A neutron star is the result of the collapse of a massive star under the effect of its clean Gravité, when it exhausted any sound Fuel nuclear. According to the Mass of the core which crumbles, it is formed, by order ascending of mass, either a white Naine, or a neutron star, or a Black hole. The release of energy which results from it produces a Supernova of the type II, Ib or Ic.

According to the circumstances, a neutron star can appear under various aspects. If it rotates quickly and that it develops powerful a Magnetic field, it then projects along its magnetic axis a thin brush of radiations, and an observer placed roughly in the direction of this axis will observe a Pulsar or a Magnétar, depend on the number of revolutions and intensity of the magnetic field. If it belongs to a binary system, it will be able to then seem a pulsar X or one source with starts γ, so from the gas matter resulting from his/her companion falls regularly on his surface. In the other cases, a neutron star is almost invisible because of its very low size, which is only of a few tens kilometers in maximum diameter, because of its extremely important density.

History

In the Years 1920, Arthur Eddington, working on the structure and the stellar evolution, did not manage to solve the problem of the end-of-life of stars, when those exhausted their nuclear fuel. In 1930, at the time of its long voyage by steamer bringing it of India to the university of Cambridge, Chandrasekhar, which did not have whereas 20 years, took again this problem by supposing that:

• the gas of electron S in the middle of these stars was a Perfect gas;
• the electrons were Relativiste S, which Eddington had not considered.

It found whereas the maximum mass M of dwarf white was worth:

$\backslash \; textstyle\; \{M\_\; \{limit\}\; =\; \backslash \; frac\; \{5,76\}\; \{\backslash \; mu\_e^2\}\; M\_S\}$ with µ = molecular Mass average by electron of star, and M being mass of the Sun.

This result made great noise, not only because it was young a 20 year old student who had solved a problem against which Eddington had butted, the large astrophysicist of the time, but also because a mass limits was fixed for these stars, and that this limiting mass depended only on one combination of fundamental constants (5,76) and μ, corresponding to the chemical composition and the ionization rate of star. This limit is now called Limite of Chandrasekhar, or Mr.

The equations also showed that the ray of dwarf white decreases when its mass increases, the equation binding these two parameters being form: $\backslash \; textstyle\; \{R\; =\; \backslash \; sqrt\; \{\backslash \; frac\; \{K\}\; \{M\}\}\}$, K being a constant. This paradoxical result is explained by the fact why the increase in the ray due to the matter increase is negligible in front of the reduction of the ray due to the additional compression caused by the increase in gravity. Consequently, the Densité of dwarf white increases considerably when its mass increases, since its size is reduced at the same time. The equations provided that when the mass of dwarf white tends towards M, its density tends towards the infinite one and its ray towards zero. To avoid this singularity, it was allowed a time that, at the time of the end-of-life of a massive star, the matter expulsion was always such as at the time of collapse the mass of the core was always lower than Mr. It should be noted that at that time the neutron was not yet discovered.

They were Zwicky and Baade, which, the first in 1934, considered the collapse of a star heart of a mass higher than Mr. the degeneration of the electrons not managing more to stop the contraction of the heart, they are linked then with the Proton S, which are transformed into Neutron S. When these neutrons are completely degenerated, i.e., when they occupy all the allowed basic cells, which cannot enfreindre the Principe of exclusion of Pauli, they exert then a pressure of origin not-thermics, able to stop gravitational collapse, this phenomenon appearing for densities of about 10 17 kg/m 3 . This scenario is all the more remarkable well, that it was described and put in equation, before a neutron star was observed, since the first Pulsar discovered (CP 1919) was it only in 1967.

Mass limit

M define the border between the dwarf white ones and neutron stars. Its equation being: $\backslash \; textstyle\; \{M\_\; \{CH\}\; =\; \backslash \; frac\; \{5,76\}\; \{\backslash \; mu\_e^2\}\; M\_S\}$, to obtain a numerical value from it, it is enough to know μ, which is the average molecular mass by electron of star. But in practice, this parameter is difficult to appreciate, because it depends mainly on the chemical composition of star. However, at this stage, the star passed by the phases of combustion of the Hydrogène, the Hélium, the Carbone, the Néon, etc until the Fer, and its chemical composition is complex, the cores of atomic masses ranging between 50 and 60, and among them mainly iron, being undoubtedly mainly represented. Moreover this parameter is undoubtedly not the same one in any point of star.

Thus, as example, for the Sun:

• μ = 1,18 for the whole of the star
• μ = 1,54 in the center of the star

By taking μ = 2, one obtains: M = 1,44 Mr. This value, calculated thanks to some approximations carried out in a purely theoretical context (the gas of electrons is a perfect gas, and μ = 2), appeared remarkably in conformity thereafter with the later results provided by the observations. Indeed, the masses of the neutron stars which could be measured are very close to 1,4 Mr. All these stars belong to a double system (it is the condition so that one can measure the mass of it), even if, in the table below, the mass of their companions were not always indicated. Some of these companions are probably themselves of neutron stars.

Sources: University of Heidelberg (http://www.lsw.uni-heidelberg.de/users/mcamenzi/NS_Mass.html) and Philip Charles and Frederick Seward, in Exploring the X-Ray Universe pages 164 and 165.

The Median value of these masses is of 1,43 M, and them standard deviation of 0,23 Mr.

In spite of these results close to the theory, one could be astonished to find neutron stars of mass lower than M, because the theory announces that for the moment collapse, it is necessary that the mass of the core is higher than this value to lead to a neutron star. A less heavy core should finish dwarf white. In fact, in 1939, Robert Oppenheimer and its Canadian college George Volkoff of the University of Berkeley had been the first to calculate the configurations of balance of neutron stars, starting from an equation of take state into account a degenerated relativistic gas. They found that a neutron star is stable, i.e. it preserves its neutron star state, for masses ranging between 0,1 M and 2 to 3 Mr. This limit higher is called besides Masse of Oppenheimer-Volkoff or Mr. Beyond this limit, a cold body cannot preserve its stability and would crumble in a Black hole.

This result does not call into question the Limite of Chandrasekhar (during a gravitational collapse it is necessary that the mass is higher than M to form a neutron star), but it makes it possible to envisage two situations.

• if a “normal” neutron star (of mass > M) lost matter for an unspecified reason, it would preserve its neutron star nature up to 0,1 Mr. Normalement no phenomenon would not allow this massive loss, but it is a kind of experiment by the thought .
• if, in an explosive process, a matter mass higher than 0,1 M were compressed by the explosion until the neutron star state, once the shock wave passed, this matter would continue to exist in this form. It is a completely plausible scenario starting from the explosion of the Supernova S, in which the compressed heart can extremely well have a mass lower than that of Chandrasekhar.

However, this result remains for the moment of the purely theoretical and speculative field, the observations not having never revealed so far the existence of “dwarf” neutron star; it would be in any rigor of neutron stars of low mass , but larger from the opposite relation/mass cuts (see below), to the surroundings of 1000 km for 0,1 Mr. the measured values slightly lower than M, appearing in the table, could be explained by the approximations of the theory and uncertainties of measurement of the observations (see http://www.lsw.uni-heidelberg.de/users/mcamenzi/NS_Mass.html for the beaches of uncertainty).

Cut

Just like the dwarf white ones, the neutron stars have a ray which varies in a way inversely proportional to their mass. If it is supposed that the gravitational force is compensated by a perfect gas of degenerated neutrons, the ray R of a neutron star is given by the formula: $\backslash \; textstyle\; \{R\; \backslash \; (in\; \backslash \; km)\; =\; 16\; \backslash \; sqrt\; \backslash \; frac\; \{M\_S\}\; \{M\}\}$. The numerical value 16 is here resulting only from one combination of constant fundamental physics, without having to appreciate, as for the dwarf white ones, the parameter μ, since it is replaced in this case by Y, average molecular weight by neutron of the star, which is worth 1 per definition. It should be underlined nevertheless that this result is to date very approximate, because it rests on debatable assumptions: interactions between ignored neutrons and relativistic effects, ignorance of the behavior of the matter for densities higher than 10 17 kg/m 3 .

Despite everything, to give an order of idea of the value of the ray of these stars and way in which it varies, the table below indicates the value of the rays for some values of mass of a neutron star, without prejudging if these masses are compatible or not with these bodies.

A neutron star is approximately 2000 times smaller than dwarf white. One finds however the paradoxical behavior of these last: the ray of star decreases when its mass increases. That is explained by the fact that the tendency to the increase in the ray due to the matter addition is less than the reduction of the ray due to the additional compression undergone by star, following the increase in the gravity caused by this matter addition.

Limit with the black holes

Because of its small size and its raised density, a “traditional” neutron star of size has on its surface a field of gravity approximately 2 (200 billion) of times more important than that reigning on the Ground, and its Escape velocity is about half of the Speed of light. It is easy to imagine that if matter is added to him, its field of gravity will increase quickly because of the increase in the mass and the reduction of the ray. When its escape velocity reaches that of the light, the neutron star will have become a Black hole.

This maximum mass of a neutron star, at the border with the black holes, is difficult to calculate and to even appreciate, because, in particular, of our ignorance of the compressibility of the matter to these very high densities. It is estimated that this value is probably around 3M, and that it is almost certainly lower than 5 M, thus showing our great uncertainty in these extreme fields.

Composition

The Matière on the surface of a neutron star is made up of atomic nuclei Ion ized and of electron S. While approaching the center, these cores are increasingly rich in Neutron S, such cores would disintegrate quickly on Earth, but are stabilized by the gigantic Pression which reigns there. Still more deeply, one arrives at a point where the pressure does not manage any more to stabilize the cores what makes it possible the neutrons to be dissociated from the atomic nuclei. In this area the matter is made up of electrons, atomic nuclei ( déliquescents ) and of free neutrons.

The true nature of the matter superdense existing in the core of a neutron star is not yet well-known. Probably, it is composed of three layers, named by analogy with the Earth:

• a external crust solid, thick from approximately 1 km,
• a coat which could contain a mixture Superfluide of neutrons, electrons and of a little Proton S, sometimes called Neutronium in the popular literature,
• a core from approximately 1 km of ray, perhaps composed of Hypéron S; other particles, such as pawn S or Kaon S, could also be present, but currently, this could be neither confirmed nor cancelled by observations.

Number of revolutions

Another characteristic of neutron stars is their extremely fast rotation. Their Period of rotation generally varies between 30 second S and a hundredth of second. This is explained by the conservation Angular momentum: as the star contracts, its number of revolutions increases.

For example, if the Sun (ray = 7 km, period of rotation approximately a month) were transformed into neutron star by preserving its mass, its ray would be worth 16 km then, and it would rotate 1000 times a second.

A lately formed neutron star turns quickly; with time this speed decreases because its Magnetic field dissipates energy. An old star can take several seconds, even a few minutes to carry out a full rotation on itself. The rate of decrease number of revolutions of a neutron star is normally constant and very weak: the rates observed are of 10 -12 to 10 -19 second by second.

The number of revolutions of a neutron star can undergo abrupt increases sometimes. This increase is the effect of the internal reorganization of the matter composing star, a little like the equivalent of a Earthquake. Such a Tremblement of star would correspond to a magnitude from 20 to 25.

Formation

A star, during the longest part of its life, uses hydrogen like nuclear fuel. When this one is exhausted, and if the star is sufficiently massive, the star contracts, its central temperature rises, allowing the use of helium like new fuel. Then when helium is exhausted, carbon takes over, and so on: the residues of a phase being used as fuel for the following phase, and the phases following one another at increasingly fast intervals, as shows it the following table:

Source: A.C. Philips, in The Physics off Stars pages 26 and 131.

After the last period, the energy production is not possible any more, since the synthesis of atomic nuclei located beyond iron claims energy. However the temperature is then sufficient to start the disintegration of iron and the close elements by the reactions:

$\backslash \; textstyle\; \{\backslash \; gamma\; +\; Ni^\; \{56\}\; \backslash \; rightarrow\; 14\; \backslash \; He^4\}$

$\backslash \; textstyle\; \{\backslash \; gamma\; +\; Fe^\; \{54\}\; \backslash \; rightarrow\; 13\; \backslash \; He^4\; +\; 2n\}$

$\backslash \; textstyle\; \{\backslash \; gamma\; +\; Fe^\; \{56\}\; \backslash \; rightarrow\; 13\; \backslash \; He^4\; +\; 4n\}$

etc

These processes, which claim energy, break balances thermics and hydrostatic heart of star. The radiation is not then sufficient any more to be opposed to the gravitation, and star centers it crumbles literally under its own weight. Instability being propagated with all star, the implosion of the center is accompanied by an explosion of the external layers, causing an enormous loss of mass of star, and giving place to a supernova.

The evolution of star depends then on the remaining mass of the core which implosé.

• If this mass is lower than M, also called Limite of Chandrasekhar and who is worth approximately 1,4 times the solar Masse, the remainder of star finishes dwarf white.
• If this mass is higher than roughly 3 solar masses, the remainder of star finishes as a black hole
• If, finally, this mass lies between the two preceding thresholds, the remainder of star finishes out of neutron star.

In this last case, the pressure of gas of electrons degenerated of the heart is not sufficient to stop gravitational collapse. The density becomes such as the electrons are massively absorbed by the protons, and the increase in the number of neutrons in the cores makes decrease their binding energy. The neutrons end up escaping from it, and form a “soup”. The pressure of gas of degenerated neutrons then manages to stop collapse. The unit stabilizes under an extremely small volume, since the remainder of star holds in a sphere of a few tens kilometers in diameter, 2000 times smaller than dwarf white.

The release of energy during the few seconds that collapse lasts is gigantic, about thousand times the energy released by the Sun during all its life. The major part (>95%) of this energy is released in the form of Neutrino S according to process URCA describes by Mário Schenberg:

$\backslash \; textstyle\; \{(Z,\; A)\; +\; e^\; \{-\}\; \backslash \; rightarrow\; (Z-1,\; A)\; +\; \backslash \; nu\_e\; \backslash ,\}$

$\backslash \; textstyle\; \{(Z-1,\; A)\; \backslash \; rightarrow\; (Z,\; A)\; +\; e^\; \{-\}\; +\; \backslash \; overline\; \{\backslash \; nu\_e\}\; \backslash ,\}$

The power of this reaction is in T 8 , the emission of neutrinos and cooling resulting from star are thus very fast.

Observations

Various types of neutron stars

The neutron stars being able to be observed are:

• the Starts rays-X and starts gamma
• the Pulsar S
• the Magnétar S

Pulsars

See also: Pulsars

A neutron star can appear to pulsate because of the electrons accelerated around the magnetic poles, which are not aligned with the axis of rotation of star. These electrons moving away from star, but always undergoing its powerful magnetic field, must turn with this one.

However, there exists a distance beyond which these electrons should move at a speed higher than the Speed of light in order to continue to turn. At this distance the electrons cannot continue any more to follow star and release to them kinetic energy then in the form of x-rays or of gamma rays. An observer can see this radiation with each time the magnetic pole of star is directed towards him. If this alignment is possible, it reproduces with the same period as the period of rotation of star.

There the neutron stars which produce such periodic glares are called Pulsar S. When the first pulsar was discovered in 1967 by Jocelyn Bell and Antony Hewish, some believed to see the signs of the existence of a extraterrestrial Intelligence. Indeed, these very regular signals could be interpreted as those coming from a kind of marks out, but the discovery many other pulsating radio sources eliminated this assumption quickly. Today, several hundreds of pulsars are indexed.

Magnétars

See also: Magnétar

There exists another neutron star class, known under the name of Magnétar . A magnétar has a magnetic field of more than 10¹⁴ G: it is enough to erase your credit card since a distance higher than that of the Sun or to be mortal since the the Moon. In comparison, the Terrestrial magnetic field is only of 0,5 G (50 microteslas), while magnétars can reach 10 gigateslas. The phenomenon at the origin of the magnétars implies the increasingly dense rolling up of the lines of field around star until the appearance of a magnetic field.

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