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Generation of Ultrahigh-Energy Gamma Rays in Accreting X-Ray Pulsars YU.N. GNEDIN AND N.R. IKHSANOV Central Astronomical Observatory ABSTRACT Relativistic protons producing ultrahigh-energy gamma rays as a result of nuclear collisions are expected to generate close to the neutron star surface as a result of accretion. The high efficiency of He accreting matter's gravitational energy conversion into the acceleration energy and high efficiency of the acceleration itself are the mam peculiarities of the considered mechanism. It Is shown that a distribution of the "loss cone" type accreting protons takes place during accretion onto a neutron star with a strong magnetic field. This distribution effec~vetr generates small-scale Alfven, proton cyclotron waves, and non-linear waves (magneto-acoustic and Alfven solitons) due to instabilities. The electric field of the moving solitons may accelerate the protons to energies > 10~5 eV. The region of acceleration covers the Amen surface to distances of 2-3 radii of the neutron star from its surface. New possible sources of ultrahigh~nergy gamma-rays are predicted. They may be binary X-ray systems with neutron stars permeated by magnetic fields of ~ 109 Gauss. INTRODUCllON One of the recent and most interesting astronomical discoveries was the detection of very high-energy (10~2 to 1014 eV) and ultrahigh-energy (lOl4 to 1016 eV) Gamma rays from X-ray binaries. Radiation of ultrahigh- energy quanta of four binary systems (Her X-1, 4U0115+63, Vela X-1, and Cog X-3) have been observed by at least two independent groups (Lamb and Weekes 1987~. The radiation detected pulsates with He star's rotation 144
HIGH-ENERGY ASTROPHYSICS 145 period. bible 1 gives the basic characteristics of these sources. As it follows from this table, the main physical properb luminosity in the gamma-ray range: x-ray range ratio-is within L,/Lr > 10-3 (1) and perhaps ~ 1. It is evident that such a traditional model as radiation of relativistic particles generating in the electric and magnetic fields of a fast-rotating neutron star, will not do for this physical situation. The rotation rate of neutron stars ~ Her X-1 and 4U0115163 is too small to provide the necessary energy. Thus, relativistic protons and electrons originating very high-energy gamma rays should generate close to the neutron star's surface as a result of accretion. At present there is no general theoretical conception of the mechanism of relativistic proton generation near the surface of the Secreting neutron star, although there are quite a few ideas (see Brecher 1987; Hillas 1987~. The main peculiarities of such a mechanism should be as follows: 1. High efficiency of gravitational energy conversion of accretion mat- ter into fiche acceleration source energy, since the ratio of the ultrarelativistic particle energy power to the X-ray emission energy power can be rather large: Ln/Lm < 1 and even Lp/L:; > 1 r, (2) Tomb and Weekes 1987; Hillas 1987~. 2. High efficiency of the mechanism of acceleration, since the char- acteristic time of energy losses due to synchrotron radiation of protons is very short tSyn ~-4.4 x 10-l2E~siB-2 where E15 is the proton energy given in 1015 eV and B12 is the magnetic field measured in 10~2 Gauss. 3. Another essential difficult for acceleration is the high density of the accelerated plasma which prevents accumulation of the energy of the accelerating particle because of frequent coulomb collisions. There must be a mechanism in the Faceting plasma, which causes a strong inhomogeneity of the plasma such as dense and small plasma drops. The goal of the present paper is to End such a mechanism of conversion of fiche accreting plasma gravitational energy in the neutron starts magneto- sphere into the relativistic proton energy. This conversion should provide for the necessary energy and high efficiency of acceleration. Such a mech- anism is generation of non-linear waves (Al~en and fast magneto-acoustic
146 J o C, ~ - ._ o ._ 8 .° C) ~ _ C) P~ ~ .~ o o ~o .- 4) C) C~ ° o C\. - _ C'2 o o o _ _ _ . , _ ~_ o o o o _ _ _ _ ~o ~ o o o _ _ _ _ 1 1 1 1 o o o ~ _ _ '_ _ C~ C~ C ~o~ C7` oo ~, ~- ~t _ ~o 8 _ C ~o o C~ ~o _ _ , ~o C} := - t~ X X a~ e~s ;> ~ C, ~; _ _ C _O _ . o C) - . o :^ ~o . - 11 ~ C) D o o _ - C~ O O _ - :L _' ~- o ~o _ _ t`' - - ~O" ~ _ ~_ X O q" =' =' ~ c ~_ _ X X ¢: V _ ~: ~: C'3 C, .~ ._ ~D 4, >< - C~ X ._ ~C ~ox _ o _ o ~_ _ z U) O -~D ~ - Q, C) ~ ~ ._ C) ~ ._ ~ O ~ 3 ~ _ U, ~ ~ os CJ _ os ~ ,= o C, 2 ~ C) U' D O ~: ;~ 5: as ._ D - .= C, D - ~C - Q) ;- - U) C, :: o U) C) C) - C~
HIGH-ENERGY ASTROPHYSICS 147 solitons) in the accreting plasma. The accreting plasma automatically be- comes essentially mhomogeneous. MEClIANISM OF lam CONVERSION OF GRAVITATIONAL ENERGY TO ULTRA-REIATIVISTIC PROTON ENERGY lithe idea of the proposed mechanism lies in the assertion that a dis- tribution of accreting protons of "the loss cone" type takes place during accretion onto the neutron star with a strong magnetic field (Leroy and Mangeney 1984; Benz and Thejappa 1989~. This distribution is character- istic for generation of Stabilities and given by F(P1,P~) = Cexp [_(P~ P2~) _ (Pl P2l0) ~ /\Pl ~ /\pl~2 (4) where C= [7r3/27\pl~p~i Tempo_ Pol )+~ Pol t! + erf ~ Pol )] )] _ (5) In the case of sperical accretion P = me x Vff, where mp is the proton mass and Vff is the free-fall velocity of the accreting plasma. What is the physical justification of the above assertion? First of all this distn~ution (4) can take place at the entrance of the accreting plasma onto the cusp level of the magnetized neutron star due to the conservation of the adiabatic invariant AP' /B = Const. Another possible reason for this distribution may be plasma reflection from a strong shock wave formed doling the accretion. One can note three possible locations of the shock wave: Alfv~n surface where the shock wave is formed as a result of the interaction of the accreting matter with the neutron star's magnetospheric plasma, in the region of the so-called magnetopause. The protons may resect from the magnetopause forming distribution (4) or a bit different distribution (Leroy and Mangeney 1984~. This reflection may take place deep in the magnetosphere closer to the neutron star's surface as a result of the formation of a shock wave or a strong narrowing of the magnetic cusp in the region of the accretion energy release. In the latter case, we have tO deal with the reflection from a magnetic mirror (Vlahos 1987~. As to the shock wave, it can be formed due to the radiation pressure if its strength is close to the Eddington limit (Basko and Sunyaev 1976~. The cross section of the photon scattering by the electron is resonant at the Cyclotron frequency Gibe in the magnetic field of the neutron star. This
148 AMERICAN AND SOVIET PERSPECTIVES increases the pressure in comparison with the case without the magnetic field (Mitrophanov and Pavlov 1982; Gnedin and Nagel 1984; Zheleznyakov and Litvinchuk 1986). A distribution of the (4) type is unstable and generates small-scale Alfven, proton Cyclotron and hybrid waves (Meerson and Rogachevsldi 1983; Machabeli et ale 1987) as well as nonlinear waves: solitons which are magneto-acoustic and Alfven vortices in plasma (Petviashvili and Pohotelov 1973~. Solitons are effectively generated at the moment of the resection e.g., from the magnetic wall or in the region of the shock wave formation (Alsop and Arons 1988; Arons 1988) of the moving plasma. The frequency of the excited linear waves is given by LO) ~ ~ giVA/v where win Is the ion cyclotron frequency, VA is the Alf~en velocity, and V is the plasma beam velocity equal to Vf I. The instability increment is equal to (Zaitsev and Stepanov 1985) ~ ~ 0.4(8~Wp/B2)Wff (6) where Wp is the energy density of the proton beam causing instability. In our case we may assume this value to be close to the densitr of the accreting plasma gravitational energy, i.e., Wp < Wff = 1/2pVff (~7~) where p is the accreting plasma, with density depending on accretion rate M. The generated waves become more intensive in direction close to that of the magnetic field lines: Kit < (~/wB~/2. On the Aliven surface VA ~ Vff and w ~ Alibi, be., ion cyclotron waves are effectively generated. Within the magnetosphere: ~ > win. A soliton as a magneto-acoustic vortex may be considered as a nonlin ear packet of fast magneto-acoustic waves. This packet is an axial-symmetric formation, propagating along the magnetic field B. Its dimensions in the direction of ache propagation ~: and in the direction of the radius ~ are given by id ~ `, A2 ;tr ~ `~, A3 where A is the dimensionless amplitude of the vortex Since A < 1, as a rule, the vortex is hastened along the magnetic field lines. The magnetic field of the magneto-acoustic vortex is mainly radial, ABr = AB, and its propagates with the velocity, V5 = VA (1 A2) The Alf¢6n vortex on the contrary, is elongated along B. (¢: ~ tr) and its magnetic field Is predominancy azimuthal 1\B`' = AB. It can be
HIGH-ENERGY ASTROPHYSICS 149 considered as a waveguide along the direction of the B radius p = 1/AK' 3 . There are other types of Alfv~n solitons (see Mihailovsky et al. 1976; Ovenden et al. 1983~. In order to provide for effective development of the instabilities of the (4~-~6) type one should have: byte > 1, where tD is the characteristic dissipation time of the process in question. This dissipation leads to damping of linear and nonlinear waves and, in particular, to breaking of solitons. One of the effective channels of dissipation is coulomb collisions: tD ~ 1/ue ~ Ff3f/Ne (9) where me is the effective frequency of collisions of the accreting proton beam with the background plasma. AD ~ 104 for the Alf~en surface, i.e., mechanism (43 operates electively. This condition AD > 1 is also satisfied near the neutron star's surface. The mechanism of soliton dissipation is widetr discussed in scientific literature, although the problem has not yet been finally solved. We can put down the final conclusion as follows: the conversion of the accreting flux gravitational energy into the ultrarelativistic particle energy as a result of the development of the "loss cone" type instability (43 takes place at a characteristic distance to the neutron star. This generation radius 1S: R3, ~ Rgen < RA (10) PROTON ACCELERATION TO ULTRARELAIIVISTIC ENERGIES IN THE REGION OF THE "LOSS CONE" lYPE INSTABILITY GENERATION The electric field of a fast solution can be the most effective mechanism of the proton acceleration to ultrarelativistic energies: E = 1/Ct~A^B]; AB = AB (11) On the Alfven surface VA ~ Vff; that is, it is equal to the plasma free-fall velocity. Inside the accretion column VA ~ C. Since the magnetic field of the magnet~acoustic soliton is radial IBM ~ 0, and that of the Alfven soliton is azimuthal FIB<,, ~ O relative to the magnetic field lines of the _ _ neutron star B. the electric field acts transverse to the magnetic field B lines in accordance with (11~. It is the azimuthal E<' ~ O in the case of the generation of magneto-acoustic solitons and the radial En ~ O in the case of the Alf~en solitons. Therefore, the main source of energy losses of the accelerating protons is synchrotron radiation
150 AMERICAN AND SOVIET PERSPECTIVES The equation for the accelerating proton energy acquired due to the electric field E has the form dE -_ _ = cEu (12) where ~ Is the accelerating proton velocity ~ ~ c. Solution (12) accounting for (11) gives: E1s = 0.2(A/B12) /, if it is the characteristic time of the proton synchrotron losses. Coulomb collisions only slightly influence the propagation of protons. Nuclear collisions become important for them. Hence, the presence of a very inhomogeneous distribution of plasma Is needed, for instance, in the region of the accretion column, to provide for the escape of ultrarelativ}stic protons from the acceleration region. It should be noted that an analysis of observational data on X-ray pulsars lead many authors (Basko and Sunyaev 1976; Bai 1980) to the conclusion that the plasma distribution is inhomogeneous in the Alfv~n range and within the accretion column. In X-ray binary systems where the compact object is a magnetized white dwarf (objects of AM Her type or "polars") a noticeable excess of soft X-ray radiation in comparison with the hard X-ray radiation, i.e., Lath > 1~ observed. Rota ~ al. (19~) interpreted this result in a model of very inhomogeneous accretion, when the accreting matter arrives in either magnetic pole region of the white dwarf as separate blobs elongated along the magnetic field lines. Note, that the mechanism of soliton generation causes the accretion inhomogeneity, because the plasma density inside a soliton is noticeably greater than outside of the soliton: Lip ~ (/\B)2. The difficulty of the ultrarelativistic protons escape from the generation region can be overcome, if one assumes that the source of gamma rays is neutrons, not protons. The neutrons are formed in the generation region as a result of nuclear collisions formed in the generation region as a result of nuclear collisions of ultrarelativistic protons with the surrounding plasma. In conclusion, we would like to emphasize the fact that soliton mech- anism explains also the freezing-in of the Secreting plasma to the strong magnetic field of the neutron star, since the magnetic field will penetrate quickly to plasma blobs, formed by solitons. OBSERVATIONAL CONSEQUENCES OF THE PROPOSED MECHANISM The lllrninosity of the X-ray pulsar in a binary is fully determined by the rate of accretion on the neutron star according to the traditional theory (13)
HIGH-ENERGY ASTROPHYSICS 151 Lo = GM~M/R5. (14) The main parameter of our model is the ratio of the power of ultra-high energy protons to the X-ray luminosity: WE (Rg (Rgen ) R Lo AWgr(R) Rgen (15) The value ~W,v(Rgen) takes into consideration the resection of the ac- creting plasma in the region of the interaction (e.g., polar cusp) and can considerably exceed the portion of the gravitational energy released in the X-ray range. Hence, the coefficient ~ can be larger than unit 77(Rgen) > 1. Let us analyse the case when the ultrarelativ~stic protons are generated on the Aliven surface: Rgen ~ RA. Then from most typical conditions for X-ray pulsars: M = 10-8 Midyear, B. = 10~2 the ratio is LF/L~ ~ Rs/RA ~ 10-2 . (16) This ratio is characteristic for a number of sources from Table 1, if one accepts ~ 10% for efficiency of Me generation of gamma rays. As to pyg X-3, this ratio is close to 1. This means that according to (17) the Elfin radius RA ~ RS, which corresponds to the value of the magnetic field on the neutron starts surface Bs ~ 109 Gauss. This result is well confirmed by the recent observational data, which indicate that the neutron star in the Cyg X-3 system is a millisecond pulsar (Watson 1987; Zyskin et al. 1987~. In accordance with (15) and (163 one should expect noticeable fluxes of ultrahigh-gamma-rays from such X-ray binanes, whose compact com- panions are neutron stars with comparatively weak magnetic fields (= 109 Gauss). Possible candidates of that We can be Car X-1, SS433, Sco X-1, LSI+61°30~. Recent there was an announcement concerning the discov- e~y of a variable gamma-ray radiation of ultrahigh energy from Cir X-1 and 2A 1822-37,1 (Ciampa and Clay 198~, Ciampa et al. 1989~. REFERENCES Alsop, D., and J. Aronse 1988. Phys. Fluids. 31:839. Arons, J. 1988. Page 1. Proceedings of the Joint Varenna-Abastumani Workshop on Plasma Astrophysics. Varenna. Bai, ~ 19%0. Astrophys. J. 239:299. Basko, M.M., and RN Sunyaev. 1976. Mon. Nat. R. est. Soc. 175:395. Benz, A O. and G. Thejappa. 1988. Preprint. Institute of Astronomy, EIH, Zurich. Ciampa, D., and R.W. Clay. 1989. Preprint. Department of Physim and Mathematical Physim, University of Adelaide. Ciampa, D., R.W. Clay, and P.G. Edwards. 1989. Astrophys. J. Ill press. Gnedin, Yu.N., and W. Nagel. 1984. Astron. Astrophys. 138:356.
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