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Method of conformal mappings for calculation of electric currents in magnetospheres of compact stars

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Abstract

In the two-dimensional approximation with the method of conformal mappings, we analyze the magnetic-field structure in the magnetosphere of a compact star. The dependence of the solution on the input parameters of the model is investigated. The direct and reverse electric currents are calculated in the magnetosphere.

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References

  1. J. D. Cole and J. H. Huth, “Some interior problems of hydromagnetics,” Phys. Fluids, 2, No. 6, 624–626 (1959).

    Article  MATH  MathSciNet  Google Scholar 

  2. A. A. Galeev, R. Rosner, and G. S. Vaiana, “Structured coronae of accretion disks,” Astrophys. J., 229, No. 1, Pt. 1, 318–326 (1979).

    Google Scholar 

  3. J. Heyvaerts, in: Advances in Solar System Magnetohydrodynamics, Cambridge Univ. Press, Cambridge (1991).

    Google Scholar 

  4. T. Kudoh, R. Matsumoto, and K. Shibata, “Magnetically driven jets from accretion disks: The effect of magneto-rotational instability,” Adv. Space Res., 23, No. 5/6, 1101–1104 (1999).

    Article  Google Scholar 

  5. M. A. Lavrentyev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  6. V. M. Lipunov, “Disk accretion onto magnetized compact objects,” Astrometriya Astrofiz., 36, 8–12 (1978).

    Google Scholar 

  7. V. M. Lipunov, “Magnetospheres of accreting compact stars with multipole magnetic fields,” Astron. Zh., 55, No. 6, 1233–1240 (1978).

    Google Scholar 

  8. V. M. Lipunov, Astrophysics of Neutron Stars [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  9. V. M. Lipunov, E. S. Semenov, and N. I. Shakura, “Accretion disk orientation in binary X-ray pulsars,” Astron. Zh., 58, No. 4, 765–770 (1981).

    Google Scholar 

  10. V. M. Lipunov and N. I. Shakura, “Interaction of the accretion disk with the magnetic field of a neutron star,” Sov. Astron. Lett., 6, No. 1, 14–17 (1980).

    Google Scholar 

  11. K. Mukerjee, P. Agrawal, B. Paul, et al., “Pulse characteristics of the X-ray pulsar 4U 1907+09,” Astrophys. J., 548, No. 1, Pt. 1, 368–376 (2001).

    Google Scholar 

  12. P. Oberts, “The two-dimensional problem of the shape of the magnetosphere,” Geomagnetizm Aeronomiya, 13, No. 5, 896–905 (1973).

    Google Scholar 

  13. A. V. Oreshina, I. V. Oreshina, B. V. Somov, and N. I. Shakura, “A two-dimensional model of the magnetosphere of a compact star with an accretion disk,” Prikl. Mat. Mekh., 68, No. 3, 452–461 (2004).

    MATH  Google Scholar 

  14. I. V. Oreshina and B. V. Somov, “The method of conformal mappings for solving problems of cosmic electrodynamics,” Izv. Ross. Akad. Nauk. Ser. Fiz., 63, No. 8, 1543–1549 (1999).

    Google Scholar 

  15. M. Romanova, G. Ustyugova, A. Koldoba, V. Chechetkin, and R. V. E. Lovelace, “Dynamics of magnetic loops in the coronae of accretion disks,” Astrophys. J., 500, No. 2, Pt. 1, 703–713 (1998).

    Google Scholar 

  16. K. Shibata and T. Kudoh, “Formation and collimation of jets by magnetic forces,” in: T. Nakamoto, ed., Proc. Star Formation, Nobeyama Radio Observatory, Nobeyama (1999), pp. 263–268.

    Google Scholar 

  17. N. R. Sibgatullin, Oscillations and Waves in Strong Gravitational and Magnetic Fields [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  18. N. R. Sibgatullin, I. N. Sibgatullin, A. A. Garcia, and V. S. Manko, “Magnetic fields of pulsars surrounded by accretion disks of finite extension,” Astron. Astrophys., 422, 587–590 (2004).

    Article  MATH  Google Scholar 

  19. B. V. Somov, Plasma Astrophysics. Pt. I: Fundamentals and Practice, Springer, New York (2006).

  20. B. V. Somov, A. V. Oreshina, and I. V. Oreshina, “Magnetic reconnection in the corona of the accretion disk of a compact star,” Izv. Vyssh. Uchebn. Zaved., Radiofiz., 44, No. 9, 796–805 (2001).

    Google Scholar 

  21. B. V. Somov and S. I. Syrovatskii, “The formation of a current (neutral) layer accompanying the motion of a plasma in the field of a plane magnetic dipole,” Zh. Eksper. Teor. Fiz., 61, No. 5, 1864–1875 (1971).

    Google Scholar 

  22. B. V. Somov and S. I. Syrovatskii, “Hydrodynamic flows of a plasma in an intense magnetic field,” Neutral Current Layers in a Plasma. Tr. Fiz. Inst. Akad. Nauk. 74, 14–72 (1974).

    Google Scholar 

  23. S. I. Syrovatskii, “The formation of current layers in a plasma with a frozen-in strong magnetic field,” Zh. Eksper. Teor. Fiz., 60, No. 5, 1727–1741 (1971).

    Google Scholar 

  24. C. Thompson and R. Duncan, “The soft gamma repeaters as very strongly magnetized neutron stars. II. Quiescent neutrino, X-ray, and Alfv´en wave emission,” Astrophys. J., 473, No. 1, Pt. 1, 322–342 (1996).

    Google Scholar 

  25. P. M. Woods, C. Kouveliotou, E. Göğüş, et al., “Evidence for a sudden magnetic field reconfiguration in soft gamma repeater 1900+14,” Astrophys. J., 552, No. 2, Pt. 1, 748–755 (2001).

    Google Scholar 

  26. V. N. Zhigulev, “The phenomenon of the magnetic ‘squeezing out’ of a flow of a conducting medium,” Dokl. Akad. Nauk SSSR, 126, No. 3, 521–523 (1959).

    Google Scholar 

  27. V. N. Zhigulev and E. A. Romishevskii, “The interaction of flows of a conduction medium with the Earth’s magnetic field,” Dokl. Akad. Nauk SSSR, 127, No. 5, 1001–1004 (1959).

    Google Scholar 

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Authors and Affiliations

  1. Sternberg Astronomical Institute, Moscow State University, Moscow, Russia

    I. V. Oreshina & B. V. Somov

Authors
  1. I. V. Oreshina
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  2. B. V. Somov
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Correspondence to I. V. Oreshina.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 15, No. 6, pp. 141–150, 2009.

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Oreshina, I.V., Somov, B.V. Method of conformal mappings for calculation of electric currents in magnetospheres of compact stars. J Math Sci 172, 852–858 (2011). https://doi.org/10.1007/s10958-011-0228-7

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