Plasma model for pulsar radiation тема автореферата и диссертации по астрономии, 01.03.04 ВАК РФ

Abastumani Astrophysical Observatory Georgian Academy of Sciences

George Ivan Melikidze

Plasma Model for Pulsar Radiation

0Î.03.04 - Plasma Astrophysics

Abstract of Doctoral Dissertation in Physical and Mathematical Sciences

Tbilisi, 1996

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Dissertation is completed:

In the Abastumani Astrophysical Observatory, Georgian Academy of Sciences

Consultant: Expert:

Official Opponents:

George Z. Machabeli, Doctor of Physical and Mathematical Sciences

Alexandre I. Tughushi, Doctor of Physical and Mathematical Sciences, professor.

Givi I, Suramlishvili, Doctor of Physical and Mathematical Sciences

Vladimer V. Usov, Doctor of Physical and Mathematical Sciences, professor.

Archil G. Khantadze, Doctor of Physical and Mathematical Sciences, professor.

Leading Organisation:

Date and Place of Defence:

Dissertation is available

Radio Astronomical Station of the Astro Space Center of P.N. Lebedev Physics Institute of the Russian Academy of Sciences

December 26, 1996, p.00 p.m., at the meeting of the Dissertation Council of Abastumani Astrophysical Observatory Ph.M.01.03.c N1 AI. Kazbegi ave.2a, Tbilisi

in the library of the Abastumani Astrophysical

Observatory

Abstract was distributed on November 26, 1996 Secretary of the Dissertation Council, ,

Candidate of Physical and Mathematical Sciences ^ \ K.Chargeishvili

General Characterization of the Thesis

Actuality of the Subject. Pulsars rank among the most interesting objects in our universe. Physicists from various fields have been attracted by the extreme conditions, which prevail in pulsars and their magnetospheres. For example, the magnetic field of a pulsar reaches 10l2-i-1013 G: the mass density in the star itself is of the order of the density of nuclear matter 10H -r 1015 g cm-3; and the energy of the particles in the magnetosphere is ultrarelativistic (107 mc2).

Presently about 750 pulsars arc known, and they have a lot of features in common. It has not been more than a year since their discovery that pulsars were identified with rotating neutron stars. According to this model, the emission comes from bounded region such as the polar caps of the pulsars. As the star rotates, an observer coming into the directional pattern of the emission sees pulses, which are repeated at a period equal to the rotation period of the star.

Soon after the discovery of pulsars it became obvious that they are one of the most active objects in the local galaxy. Their brightness temperature, estimated from the radio emission of pulsars, exceeds the brightness temperature of other sources of radiation. Furthermore, 7-einissiou has been detected from the pulsar PSR 0531+21 in the Crab Nebula and from the pulsar PSR 0833-45 ill the constellation Vela. These pulsars are surrounded by the remnants of supernovas, and in their magnetic field there is the synchrotron emission by high-energy particles from the pulsar with a Lorentz factor of 107 4- 10s. All these arguments suggest that the emission of pulsars must be generated in a highly relativistic plasma. Here only rotationally powered pulsars are studied.

Pulsars are believed to pulse because their spin causes a highly directional beam of emission 10 sweep around the sky, illuminating a favorably situated observer once per rotation. The observed waveforms ( slices through the directional patterns of the beams ) have varied shapes but. in the great majority of cases they have common feature of a small duty cycle ( pulse width divided by period ), and this cycle usually is not more than a few percents.

As early as in 1969 it was established that pulsars must be rapidly rotating highly magnetic neutron stars. No other model lias been proposed that accounts satisfactorily for the extremely high degree of timing stability. As neutron stars, pulsars must be born in supernova explosions or in binary System in which the accretion of matter onto the surface of a

white dwarf pushes it over the Chandrasekar mass limit and causes it to collapse without Visible fireworks. The energy of the radio emission of pulsars comes from the energy, which is released as the rotation of the pulsar slows down. This slowing is observed for almost all pulsars. Exceptions are the pulsars in a close binary system, which accelerate due to interaction with the companion.

The magnetosphere of pulsars has an extremely complex structure. Study of this structure requires the solution of many problems, which combine different fields of physics, ranging from quantum field theory to plasma theory. The creation of a self-consistent theory of the pulsar magnetosphere is connected with many difficulties. Meanwhile according to general energetic considerations and observational data it seems possible to assume, that a high density relativistic electron-positron plasma is generated in the polar regions of the pulsar magnetosphere.

It is widely believed that all the waves observed as the pulsar radiation on the Earth must be generated in this plasma in the region of the open field lines. All the characteristics of the observed radiation like the polarization properties, behavior of the position angle, the subpulse drifting phenomena should be determined in this medium.

There is not a full understanding of the pulsar radioemission mechanism despite a lot of attempts. On the other hand pulsars clinch two Nobel Prizes, and they are very interesting physics laboratories for many reasons. So, creation of a self consenting theory of pulsar radiation and explanation of their observation features is one of the most actual problems in the modern astrophysics.

Aim of the Thesis. The aim of the theory presented in the Thesis is studding of the pulsar emission mechanisms and formation of their observable features, such as polarization properties, subpulse drift phenomenon, nulling and etc. We believe that our theory can naturally explain not only pulsar activity but also many peculiarities of observed radiation. For this purpose we study the theory of the ¡«homogeneous relativistic electron-positron plasma, wave generation and propagation, and their polarization.

Scientific novelty. The following new results are obtained in the Thesis:

1. The permetivity ten/or of the relativistic electron-positron plasma in the inhomogeneous strong magnetic field taking into account the drift ¡notion is obtained.

2. Pol/iri/ation and propagation of waves in the pulsar magnetosphere are studied. All the possible instabilities in the magnetospheric plasma is considered and it was found that only three instabilities are possible to lie developed in the stationary magnetosphere. These mechanisms are

in

responsible for all types of pulsar radiation.

3. Ill addition the possibility of radioeniission by means of curvature radiation of Lagiiiuir solifons is considered. The Laiigmtiir waves could be exited due to two stream instability ill non-stationary magnetospheie.

4. The mechanism for formation of the polarization characteristics of both linearly and circularly polarized radiation is given. Linear polarization is naturally explained by excitation and oblique propagation of the plasma waves. Behavior of the position angles in this case is defined by relative disposition of \vave vectors and magnetic field lines towards each other { in opposite of the Radhakrishnan-Cooke model where the position angle depends on the geometry of the emission zone ).

5. The properties of the observed circular polarization ( CP ) is explained taking into account the relative motion of electrons and positrons in the pulsar magnetospherc. In particular: the existence of low moderate amounts of CP in the 'core' type emission; the high degree of nonpolarized emission in some pulsars; the fact that the intensity maximum of the circular polarization in average profiles falls mainly in the center of the pulse; the decrease of the circular polarization intensity to minimum at minimal impact parameters: presence of the sense reversal circular polarization in some pulsars and the one sense circular polarization in the others; two sense reversals within a pulse window observed in very few pulsars ( virtually only PSR 1541+09 provides a good example ); correlation of the antisymmetric circular polarization with linear polarization; the transitions +/- ( changing of left-handed to right-handed polarization ) is accompanied by the decrease of the linear polarization position angle, and for the transitions -/+ on the contrary; high percentage of circular polarization in PSR 1702-19 (GO %) and one sense of circular polarization in both the main pulse and the interpulse.

6. There was found the mechanism that can serve as an explanation of the subpulse drift phenomena. This mechanism does not need any additional assumptions. The drift, wave propagating almost transversely to the magnetic field can affect the fulfillment of the radiowave generation conditions. If the pulsar angular velocity is near to the frequency of the drift wave (ii « u) one should observe regular drift phenomena. Otherwise (i! < or w) random appearances of subpulses along the pulse window should he observed. Within this mechanism the different directions and reversals of subpulse drifting, different values of P3 even for the same pulsar is explained.

7. There was suggested the mechanism for the pulsar nulling. When the peak of the beam distribution function shifts towards lower Lorentz-factors

the radio emission mechanisms snitch oft" and cause nulling. The emission resumes immediately after the gap closes up. Depending on the primary beam distribution function the process ( which starts from the broadening and finishes with the closing up of the gap ) can proceed with different speed. If this process takes less time than the pulsar period, only a short time scale variability of the emission would be observed. In the opposite case we observe nulling. The decrease of -¡k causes not only the emission disappearance but also the slowing down of the drift wave phase velocity at nulls. As for large decrease of jt the phase of the drift wave and the place of the pulse in the pulsar window is 'remembered'. The shorter the mill the better the place is remembered. At long nulls and slight change of the phase memory does not take place. Instead of the phase memory there should be drift velocity memory, i.e., after the emission resumes the subpulse should appear near the place where it might have been in the case of 110 null. It was shown-that 'core' single profiles should be less affected by nulls than 'conal' profiles. This conclusion is in a good agreement with observations.

8. The correlation of intensity temporal variations between components I and II of the 'conal' double profile is explained as one of the natural consequences of the theory. The 'hollow cone' model cannot explain that kind of correlation. The results of observations defining the spatial structure of the emission sources are explained on the basis of the offered model. The superdispersion pulse delay phenomena is explained as magnetic field line 'sweepback'.

9. The mechanism of the pulsar PSR 0531+21 optical radiation is suggested. In the framework of this mechanism, the main features of the optical radiation of PSR 0531+21 are explained: the anomalous narrowness of the main pulse top, the existence of linear polarization and the changes of its degree, variations of the position angle, lion-coincidence of the polarization degree minimum with the intensity maximum, the intensity fall in the infrared region.

Approbation of results. The results presented in the Thesis were reported at International Conference on Plasma Physics ( Lausanne, Switzerland, 1981 ), The Joint Varenna-Abastumani International School and Workshop on 'Plasma Astrophysics ( Yarcnna, Italy, 193,8 ), All-Union Seminar on Physics of Neutron Stars ( Leningrad. Rusia, 1988 ), International Simposium Principle of invariance and its application ( Erevan, Armenia, 1989 ). U.S.-USSR Workshop on High-Energy Astrophysics { 1989 ), IAU Colloquial No 128 ( Ziclona Gora. Poland, 1990 ), The Joint Varenna-Abastumani-ESA-Nagoya-Potsdam International School and Workshop on

'Plasma Astrophysics ( Telavi. Georgia, 1990 ). As well as 011 seminars at Radio Astronomy Department of P.N.Lebedev Physics Institute ( Pushchino, Russia ), Institute of Cosmic Research ( Moscow, Russia ), Raman Research Institute ( Bangalore, India ), Centre D'Etudes Nucleares de Saclay ( Paris, France ). Ecole Polite( lmique ( Paris, France ), Astronomical Center ( Zielona Gura, Poland ).

Size of the Thesis. The Thesis contains G Sections, 125 pages, 15 figures. Section 'Reference' includes 201 citations.

Content of the Thesis

In the Section 1 ( Introduction ) the aim of the Thesis is described. The following problems are discussed there: a short story about pulsar discovery and early models; the main properties of observed emission; brief description of the standard model for pulsars; physical processes leading to the formation of the relativistic electron-positron plasma in the open magnetic field region: difficulties 011 the way of creation of the self-consistent, theory for the pulsar maguetosphere; different- possible mechanisms for pulsar radiation; what kind of requirements the successful mechanism has to meet. The parameters of the magnetospheric plasma an1 given. The framework of the model which is used as a base for further consideration is discussed. The main parameters of the electron-positron plasma of the pulsar maguetosphere are as follows: The magnetic field is assumed to be dipole field in the radiation region. The magnetic held can be considered as a slightly nonuniform. The distribution function of the ¡¡articles is one dimensional. The Lorentz factors of.the particles are ~ 3 4- l(i"\ ~ 10'1 -j-105 and 7, ~ 10(> -j- 10' for the plasma, tail and beam particles respectively. The distribution functions of electrons and positrons are shifted with respect to each other. The ring of the magnetic field lines is considered and is supposed that the width of the ring is much smaller than the curvature radius of the field lines, but it is much more, than the length of the waves. The latter implies that the boundary effects are negligible.

The Section 2 ( Empirical theory of the pulsar radiation ) deals with the features of pulsars that follows from the observations and the system of their classification. Peculiar features the explanation of which are the most important for all successful radiation models are discussed there. To those features belong: polarization characteristics, polarization angle behavior, pulse drifting and nulling phenomena etc. Difficulties related to the explanation of these features in the frame of the hollow cone model are considered, especially phenomena which can be explained only by our

model.

In the Subsection 2.1 ( Mean pulse profiles ) the classification of pulsars by means of the mean pulse profiles is given. The physical background of this classification is discussed. The characteristics of the components are described. In the Subsection 2.2 ( Polarization in the pulsar emission ) polarization properties of radiation is discussed, such ¡is presence and amount of linear and circular polarization, position angle behavior. Especially those features which cannot be explained by the hollow cone model are considered ( for example the mode switching, presence of the orthogonal polarization mode, fast changing of position angle etc. ).

In the Subsection 2.3 ( Nulling, subpulse drift, phase memory and mode changing phenomena ) the phenomena which are observed in individual pulses are discussed. The theory presented in the Thesis naturally explains ( without any additional assumption ) those phenomena. On the other hand most previous attempts for their explanation faced the unsolvable problems. This kind of observable feature is the correlation of subpulses in emission which is described in the Subsection 2.4.

In the Section 3 ( Waves in the Magnetospheric Plasma of a Pulsar ) the permeability tenzor of the relativistic electron-positron plasma in the inho-mogeneous strong external magnetic field is investigated and contribution of the magnetic field line curvature is discussed.

In the Subsection 3.1 ( Permittivity tenzor of the magnetospheric plasma ) the tenzor is obtained using a cylindrical coordinates. In order to take into account the curvature of magnetic field lines correctly the cylindrical symmetry is used. The relativistic equation of the motion is solved in such environment and using the method of integration along the particle trajectory the dispersion equation of the magnetospheric plasma is obtained.

In the Subsection 3.2 ( Polarization of waves propagating in pulsar inag-netosphere ) polarization of plasma waves'is investigated. It was shown that taking into account the inequality of distribution functions of electrons and positrons there is possible presence of circularly polarized waves. When the angle between wave-vector and the external magnetic field 0 satisfies following condition

' ■ (1)

r

two circularly polarized waves exist. ( Here 7 is the average Lorentz-factor of the bulk of plasma and A determines the difference in energies of electrons and positrons. ) In the opposite case there are two linearly

2:1

polarized waves: t and lt-waves. The polarization plane of the lt-waves lies in the same plane where the curved magnetic field, while the polarization plane of t-waves is perpendicular to this plane.

In the Subsection 3.3 ( Wave propagation in the pulsar maguetosphere ) the dispersion relation of plasma waves are obtained. It should be mentioned that t-wave is purely transverse wave ( electromagnetic ) and its dispersion relation is:

v = kc(\-6), • (2)

where 2

6 = (3)

' p H

This is analogous of the magnetosonic wave. In the case of longitudinal propagation t and /¿-waves coincide with each other. Low-frequency waves propagating nearly transversely to the magnetic field are also studied in this section. These waves are used in order to explain the subpulse drift phenomena.

The Subsection 3.4 (Possible instabilities of the magnetospheric plasma) deals with the instabilities which can serve as radiatioi; mechanism. It was found that there exist only three type of instabilities in the stationary maguetosphere that can be used for explanation of pulsar activity. The conditions for the wave damping in the magnetospheric plasma is given. The resonance conditions and growth rates for these instabilities are obtained.

In the Section 4 ( Plasma Mechanisms of the Pulsar Radiation ) so called plasma model for pulsar radiation is described. It should be mentioned th

at this model in scientific literature is often referred as the Georgian model. The model could be described as follows: In a sufficiently narrow ( in comparison with the whole maguetosphere dimensions ) region in the vicinity of the last open field line the wave generation via three different mechanisms is possible ( in the stationary maguetosphere ). The first mechanism is connected to the t-wave excitation at the anomalous Doppler effect when the resonance condition

u.' - k^c - kzUdn + = 0. (4)

7

is satisfied. For the development of the instabilities in the maguetosphere of a pulsar it is necessary to satisfy the following conditions: the resonance condition should be fulfilled inside the light cylinder and the growth rate of the instability should be sufficiently large, i.e. the characteristic time of

the instability development r ~ T-1 should be move t]ian the time which is necessary for the plasma to leave the wave generation region ( re > i? ).

The resonant condition (4) is satisfied only if l/272„ < 6. This is possible if the resonance is carried out for the particles of the both the 'tail' of the distribution function and the primary beam. For the parameters of typical pulsars (P = Is) the expression (4) is fulfilled at the distances 109 cm < R < 5 • 109 cm in a rather limited region the width of which is of the order of 107 + 108 cm. Note, that in this mechanism the limitation on 9 angle is only from above 92 < 25. Hence the emission region will give the entire circle ( 'core' type emission ). The t-wave generation is possible by the particles of the 'tail' of the distribution function yr = 7, ~ 103 -f 104 and it occurs at the distances R/Rc ~ 0.5 + 1. The frequency of the excited waves falls within the range 10s < uj'0 < 1010 Hz. Note, that the frequency of the excited t-wavcs is restricted from above u>l0 < 2ypu)B. The t-wave generation takes place by the particles of the primary beam with the parameters yr — 7, ~ 105, 7p ~ 3, -yT ~ 103 at the distances R/Rc 0.1 4- 0.3. There is a possibility of It-wave generation at the . anomalous Doppler-effect resonance with the same growth rate and on the same angles as for t-waves. However, the frequencies are restricted by

The next mechanism is connected to the possibility of the wave generation at the Cherenkov resonance

due to the beam particle drift motion. It was shown that for the parameters 7, ~ 10fi,7 ~ 3,7T ~ 10" the generation of both t and It-waves takes place in the angles restricted from above and from below 0\ < 0 < O2. Hence the rays will compose a hollow cone, i.e. 'cone'- type emission. The frequency of waves depends 011 the distance from the stellar surface as

The drift velocity of beam particles moving from the pulsar to the light cylinder'increases since n,i oc (R/Rsi)". where a ~ 2 relying on the'dependence of pcr on R. I11 the region where u,i > <I> for the typical pulsars parameters the drift motion causes t and /Mvaves excitation at distances R ~ 10s -r 10'Jcm, corresponding to the radio emission in the frequency range uj0 ~ 10s to 1010 Hz.

The third mechanism works only if the t and It-waves were being excited at the resonance (3) by the beam particles. The subsequent interaction of

JJ < 23'\u;p.

>^'0 ~ kfVtp — kTitjn — 0

(5)

7/2

(6)

these waves with the beam particles causes their quasilinear diffusion. Thus the beam particles obtain lion-zero effective pitch-angle <I\

There was shown that the wave exc itation is possible only in the highly limited region of the magnetosphere. It is easy to estimate the longitudinal size ( along the magnetic field lines ) of a source ¡is /?., < 108 cm. The possibility of the wave excitation highly depends on the curvature radius of the field lines. Hence the generation region is limited ill transverse dimensions also. It. is important, to mention that the waves are exited in the strongly limited angle 0, which is determined by the resonance conditions and the value of the growth rate. The waves propagating along a straight line create cones. The cones are put into each other and bases of cones are directed to an observer. So a cross section of the radiation pattern may be presented ¡us two concentric rings with the continuous central part. This model can produce all types of subpulses. The third mechanism is possible only for the old pulsars. So the five component profiles like PSR 0C21-04 are moderately old.

Development of ¡ill these mechanisms depends very much on the value ■of and consequently 011 the structure of the pulsar magnetic field at the stellar surface. I11 the case of the dipole magnetic field neither the cyclotron nor the Cherenkov instabilities have enough time for development, inside the light cylinder. I11 this rase the excitation of plasma waves is possible ( Langmuir waves ) due to non-stationarity of the plasma outflow from the polar cap. In the Subsection 4.2 ( Langmuir .soliton ) the possible radiation mechanism due to Langmuir wave excitation is discussed. There was shown that, after development of Langmuir turbulence due to inodulational instability Langmuir soliton is formed. The soliton causes charge separation and as it moves along the curved magnetic field lines it emits curvature radiation. The spectra and power of this radiation was calculated. In this approach, in contrast with those taken in previous studies, the question of the formation of the bunches is resolved automatically. Because of the relative motion of the centers of mass of the electrons and positrons, the pondemotorive force acts differently on these different, particles, redistributing the charges over the volume of the soliton. The polarization of the waves emitted by the soliton is the same as that of an //-waves.

The Section 5 ( Interpretation of the Observational Data ) is devoted to the application of the developed theory.

In the Subsection 5.1 ( Formation of the polarization properties of pulsar radiation ) a model explaining the existence and properties of the linear and circular polarizations in pulsar emission is offered. Two orthogonal polarization modes are naturaly explained by t and lt-waves. These waves are

exited simultaneously due to II and III mechanisms. So an observer may observe both polarization modes radiated from the same places. Changing of the position angle is determined by the relative orientation of the magnetic field lines and wave vector.

It was shown that if the circular polarization exists it should be confined to small angles and observed in the 'core'-type emission, the place of the maximum intensity of the circular polarization in the profile window should be near the place of intensity maximum of the "core'-type emission.

In the Subsection 5.2 ( The nature of pulsar subpuLsc drift ) the theory explaining the subpulse drift, phenomenon is presented. Observational data show that subpulse drift is pronounced in 'conal'-type radiation. According to-the theory presented in the thesis "conar radiation is generated on the Cherenkov resonance. As it was shown the subsection 3.3 the low frequency waves propagating across the external magnetic field could exist in the maguetosphere. This waves mainly affect on the curvature of the magnetic field lines changing the curvature radius. At the same time the angle between wave-vectors and magnetic field lines depend on the drift velocity which is determined by the curvature radius. So if frequency of the low frequency waves is of the same order as the frequency of the pulsar rotation a regular drift of subpulses could be observed. In opposite cases there would be random blinking. This model could explain a different direction of subpalse drift which could not be explained by the spark theory. Direction of the subpulse drift depends 011 difference between the frequency of waves and the frequency of rotation. Furthermore, we can observe the drifting subpulses with different drift velocity if those components are generated in different places, where the frequency of drift waves should differ too. Let us mention that in our model subpulses are determined by the peculiarities of wave generation, not by the sparks.

In the Subsection 5.3 ( A model for pulsar millings and phase memory phenomenon ) depandence of the radio emission generation 011 the paramiters of the magnetospheric plasma is di- ussed. It was shown that if Lorentz-factor of priiary beam decreases II and III Mebxanism for wave generation should switch off and a pulsar should enter a null state. At the same time decrease of the beam Loretz-factor couses decrease of frequency of the drift waves. As a result for short nulls phase memory phenomena would be observed.

Thus finally the following model could be established: the low-frequency drift wave which propagates across the magnetic field and encircles the maguetosphere, is generated along the radio emission. This wave changes the curvature of the magnetic field lines in the radio wave generation region.

Therefore the suhpulse generation region is transported together with the drift wave phase and the suhpulse drift is observed.

The waves are generated in the plasma for quite a narrow range of parameters. Therefore the processes leading to the plasma formation in the gap should affect the generation process. During the particle extraction from the surface the primary beam distribution function is formed. The most energetic particles of this distribution give birth to the electron-positron pairs inside the gap. Positrons are accelerated towards the stellar surface. They heat it, cause the thermoemission of electrons and hence broaden the tale of the primary beam distribution function. This process can be repeated several times. Because of this the electric field in the gap weakens gradually each time and therefore the energy of the bulk of the beam does not obtain enough energy for the pair creation. This process continues until the density of the extracted particles exceeds the GoldreichJulian density. Then negative potential appears screening the electric field and closing up the gap. The gap function is analogous to triode.

When the peak of the beam distribution function shifts towards lower Lorentz-factors the radio emission mechanisms switch off and cause nulling. The emission resumes immediately after the gap closes up.

Depending 011 the primary beam distribution function a process (which starts from the broadening and finishes with the closing up of the gap) can procecd with different speed. If this process takes less time than the pulsar period, only a short time scale variability of the emission would be observed. In the opposite case nulling could be observed.

The decrease of 7, causes not only the emission disappearance but also the slowing down of the drift wave phase velocity. Hence during short, nulls and at large decrease of 7t the phase of the drift wave and the place of the pulse in the pulsar window is 'remembered'. The shorter the null the better the place is remembered. At long nulls and slight change of 7, the phase memory does not take place. Instead of the phase memory there should be drift velocity memory, i.e., after the emission resumes the subpulse should appear near the place where it might, have been in the case of no null.

In the Subsection 5.4 ( Spatial structure of the emission sources and subpulse correlation of PSR 1133+16 - the model ) the observation data discussed in Subsection 2.4 are explained. One of the natural consequences of the model is that the temporal intensity variations in components I and II of the 'conal' double profile should be correlated due to the fact that both component are produced by the radiation coming almost from one and the same place, meaning - by almost the same particles. Note that in the 'hollow cone' model where the particles producing radiation for component

I and the particles producing component II are separated by the whole magnetosphere transversal dimensions it would be difficult to understand such correlation.

The observations were carried out to check this prediction. Using the method of cross correlation function there was shown that indeed the intensity temporal variations are highly correlated between I and II components but not between them and the central one'.'

In the Subsection 5.5 ( Optical radiation of the Crab pulsar PSR 0531+ 21) the wave generation mechanisms are applied to Crab pulsar. It was shown that cyclotron instability can develop in the magnetosphere and excited waves fall in the optical region. So the physical nature of the Crab pulsar optical emission is the same as the radio emission of typ'ical pulsars. These residts could be easily applied for new-born pulsars. The detection of neutrinos from the supernova 1987A suggests the formation of a neutron star in its interior. Thus if the pulsar in SN 1987A is formed having the considered parameters it should produce the energetic radiation having much in common with Crab pulsars. The range of emitted frequencies . generated at cyclotron instability decrease with the pulsar slow-down and if P > 0.1 — 0.2 s the frequency range will lower to radio frequencies and soft A'-rays or UV (for radiation produced by synchrotron mechanism). The luminosity of the pulsar in SN 1987A should not resemble that of Crab.

Acknowledgments. This work was partially supported by grants R.VI000 and RV200 from the International Science Foundation and 94-3097 from INTAS.

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The main results of the thesis are published in the following papers

1. Melikidze G.I. ¿c Pataraya A.D., Langmuir soliton propagated in the relativistic plasma at an angle to the external magnetic field, As-trofiziku, 20. pp.157-163 (1984)

2. Lominadze J.G.. Melikidze A.P. ¿c Pataraia A.D.. Plasma mechanisms for the pulsar radiation: Proe. of the. Intel-national Confe.icncc on Plasma Physics ( Lausanne. Switzerland ), Invited papers, Vol. 2, PP.1043-104G (19S4)

3. Melikidze G.I., Pataraia A.D. ^ Chagelishvili G.D., Soloton of low-fre<iuennv electromagnetic waves in the electron-positron plasma. Bulletin of the Ganyian Academy of Sen net -;. 114, pp.290-292 (1984)

4. Lominadze J.G., Machabeli G.Z., Melikid/.e G.I. Ic Pataraya A.D., Magnetospheric plasma oi a pulsar, Sov. ./. Plasma Phys., 12, pp.712721 (19SG)

5. Machabeli G.Z. Melikid/.e Ci.I.. On the mechanism and some peculiarities of optical radiation of PSR 0531+21, Sov. Astronomical J., G5, pp.741-745 (1988)

G. Kazbegi A.Z., Machabeli G.Z. i: Melikidze G.I., On the mechanism of formation of the polarization characteristics of pulsar radiation, In: Proc. of tin- .hunt Van i:mi-Abw>fHmti.ni Intelnational School & ■ Workshop on P'tmini A^tii'i'ln/sies. ed. T.D. Guyenne, ESA SP-285, Vol. I ( Paris: European Space Agency ). pp.277-280 (1988)

7. Melikidze G.I.Pataraya A.O.. Xonlinear waves in the magnetosphere of pulsars. Pux:. of the Symposium Principle, of invariance.■ and its applications, ( Erevan ) pp.42G-430 (1989)

8. Kazbegi A.Z.. Machabeli G.Z. L' Melikidze G.I.. On the posibility of discovering pulsed liigh-energy radiation from SN 1987, In: AH-Union Seminar oil Physics of Neutron Stars, ed. D.A. Varshalovich ( Leningrad: PTI ). 1 pp.9 1-99 (19S8)

9. Kazbegi A.Z.. Machabeli G.Z. k. Melikidze G.I., On the existence of circular polarization in the pulsar magnetosphere, In: Proc. of the Joint, Van nna-Abastumaui-ES N ayoya-Pot sdam Workshop on Plasma Astrophysics, ed. T.D.Guyenne, ESA SP-311, ( Paris: European Space Agency ), pp.227-233 (iooi))