Rotating relativistic electron-positron plasma stream dynamics in the pulsar magnetosphere тема автореферата и диссертации по астрономии, 01.03.04 ВАК РФ

Abastumani Astrophysical Observatory Georgian Academy of Sciences

Irakli Sulkhnn Nanobashvili

Rotating Reiativistic Electron-Positron Plasma Stream Dynamics in the Pulsar Magnetosphere

01.03.04 -Plasma Aarophysics

Abstract of Candidate Dissertation in Physical and Mathematical Sciences

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Tbilisi, 1997

Dissertation is completed:

la the Abastumani Astrophysicsl Observatory', Georgian Academy of Sciences

Scientific Supervisor: George Z. Machabeli, Doctor of Physical sad Mathematical Sciences

Expert: Luli Kk, Shatashvili, Doctor of Physical- and Mathematical Sciences

Official Opponents: Alexandre I. Tugushi, Doctor of Physical iad Mathematical Sciences, Professor

David P. Garuchava, Cendidst of Physical tsd Mathematical Sciences

Leading Organisation: Tbilisi State University

Date sad Place of Defence: June 1997, p.m., at the meeting of

Dissertation Council of Abastumani Astrophysical Observatory l?£i.fvl.01.03.cNJ A. Kazbegi ave.2a, Tbilisi

Dissertation is available: in the library of the Abasrutnzni Astrophysical Observatory

Abstract wss distributed on May 20, 1W

Secretary of the dissertation council,

Candida ofPhysical end Mathematical Sciences A - K.B. Cfcargeishviii

General characterization of the thesis:

The actuality of the subject:

During the common process of the matter continuous transformation in the universe the stars appear, live and die. Pulsars are the rapidly rotating neutron stars and, like other stars, they are also born, then they live and die. The discovery of these objects in the sixties of the twentieth century was one of the most eminent discoveries in the human history, which has significantly broaden our knowledge about the forms of the matter existence and its transformations in the universe.

Nowadays more than 750 pulsars are discovered. Soon after their discovery pulsars have been identified with the rapidly rotating neutron stars. \t present it is widely accepted the model, according to which the pulsar is a compact object, the radius of which is about 10 km. The matter density inside it is very high and equals to the density of the nuclear matter. 10" -1015 g/cm3. Pulsars have the huge magnetic fields of the order 10" -10" G. As a rule, the pulsar rotation axis and the magnetic axis form some angle between each other. The electromagnetic waves are radiated from the region of the pulsar magnetic poles (polar caps) in a small angle around the magnetic axis and, when the magnetic axis is directed to the Earth, the observer registrates the radiation. The period of the pulsation varies from 1.5 msec till several seconds and the frequency from radiowaves till 7-radiation.

According to the present model, there are distinguished three regions inside pulsar. They are the cristalic crust, the thickness of which is about 1 km. It mainly consists of iron atoms. In the second, so-called intermediate region, the matter is mainly presented in the form of neutrons. The last third region is the pulsar nucleus, which, as the scientists think, consists of the heavy elementary particles — hyperons. The 99 per cent of the pulsar mass is presented in the form of the superfluid neutron liquid. By this reason the

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pulsars are called the neutron stars. Desides, puisar — the neutron star — is surrounded by the magnetosphere, which has the rather complicated structure and properties. In the magnetosphere the charged particles, electrons and positrons, with very high energies are born and they are responsible for the pulsar radiation.

Just after their discovery the intense investigations of pulsars have been started in the leading astrophysical centers all over the world and also in the Abastumani Astropbysical Observatory. There were suggested a number of models for tiie explanation of tiie pulsar birth, its structure and properties of its observed radiation. Large number of the original papers in the scientific literature and books have been published. From the review of these papers the great results are clearly seen, which have been obtained by a number of the scientists all over the world. But it is also evident, that generally it is still a lot of work on the way of the investigation of pulsars. In particular, the investigations of the pulsar magnetosphere structure and the processes, which take place in it, are very far from the end. It is especially interesting the investigation of the processes, which take place in the pulsar magnetosphere relativistic electron-positron plasma, for example, the instabilities, the generation of the electric and magnetic fields and the electromagnetic waves, their influence on the magnetosphere structure, etc. Just some of these problems defined the subject of the investigations, presented in the present thesis.

* The inaia purpose of (he investigation presented in this thesis is the following:

1) The magnetohydrodynainica! investigation of the relativistic. electron-positron plasma stream, which corotates with the pulsar'magnetosphere.

2) The study of the influence of the centrifugal force on the relativistic plasma stream behaviour.

3) The investigation of the stability of the pulsar magnetosphere relativistic plasma with respect to the radial potential perturbations and the possibility of the zptriodic instability development.

4) The analysis of tlx- possible changes of the pulsar magnetosphere structure because of the aperiodic instability development.

5) The consideration of the aperiodic instability role in the process of the transformation of the energy, released during the pulsar rotation slowing down into the energy of the magnetospheric plasma.

On the defence there are presented the following propositions nntl results:

1) The effect, unknown before for the relativistic plasma stream, which corotates with . the pulsar magnetosphere. In particular, this is the effect of the plasma stream radial braking, when the stream radial velocity exceeds the critical value. This effect appears, when we take into account the centrifugal force in the equation of the plasma stream motion, written in the noninertial rotating frame.

2) The possibility of marking out the centrifugal force from the Lorentz force in the limits of the drift approximation during the consideration of the same processes in the rest inertial frame, when the inhomogeneity of the magnetic field in this frame is taken into account. This centrifugal fofce again gives rise to the effect of the plasma stream radial braking, when the stream radial velocity exceeds the same critical value, as it was in the previous ease.

3) The critical value of the plasma stream radial velocity (V, = cfsfi), for which the centrifugal force, acting on the stream, and its radial acceleration change their sign and the stream radial braking begins.

4) The stability of the pulsar magnetosphere relativistic electron-positron plasma with respect to the radial potential perturbations and the possibility of the aperiodic instability development, which causes the generation of the exponentially increasing radial electric field along the pulsar magnetic field lines (radius).

5) The mechanism of the toroidal magnetic field generation in the pulsar magnetosphere relativistic electron-positron plasma, which is based on the effcct of the plasma stream

radial braking and the existence of the electric field, generated in the magnetospheric plasma because of the aperiodic instability development.

6) The transformation of the energy, released during the pulsar rotation slowing down into the energy of the pulsar magnetosphere plasma and the energy of the toroidal magnetic field, generated in it because of the effect of the pulsar magnetosphere plasma stream braking and the existence of the electric field, generated in the magnetospheric plasma as a result of the aperiodic instability development.

T) The change of the pulsar magnetic field structure from the radial to the spiral one, which causes the viol&tiou of the corotation in the pulsar magnetosphere. The violation of the corotation itself causes the limitation of the growth of the electric field and the toroidal magnetic field, generated in the magnetospheric plasma because of the aperiodic instability development.

The scientific novelty and the practical value of the obtained results:

1) The magnetohydrodynamical investigation of the relativistic plasma stream, which corotates with the pulsar magnetosphere is performed. It is shown, that taking into account the centrifugal force in the equation of the plasma stream motion, written in the

, noninertial rotating frame, gives rise to the effect, unknown before for the plasma'stream. In particular, this is the effect of the plasma stream radial braking, when the radial velocity of the stream exceeds the critical value c/v/2.

2) The stability of the pulsar magnetosphere relativistic electron-positron plasma with respect to the radial potential perturbations is investigated and it is shown the possibility of the aperiodic instability development in such a plasma. The development of this instability means the generation of the exponentially increasing radial electric field along the pulsar magnetic field lines (radius).

3) The mechanism for the toroidal magnetic field geuc ration in the pulsar magnetosphere plasma is suggested. This mechanism is based on the effect of the p.lasma stream ; adial

braking and the existence of the electric field, generated in the magnetospheric plasma because of the aperiodic instability development in it. The appearance of the toroidal magnetic field causes the change of the pulsar magnetic field structure from the radial to the spiral one.

4) It is shown, that the change of the pulsar magnetic field structure from the radial to the spiral one causes the violation of the corotation in the pulsar magnetosphere. The violation of the corotation itself causes the limitation of the growth of the electric field, generated because of the aperiodic instability development in the pulsar magnetosphere plasma and the toroidal magnetic field, connected with the appearance of this electric field.

5) It is shown, that, because of the effect of the pulsar magnetosphere plasma stream radial braking and the development of the aperiodic instability in it, the energy, released ■ during the pulsar rotation slowing down, is effectively transformed into the energy of the pulsar magnetosphere plasma and the toroidal magnetic field, generated in it.

The size of the thesis:

The thesis consists of introduction, 3 chapters and conclusion. It is printed on the 91 pages, contains 6 figures and 103 citations.

Content» of the thesis:

In the first chapter of the thesis it is considered the present model of pulsars. In the first paragraph the theory of the pulsar birth and its inner structure is presented. In the second paragraph we shortly review the mechanisms of the pulsar radiation! As it is well known, pulsar is surrounded with the magnetosphere, which has the rather complicated structure. In the third paragraph is considered the structure of the pulsar magnetosphere.

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the mechanism of its filling with the relativistic electron-positron plasma and the difficulties, which one meets oil the way of the investigation of the pulsar magnetosphere relativistic plasma.

The second chapter of the present thesis is devoted to the niagnetoliydrodyiidiitical investigation of the pulsar magnetosphere relativistic electron-positron plasma. In the first paragraph is presentee! the simplified geometrical model of the pulsar magnetosphere, which we use. In particular, we discuss the case, when the pulsar rotation axis and its magnetic axis are perpendicular to each other. The pulsar magnetic field lines are considered as the radial straight lines, located in the plane, which is perpendicular to the pulsar rotation axis. This assumption is justified, because v.'e discuss the physical processes in the magnetospheric layer, the thickness of which is much less than the curvature radius of the pulsar magnetic field lines. In the magnetic field of such a structure the dynamics of the single charged particle is considered. It is shown, that this problem can be reduced to the simple mechanical problem, when the bead moves without the friction in the long rotating pifie the axis of which is perpendicular to the rotation axis. It is assumed that the pipe is absolutely rigid aw;l its mass is eijual to zero. In such a case the bead will move along the pipe and corotatc with it, and the centrifugal force will play the major role in the dynamics of the bead. Of course, this is more mathematical idealisation than the real physical problem, but during its consideration there appear the interesting peculiarities of the particle motion, which will be useful in the investigation of the pulsar magnetosphere relativistic plasma magnctohydrodynamioi. We consider two cases, when the angular velocity of the pipe rotation is constant, i.e. the energy of the rotation source is infinitely large and when the angular velocity of the pipe rotation is not constant, i.e. the energy of the rotation source is finite. In the first case the bead motion is oscillatory. If in the starting moment t — 0, the bead is located just above the rotation axis, i.e. in the point r = 0 and has the nonzero initial velocity Vo. it moves outwards in the direction of the light cylinder (the light cylinder is the surface, oil which the azirnuthal velocity of rotation

equals to the speed of light) and initially both, the radial and azimuthal velocities of the bead increase. After some time the radial velocity reaches its maximal value and after this it begins to decrease. At the same time the azimuthal velocity of the bead goes on its increasing. On the light cylinder the radial velocity of the bead equals to zero, hut the azimuthal velocity equals to the speed of light. After this the bead turns around and moves in the direction of the rotation axis. During this motion the azimuthal velocity of the bead monotonically decreases and 011 the rotation axis it equals to zero. As for the radial velocity, its modulus behaves just in tlie same manner as it was in the case of the bead motion in the direction of the light cylinder. When the bead reaches the rotation axis, it does not stop, but continues the motion in the opposite direction just in the same manner as it was described above, etc. Thus, the motion of the bead is really oscillatory. The equation of the bead motion has the following form:

The general solution of the equation of the motion can be expressed by the Jakobian elliptical functions. In the case of the nonrelativistic velocities it can be expressed by

In the left hand side of the equation of the motion we have the radial acceleration of the bead and in the right hand side the centrifugal force, acting on it. As it is evident from the equation of the motion, when it is fulfilled the following condition:

then the centrifugal force, acting on the bead, and its radial acceleration change their sign and the bead radial braking begins.

In the case, when the angular velocity of the rotation is not constant, the bead motion does not remain oscillatory. Before the light cylinder the azimuthal velocity of the bead

the hyperbolic functions and in the case of the large relativistic velocities by the usual tf-igonometric functions.

increases, but beyond the light cyliuder it decrease*. As for the radial velocity of the. bead, initially it increases, but, when the condition Vr > is fulfilled, it begins to decrease. Beyond the light cylinder the radial velocity of the bead again increases.

In the second paragraph the behaviour of the pulsar magnetosphere relativistic plasma in the noninertial rotating frame is considered. The conductivity of the pulsar magnetosphere plasma is very high and it can be assumed to be infinitely large. Because of this the pulsar rfcagnetic field lines are frozen in it. It is shown, that near the neutron star surface the pulsar magnetic field lines act on the magnetospheric plasma particles just like the pipe acts on the bead located inside it. The reason of this is the electric drift. Really, because of the pulsar corotation with its magnetic field (the matter- in the inner layers of pulsar is in the superconductive state, so the magnetic field lines are frozen in it and corotate with it), the electric field is,generated, which is directed across the pulsar magnetic field lines. In the crossed electric and magnetic fields the electric drift takes place, which forces the magnetospheric plasma particles to corotate with the magnetic field lines. -In such a case the centrifugal force plays the major role in the pulsar magneto*-sphere plasma dynamics. Takiug into account this force we will get the same equation of the motion, which we had in the case of the consideration of the single particle dynamics. Thus for the pulsar magnetosphere relativistic plasma the effect of the radial braking will take place under the same condition as it was in the case of the single particle, i.e. when Vr > c/,/2.

In the third paragraph the behaviour of, the pulsar magnetosphere relativistic plasma is considered in the rest inertia] frame. In this case in the equation of the motion of the magnetospheric plasma there is only the Lorentz force, the centrifugal force does not exist .in it in the evident form. It is shown, that the reason of this is the iohomogeneity of the magnetic field in the rest inertia! frame. Really, if we take into account the inhomogeneity of the magnetic field, it is possible in the limits of the drift approximation to mark our from the Lorentz force the centrifugal force in the evident form. Thus, in the rest inertial

frame we will get the same equation of the motion for the pulsar magnetosphererelativistic plasma as it was in the noninertial rotating frame. So, in the rest inertial frame the efTed of the plasma radial braking will take place under the same conditions.

In the third chapter the mechanism of the electric field generation in the pulsar magnetosphere relativistic electron-positron plasma and the possible changes of the magnetosphere structure, caused by the appearance of this electric field, are considered. In the first paragraph the stability of the magnetospheric plasma with respect to the radial potential perturbations is investigated. The effect of the plasma stream radial braking, which take's place in the pulsar magnetosphere makes the plasma unstable and when the following condition is fulfilled:

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the aperiodic instability is developing in the pulsar magnetosphere plasma, i.e. the exponentially increasing electric field is generated along the pulsar magnetic field lines. In the steond paragraph the mechanism-of the toroidal magnetic field generation in the pulsar magnetosphere relativistic electron-positron plasma is presented, which is based on the effect of the pulsar magentosphere plasma braking and the existence of the electric field, generated in the plasma because of the aperiodic instability development in it. The electric field causes the additional braking of the charged particles of one sign and the decreasing of the braking of the charged particles of the another sign. Because of this the increasing radial electric current and correspondingly the toroidal magnetic field appear in the pulsar magnetosphere. It is shown, that the effect of the pulsar magentosphere plasma braking and the aperiodic instability, which is developing in it, cause the effective transformation of the energy, released during the pulsar rotation slowing down, into the energy of the magnetospheric plasma and the toroidal magnetic field, generated in it. As a result of the toroidal magnetic field generation, the structure of the pulsar magnetic field changes from the radial to the spiral one. The pulsar magnetosphere plasma parti-

clcs follow the neutron star magnetic field lines, and because of this, such a change of the pulsar magnetic field structure will cause the violation of the solid body type rotation, corotation of the pulsar, its magnetic field and the magnetospheric plasma. The violation of corotation will also cause the limitation of the growth of the radial electric field, generated because of the aperiodic instability development in the pulsar magnetosphere plasma, the corresponding radial electric current and the toroidal magnetic field.

The main results of the thesis:

1) The (-((nation of the motion of the relativistic electron-positron plasma, which coro-tates with the pulsar magnetosphere, is considered in the noniniertial rotating frame. The importance of taking into account the centrifugal force is shown. This gives rise to the unknown effect for the rotating relativistic plasma stream. In particular, when the stream radial velocity exceeds the critical value, the centrifugal force, acting on the stream, and

.its radial acceleration change their sign and the stream radial braking begins.

2) The equation of the plasma stream motion is also discussed in the rest inertial frame. In the contradistinction with the previous case, in the equation of the motion there exists only the Lorentz force. It is shown, that, if we take into account the inhomogeneity of the magnetic field in the rest inertial frame, it is possible in the limits of the drift approximation to mark out from the Lorentz force the centrifugal force in the evident form.

3) It is found the critical value of the radial velocity, for which the plasma stream radial braking begin and it equals to cjsfi..

4) The stability of the pulsar magnetosphere relativistic electron-positron plasma with respect to the radial potential perturbations is investigated and the possibility of the aperiodic instability development, i.e. the generation of the exponentially increasing radial electric held in this plasma is shown.

5) The mechanism of the toroidal magnetic field generation in the pulsar magnetosphere ' plasma is suggested, which is based on the effect of the plasma radial braking and the existence of the electric field, generated because of the aperiodic instability development

in the plasma. The appearance of the toroidal magnetic field causes the change of the pulsar magnetic field structure from the radial to the spiral one and the violation of the solid body type rotation, corotation of the pulsar, its magnetic field and the magneto-spheric-plasma. The violation of the corotation causes the limitation of the growth of the radial electric field generated because of the aperiodic instability development and the. corresponding radial electric current and the toroidal magnetic field. 0) It is shown, that the effect of the plasma stream radial braking and the aperiodic instability development in it cause the effective transformation of the energy, released during the pulsar rotation slowing down into the energy of the pulsar niagnetosphere plasma and the toroidal magnetic field, generated in it.

The publications and the approbation of the results!

The main results of the thesis were reported on the Second Volga International Summer School on Space Plasma (Nizhni Novgorod/Volga River, Russia, 1995), on the tith International Conference oiv High Power Particle Beams, "BEAMSW (Prague, Czech Republic, 1996), on the International Conference on Plasma Physics, "FARAW (Prague, Czech Republic, 1996), on the scientific councils of the Abastumani Astrophysical Observatory and on the seminars of the theoretical department of the Observatory, on the seminar of the Institute of Plasma Physics, Czech Academy of Sciences, and are published in the following papers:

1. O.V.Chedia, T.A.Kahniashvili, G.Z.Machabeli, l.S. Nanobashvili, "On the kinematics of a corotatiug relativistic plasma stream in the perpendicular rotator model of the pulsar magnetosphere", Astrophys. Space Sci., 233, pp.57-6-1, 1996.

2. O.V.Chedia, T.A.Jiahniashvili, G.Z.Machabeli, l.S. Nanobashvili, "Mjjgnetohydro-

dynamics of a rotating relativistic plasma stream", J. Goergian Phys. Soc., 3, pp.3745, 1996.

3. O.V.Chedia, T.A.Kahniashvili, G.Z.Machabcli,,I.S. Nanobashvili, "Relativistic electron beam dynamics in the pulsar niagnetosphere", Proc. of the 11th Int. Conf. ou High Power Particle Beams, "BEAMS"96\ Prague, 2, pp.1035-1038, 1996.

4. G.Z.Machabeli, I.S.Nanob&shvili, A.D.Rogava, "Centrifugal acceleration surprises", Izv. Vuz. Radiofizika, 39. pp. 39-45, 199C.

5. I.S.Nanobashvili, "Description of the relativistic plasma stream corotatiug with the pulsar inagnetospbere\ Czech. J. Phys., 47, pp. 217-221, 1997.

6. T.A.Kahniashvili, G.Z.Machabeli, I.S.Nanobashvili, "Generation of the electrostatic field in the pulsar magnetosphere plasma", Phys. Plas., 4, pp. 1132-1135, 1997.

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