Найден пульсар, устроившийся на полставки
Британские астрономы выявили очень странный пульсар, который, вероятно, поможет в будущем разгадать многие загадки этих необычных "космических маяков" и проверить имеющиеся теории пульсаров.
Британские астрономы выявили очень странный пульсар, который, вероятно, поможет в будущем разгадать многие загадки этих необычных "космических маяков" и проверить имеющиеся теории пульсаров.
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Nss were first theoretically proposed by Baade and Zwicky in their work on SNae . And firat calculations on nss though were done by Oppenheimer and Volcov focusing on theoretical predictions of their properties assuming matter to be composed by an ideal gas of neutrons at high density . And their discovery however took place almost 20 years , in 1968 Hewish and Bell discovered radiopulsars , wich were indeficated by Gold as rotating nss . And now we will say this: -Neutron stars are the collapsed cores of some massive stars. When the core of a star uses up the nuclear energy, radiation pressure can no longer balance the gravity. Смысл классификации н.з. заключется , в том , что при наблюдении за ними это , в какой-то степени помагает понять не только их природу но и дальнейшую эволюцию, хотя,информация о нейтронных звёздах пока от той чёткости,к-рая присуща классификациям,ещё очень далека, поэтому любая классификация может иметь очень приблизительный характер. Проще всего классифицировать NS , полагаясь на физический смысл различий между ними. Что же касается всех возможных сочетаний параметров, то носители не всех таких сочетаний наблюдались к настоящему времени далеко не все.Несмотря на то, что ,начиная с момента открытия первого пульсара, было получено довольно много интересной инф,знания по теоретической физике(и в астрофизике, в том числе и по н.з.),как и возможности современной астрономии продвинулись намного вперёд, вопросов в данном случае пока ещё больше , чем ответов.…Well let's start with the classification. Well, the classification of neutron stars is very conditional, because all these stars belong to the same family .. Well, here will be presented subtypes:
1. One of most the intersting subtype is the protoneutron star (PNS)
2. Radio-quiet neutron stars. Or one can call it jokingly,let it be a "radio-quiet boy '
3. Radio loud neutron star ( Radio loud "neutronca")
4. Single pulsars–general term for neutron stars that emit directed pulses of radiation towards us at regular intervals (due to their strong magnetic fields).
5.Rotation-powered pulsar ("radio pulsar")
6. Magnetar–it is a "neutronca" with an extremely strong magnetic field .
7. Soft gamma repeater (SGR)
8. Anomalous X-ray pulsar (AXP) is also an intersting ns
Well, of course, that the double star systems containing neutron stars will be very interesting. There are the next subtypes of nss: -
9.Binary pulsars
10.Low-mass X-ray binaries (LMXB)
11.Intermediate-mass X-ray binaries (IMXB)
12.High-mass X-ray binaries (HMXB)
13.Accretion-powered pulsar ("X-ray pulsar")
14.Millisecond pulsar (MSP) ("recycled pulsar")
15.Sub-millisecond pulsar
16.There is another class of neutron stars, which stand out . These are the following types: There are exotic stars:-
Quark star–currently a hypothetical type of n s composed of quark matter, or strange matter. As of 2008 ( or 2007), there are three candidates .The quark stars or strange stars are hypothetical types of exotic stars composed of quark matter, or strange matter. These are ultra-dense phases of degenerate matter theorized to form inside particularly massive neutron stars. They can still be considered one of the varieties of the forerunners of black holes .
Electroweak star–currently a hypothetical type of extremely heavy neutron star, in which the quarks are converted to leptons through the electroweak force, but the gravitational collapse of the star is prevented by radiation pressure. As of 2010 (or of 2009), there is no evidence for their existence.
Preon star–currently a hypothetical type of neutron star composed of preon matter. If I can, I 'll talk about it :- A typical neutron star has a mass between 1.5 and about 2.0 solar masses . , with a corresponding radius of about 10 km if the Akmal-Pandharipande-Ravenhall EoS(APR EOS) is used. Well, one can talk about this later . These stars have the strongest magnetic fields in the known universe. The strongest inferred neutron star fields are nearly a hundred trillion times stronger than Earth's fields, and even the feeblest neutron star magnetic fields are a hundred million times Earth's, which is a hundred times stronger that any steady field we can generate in a laboratory. N ss are extreme in many other ways, too. For example, if one can imagine the thrill of the high-temperature superconductors, with critical temperatures around 100 K. Ok. The protons in the center of neutron stars are believed to become superconducting at 100 million K, so nns are the real high-T_c champs of the universe. The gravitational field at the star's surface is about 2×10^11 times stronger than on Earth. The escape velocity is about 100,000 km/s, which is about one third the speed of light. Such a strong gravitational field acts as a gravitational lens and bends the radiation emitted by the star such that parts of the normally invisible rear surface become visible . . The gravitational binding energy of a neutron star with two solar masses is equivalent to the total conversion of 0.5 solar mass to energy ( it is from the law of mass-energy equivalence, E = mc^2). That energy was released during the supernova explosion. . Shorter and more precise: - the nss are a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed of neutrons (as a rough approximation) , which are subatomic particles without electrical charge and a slightly larger mass than protons. Neutron stars are very hot and are supported against further collapse because of the Pauli exclusion principle. This principle states that no two neutrons (or any other fermionic particle) can occupy the same place and quantum state simultaneously. Nss encompass "normal" stars with hadronic matter exterior in which the surface pressure and baryon density vanish ( the interior may contain any or a combination of exotic particles permitted by the physics strong interactions), and strange quark matter(SQM). An SQM star could have either a bare quark-matter surface with vanishing pressure but a large supranuclear density , or a thin layer of normal matter supported by Coulomb forces above the quark surface . In a theoretical treatment of compact object as the ones described above , aiming at a high degree of accurency and and contact with reality , one would have to include all different layers of hadronic and quark matter and the corresponding particles , like leptons , such as the electron and the muon , other than nucleons.. Let us tell about it a bit latter.The name "SQM-star" originates from the conjecture that quark matter with up, down and strange quarks ( but the charm , bottom , and top quarks are too massive to appear inside nss) might have a greater binding energy per baryon at zero pressure than iron nuclei have. Some of these quarks may then become strange quarks and form strange matter.
Recent theoretical research has found mechanisms by which quark stars with "strange quark nuggets" may decrease the objects' electric fields and densities from previous theoretical expectations, causing such stars to appear very much like—nearly indistinguishable from nss. But the team of P. Jaikumar, S.Reddy and A W. Steiner made some fundamental assumptions and it led to uncertainties in their theory large enough that the case for it is not yet solid. More research, both observational and theoretical, remains to be done on "strange stars"( and "quark stars" too ) in the future. Thus the nss are some of densest manifestation of massive objects in universe . And they are ideal astrophysics laboratories for testing theories of dense matter physics , and provide connections among nuclear physics, particles physics, and astrophysics . Well, as they are a good example for observing the gravitational effetsts (ie, one can test the theory of relativity) . Neutron star relativistic equations of state provided by Jim Lattimer include a graph of radius vs. mass for various models .. So can talk a bit about general relativity and gravitation theory of Newton . When it comes to classical mechanics, then one should say the notion that a body's motion can be described as a combination of free (or inertial) motion, and deviations from this free motion. Such deviations are caused by external forces acting on a body in accordance with Newton's second law of motion, which states that the force acting on a body is equal to that body's (inertial) mass times its acceleration. The preferred inertial motions are related to the geometry of space and time: in the standard reference frames of classical mechanics, objects in free motion move along straight lines at constant speed. Simply put, their paths are geodesics, straight world lines in spacetime . Well, one might expect that inertial motions, once identified by observing the actual motions of bodies and making allowances for the external forces (such as electromagnetism or friction), can be used to define the geometry of space, as well as a time coordinate. However, there is an ambiguity once gravity comes into play. According to Newton's law of gravity, and independently verified by experiments such as that of Eötvös and its successors, there is a universality of free fall (also known as the weak equivalence principle, or the universal equality of inertial and passive-gravitational mass): the trajectory of a test body in free fall depends only on its position and initial speed, but not on any of its material properties. Well, one could consider a simplified version, known to all at school. A simplified version of this is embodied in Einstein's elevator experiment .... I will not recount in detail the essence of this experiment, just say that: - In this case Einstein formulated the equivalence principle that would be the foundation of General Relativity. It states that `` there is no experiment a person could conduct in a small volume of space that would distinguish between a gravitational field and an equivalent uniform acceleration''. A consequence of this is that if an elevator is falling freely toward the ground because of gravity, an occupant inside will feel weightless just as if the elevator was far away from any planet, moon, or star. No experiment would help us distinguish between being weightless far out in space and being in free-fall in a gravitational field. One can express the Relativistic generalization as follows: -As intriguing as geometric Newtonian gravity may be, its basis, classical mechanics, is merely a limiting case of (special) relativistic mechanics. In the language of symmetry: where gravity can be neglected, physics is Lorentz invariant as in special relativity rather than Galilei invariant as in classical mechanics. (The defining symmetry of special relativity is the Poincare group which also includes translations and rotations.)
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The differences between the two become significant when we are dealing with speeds approaching the speed of light, and with high-energy phenomena. With Lorentz symmetry, additional structures comes into play. They are defined by the set of light cones .The light-cones define a causal structure: for each event A, there is a set of events that can, in principle, either influence or be influenced by A via signals or interactions that do not need to travel faster than light and a set of events for which such an influence is impossible. These sets are observer-independent. But the light-cones, in conjunction with the world-lines of freely falling particles, contain even more information: they can be used to reconstruct the space-time's semi-Riemannian metric, at least up to a positive scalar factor. In mathematical terms, this defines a conformal structure. Special relativity is defined in the absence of gravity, so for practical applications, it is a suitable model whenever gravity can be neglected. Bringing gravity into play, and assuming the universality of free fall applies: there are no global inertial frames. Instead there are approximate inertial frames moving alongside freely falling particles. Translated into the language of spacetime: the straight time-like lines that define a gravity-free inertial frame are deformed to lines that are curved relative to each other, suggesting that the inclusion of gravity necessitates a change in spacetime geometry. Thus, having formulated the relativistic, geometric version of the effects of gravity, the question of gravity's source remains. If it comes about Newtonian gravity, then in this case, the source is mass. In special relativity, mass turns out to be part of a more general quantity called the energy-momentum tensor, which includes both energy and momentum densities as well as stress (that is, pressure and shear). Using the equivalence principle, this tensor is readily generalized to curved space-time. And the picture should be represented similarly with geometric Newtonian gravity, it is natural to assume that the field equation for gravity relates this tensor and the Ricci tensor, which describes a particular class of tidal effects: the change in volume for a small cloud of test particles that are initially at rest, and then fall freely. In special relativity, conservation of energy-momentum corresponds to the statement that the energy-momentum tensor is divergence-free. This formula, too, is readily generalized to curved spacetime by replacing partial derivatives with their curved-manifold counterparts, covariant derivatives studied in differential geometry. With this additional condition—the covariant divergence of the energy-momentum tensor, and hence of whatever is on the other side of the equation, is zero— the simplest set of equations are what are called Einstein's (field) equations:-Rab-(1/2) Rgab=kTab ...Well on the left-hand side is the Einstein tensor, a specific divergence-free combination of the Ricci tensor Rab and the metric. Still, the Ricci tensor itself is related to the more general Riemann curvature tensor .... If R is the curvature scalar than in this case R=Rcdg^(cd), and Rab=Rabd ^d . On the right-hand side, Tab is the energy-momentum tensor. Matching the theory's prediction to observational results for planetary orbits (or, equivalently, assuring that the weak-gravity, low-speed limit is Newtonian mechanics), the proportionality constant can be fixed as κ = 8пG/c ^4, with G the gravitational constant and c the speed of light . If the energy-momentum tensor vanishes, then one can obtain the vacuum Einstein equations.( ie in case if Rab=0) ..... The Einstein field equations (EFE) are the core of general relativity theory. With their help (ie EFE) one can describe how mass and energy (as represented in the stress-energy tensor) are related to the curvature of space-time (as represented in the Einstein tensor).I love this theory. But here I have to crumple this theory .... And the basic equations neochen something and brought forth. So just write it down, relying on memory .
Although, quite honestly, I absolutely have nothing to remember, that anything like that narosat;-)))). Ie write quickly, without straining my memory: - In short, I should say that : the EFE reads as follows ( in abstract index notation) :Rab-(1/2) Rgab+gab^= (8пG)/c^4)) Tab where Rab is the Ricci curvature tensor, R- is the scalar curvature , gab the metric tensor, ^ -is the cosmological constant ,G is Newton's gravitational constant , c is the speed of light, and Tab is the stress-energy tensor....And taking into account that the Einstein tensor is correlated to the expression :Rab-(1/2) Rgab , or rather it is the identity to this expression (that is : Gab =Rab-(1/2)gabR,one should write the EFE in a more compact form by defining the Einstein tensor: Gab+^gab= (8пG)/c^4)) Tab . However the Einstein tensor is symmetric second-rank tensor that is a function of the metric. The EFE can then be written as Gab=(8пG)/c^4)) Tab, where in this case the cosmological term will be absorbed into the stress-energy tensor as dark energy. And if we're using geometric definitions where G = c = 1, this can be rewritten as :Gab=8пTab . On the left part (of this equation)represents the curvature of spacetime as determined by the metric and the expression , and on the right represents the matter / energy content of spacetime (If this expression wil be considered). The EFE can then be interpreted as a set of equations dictating how the curvature of spacetime is related to the matter/energy content of the universe. And together with the geodesic equation, these equations will form the core of the mathematical formulation of GR (if one can say without details)...Well, one should note that G R is very big .... And we should outline only a few moments, which flows out of it, and only .....The existence of gravity is indisputable, but its cause is quite another matter. The complete description of gravitational forces is only possible if the geometry of space itself is well understood, and this can be very difficult to ascertain. While the dimensionality of space on Earth, at a human scale of size, is relatively simple to understand, the way reality behaves for things which are exceedingly small, or extremely large, is a different matter entirely. This is not the biggest problem, however. Certain basic considerations make it nearly impossible to see the stage upon which events in our universe unfold. It is hard to look at the arena of events directly, at least without the players getting in the way. In addition, the act of observing can influence the outcome of things. The Gravitational force has a powerful influence, but unlike the other fundamental forces, it does not have an intermediary which we have been able to directly observe. There are two principal approaches to investigating NSMs. These are models that consider Newtonian gravity with weak field (quadrupolar) or post-Newtonian corrections for the effects of gravitational radiation, and fully relativistic hydrodynamics models with dynamically calculated spacetimes. One of the research groups is addressing both approaches, and its research has focused on Newtonian and post-Newtonian models. Significant progress can be made with Newtonian and post-Newtonian simulations, and comparing Newtonian-like simulations with fully-relativistic simulations will determine how significant general relativistic effects are in the gravitational waveform of the merger. From this comparison the researchers hope to gain a better understanding of the limits of Newtonian and post-Newtonian theories. Well, a little grab this theme, as the Post-Newtonian formalism. It is a calculational tool that expresses Einstein's (nonlinear) equations of gravity in terms of the lowest-order deviations from Newton's theory. This allows approximations to Einstein's equations to be made in the case of weak fields. Higher order terms can be added to increase accuracy, but for strong fields sometimes preferable to solve the complete equations numerically. Some of these post-Newtonian approximations are expansions in a small parameter which is the ratio of the velocity of matter, forming the gravitational field, to the speed of light, which in this case is better called the speed of gravity. In the limit, when the fundamental speed of gravity becomes infinite the post-Newtonian expansion reduces to Newton's law of gravity. Examples of the process of applying PPN formalism to alternative theories of gravity can be found in Will (at the end of the last century).
This is a very interesting approach to the situation (Look at here:-www.stanford.edu/group/chugroup/amo/amo.paper/PRL2008_LV.pdf) . But now we are going to tell about the predictions of Einstein's theory, coupled with the observations for our heroes . Early tests of GR were hampered by the lack of viable competitors to the theory: it was not clear what sorts of tests would distinguish it from its competitors. One should note that: GR is the most successful of all known gravitational theories. No discrepancy with the predictions of this theory was until today. But there are some unresolved issues (equations) within this theory. Therefore, one can say, about this theory that it is wonderful, but imperfect, because it is not yet complete (and one can say that and of all other fundamental theories). Well, roughly speaking one can note that: Post-Newtonian corrections can be viewed as a consequence of GR . In any case, they are based on this theory (it is named one of the cornerstones). Without knowing the theory of relativity no one should approach the post-Newtonian corrections . Но только если достаточно хорошо знать теории гравитации , как таковые, то можно легко убедиться, что они оченьпростые ;-))). GR tests of gravity :- In at least one case, the binary pulsars are one of the few objects which allow physicists to test general relativity in the case of a strong gravitational field. Although the binary companion to the pulsar is usually difficult or impossible to observe, the timing of the pulses from the pulsar can be measured with extraordinary accuracy by radio telescopes. A relatively simple 10-parameter model incorporating information about the pulsar timing, the Keplerian orbits and the post-Keplerian corrections (there are required five parameters to refer the TOAs to the binary barycenter :1) the orbital period Pb , 2) the projected semi-major orbital axis, ap sin i, 3)the orbital eccentricity , e ,4) the longitude of periastron omega small , 5) the epoch periastron passage , T0) is sufficient to completely model the pulsar timing .( Ну по русски, чтоб подчеркнуть, так основной грав. Теорией на сегодняшний день яв-ся Нютоновская и ОТО, то мы рассматриваем делая равнения на ОТО . И там в ОТО 5 наиболе важных ПК параметров в первом постньютоновском приближении ( и/или 3 в любой из альтернативных вариантах) .. Ну в случае когда свободными параметрами будут только массы наших звёзд , при измерении 3х и более ПК -параметров независимо от теорий должны пересекаться в одной точке :О(v^2/c^2) ). The clock stability of pulsar means that though precise monitoring of pulsar rotations one can study a rich variety of phenomena that affect the propagation of their pulses . While the basic spin and astrometric parametres can be derived for essentially all pulsars , millisecond pulsars are the most useful objects for more exotic applications. Their pulse arrival times can be measured much more precisely than for normal pulsars( scaling essentially with the pulse period ) and their rotation is also much smoother , making them intrinsically better clocks. The key quantity of interest is the time arrival (TOA) of pulses at the telescope . However , since individual pulses are usualy too weak to be detected, and since they also show a jitter in arrival time within a window given by the extend of the pulse profile , it is the latter which is used for the timing . The stability of pulse profiles allows us to compare the observed profile with a high-signal-to noise ratio template that is constructed from pervious observations .
The time-offset between template and profile determines the TOA . Becouse one can use pulse profiles rather than individual pulses , the TOA refers to some fiducial point on the profile . Ideally , this point coincides with the plane defined by the rotation and magnetic axes of the pulsar and the line of sight to the observer wich is defined geometrically and independent of observing frequency or propagation effects. The aim of pulsar timing is count the number of ns rotations between two observations . Each TOA can therefore be assigned with a pulse number N which depends on rotation frequency nu and TOA t as :- N=N0+nu0( t-t0) +(1/2) nu* (t-t0) ^(2) +(1/6) nu** (t-t0)^(3)+..+ [eq. R] where N0 is the pulse number at the reference epoche t0 . If t0 coincides the arrival of pulse and a pulsar with spin-down (ie nu and nu* )is known accurately, the pulses should appear at integer values of N when observed in an inertial reference frame .... The time transformation also corrects for any relativistic time delay that occurs due to the presence of masses in the Sol system. Given a minimal a set of starting parameters , least squares fit is needed to match the measured arrival times to pulse number according [eq. R] , one can minimise the expression : x^2= Sum(i) [(N(ti)-ni)/ σ i]^(2) where ni is the nearest integer to N (ti) and σ i is the TOA uncertainty in units of pulse period (turns) . The aim is to obtain a phase-coherent solution that accounts for every single rotation of the pulsar between two observations . One starts off with a small set of TOAs that were obtained sufficiently close in the time so that accumulated uncertainties in the starting parameters dont exceed one pulse period . Gradually, the data set is explained maintaining coherence in phase . When successful , post-fit residuals expressed in pulse phase show a Gaussian distribution around zero with a root mean square that is comparable to the TOA uncertainties . A good test for the quality of the TOAs and their fit is provided by creating a new set of mean residuals each from by averaging n avg consecutive post-fit residuals . The root mean square calculated from the new set should decrease with srf n avg if no systematics are present. After starting with fits for only period and pulse reference phase over some hours and days, longer time spans slowly require fits for parameter like spin frequency derivative(s) and positions . Incorrect or incomplete timing models cause systematic structure in the post-fit residuals identifying the parameter that needs to be included. The precision of the parameter with length of data span and the frequency of observation , but also with orbital coverage in the case of binary pulsars. A binary pulsar is a pulsar with a binary companion, often a white dwarf or n s.
Binary pulsars are one of the few objects which allow physicists to test general relativity in the case of a strong gravitational field. It should be emphasized what:-Ну что мы там можем ну сказать в «более простом варианте» ? Ну для точечных объектов с пренебрежительно малым влиянием вращения звёзд ПК параметры в любой теории яв-ся функциями заранее неизвестных масс обеих вёзд и измеряемых с большой точностью кеплеровских параметров ну таких , как орбитальный период , обозначим это Pb и эксцентриситет е . Observations of pulsars in binary orbits show a periodic variation in pulse arrival time . The timing model therefore needs to incorporate the additional motion of the pulsar as it orbits the common center of mass in the binary system . For non-relativistics binary systems , the orbit can be described using Kepler's laws . But for a number of binary systems the Keplerian description of the orbit is not sufficient and relativistic corrections should be applied . For pulsars in th close binary systems about w. ds. ( white dwarfs) and other nss or perhaps eventually bhs , relativistics effect due strong gravitational fields and high orbital velocities produce observable signatures in the timing residuals . Even though GR appears to be the best description of the strong-field regime to data , alternative theories of gravity nevertheless should be considered and tested against it . A straightforward means of comparison is to parameters the timing model in terms so-called "Post-Keplerian" (or PK) parameters . For point masses with negligible spin contributions , the PK parameters in each theory should only be functions of the priori unknown pulsar and its companion mass , Mp and Mc and easely measurable Keplerian parameters and with two masses will already determine as the only free parameters in the theory independent timing model to TOA measurements , the PK parameters are determined from a different theories of gravitation . In GR, the five of them most important ( As it was noted above in Russian laguage). And well, let it be shown schematically is very inaccurate and too roughly : омега малая =3 То^(2/3)[Pb/2п]^(-5/3)[(1/(1-e^(2))] (Mp+Мc)^(2/3) , y=To^(2/3) [Pb/2п]^(1/3) [(eMc( Mp+2 Mc)/(Mp+Мc)^(4/3)) ], Pb=-[(192п/5] То ^(5/3) [(Pb/2п)^(-5/3)] [(1/(1-e^2)^(7/2)] [(1+(73/24(?))e^2+(37/96(?))e^4)][(1-e^2)^(-7/2)]x T o^(5/3)[MpMc/(( Mp+Mc)^(1/3))], or :- it can also be written as follows:Pb=-[(192п/5] (2п Mfb) ^(5/3) Fe , item :-r=To Mв , and :-s=x To^(-1/3) [Pb/2п]^(-2/3) [((Mp+Mc)^(2/3)/ c] , well, in short ,these formulas are not very accurate .Hу там просто показано , что как раз Pb ,е и х-это в данном случае есть период , эксцентриситет и большая полуось орбиты двойной системы , они получаются из наблюдений . Ну а величины Mс и Mр ну эт будет массы наших двойных объектов( не пульсаров) ну, там пульсар и его , какой нибудь «приятель»;-)))), не важно нейтронка , нормальная звезда, белый карлик и/или чёрная дыра. То- это есть постоянная , к-рая будет определятся в виде То=G Mo/c^3 ~4.9mu s,G &c-ньютоновская и скорость света . Ну первый параметр измеряется легко – это есть скорость релятивскгого поворота лини апсид , по этому измерению (омега малая) можно определить полную массу наших космических объектов . Notice that, by virtue of Kepler’s third law, (2п fb)^(2)=m/a^(3) ,(2пfb)^(2/3)=m/a ~э, thus the first two post-Keplerian parameters can be seen as O(э) or 1PN corrections to the underlying variable, while the third is an O(э^(5/3))... The parameter y denotes the amplitude of delays in arrival times coursed by the varying effects of the gravitational redshift and time dilation (second order of Doppler) as the pulsar moves in the elliptical orbit at varying distances from the companion and with varying speeds . And the other two parameters r and s are related to Shapiro delay caused by the gravitational field of the companion .
Pulsar radio emission mechanisms & Electrodynamics
And evolution of nss.: -Well, this introduction will not be over: In begining ,one can digress a bit and tell about the dynamo mechanism, which is responsible for the generation of the magnetic field. Well, because it is assumed that this mechanism underlies the formation of magnetic fields in cosmic objects. (And one should note that this mechanism is not considered to be the only one who has to answer for the generation of magnetic fields of neutron stars. But most of this mechanism is accused of such a malicious crime). The dynamo theory proposes a mechanism by which a celestial body such as the Earth or a star generates a magnetic field. The theory describes the process through which a rotating, convecting, and electrically conducting fluid can maintain a magnetic field over astronomical time scales. Dynamo theory describes the process through which a rotating, convecting, and electrically conducting fluid acts to maintain a magnetic field. This theory is used to explain the presence of anomalously long-lived magnetic fields in astrophysical bodies. Dynamo theory of astrophysical bodies uses magnetohydrodynamic equations to investigate how the fluid can continuously regenerate the magnetic field. It was actually once believed that the dipole, which comprises much of the Earth's magnetic field and is misaligned along the rotation axis by ~ 11 degrees, was caused by permanent magnetization of the materials in the earth. This means that dynamo theory was originally used to explain the Sun's magnetic field in its relationship with that of the Earth. However, this theory, which was initially proposed by J. Larmor has been modified due to extensive studies of magnetic secular variation, paleomagnetism (including polarity reversals), seismology, and the solar system's abundance of elements. Also, the application of the theories of Gauss to magnetic observations showed that Earth's magnetic field had an internal, rather than external, origin. There are three requisites for a dynamo to operate: first of them is an electrically conductive fluid medium, second of them is kinetic energy provided by planetary (or stars) rotation, and third is an internal energy source to drive convective motions within the fluid . In our case for example - pulsars are the prototypes for a class of astrophysical object that emit most of their spin-down energy in the form of electrodinamics flux. Such objects typically consist of central conducting body surrounded by a highly magnetized rotating magnetosphere and a relativistic outflow .
Understanding the structure and inner working of pulsar magnetospheres is therefore important not only for interesting the vast and constantly growing collection of observations of pulsars and their winds as a keystone to understanding the processes in the magnetospheres of the magnetically dominated systems , such as magnetars and accretion disks. Pulsar spindown:- the underlying mechanism for converting rotational energy into the electromagnetic energy loss from a pulsar is unipolar induction from a rotating magnetize sphere. Rotation at the angular frequency Ω (Omega big) of a conducting sphere in a magnetic field generates potential difference between the pole and equator V ~ Ω Psi big, where the Psi big is the inclosed magnetic flux. This potential is due to the Lorenz force separating the charges inside of a rotating conductor. .. Induction or creation of magnetic field is described by the induction equation: delta big B / delta t = η Laplace ^ 2 B + Laplace x (ux B), where u is velocity, B is magnetic field, t is time, and η = 1 / σμ is the magnetic diffusivity with σ electrical conductivity and μ permeability. The ratio of the second term on the right hand side to the first term gives the Magnetic Reynolds number, a dimensionless ratio of advection of magnetic field to diffusion (Note: - the Magnetic Reynolds number is a dimensionless group that occurs in magnetohydrodynamics. It gives an estimate of the effects of magnetic advection to magnetic diffusion.). In kinematic dynamo theory the velocity field is prescribed, instead of being a dynamic variable. This method cannot provide the time variable behavior of a fully nonlinear chaotic dynamo but is useful in studying how magnetic field strength varies with the flow structure and speed. Using Maxwell's equations simultaneously with the curl of Ohm's Law, one can derive what is basically the linear eigenvalue equation for magnetic fields (B) which can be done when assuming that the magnetic field is independent from the velocity field. One arrives at a critical magnetic Reynolds number above which the flow strength is sufficient to amplify the imposed magnetic field, and below which it decays.
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There is still one of the way to display the agreement with GR is by comparing the observed phase of the orbit with a theoretical template phase as a function of time.One can tell about it even less detail. If fb varies slowly in time, then to first order in a Taylor expansion, the orbital phase is given by: Fb (t) = 2pfbot + pfb `ot ^ 2. The time of periastron passage tp is given by Fb (t) = 2pN, where N is an integer, and consequently, the periastron time will not grow linearly with N. Thus the cumulative tp difference between periastron time and, the quantities actually measured in practice, should vary according to tp-N/fbo =- f `obN ^ 2/2fbo ^ 3 ~ - (f `ob/2fbo) t ^ 2. If we are using a schematical picture, then the dots are the data points, while the curve is the predicted difference using the measured masses and the quadrupole formula for f `ob in this scheme .. The parameters r and s are not separately measurable with interesting accuracy for B1913+16 because the orbit’s 47°inclination does not lead to a substantial Shapiro delay.. And these parameters are only measurable , depending on timing precision if the orbit is seen nearly edge- on. Strong field tests :- The first binary pulsar used to test GR in this way was PSR B 1913+16 discovered by Hulse & Taylor . As such these pulsars act like very accurate clocks which allow very precise monitoring of their orbital motions. Observations of pulsars in orbit around other stars have all demonstrated substantial periapsis precessions that cannot be accounted for classically but can be accounted for by using general relativity. For example, the Hulse-Taylor binary pulsar PSR B1913 +16 (a pair of neutron stars in which one is detected as a pulsar) has an observed precession of over 4o of arc per year. This precession has been used to compute the masses of the components. arxiv.org/PS_cache/astro-ph/pdf/0407/0407149v1.pdf
The most functional feature of kinematic dynamo theory is that it can be used to test whether a velocity field is or is not capable of dynamo action. By applying a certain velocity field to a small magnetic field, it can be determined through observation whether the magnetic field tends to grow or not in reaction to the applied flow. If the magnetic field does grow, then the system is either capable of dynamo action or is a dynamo, but if the magnetic field does not grow, then it is simply referred to as non-dynamo. The kinematic approximation becomes invalid when the magnetic field becomes strong enough to affect the fluid motions. In that case the velocity field becomes affected by the Lorentz force, and so the induction equation is no longer linear in the magnetic field. In most cases this leads to a quenching of the amplitude of the dynamo. Such dynamos are sometimes also referred to as hydromagnetic dynamos. Virtually all dynamos in astrophysics and geophysics are hydromagnetic dinamos or are they considered as such .. Numerical models are used to simulate fully nonlinear dynamos. A minimum of five equations are needed.
One can represent them something like this: 1) Maxwell's equation, 2) The Boussinesq conservation of mass (sometimes) 3) the Boussinesq conservation of momentum, also known as the Navier-Stokes equation: in this case, such quantities are counted as: ν it is the kinematic viscosity, ρ 'is the density perturbation that provides buoyancy (for thermal convection ρ' = αΔT, Ω is the rotation rate of the space object, and is the electrical current density, 4) a transport equation, usually of heat (sometimes of light element concentration): delta bigT / delta big t = k Laplace ^ 2 T + E, in this case T is temperature, κ = k / ρcp is the thermal diffusivity with k thermal conductivity, cp heat capacity, and ρ density, and ε is an optional heat source. In this case often the pressure is the dynamic pressure, with the hydrostatic pressure and centripetal potential removed., And 5) Rα = (gα TD ^ 3) / nuk, E = nu / (omega big D ^ 2), Pr = nu / k, Pm = nu / eta. In these equations: Ra is the Rayleigh number, E the Ekman number, Pr and Pm the Prandtl and magnetic Prandtl number. Magnetic field scaling is often in Elsasser number units B = ρΩ / σ. A stellar magnetic field is a magnetic field generated by the motion of conductive plasma inside a main sequence (hydrogen-burning) star. This motion is created through convection, which is a form of energy transport involving the physical movement of material. A localized magnetic field exerts a force on the plasma, effectively increasing the pressure without a comparable gain in density. As a result the magnetized region rises relative to the remainder of the plasma, until it reaches the star's photosphere. Magnetic stars: - Compact and fast-rotating astronomical objects (white dwarfs, neutron stars and black holes) have extremely strong magnetic fields. The magnetic field of a newly born fast-spinning neutron star is so strong (up to 10 ^ 8 teslas) that it electromagnetically radiates enough energy to quickly (in a matter of few million years) damp down the star rotation by 100 to 1,000 times .Matter falling on a neutron star also has to follow the magnetic field lines, resulting in two hot spots on the surface where it can reach and collide with the star's surface. These spots are literally a few feet (about a metre) across but tremendously bright. Their periodic eclipsing during star rotation is hypothesized to be the source of pulsating radiation. An extreme form of a magnetized neutron star is the magnetar.- Pulsars are rapidly rotating highly magnetized neutron stars / They have resulted in many applications in physics and astronomy . A theory of pulsars must explain all observed phenomena : the periodic, radiation and beaming mechanisms . Well, we'll come back to the evolution of neutron stars a few times. But now we have to tell u that's: - Pulsars are forget in spectacular Type II SN explosions following the catastrophic gravitational collaps of massive star> 8Mo. It all begins ironically with the death star. After a star has depleted all the hydrogen in the core. Well, this is one of the common views about origin the rapid rotation, and ultra strong magnetic field that (or/it is rather one of many popular approaches ) :- the origin of pulsars rapid rotation and ultra strong magnetic field permeating its structure is inherently related to the gravitational collapse of the progenitor star . Most main sequence stars are observed to possess a magnetic field presumable generated by the motion of conducting material in its interior , exempli gratia Bo~10^2G . With the deth of the star has a radius 10^9 m and surface magnetic flux density B~10^2 G and newborn ns of radius 10^4 m would processes a surface magnetic flux density B~10^8 G. The rapid rotation of the pulsar results from the conservation of angular momentum during collapse . The maximum theoretical spin rate of any object held together by gravity , such as a ns, before a centrifugal break-up is ~0.1 ms . In the rotating ns model the magnetic field is misaligned with the rotation axis , resulting in the release of pulsars rotational energy through the induced electromagnetic radiation due to rotations. Well one can tell about the calculations of the evolution of the rotation period of neutron stars. There are the most well-studied parameters of neutron stars . And it can be considered as a separate topic of conversation :- There are four main stages the evolution of these parameters of neutron stars. : 1) ejector; 2) propeller, 3) the accretor and 4) the georotator (Ejector .--.> Propeller .--.> Accretor .--.> Georotator) . Well, what there may be ....
Well, what there may be .... Well, in general it may be so, hm:- A ns passes through several evolutionary phases. Typical representatives of the phase of ejector is a radio pulsar, at wich a ns depends on relation between several critical radii: the gravitational capture radius-Rg=2GM/v^2, light cylinder radius Rl=c/ ω, Alfven radius-Ra, co-rotation radius Rco=(GM/ ω ^2)^(1/3), and the Shartsman radius Rsh. But the phase of the radiation will be a precursor to the phase of ejector. Well let's talk a bit about the "remaining" phases: One can assume that , the all of nss are born in the ejector stage. Rapid rotation of the magnetosphere will be observed at the stage of the propeller and the accretion will be impossible in this case .In some cases one can expected one of the most interesting situation due to high level of asymmetry system,and/ or due to rapid changes parameter of surruondind medium / In normal interstellar medium ( it is called ISM in an abbreviation) such an object would be on the Propeller phase, but usual one as Rg < Ra, and in the case of a highly magnetised ns (with B~10^15 G) and velocity 150-200km/s it would be Georotator stage (Another name of this stage is “a-non-gravitational propeller”) And one must say that :- Georotator stage occurs with the reversed relation between Rco and Ra . Here one can be interested by the case Rg, Rco < Ra < Rl /. At the magnetospheric boundary gravity is not important in the case of the Georotatos stage . And accretion stage mey be impossible when Ra > Rco…. . There is some suggestion which is actively discussed by several authors . That is the following possibility if one of the propeller stage coolling the matter around the rotating magnitosphere is efficient enough (for example as synchrotron emission of thermal electrons on the magnetic field frozen in can be important, and the main problem here is that the frequency for large magnetosphere radius ), than not static atmosphere, but a dence envelope with growing mass is formed on top magnetospheric boundary . А на стадии георотора радиус магнитосферы настолько большой , что вещ-во не захватывается н.з.;-))).. So, what can one say about the periods of evolution? All of n ss are assumed to be born with aperiod P (0) = 0.02 . As pulsars are provided by their rotational energy, their spin frequency decreases with the spin -frequency decreases by v`=-const v^n where the exponent n is known as the breaking index . For magnetic dipole emission as main energy loss one may expect n=3 . Measuring a second spin-frequency derivate v``, one can obviously determine the breaking index via : n=vv``/v`^2 so that the assumption the dipole breaking can be tested .
The key to underatanding the complex emission mechanism is an explicit underatanding of the pulsar magnetosphere . Consider the pulsaras a conducting sphere that then non-rotating, has a dipolar magnetic field . As a result rotation each free charge in the stellar interior experiences the force q(Ωxr)xB/c , where Ω is the angular velocity of the pulsar . In response the charge within the pulsar redistributes itself , estabilishing an electric field in oder to gain equilibrium and a force free system.
The induced surface charges on the stellar surface constitute an external electic field wich , at the surface of the pulsar exeeds that gravity resulting in copius amounts of electrons being stripped from the pulsar and occupying the magnetosphere .It is assumed that the liberated charged particles are accelerated in the external electric field , emited photons as they go. If the photons acquir the appropriate energy and interact with magnetic field they produce an electron-positron pair. These produced pairs go on to produce more pairs and a cascade effect is initiated that populates the magnetosphere with a pair plasma . And this plasma redistributes itself in order to produce a force-free scenario experience the same ExB as in the interior of the pulsar , forcing the pair plasma to co-rotate with the pulsar . Co-rotation can only be sustained up to a certain radius from the star where the plasma speed reaches the speed of light , this defines an imaginary boundary known as the light cylinder. The light cylinder defines closed-field lines and open-field lines as the magnetic field lines that close and don’t close within the light cylinder respectively . The open field lines define a region above the magnetic poles known as the polar cap. The pair plasma that resides within the magnetosphere is the soutrce of the broadband electromagnetic radiation observed from the pulsar.The distinguishing feature between incoherent and coherent emission mechanisms is the brightness temperature of the source . For incoherent emission , where the particles comprising the source emit out of phase with each other , the brightness temperature is Tв ~ 10^12K . For a pulsar with a flux density ~1 Jy , at distance of 1kpc and size of 10 km , the brightness temperature Tв~10^20-10^30 K ,of pulsar radioemission implies that a coherent emission mechanism must be at work , that is a large number of particles emitting in phase . The mechanism , as well, as successfully describing the observed brightness temperatures must also satisfactorily encompass the high degree of polarisation and the broadband nature of the emission . Existing candidates for the pulsar coherent emission mechanisme are referred to as an antenna mechanisms involve the emission radiation by a population of particles , all radiating in phase . A family of N- particles ,each of charge q that are confined to a volume of dimension less than emitted wavelength , will act like a particle of charge Nq and all radiate in phase .As result the radiated power of the source will be greater than that from an individually emitting particle by a factor N^2 . The favoured antenna mechanism in the pulsar contex is curvature emission , despite it being a relatively inefficient emission process . Curvature radiation is the radiation emitted by a charge particle when it moves along a curved magnetic field line . If the magnetic field is sufficialy strong the particles will be unable to move perpendicular to the field , as a result if the magnetic line curves the paricles will be accelerated and hence radiate electromagnetically . Curvature radiation is insensitive to the mass and charge of the particle and radiates at a specific frequency . It is regarded as a natural and unavoidable emission process in pulsar magnetospheres. Komisaroff was one of first to discuss the concept of curvature radiation in the context pulsar emission. His pulsar emission model is assuming that groups of charged particles are accelerated along the open field lines at the magnetic pole , radiating by the curvature mechanism . The main issue with coherent curvature radiation is finding a reasonable mechanism that creates and sustains the required particle bunches for the timescale required .
Particle bunching can occur in the magnetospheric pair or pairing plasma ,yielding a suitable bunching mechanism . However it is argued that the radiation back reaction tends to disperse the particles bunch that created it acting against the coherent process . Relativistic plasma emission is the generation of electromagnetic radiation near the local plasma frequency or its harmonics . It operates in two phases: the generation of Langmuir waves (or Alfven –type waves ); a non-linear process that converts the wave energy into a desirable propagating electrostatic plasma oscillation : these waves cannot escape the plasma region since they are not electromagnetic in nature and require a plasma to sustain them . To produce escaping radition a process must exist that converts the mode into a propagating electromagnetic Ordinary or Extraordinary mode . Within pulsar context a pair plasma above the polar caps is considered to be relativistic and streaming . The plasma particles are assumed to radiate all their energy perpendicular to the ambient magnetic field so that the plasma one-dimensional . This type of plasma is referred to as a pulsar plasma ...Neutron stars marked the entrance into physics and astrophysics of objects having magnetic fields whose strength exceeds by many orders of magnitude anything one could even dream of producing in a laboratory. 10 ^ 12 G, typical for a pulsar, is way above the atomic critical field BA = m ^ 2e ^ 3c / h ^ 3 = 2.4 x10 ^ 9 G where atomic structure is strongly altered, and magnetars, with fields above 10 ^ 14 G, are well into the quantum relativistic regime marked by the Schwinger field BQ = m ^ 2c^3/eh = 4.5x10 ^ 13 G. Physics in such fields is alien to everyday experience and constitutes a challenge to the intelligence. Moreover, understanding the neutron star surface is a prerequisite to study the properties of matter at the extreme densities (> 10 ^ 15 g/cm^3) reached in the stellar core since an increasingly larger part of the information we have on these stars is coming from detection of their surface thermal emission.
Let's look at the lighthouse model :- As the n s spins , charged particles are accelerated out along magnetic field lines in the magnetosphere . The accelerated particles emit electromagnetic radiation , most readily detected at radio frequencies as sequence of observed pulses produced as the magnetic axis (and hence the radiation beam ) crosses observer's line of sight each rotation . The repetition period of the pulses is therefore simply the rotation period of ns . N ss are essentially large celestial flywheels with momenta of intertia ~ 10^38 kg m^2 . The rotation ns model predicts a gradual showdown and hence an increase in the pulses period as the outgoing radiation carries away rotational kinetic energy . So, as the conclusion one can say following :- In our case, this mechanism will be :- The magnetic dipole with momentum M rotating in a vacuum with angular frequency Ω radiates electromagneti radiation of frequency Ω and power :W=(2/3)[ Ω^(4)M^(2)/c^(3)] sin^(2)x [eq I], here x is the indicated angle, ie this is the angel between the vector M and Ω( this is a resume , for what reason the repeat is inevitable) . The mechanical rotation energy and the angular moment of a star are converted to the electromagnetic energy and angular momentum ( as previously it was mentioned ) . And this conversion is realized by electric currents following on a star surface . The issue is that the electric and magnetic fields inside and out side a stare are different . The fields inside are determined by the magnetic field sourse given by the dipole magnetic moment M and also by the properties of the star matter . And one can suppose first that the conductivity of ns crust is high (ie if σ.--.> infinit.) and in that case the electric field is related to magnetic field inside the star : E= -(1/c)[ Ωr]B] .It means the disappearance of electric field E’ in the frame rotating together with the star . Outside the star in vacuum the fields are satisfied by wave equation and the relation between the fields E and B follows from Maxewell equation (E, B--- exp{i Ωt } ): E=( ic/ Ω)curl B . The condition of continuity of companent of the magnetic field Br normal to the star surface and the tangential components of electric field Et determines the amplitude of the magnetodipole radiation in vacuum ( there also the electroquadriupole radiation of ΩR/c is smaller than the magnetodipole one) .
The observational appearance of isolated ns (INSs) ,wich accrete material from the interstellar medium ,is a subject of intensive theoretical investigation . It is a presently established that the initially fast rotating INSs under certain conditions , are able to switch thrir state from ejector to propeller within the Hubble time t< Th~10^10yr. And even to reach periods at with coratational radius Rcor=(GMns/omega small^2)^(1/3) exceeds the magnitospheric radius of the star :Rm=(mu^(2)/Mc srf:2GM)^(2/7), here Mns, omega small=2п/Ps , and μ are tha mass , the agular velocity ,and the dipole magnetic of the ns, respectively. Mc is the mass capture rate by the star from the interstellar medium , wich can be expressed as Mc~п R^2 ro V infinity , V infinity is the relative velocity of the ns to the surrounding material , ro is the density of the interstellar material and Ralfa is accretion radius of the star: Ralfa=2GMns/, V infinity^2 .Limiting ρ <10^(-24)g/cm^(3) , and V infinitive>Vs, where Vs is the thermal velocity in the interstellar material ( according to SB Popov et. Al), have estimated the maximum possible rate of mass capture by an isolated ns as Mc~/< Mmax~10^12 ρ -24 m^2 1/V6 g/c . Here m is the mass of the star expressed in units of M0 , ρ -24= ρ /10^(-24) g/cm^(3) and V6= V infinit./10^6 g/c . In this case all material captured by the star is accreted onto surface , and they have suggested that the accretion luminosity of INSs can be as high as MmaxGMns/Rns~10^32 erg/s . According to Shvartsman 's scheme, wich was proposed in the seventies of last century , the evolution track of a rotating magnetized ns can be presented in the from following sequence of this states : Ejector.--.> Propellrer .--.> Accretor . Within the scheme , the rotational rate of a newly born fast rotating star decreases , initially by the generation of the magneto-dipole waves and the ejection of relativistic particles ( pulsar-like- spin down) , and later by mean of the interaction between its magnetosphere and the surroding matterial (propeller-spin down) .
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The first state transition occurs when the pressure of the material ejected by the star can not longer balance the pressure of the surroundig gas , and the later penetrating into accretion radius of the star interacts magnetosphere with the stellar magnetosphere . The spin evolution of a spherically accreting strongly magnetised ns is the state of propeller has been investigated by Davies , Fabian and Pringle . As they shown , two sub – states of the propeller state can be distinguished : the supersonic and subsonic propeller . And in both cases ns is spining down due to the interaction between its magnetosphere and the surrounded by a spherical quasi- static atmosphere , in wich the plasma temperature is of order of the free-fall temperature Tff(r)= GMnsmp/kr , Here G, mp, k are the gravitational constant ,the proton mass and the Boltzman constant , respectively . The atmosphere is extended from magnetospheric boundary up to accretion radius of the ns . The rotational energy loss by the ns is convected up through the atmosphere by the turbulent motion and lost through its outer boundary . The formation of the atmosphere in the first approximation pervents the surrounding gas penetrating to within the accretion radius of the star . As the ns moves through the interstellar medium , and the interstellar gass overflows the outer edge of the atmosphere wich is traditionally called the stength of the stellar wind and denotes the maximum possible mass capture rate by the ns . As long as the angular velocity of the ns is large enough for corrotation radius to be smaller than the magnetosphere radius , the star is in contrifugal inhibitor regime ( ie the centrifugal acceleration at the magnetospheric boundary , omega small^2 Rm , dominates the gravitational acceleration GM ns/Rm^2) . The centrifugal inhibition is not effectve only within the bases of the corrotational cylinder . However , the accretion material onto the stellar surface through thes regions does not occur only if the angle between the magnetic and rotational axes is small enough and if magnetic field of the ms is weak enough for the magnetospheric radius to exceed the star radius . Excecpt the bases of the corrotational cylinder , the linear velocity at the boundary of the magnetospher e wich is co-rotating with the star in this case is larger than the sound speed in the atmospheric plasma . That is why this state is refereed to as supersonic propeller . Subsonic propeller :- as the star is spinning down , its co-rotational radius increases and reaches the magnetospheric radius when Ps=Pcd . Under the condition Ps>Pcd the centrifugal barrier is not effective : the atmospheric plasma penetrating into the magnetic field of the star is able to flow along the magnetic field lines to accrete onto the star surface . The rate of plasma penetration into the magnetosphere of spherically accreting strongly magnetised ns can be high as Mc only if the magnetospheric boundary is unstable with respect to interchange (e.g. Rayleigh- Taylor) instabilities . Otherwise , the rate of the plasma penetration is limited to the diffusion rate , wich is a few orders of magnitude smaller than Mc. For instability to occur the sign of effective gravitational acceleration at the magnetospheric boundary should be positive : geff=[GMns/R^2]cost eta big-[Vti^(2)(Rm)/Rcurv.teta]>0 [ the condition I] . The Rcurv is the curvature radius of field lines , teta big is the angle between the radius vector and outward normal to the magnetosphere boundary and Vti(Rm) is the ion thermal velocity of the accreting plasma at the boundary . The condition [I ]can be expressed in terms of plasma temperature at the magnetospheric boundary as T
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The colling of the atmospheric plasma is governed by the bremsstrahlung radiation and the convective motion . For this process to dominate the energy input into the atmosphere due to the propeller action by the star, the spin period of the star should be Ps>/~Pbr . Where Pbr is a so-called braak period . The conditions of interest , the break –period significantly exceeds Pcd . In other words this means that the state transition supersonic propeller .--.>steady accretor may occur only via an additional intermediate state , wich is called the sub-sonic propeller . This term reflects the fact that the rotation velocity of the magnetosphere during this state is smaller than the termal velocity in the surrounding gas . If the propeller actions were the only source of the heating of the atmospheric plasma , the magnetospheric boundary of the ns would be able to switch its state from subsonic propeller to accretor as its spin period reaches Pbr . Although the interchange instabilities of the magnetospheric boundary during the subsonic propeller state are suppressed the “magnetic gates ” are not closed completely , and the atmospheric plasma is able to penetrate into star magnetic field due to diffusion . A magnetised INS is able to switch its state from subsonic propeller to steady accretor only if the mass capture rate by this star from interstellar medium is Mc>/~ M0 . Otherwise , the corresponding state transition does not occur and the star remains surrounded by the hot atmosphere . And in this case the mass accretion rate onto the star surface is limited M~/8Mo at the end of its life , wich triggers a type II supernova explosion .Thermonuclear runaway : there is a general agreement on the scenario of classical sn explosions : a low luminosity wighte dwarf accretes hydrogen - rich matter in cataclisme binary systeme, as result of Roche lobe overflow of its main sequence companion .Explosive hydrogen burning synthesizes some beta^+ - unstable nuclei of short lifetimes(N13,O14 ,O15, F17) wich are transported by convection to outer envelope, where they are preserved from distuction . But one should note that : the detailed explosion mechanisme of Type II SNae is not understood , but m it is probable that neutrinos play a crucial role . One of the most remarkable aspect is that neutrinos become temporarily trapped within the star during collapse . The typical neutrino – matter cross section is σ~ 10^(-40)cm^2, resulting in a mean free path ^~1/( σn)~10cm , where the baryon number density is n~2 to 3no . This length is much less than the proton-neutron star radius , wich exceeds 20 Km . The gravitational collapse of the progenitor star’s white dwarf-like core to ns is about 3GM/5R^2~ 3x10^53erg(G is gravitational constant), wich is about 10% of its total mass energy Mc^2. Newly born nss and proto-nss are rich in leptons, mostly e- and nu e .The kinetic energy of the expanding remnant is order 10^51 erg …. Core collapse halts when the stars interior density reaches no, wich triggers the formation chock wave at the core's outer edge . The chock wave propagates only about 100-200 km before it stalls , having lost energy to neutrinos and from nuclear dissociation of the material it has plowed through . Apparently, neutrinos from core assisted perhaps by rotation , convection , and magnetic fields . The force of impact would likely destroy the object's component atoms, rendering all its matter identical, in most respects, to the rest of the star....Global structure of nss . Global aspects of nss , such as mass and radius (M-R) relation , are determined by the equation of hydrostatic equilibrium . For spherical object in GR , these so called TOV(Tolman-Oppenheimer-Volkov) equation : dP/dr=-(Gm/r)[ ρ (r)+(P(r)/c(2)][ m(r)+4п r^(3)P(r))/c(2)])( ρ +P/c^2)/(1-(2Gm(r)/rc^(2)); dm/ dr=4пr^(2) ρ r^2 . Where P and ρ are the pressure and mass –energy density , respectively , and m(r ) is the gravitational mass enclosed within the radius r . Although a few exact solutions are known for realistic P- ρ relation(equation of state , eos) this equation must be numerically solved to obtain the M-R relation . For normal ns , the radius is relatively insensitive to mass in the vicinity of 1—to—1.5 Mo unless the maximum mass is relatively small . A simultaneous measurement of mass radius of an intermediatemass star could help to discriminate among the families of possible EOSs .
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Heated plasma radiates primarily in the X-ray band. In general the magnetic axis does not coincide with the spin axis, so that the n s is like a lighthouse which pulses when one or two poles of it is/are on our line of sight. In other words, one can expect to see X-ray pulsations from such a n s .A n s is a product of a supernova explosion. If more than half of the mass of the binary system is ejected during the explosion, binary system will be separated. N ss of this type are called accretion powered pulsars .Accreted plasma also carries angular momentum to the neutron star so that the ns is exerted torque causing a change in the spin period. As the moment of inertia of the n s is much smaller than a non-degenerate star, one can expect to observe changes in the spin period. Observations of changes in X-ray ux of accretion powered pulsars is also important to analyze plasma near the ns. Change in X-ray is an indicator of the change in mass acretion rate and physical characteristics of plasma .Since plasma carries angular momentum to the n s change in plasma accretion may change the torque exerted on the n s wich can be seen by analyzing the changes in the frequency derivative found from the frequency history of the pulsar. To understand the nature of accretion on n ss, firstly it must be , firstly it must be emphasized that neutron stars have very large surface dipole magnetic field (10^9,10^12 Gauss, while the surface magnetic eld of the Sun is about 1 Gauss) . Moreover, the strong gravitational field with a surface gravitational acceleration of about 10^14 cm.s^2 .
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