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On the Nature of Pulsar Radiation NZ. Kazbeg~, G.Z" Machabeli, and G.I. Melikidze Abastumani Astrophysical Observatory INTRODUCTION A key question in the interpretation of the emission of pulsars is that of the excitation and propagation of waves in a magnetospheric plasma. The magnetosphere of a pulsar has an extremely complex structure and there are many difficulties in the development of its self-consistent model, the bases of which were considered in Goldreich and Julian (1969~; Sturrock (1971~; and Ruderman and Sutherland (l975~. At present there exist some sufficiently well-grounded models not exactly agreeing with each other (e.g. Ruderman and Sutherland 1975; Cheng and Ruderman 198~, Arons and Sharlemann 1979; and Arons 1981~. However, the creation of a dense, relativistic, electron-positron plasma in the polar regions of rotating neutron star magnetospheres is the point of similarity among these models. The pulsar radiation should be generated in such a plasma. A spinning magnetized neutron star generates the electric field which extracts electrons from the star surface and accelerates them forming low density (nb = 710-2 BoP~i, where P is the pulsar period and Be the magnetic field at the star surface) and the energetic (the Lorentz-factor of particles is orb = 3.106 . - 107 for Apical pulsars) primal beam. In a weakly curved magnetic field, electrons generate Quanta which produce in turn electron-positron pairs. Further energetic radiation will be produced, and this will go on to produce more pairs and so on until the plasma becomes dense and screens the electric field (Goldreich and Julian 1969; Sturrock 1971~. As a result, sufficiently dense (no ~ l0i6 _ 10~7 cm~3) electron-positron plasma with an averaged Lorentz-factor up = 3 - 10 is formed. The investigation of He kinetics of this avalanche process shows 225

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226 AMERICAN AND SOVIET PERSPECTIVES that the plasma flowing along the open magnetic force lines possesses the aysmmetrical distribution function with a tail stretched out in the direction of the positive momenta (from the pulsar to the observer, e.g., Arons 1981~. Due to the strong magnetic field, the transversal components (with respect to the magnetic field Bo) of the particles momenta p ~ decay, and the distribution function tends to be one-dimensional. Most probably the magnetic field near the pulsar has a complicated structure differing greatly from a dipole. Though at a sufficiently large distances from the stellar surface up to the light cylinder, the magnetic field can be considered as dipolar: B = Bo(Ro/R)3 if Ro << R < c/Q, where Ro = 106 cm Is a neutron star radius, Q is the pulsar angular velocity. The dependence of the plasma density from the distance Is the same n = n<~(RO/R)3, where index "O" denotes the values taken at the star surface. In our opinion the maser emission mechanisms (Ginzburg and Zhelez- niakov 1975) are the only valid and well-grounded among the others (e.g. antenna mechanisms; for more details see Lominadze et al. 19861. ~ consider the curvature of the magnetic field lines exactly the pylin- dnc coordinates x, r, S will be used below. The x-axis is directed transversely to the plane where the curved field lines lie, r- is the radial and A- the azimuthal coordinates. The latter describes the curvature of the field line (torsion is neglected and BRB/0r = 0, RB - is the curvature radiUS of the field line). In such geometry one has the following integrals of motion: A, pa - W,B~ r/c, pa r. Here pi = vi y/c and vi are the particle momentum and velocity, wale = en B/m c. The particle distribution function should depend on the integrals of motion. Using the method of integration along the par- ticle trajectory one obtains the components of the dielectrical permeability tensor: zz 1 '2 ~ w2 J ~ :`w k~v~-2k~u2/c)( 1+ ~1 of +2w' 2 Q7o of A; Err = 1 - 2 ~ P2 | dry Tt,, _ ~ it, _ ~ it, Nt 1 1 c~ = 1 + ~ Pa a l tow-Have-Aria) He+ T Q_ J Jay, J dip 2QO it; _ 1_ ~ PO / PA T(W-k~v~-kru=) i Q+-Q_ ) fa i; ~J ~ i'

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HIGH-ENERGY ASTROPHYSICS 6'Z = - 2 ~ P2 J PY {(A-kyvy-2kyu2/c)(Q+ _ Q_)f~}; 1 p2 dry vy 1 1 1 1 6=Y = 2 ~ w2 J ~ C ([kSc(Q+ + Q_)-ikrc((Q+ _ Q )] If +2w UP ~ aft ); 1 Spa ~ rln t, /1 6/p; + (pa-u~/cj2; the sum over car Is taken over the particle species and the integration from ooto +oo; vie-iS the particle velocity along the field line, pi' = vamp ,/c, up = / v PRe C iS the particle drift velocity caused by the weak inhomogeneity of the magnetic field and directed along the x-ens for positrons (hereafter for the values without the subscript cat the sign of the charge is assumed to be positive). For the particles of the bunk of plasma, the drift velocity u tends to be zero. Hence, if one assumes up = 0, then equation (1) reduces to the standard form which we designate as (Pj. In the electron-positron plasma deserted by (j, there exists two types of waves: the purely transversal electromagnetic t-wave with an electric vector Et directed transversely to the plane where the magnetic force line lies, and the potential-nonpotential it-wave with the electric field Elf in the plane of k and Bo. The spectra of me waves are as follows:

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228 AMERICAN AND SOVIET PERSPECTIVES ( 4/~)B 4) my ( 16~) (2) (3) note that formulae (2) and (3) are obtained for co < Up, and expression (3) describes only the low-frequency branch of the it-waves. The phase velocity of the high-frequengy branch exceeds the speed of light and cannot interact with particles. The pulsar emission mechanisms provide infor- mation on wave excitation and propagation in the magnetosphere plasma along with their emergence in vacuum. The electromagnetic waves leave the magnetosphere without transformation. THE PULSE RADIATION MECHANISMS Sagdeev and Shafranov (1960) were the first to point out the existence of the cyclotron instability in plasma with the anisotropic temperature. Let us invest/gate the possibility of t-wave generation on me Cyclotron resonance: -k~c-knurl BE =0 (4) Substituting formula (2) and the expressions k = k~(1 + kl2/2k~p2) and v<,, = c(1 - 1/2~2 - u2/2c2) in formula (4) one obtains: k2 + 1 ~ 1 (k~ 2k2 272e5 2 ~ kit ~ 2 UC! ~ _ ~ = ~ B (5) c J k~pc~re~ As it was shown by Machabeli and Usov (1979) the l-waves are being excited in the pulsar magnetosphere only at the anomalous Doppler-effect (upper sign of the equation (5)). The lower sign of equation (5) corresponds to wave damping. In the plasma rest frame these conditions are fulfilled for the velocities satisfying the condition (Lominadze et al. 1986): v cL'ok~v~+ ~ COB ~ ~WB + k2 V2 _ w2 C= ~)B + k2 V2 (~6) It is obvious that for the whole range of frequencies we = kc < ~B7p damping (lower sign in formula (6)) can occur only on particles having negative velocities, and for the distribution function given on Figure 1, at we << Wisp it is absent. In the case when the resonance condition we - live,-Mu - CUB/7 = 0 is nevertheless fulfilled, waves are strongly

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HIGH-ENERGY ASTROPHYSICS f l / l l / / I I _ - _ up ~fib FIGURE 1 The particle distribution function in the pulsar magnetosphere. 229 damped and cannot reach an observer. Hence, for energetic particles only the resonance at the anomalous Doppler-effect (upper sign of equation (5~) can be satisfied. Assuming that the electron and positron distribution functions are about the same, and considering the perturbations propagating nearly along the magnetic field in the k ~ v ~ /wB ~ 1 approximation one obtains the following dispersion relation for t-waves: k2c2 2 = e== Cat (7) For the development of the cyclotron instability it is necessary to satyr the following conditions (Machabeli and Usov 1979~: 1. The distance R between the star and the instability development region should be less than the pulsar light cylinder radius: ( ) ~ ( ) ~ (8) 2. The characteristic time He of the instability development should be less than me time of We plasma escape from the light cylinder ret Using the definition of the rib (Goldreich and Julian 1969) and that rip nip the condition (8) can be rewritten in me following way: ~p<5 10 orb (~012G) (Is) (9)

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230 AMERICAN AND SOVIET PERSPECTIVES In the case of the "typical" pulsar (Be ~ 10~2G, P ~ Is) for the beam particles we have the following limitation on the average Lorentz-factor of the particles of the bunk of plasma up < 5~, as for the particles of the tail the limitation is Up < 10. The value of up and consequently the satisfaction of the condition (8) (or its equivalent (9~) depends on the configuration of the external magnetic field of the pulsar. As it was shown earlier (Lominadze et al. 1983) in the dipole magnetic field the cyclotron instability can develop only in the magnetospheres of the rapidly rotating pulsars (like PSR 0531~21 and PSR 0833~5~. Besides the energy flow earned away by the particles from the pulsar should be of the same order as the energy released when the rotation of the pulsar slows down. The difficulty for the pulsars with a dipole magnetic field to satisfy the condition (9) is due to a very large value of up > 102 . 103 (Cheng and Ruderman 1980~. On the other hand it seems more probable that the magnetic field of a neutron star near the stellar surface differs greatly from the dipole one, and the curvature of the field lines RB is on the order of Ro (Ruderman and Sutherland 1975~. Observational data on pulsars (Davies e! al. 1g84) and Faceting neutron stars in Me binary systems, such as Her-X1 (Pines 1980) testier to the above assumption. In the magnetic field with RB ~ RO one obtains Up < 10. Consequently in the magnetic field of this configuration the region of the cyclotron instability development may be inside the light cylinder both for the beam of the primary particles and for the high-energy tail of the plasma particles. The resonance condition (5~(the upper sign) is satisfied only if 2 2 Ores (10) The latter is fulfilled at k ~ ~ 0. Thus the waves are being excited in very narrow angles. The grown rate of Cyclotron instability is `~2 1 u2 ~o^JT 2 C and ~ = ~"s ~ . at that the resonant frequency is defined as CaB To ~ Unfree (11) (12) (13) (7T and tree are the thermal spread and the average Lorentz-factor of the resonant particles respectively). As for the damping of t-waves, it occurs

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HIGH-ENERGY ASTROPHYSICS 231 on the particles of the bulk of plasma and the corresponding decrement is given by: A,__ P 1 24)oC0B )~' (14) the frequency of damped waves is we ~ 2yp~B. However, as it was already mentioned above, the damping for the distribution function given on Figure 1 and at we at< Pub iS absent Note that the expressions (11) and (12) are valid only if the resonance width is more than the growth rate (the so-called condition of kinetic approximation). This leads to the following limitation on << wig AT V I red (15) From the expressions (11), (12), and (IS) it follows that for the particles of the tail, the excitation of l-waves is possible at the distances R ~ 108 cm from the center of the pulsar. As for the particles of the primary beam the distance R is: R ~ 109 cm. The interaction of the excited l-waves with the beam particles brings about the quasilinear diffusion of particles in the momentum space. As a result the beam particles acquire non-zero pitch-angles (tg; = p ~ lips). Besides the particles in the inhomogeneous magnetic field B(R) drift with the velocity us. As it is shown by Machabeli and Usov (1979) in the central parts of the magnetosphere the value of I,6 of RB2 and so it may exceed us. In this case the resonance condition we - k~v~ - k~u~ = 0 due to the fact that v~/c = 1 ~ll27re,2 - Nb2/2 - U=2/2C2 will take the following form: (k )2 (16) This type of Cherenkov resonance can be easily fulfilled. Let us consider the possibility of the t-wave excitation by the beam particles at a Cherenkov resonance (Kazbegi et al. 1987~. Solving the imaginary part of the dispersion relation we obtain the growth rate of t-waves: ~ _ 1rW', {klPlOC)2 2 fib (6f~p) t"' - 2 `~72 ~2wg J pro 1 + p2' 0 <0p

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232 AMERICAN AND SOVIET PERSPECTIVES The condition of the kinetic approximation yields tO - < 1627T ~ 10 - 4 - 10 - 5 WO fib (19) The comparison of the forlllulae (16) through (19) gives an estimate rho ~ 54/3, which shows the possibility of the instability development on the distance R ~ 5108 -. 109 cm. The substitution of the it-waves spectrum (3) in the Cherenkov reso- nance condition yields to ok j2 w2 And the growth rate of the it-waves, when ~f 0 is given by r it, ~ 2 ~ k ~ 2 ~ (20) (21) The kinetic approximation condition is the same, i.e. (19~. Note that when k ~ ~ O it- and l-waves turn into one purely electromagnetic branch describing the perturbations with an arbitrary polarization. According to its definition the drift velocity us of the beam, with the motion of particles from a pulsar to the light cylinder increases (us or (~Ro~a, where a ~ 2 depending on the dependence of RB from R). In the region where us > ~ the Cherenkov resonance condition looks like [_ k2 _ 1 (U=_ k~52 a for the l-waves and (22) U2 _ _ _ _ , _ . C2 k2 8wp27p ~ us (23) for the it-waves. Making use of form. (1) one obtains the growth rate of the t- and it-waves that equal each other in this case: ~ ~ sib orb ~ kr Wo Stop AT k' (24) The condition of the ldnetic instability for both types of waves is given by: r {U2~2 AT wo c J orb (25)

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HIGH-ENERGY ASTROPHYSICS 2~33 It is clear that for the considered parameters of the typical pulsar the drift motion causes the I- and it-wave excitation at the distances R ~ 109 cm and in the radio frequency range we ~ 108 10~ Hz Therefore, the wave excitation in the plasma of the pulsar magne- tosphere is possible. The first possibility originates when the cyclotron instability develops at the anomalous Doppler-effect resonance between the l-waves and both the particles of the beam and the high-energetic par- ticles of the tail of the distn~ution function. The excited waves propagate along the magnetic force lines with k' ~ O producing the "core"-~e emission Note that this mechanism is most stable among the others and can be applied to the young pulsars. The development of the cyclotron instability is accompanied by the quasilinear diffusion of waves with the energetic particles. As a result, the beam particles obtain non-zero pitch angles (p ~ ~ 0~. At the same tune and the same distance (R ~ 109 cm for the typical pulsars) the particle drift motion caused by the magnetic field inhomogeneity becomes substantial. In this case the Cherenkov resonance can be satisfied in different parts of the magnetosphere: in the central part taking into account that ~ > Tic, and at the edges where ~ < uric. In both cases I- and it-waves are being excited. These mechanisms are valid mainly for pulsars with P > 0.1 s producing the "cone"-bpe radioemission. APPLICATION TO 1ME CENTRAL OBJECT IN SN1987A REMNANT The detection of neutrinos from supernova 1987A suggests the for- mation of a neutron star in its intenor. While the star left over from the supernova explosion is now obscured by the ejects material, a pulsar can be detected within the next few years. The period of a new-born pulsar can be even 1 -. 2 ms (Friedman et al. 1986; Ostriker 1987~. But such values of periods require very high luminosities of a pulsar L ~ 104 104i e/s. By this moment one can put an upper limit on the possible luminosity L < 1038 e/s. Hence the period increases too. The recently discovered radioem~sion from SN (Chin) et al. 1988) suggests the following parameters of a pulsar: P = 43 ms and L = 1038 e/s (Salvati e! al. 1989~. At the same time it is supposed that pulsars are born having sufficiently long periods P ~ 0.1s and even more (Narayan 1987~. Let us assume that the new-born pulsar in SN1987A has the period of the order of P ~ 0.05 . 0.1s. Our task is now to predict the range of frequencies in which the pulsar having these periods will emit. One should know the plasma parameters to apply the results of the preceding chapter to PSR in SN1987N Assume the magnetic field at the star surface Be ~ 10~2G. Then the Goldreich-Julian density is rib ~ 710 210~2 cm. The "tale" consists of the particles of the second generation

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234 AMERICAN AND SOVIET PERSPECTIVES (Arons 1981; 1hdemaru 1973~. The estimate of "tale" particles Lorentz- factor is ~ ~ 105 - 106 (Lominadze et al. 1983~. Substituting the obtained parameters ~ the fo~ulae (11), (13), and (15), one finds that the instability develops in the vicinity of the light cylinder at Me distances - R ~ 2 108 cm for P = 0.05s and R ~ 5108 cm for P = 0.1s. At these distances as it follows from eq.(l4) the following frequencies are being excited YCYC[(P = O.O5s)= 1014 . 1015 Hz and YCYC!~ = 0.1s) ~ 21011 . 1013 Hz). The development of the Cyclotron instability is accompanied by the quasilinear diffusion of the particles in the momentum space both along and across the magnetic field. The particles obtain non-zero pitch-angles of the order of fib ~ 10-2 . 10-3 (Machabeli and Usov 1979~. In this case the Inequality ~ < 1/-y' is fulfilled for the "tale" particles and the synchrotron emission peaks at the frequencies: Oman = ~b72 ~ 5 102~(P = 0.05s) . 10 (P = 0.1s) contn~uting to X-ray radiation of SN1987A that is thought lo be mainly from the decay of radioactive Co56 (Dotani et al. 1987; Sunyaev 1987~. Thus if the pulsar in SN1987A is formed having the considered param- eters it should produce the energetic radiation having much in common with Crab, Vela-pulsars and PSR 0540-69, and PSR 1509-58. The range of emitted frequencies generated at cyclotron instability decrease with the pulsar slow-down and if P > 0.1 0.2s the frequency range will lower to radio frequencies and soft X-rays or UV (for radiation produced by synchrotron mechanism), as it is in PSR 1509-58. And conversely, if the period of the new-born pulsar is in the millisecond range Christian et al. 1989) the corresponding frequencies are ~cycZ ~ 10~7 Hz and Z~yn ~ 1024 1025 Hz (Kazbegi e! al. 1988~. At the same time the luminosity of the pulsar in SN1987A should not resemble that of Crab, Vela, or PSR 054~69, being of the order of Lope ~ 103 . 1032 e/s and Lo ~ 1~5 2 1~6 e/s. Despite the optically thick shell the pulsar emission should emerge from the interior of SN1987N In our opinion (Kazbegi and Machabeli 1990) the detected radioemission from the shell with the wavelength ~ ~ 1.3 mm (Chin) 1988) is a result of hydrogen atom recombination emission at the transition from the 32 to 31 level. The photoexcitation exceeds the pulsar rotation period. In the time 109 -. 5109s after the explosion the shell should become transparent enough to detect pulsed radioemission. Thus we predict the range of frequencies in which the new-born pulsar in SN1987A with P = 0.05 . O.ls should originate. Applications to the other periods can be easily done. Eventual some conclusions can be drawn. The offered theory of pulsar radiation is based on the investigation of all plasma instabilities able

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HIGH^ENERGY ASTROPHYSICS 235 to develop in the electron-positron plasma of pulsar magnetospheres. As it was shown here and previously (Kazbegi e' al. 1989a) the only plasma instabilities are: the cyclotron developing at the anomalous Doppler-effect resonance; and Cherenkov with the consideration of the particle transversal momenta caused by the quasilinear diffusion in one case and by the drift motion in the other one. These mechanisms can produce the well-known pulse profiles (see e.g. Rankin 1983~: "core" (caused by the cyclotron mechanism) and "cone" (by the other two). On the basis of this model virtually all observational features listed in the papers by Rankin (1986) and Taylor and Stinebring (1988) can be explained: mode changing, pulse pulling and the presence of the orthogonal modes (Kazbegi et al. 1989b); the existence and behavior of the circular polarization (Kazbegi et al. 1990a); and subpulse drift (Kazbegi et al. 1990b). The analysis of the emission mechanisms' dependence on the pulsar rotation period P and its application to the expected pulsar in the interior of the SN1987A shows that it should be a source of a high-frequengy radiation. RE~:RENCES Arons, J. 1981. P=c. Varenna Summer School and Workshop on Plasma Astrophysics, ESA 273. Arons, J. and E.l: Scharlemann. 1979. Astrophys. J. 231:854. Cheng, AF., and M.A. Ruderman. 1980. Astrophys. J. 235: 576. Chini, R. 1988. IAU Circ 4652. Davies, J.G., JUG. Lyne, F.G. Smith, V.A Izvekova, ~D. Knin, Yu. P. Shitov. 1984. Mon. Not. R astr. Son 211: 57. Dotani, ~ et al. 1987. Nature. 330: 230. Friedman, J.L, J.R. Ipser, and L Parker. 1986. Astrophys. J. 304: 115. Ginzburg, V.L and V.V. Zheleznyakov. 1975. Ann. Rev. Astron. Astrophys. 13: 511. Goldreich, P. and W. Julian. 1969. Astrophy. J. 157: 869. Kazbegi, AZ, G.= Machabeli, and G.I. Melikidze 1987. Austral. J. Phys. 40: 755. Kazbegi, AZ, G.= Machabeli, G.I. Melikidze. 1988. Physics of Neutron Stars. Structure and Evolution. Leningrad. 94. Kazbegi, LIZ, G.Z Machabeli, G.I. Melikid~e, and V.V. Usov. 1989a. Proc Joint Varenna- Abastumani International School and Workshop on Plasma Astrophysics, ESA SP-285. 1: 271. Kazbegi, Am, G.^ Machabeli, and G.i. Melikidze. 1989b. Proc. Joint Varenna-Abastumani International School and Workshop on Plasma Astrophysics, ESA SP-285. 1: 277. Kazbegi, AZ, and G.Z Machabeli. 1990. Submitted to Nature. Kazbegi, Am, G.Z Machabeli, and G.I. Melikidze. 1990a. Submitted to Mon. Not. R. astr. Soc Kazbegi, AZ, G.Z. Machabeli, and G.I. Melikidze. l990b. In preparation. Kristian, J.A et al. 1989. Nature 338: 234. Lominadze, J.G., G.Z Machabeli, G.I. Melikidze, and A.D. Pataraya. 1986. Sov. J. Plasma Phys. 1~ 713 Machabeli, G.^, V.V. Usov. 1979. Sov. Astron. Lett. 5: 445. Narayan, R. 1987. Astrophys. J. 319: 162. Ostriker, J.P. 1987. Nature. 327: 287. Pines, D. 1980. Usp. Liz. Nauk. 131: 479. Rankin, J.M. 1983. Astrophys J. 274: 333. Rankin, J.M. 1986. Astrophys J. 301: 901.

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236 AMERICAN AND SOVIET PERSPECTIVES Rude~man, M.A, and P.G. Sutherland. 1975. Astrophy. J. 196: 51. Sagdeev, Rid, and P.G. Shafronov. 19~;0. ZETF. 39 181. Salvati, M., F. Papyri, E. Olivia, and R. Bandiera. 1989. Astron. Astrophys. 208: AS. Sturrock, P.^ 1971. Astrophys. J. 164: 529. Sunyaev, R^, et al. 1987. Nature. 330: 227. I5demaru, E. 1973. Astrophys. J. 183: 625. Ibylor, J.H., and D.R. Stinebring. 1988. Ann. Rev. Astr. Astrophys 24: 285.