List of neutron stars. satellite tracker

23.09.2019

The hypothesis of the existence of neutron stars was put forward by astronomers W. Baade and F. Zwicky immediately after the discovery of the neutron in 1932. But this hypothesis was confirmed by observations only after the discovery of pulsars in 1967.

Neutron stars are formed as a result of the gravitational collapse of normal stars with masses several times that of the Sun. The density of a neutron star is close to the density of an atomic nucleus, i.e. 100 million times higher than the density of ordinary matter. Therefore, with its huge mass, a neutron star has a radius of only approx. 10 km.

Due to the small radius of a neutron star, the force of gravity on its surface is extremely high: about 100 billion times higher than on Earth. This star is kept from collapse by the “degeneracy pressure” of dense neutron matter, which does not depend on its temperature. However, if the mass of the neutron star becomes greater than about 2 solar masses, then gravity will exceed this pressure and the star will not be able to withstand the collapse.

Neutron stars have a very strong magnetic field, reaching 10 12 -10 13 gauss on the surface (for comparison: the Earth has about 1 gauss). Two different types of celestial objects are associated with neutron stars.

Pulsars

(radio pulsars). These objects strictly regularly emit pulses of radio waves. The radiation mechanism is not completely clear, but it is believed that a rotating neutron star emits a radio beam in the direction associated with its magnetic field, the symmetry axis of which does not coincide with the axis of rotation of the star. Therefore, the rotation causes the rotation of the radio beam periodically sent to the Earth.

X-ray doubles.

Pulsating X-ray sources are also associated with neutron stars that are part of a binary system with a massive normal star. In such systems, gas from the surface of a normal star falls onto a neutron star, accelerating to tremendous speed. When hitting the surface of a neutron star, the gas releases 10-30% of its rest energy, while in nuclear reactions this figure does not even reach 1%. The surface of a neutron star heated to a high temperature becomes a source of X-rays. However, the fall of gas does not occur uniformly over the entire surface: the strong magnetic field of a neutron star captures the falling ionized gas and directs it to the magnetic poles, where it falls, like into a funnel. Therefore, only the regions of the poles become strongly heated, which on a rotating star become sources of X-ray pulses. Radio pulses from such a star no longer arrive, since radio waves are absorbed in the gas surrounding it.

Compound.

The density of a neutron star increases with depth. Under a layer of atmosphere only a few centimeters thick, there is a liquid metal shell several meters thick, and below - a solid crust kilometer thick. The substance of the bark resembles ordinary metal, but is much denser. In the outer part of the crust, it is mainly iron; the fraction of neutrons in its composition increases with depth. Where the density reaches approx. 4Ch 10 11 g/cm 3 , the proportion of neutrons increases so much that some of them are no longer part of the nuclei, but form a continuous medium. There, the substance looks like a "sea" of neutrons and electrons, in which the nuclei of atoms are interspersed. And at a density of approx. 2× 10 14 g/cm 3 (density of the atomic nucleus), individual nuclei disappear altogether and a continuous neutron "liquid" with an admixture of protons and electrons remains. Probably, neutrons and protons behave in this case as a superfluid liquid, similar to liquid helium and superconducting metals in terrestrial laboratories.

The substances of such an object are several times higher than the density of the atomic nucleus (which for heavy nuclei is on average 2.8⋅10 17 kg/m³). Further gravitational contraction of a neutron star is prevented by the pressure of nuclear matter, which arises due to the interaction of neutrons.

Many neutron stars have extremely high rotation speeds - up to several hundred revolutions per second. Neutron stars are formed as a result of supernova explosions.

General information

Among neutron stars with reliably measured masses, most fall within the range of 1.3 to 1.5 solar masses, which is close to the Chandrasekhar limit. Theoretically, neutron stars with masses from 0.1 to about 2.16 solar masses are acceptable. The most massive known neutron stars are Vela X-1 (has a mass of at least 1.88 ± 0.13 solar masses at the 1σ level, which corresponds to a significance level of α≈34%), PSR J1614–2230 en (with a mass estimate of 1, 97±0.04 solar), and PSR J0348+0432 en (with a mass estimate of 2.01±0.04 solar). Gravity in neutron stars is balanced by the pressure of the degenerate neutron gas, the maximum value of the mass of a neutron star is given by the Oppenheimer-Volkov limit, the numerical value of which depends on the (still poorly known) equation of state of matter in the star's core. There are theoretical prerequisites for the fact that with an even greater increase in density, the transformation of neutron stars into quark stars is possible.

By 2015, more than 2500 neutron stars have been discovered. About 90% of them are single. In total, 10 8 -10 9 neutron stars can exist in our Galaxy, that is, somewhere around one per thousand ordinary stars. Neutron stars are characterized by high speeds (usually hundreds of km/s). As a result of accretion of cloud matter, a neutron star in this situation can be visible from Earth in different spectral ranges, including optical, which accounts for about 0.003% of the radiated energy (corresponding to 10 magnitude).

Structure

Five layers can be distinguished in a neutron star: atmosphere, outer crust, inner crust, outer core, and inner core.

The atmosphere of a neutron star is a very thin layer of plasma (from tens of centimeters for hot stars to millimeters for cold ones), the thermal radiation of a neutron star is formed in it.

The outer crust consists of ions and electrons, its thickness reaches several hundred meters. A thin (no more than a few meters) near-surface layer of a hot neutron star contains a non-degenerate electron gas, deeper layers - a degenerate electron gas, with increasing depth it becomes relativistic and ultrarelativistic.

The inner crust consists of electrons, free neutrons, and neutron-rich atomic nuclei. As the depth increases, the proportion of free neutrons increases, while that of atomic nuclei decreases. The thickness of the inner crust can reach several kilometers.

The outer core consists of neutrons with a small admixture (several percent) of protons and electrons. In low-mass neutron stars, the outer core can extend to the center of the star.

Massive neutron stars also have an inner core. Its radius can reach several kilometers, the density in the center of the nucleus can exceed the density of atomic nuclei by 10-15 times. The composition and equation of state of the inner core are not known for certain: there are several hypotheses, the three most probable of which are: 1) a quark core, in which neutrons fall apart into their constituent up and down quarks; 2) hyperon core of baryons including strange quarks; and 3) a kaon nucleus consisting of two-quark mesons, including strange (anti) quarks. However, it is not currently possible to confirm or disprove any of these hypotheses.

A free neutron, under normal conditions, not being part of an atomic nucleus, usually has a lifetime of about 880 seconds, but the gravitational influence of a neutron star does not allow a neutron to decay, therefore neutron stars are one of the most stable objects in the Universe. [ ]

Cooling neutron stars

At the time of the birth of a neutron star (as a result of a supernova explosion), its temperature is very high - about 10 11 K (that is, 4 orders of magnitude higher than the temperature in the center of the Sun), but it drops very quickly due to neutrino cooling. In just a few minutes, the temperature drops from 10 11 to 10 9 K, in a month - to 10 8 K. Then the neutrino luminosity decreases sharply (it depends very much on temperature), and cooling occurs much more slowly due to the photon (thermal) radiation of the surface. The surface temperature of known neutron stars, for which it has been measured, is on the order of 10 5 -10 6 K (although the core is apparently much hotter).

Discovery history

Neutron stars are one of the few classes of space objects that were theoretically predicted prior to discovery by observers.

For the first time, the idea of ​​​​the existence of stars with increased density even before the discovery of the neutron, made by Chadwick in early February 1932, was expressed by the famous Soviet scientist Lev Landau. Thus, in his article On the Theory of Stars, written in February 1931 and for unknown reasons belatedly published on February 29, 1932 (more than a year later), he writes: “We expect that all this [violation of the laws of quantum mechanics] should manifest itself when the density of matter becomes so great that the atomic nuclei come into close contact, forming one giant nucleus.

"Propeller"

The rotation speed is no longer sufficient to eject particles, so such a star cannot be a radio pulsar. However, the rotation speed is still high, and the matter captured by the magnetic field surrounding the neutron star cannot fall, that is, the accretion of matter does not occur. Neutron stars of this type have practically no observable manifestations and are poorly studied.

Accretor (X-ray pulsar)

The rotation speed is reduced so much that now nothing prevents the matter from falling onto such a neutron star. Falling, the matter, already in the state of plasma, moves along the lines of the magnetic field and hits the solid surface of the body of a neutron star in the region of its poles, heating up to tens of millions of degrees. Substance heated to such high temperatures glows brightly in the X-ray range. The area in which the incident matter collides with the surface of the body of a neutron star is very small - only about 100 meters. This hot spot periodically disappears from view due to the rotation of the star, so regular pulsations of X-rays are observed. Such objects are called X-ray pulsars.

Georotator

The rotation speed of such neutron stars is low and does not prevent accretion. But the dimensions of the magnetosphere are such that the plasma is stopped by the magnetic field before it is captured by gravity. A similar mechanism works in the Earth's magnetosphere, which is why this type of neutron stars got its name.

Notes

  1. Dmitry Trunin. Astrophysicists have clarified the limiting mass of neutron stars (indefinite) . nplus1.ru. Retrieved 18 January 2018.
  2. H. Quaintrell et al. The mass of the neutron star in Vela X-1 and tidally induced non-radial oscillations in GP Vel // Astronomy and Astrophysics. - April 2003. - No. 401. - pp. 313-323. - arXiv :astro-ph/0301243 .
  3. P. B. Demorest, T. Pennucci, S. M. Ransom, M. S. E. Roberts & J. W. T. Hessels. A two-solar-mass neutron star measured using Shapiro delay // Nature. - 2010. - Vol. 467 . - P. 1081-1083.

Introduction

Throughout its history, mankind has not stopped trying to understand the universe. The universe is called the totality of everything that exists, all the material particles of the space between these particles. According to modern concepts, the age of the universe is about 14 billion years.

The size of the visible part of the universe is approximately 14 billion light years (one light year is the distance that light travels in vacuum in one year). According to some scientists, the length of the universe is 90 billion light years. In order to make it convenient to operate with such huge distances, a value called Parsec is used. A parsec is the distance from which the average radius of the earth's orbit, perpendicular to the line of sight, is visible at an angle of one arcsecond. 1 parsec = 3.2616 light years.

There is a huge number of different objects in the universe, the names of which are well known to many, such as planets and satellites, stars, black holes, etc. Stars are very diverse in their brightness, size, temperature, and other parameters. Stars include objects such as white dwarfs, neutron stars, giants and supergiants, quasars and pulsars. Of particular interest are the centers of galaxies. According to modern concepts, a black hole is suitable for the role of an object located in the center of a galaxy. Black holes are products of the evolution of stars that are unique in their properties. The experimental validity of the existence of black holes depends on the validity of the general theory of relativity.

In addition to galaxies, the universe is filled with nebulae (interstellar clouds consisting of dust, gas and plasma), relic radiation penetrating the entire universe, and other little-studied objects.

neutron stars

A neutron star is an astronomical object, which is one of the end products of the evolution of stars, consisting mainly of a neutron core covered with a relatively thin (? 1 km) crust of matter in the form of heavy atomic nuclei and electrons. The masses of neutron stars are comparable to the mass of the Sun, but the typical radius is only 10-20 kilometers. Therefore, the average density of the matter of such a star is several times higher than the density of the atomic nucleus (which for heavy nuclei is on average 2.8*1017 kg/m?). Further gravitational contraction of a neutron star is prevented by the pressure of nuclear matter, which arises due to the interaction of neutrons.

Many neutron stars have extremely high rotational speeds, up to a thousand revolutions per second. It is believed that neutron stars are born during supernova explosions.

The gravitational forces in neutron stars are balanced by the pressure of the degenerate neutron gas, the maximum value of the mass of a neutron star is set by the Oppenheimer-Volkov limit, the numerical value of which depends on the (still poorly known) equation of state of matter in the star's core. There are theoretical prerequisites that with an even greater increase in density, the transformation of neutron stars into quark ones is possible.

The magnetic field on the surface of neutron stars reaches a value of 1012-1013 Gs (Gs-Gauss is a unit of measurement of magnetic induction), it is the processes in the magnetospheres of neutron stars that are responsible for the radio emission of pulsars. Since the 1990s, some neutron stars have been identified as magnetars, stars with magnetic fields of the order of 1014 gauss and higher. Such fields (exceeding the “critical” value of 4.414 1013 G, at which the interaction energy of an electron with a magnetic field exceeds its rest energy) introduce a qualitatively new physics, since specific relativistic effects, polarization of the physical vacuum, etc. become significant.

Classification of neutron stars

The two main parameters characterizing the interaction of neutron stars with the surrounding matter and, as a consequence, their observational manifestations are the rotation period and the magnitude of the magnetic field. Over time, the star expends its rotational energy, and its rotation period increases. The magnetic field is also weakening. For this reason, a neutron star can change its type during its lifetime.

Ejector (radio pulsar) - strong magnetic fields and a small period of rotation. In the simplest model of the magnetosphere, the magnetic field rotates rigidly, that is, with the same angular velocity as the neutron star itself. At a certain radius, the linear speed of rotation of the field approaches the speed of light. This radius is called the radius of the light cylinder. Beyond this radius, the usual dipole field cannot exist, so the field strength lines break off at this point. Charged particles moving along magnetic field lines can leave a neutron star through such cliffs and fly away to infinity. A neutron star of this type ejects (spews, pushes out) relativistic charged particles that radiate in the radio range. To an observer, ejectors look like radio pulsars.

Propeller - the rotation speed is already insufficient for the ejection of particles, so such a star cannot be a radio pulsar. However, it is still large, and the matter captured by the magnetic field surrounding the neutron star cannot fall, that is, the accretion of matter does not occur. Neutron stars of this type have practically no observable manifestations and are poorly studied.

Accretor (X-ray pulsar) - the rotation speed is reduced to such an extent that now nothing prevents the substance from falling onto such a neutron star. The plasma, falling, moves along the lines of the magnetic field and hits a solid surface near the poles of a neutron star, heating up to tens of millions of degrees. A substance heated to such high temperatures glows in the X-ray range. The area in which the falling matter collides with the surface of the star is very small - only about 100 meters. This hot spot, due to the rotation of the star, periodically disappears from view, which the observer perceives as pulsations. Such objects are called X-ray pulsars.

Georotator - the rotation speed of such neutron stars is small and does not prevent accretion. But the dimensions of the magnetosphere are such that the plasma is stopped by the magnetic field before it is captured by gravity. A similar mechanism works in the Earth's magnetosphere, which is why this type got its name.

Supernova remnant Korma-A, at the center of which is a neutron star

Neutron stars are the remnants of massive stars that have reached the end of their evolutionary path in time and space.

These interesting objects are born from once massive giants that are four to eight times the size of our Sun. It happens in a supernova explosion.

After such an explosion, the outer layers are ejected into space, the core remains, but it is no longer able to support nuclear fusion. Without external pressure from the overlying layers, it collapses and shrinks catastrophically.

Despite their small diameter - about 20 km, neutron stars boast 1.5 times the mass of our Sun. Thus, they are incredibly dense.

A small spoonful of star matter on Earth would weigh about a hundred million tons. In it, protons and electrons are combined into neutrons - this process is called neutronization.

Compound

Their composition is unknown; it is assumed that they may consist of a superfluid neutron liquid. They have an extremely strong gravitational pull, much stronger than that of the Earth and even the Sun. This gravitational force is especially impressive because it has a small size.
All of them rotate around an axis. During compression, the angular momentum of rotation is preserved, and due to a decrease in size, the rotation speed increases.

Due to the huge speed of rotation, the outer surface, which is a solid “crust”, periodically cracks and “starquakes” occur, which slow down the rotation speed and dump “excess” energy into space.

The overwhelming pressure that exists in the core may be similar to that which existed at the time of the big bang, but unfortunately it cannot be simulated on Earth. Therefore, these objects are ideal natural laboratories where we can observe energies inaccessible on Earth.

radio pulsars

Radio pulsars were discovered in late 1967 by graduate student Jocelyn Bell Burnell as radio sources that pulsate at a constant frequency.
The radiation emitted by the star is visible as a pulsating radiation source or pulsar.

Schematic representation of the rotation of a neutron star

Radio pulsars (or simply a pulsar) are spinning neutron stars whose jets of particles move at nearly the speed of light, like a spinning beacon beam.

After continuous rotation, for several million years, pulsars lose their energy and become normal neutron stars. Only about 1,000 pulsars are known today, although there may be hundreds of them in the galaxy.

Radio pulsar in the Crab Nebula

Some neutron stars emit X-rays. The famous Crab Nebula is a good example of such an object, formed during a supernova explosion. This supernova explosion was observed in 1054 AD.

Pulsar wind, Chandra video

A radio pulsar in the Crab Nebula photographed by the Hubble Space Telescope through a 547nm filter (green light) from August 7, 2000 to April 17, 2001.

magnetars

Neutron stars have a magnetic field millions of times stronger than the strongest magnetic field produced on Earth. They are also known as magnetars.

Planets near neutron stars

So far, four are known to have planets. When it is in a binary system, it is possible to measure its mass. Of these binary systems in the radio or X-ray range, the measured masses of neutron stars were about 1.4 times the mass of the Sun.

Double systems

A completely different type of pulsar is seen in some X-ray binaries. In these cases, a neutron star and an ordinary one form a binary system. A strong gravitational field pulls material from an ordinary star. Material falling on it during the accretion process heats up so much that it produces X-rays. Pulsed X-rays are visible when hot spots on a spinning pulsar pass through the line of sight from Earth.

For binary systems containing an unknown object, this information helps to distinguish whether it is a neutron star, or, for example, a black hole, because black holes are much more massive.

The objects that will be discussed in the article were discovered by chance, although the scientists L. D. Landau and R. Oppenheimer predicted their existence back in 1930. We are talking about neutron stars. The characteristics and features of these cosmic bodies will be discussed in the article.

The neutron and the star of the same name

After the prediction in the 30s of the XX century about the existence of neutron stars and after the discovery of the neutron (1932), Baade V., together with Zwicky F. in 1933 at the Congress of Physicists in America, announced the possibility of the formation of an object called neutron star. This is a cosmic body that occurs in the process of a supernova explosion.

However, all the calculations were only theoretical, since it was not possible to prove such a theory in practice due to the lack of appropriate astronomical equipment and the too small size of the neutron star. But in 1960 X-ray astronomy began to develop. Then, quite unexpectedly, neutron stars were discovered thanks to radio observations.

Opening

1967 was a significant year in this area. Bell D., being a graduate student of Hewish E., was able to discover a space object - a neutron star. This is a body emitting constant radiation of radio wave impulses. The phenomenon has been compared to a cosmic radio beacon due to the narrow focus of the radio beam, which came from a very fast rotating object. The fact is that any other standard star could not maintain its integrity at such a high rotational speed. Only neutron stars are capable of this, among which the pulsar PSR B1919+21 was the first to be discovered.

The fate of massive stars is very different from small ones. In such luminaries there comes a moment when the pressure of the gas no longer balances the gravitational forces. Such processes lead to the fact that the star begins to shrink (collapse) indefinitely. With a star mass exceeding the solar one by 1.5-2 times, the collapse will be inevitable. During the compression process, the gas inside the stellar core heats up. Everything happens very slowly at first.

Collapse

Reaching a certain temperature, the proton is able to turn into neutrinos, which immediately leave the star, taking energy with them. The collapse will intensify until all the protons turn into neutrinos. Thus, a pulsar, or neutron star, is formed. This is a collapsing core.

During the formation of a pulsar, the outer shell receives compression energy, which will then be at a speed of more than one thousand km / s. thrown into space. In this case, a shock wave is formed that can lead to new star formation. This one will be billions of times higher than the original one. After such a process, for a period of one week to a month, the star emits light in excess of an entire galaxy. Such a celestial body is called a supernova. Its explosion leads to the formation of a nebula. At the center of the nebula is a pulsar, or neutron star. This is the so-called descendant of the star that exploded.

Visualization

In the depths of the entire space of space, amazing events take place, among which is the collision of stars. Thanks to the most complex mathematical model, NASA scientists were able to visualize the rampage of a huge amount of energy and the degeneration of the matter involved in it. An incredibly powerful picture of a cosmic cataclysm is playing out before the eyes of observers. The probability that a collision of neutron stars will occur is very high. The meeting of two such luminaries in space begins with their entanglement in gravitational fields. Possessing a huge mass, they, so to speak, exchange hugs. Upon collision, a powerful explosion occurs, accompanied by an incredibly powerful release of gamma radiation.

If we consider a neutron star separately, then these are the remnants after a supernova explosion, in which the life cycle ends. The mass of a star surviving its age exceeds the solar one by 8-30 times. The universe is often illuminated by explosions of supernovae. The probability that neutron stars will meet in the universe is quite high.

Meeting

Interestingly, when two stars meet, the development of events cannot be unambiguously predicted. One of the options is described by a mathematical model proposed by NASA scientists from the Space Flight Center. The process begins when two neutron stars are located from each other in outer space at a distance of approximately 18 km. By cosmic standards, neutron stars with a mass of 1.5-1.7 times that of the sun are considered tiny objects. Their diameter varies within 20 km. Due to this discrepancy between volume and mass, a neutron star is the owner of the strongest gravitational and magnetic fields. Just imagine: a teaspoon of the matter of a neutron luminary weighs as much as the entire Mount Everest!

degeneration

The incredibly high gravitational waves of a neutron star acting around it are the reason why matter cannot be in the form of individual atoms that begin to break down. The matter itself passes into a degenerate neutron, in which the structure of the neutrons themselves will not allow the star to pass into a singularity and then into a black hole. If the mass of degenerate matter begins to increase due to the addition to it, then the gravitational forces will be able to overcome the resistance of neutrons. Then nothing will prevent the destruction of the structure formed as a result of the collision of neutron stellar objects.

Mathematical model

Studying these celestial objects, scientists came to the conclusion that the density of a neutron star is comparable to the density of matter in the nucleus of an atom. Its performance ranges from 1015 kg/m³ to 1018 kg/m³. Thus, independent existence of electrons and protons is impossible. The matter of a star practically consists of only neutrons.

The created mathematical model demonstrates how powerful periodic gravitational interactions that arise between two neutron stars break through the thin shell of two stars and throw out a huge amount of radiation (energy and matter) into the space surrounding them. The process of rapprochement is very fast, literally in a fraction of a second. As a result of the collision, a toroidal ring of matter is formed with a newborn black hole in the center.

Importance

Modeling such events is essential. Thanks to them, scientists were able to understand how a neutron star and a black hole are formed, what happens when stars collide, how supernovae are born and die, and many other processes in outer space. All these events are the source of the appearance of the heaviest chemical elements in the Universe, even heavier than iron, unable to form in any other way. This speaks of the very important importance of neutron stars throughout the universe.

The rotation of a celestial object of enormous volume around its axis is amazing. Such a process causes a collapse, but with all this, the mass of a neutron star remains practically the same. If we imagine that the star will continue to shrink, then, according to the law of conservation of angular momentum, the angular velocity of rotation of the star will increase to incredible values. If it took about 10 days for a star to make a complete revolution, then as a result it will complete the same revolution in 10 milliseconds! These are incredible processes!

collapse development

Scientists are investigating such processes. Perhaps we will witness new discoveries, which so far seem fantastic to us! But what can be if we imagine the development of the collapse further? To make it easier to imagine, let's take a neutron star/earth pair and their gravitational radii for comparison. So, with continuous compression, a star can reach a state where neutrons begin to turn into hyperons. The radius of the celestial body will become so small that we will face a lump of a superplanetary body with the mass and gravitational field of a star. This can be compared to the fact that the earth became equal in size to a ping-pong ball, and the gravitational radius of our luminary, the Sun, would be equal to 1 km.

If we imagine that a small lump of stellar matter has the attraction of a huge star, then it is able to hold an entire planetary system near it. But the density of such a celestial body is too high. Rays of light gradually cease to penetrate through it, the body, as it were, goes out, it ceases to be visible to the eye. Only the gravitational field does not change, which warns that there is a gravitational hole here.

Discoveries and observations

For the first time from the merger of neutron stars were recorded quite recently: August 17th. Two years ago, a black hole merger was registered. This is such an important event in the field of astrophysics that observations were carried out simultaneously by 70 space observatories. Scientists were able to verify the correctness of the hypotheses about gamma-ray bursts, they were able to observe the synthesis of heavy elements described earlier by theorists.

Such widespread observation of the gamma-ray burst, gravitational waves and visible light made it possible to determine the region in the sky in which a significant event occurred, and the galaxy where these stars were. This is NGC 4993.

Of course, astronomers have been observing short ones for a long time. But until now, they could not say for sure about their origin. Behind the main theory was a version of the merger of neutron stars. Now she has been confirmed.

To describe a neutron star using the mathematical apparatus, scientists turn to the equation of state, which relates the density to the pressure of matter. However, there are a lot of such options, and scientists simply do not know which of the existing ones will be correct. It is hoped that gravitational observations will help resolve this issue. At the moment, the signal has not given an unambiguous answer, but it already helps to assess the shape of the star, which depends on the gravitational attraction to the second luminary (star).



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