify light generated within or behind them, and compact stars or exotic stars may contain material which is dark and radio silent, and as a result there is little evidence of their presence other than through their gravitational interactions.

Expectations for detection of future binary merger events

On 15 June 2016, the LIGO group announced an observation of another gravitational wave signal, named GW151226. The Advanced LIGO is predicted to detect five more black hole mergers like GW150914 in its next observing campaign, and then 40 binary star mergers each year, in addition to an unknown number of more exotic gravitational wave sources, some of which may not be anticipated by current theory.

Planned upgrades are expected to double the signal-to-noise ratio, expanding the volume of space in which events like GW150914 can be detected by a factor of ten. Additionally, Advanced Virgo, KAGRA, and a possible third LIGO detector in India will extend the network and significantly improve the position reconstruction and parameter estimation of sources.

Laser Interferometer Space Antenna (LISA) is a proposed space based observation mission to detect gravitational waves. With the proposed sensitivity range of LISA, merging binaries like GW150914 would be detectable about 1000 years before they merge, providing for a class of previously unknown sources for this observatory if they exist within about 10 megaparsecs. LISA Pathfinder, LISA's technology development mission, was launched in December 2015 and it demonstrated that the LISA mission is feasible.

A current model predicts LIGO will detect approximately 1000 black hole mergers per year after it reaches full sensitivity planned for 2020.

Lessons for stellar evolution and astrophysics

The masses of the two pre-merger black holes provide information about stellar evolution. Both black holes were more massive than previously discovered stellar-mass black holes, which were inferred from X-ray binary observations. This implies that the stellar winds from their progenitor stars must have been relatively weak, and therefore that the metallicity (mass fraction of chemical elements heavier than hydrogen and helium) must have been less than about half the solar value.

The fact that the pre-merger black holes were present in a binary star system, as well as the fact that the system was compact enough to merge within the age of the universe, constrains either binary star evolution or dynamical formation scenarios, depending on how the black hole binary was formed. A significant number of black holes must receive low natal kicks (the velocity a black hole gains at its formation in a core-collapse supernova event), otherwise the black hole forming in a binary star system would be ejected and an event like GW would be prevented. The survival of such binaries, through common envelope phases of high rotation in massive progenitor stars, may be necessary for their survival. The majority of the latest black hole model predictions comply with these added constraints.

The discovery of the GW merger event increases the lower limit on the rate of such events, and rules out certain theoretical models that predicted very low rates of less than 1 Gpc⁻³yr⁻¹ (one event per cubic gigaparsec per year). Analysis resulted in lowering the previous upper limit rate on events like GW150914 from ~140 Gpc⁻³yr⁻¹ to 17+39
−13 Gpc⁻³yr⁻¹.

Impact on future cosmological observation

Measurement of the waveform and amplitude of the gravitational waves from a black hole merger event makes accurate determination of its distance possible. The accumulation of black hole merger data from cosmologically distant events may help to create more precise models of the history of the expansion of the universe and the nature of the dark energy that influences it.

The earliest universe is opaque since the cosmos was so energetic then that most matter was ionized and photons were scattered by free electrons. However, this opacity would not affect gravitational waves from that time, so if they occurred at levels strong enough to be detected at this distance, it would allow a window to observe the cosmos beyond the current visible universe. Gravitational-wave astronomy therefore may some day allow direct observation of the earliest history of the universe.

Tests of general relativity

The inferred fundamental properties, mass and spin, of the post-merger black hole were consistent with those of the two pre-merger black holes, following the predictions of general relativity. This is the first test of general relativity in the very strong-field regime. No evidence could be established against the predictions of general relativity.

The opportunity was limited in this signal to investigate the more complex general relativity interactions, such as tails produced by interactions between the gravitational wave and curved space-time background. Although a moderately strong signal, it is much smaller than that produced by binary-pulsar systems. In the future stronger signals, in conjunction with more sensitive detectors, could be used to explore the intricate interactions of gravitational waves as well as to improve the constraints on deviations from general relativity.

Speed of gravitational waves and limit on possible mass of graviton

The speed of gravitational waves (v_g) is predicted by general relativity to be the speed of light (c). The extent of any deviation from this relationship can be parameterized in terms of the mass of the hypothetical graviton. The graviton is the name given to an elementary particle that would act as the force carrier for gravity, in quantum theories about gravity. It is expected to be massless if, as it appears, gravitation has an infinite range. (This is because the more massive a gauge boson is, the shorter is the range of the associated force; as with the infinite range of electromagnetism, which is due to the massless photon, the infinite range of gravity implies that any associated force-carrying particle would also be massless.) If the graviton were not massless, gravitational waves would propagate below lightspeed, with lower frequencies (ƒ) being slower than higher frequencies, leading to dispersion of the waves from the merger event. No such dispersion was observed. The observations of the inspiral slightly improve (lower) the upper limit on the mass of the graviton from Solar System observations to 2.1×10⁻⁵⁸ kg, corresponding to 1.2×10⁻²² eV/c² or a Compton wavelength (λ_g) of greater than 10¹³ km, roughly 1 light-year. Using the lowest observed frequency of 35 Hz, this translates to a lower limit on v_g such that the upper limit on 1-v_g /c is ~ 4×10⁻¹⁹.