A novel look at the pulsar force-free magnetosphere

Original Article


The stationary axisymmetric force-free magnetosphere of a pulsar is considered. We present an exact dipolar solution of the pulsar equation, construct the magnetospheric model on its basis and examine its observational support. The new model has toroidal rather than common cylindrical geometry, in line with that of the plasma outflow observed directly as the pulsar wind nebula at much larger spatial scale. In its new configuration, the axisymmetric magnetosphere consumes the neutron star rotational energy much more efficiently, implying re-estimation of the stellar magnetic field, \(B_{\mathrm{new}}^{0}=3.3\times10^{-4}B/P\), where \(P\) is the pulsar period. Then the 7-order scatter of the magnetic field derived from the rotational characteristics of the pulsars observed appears consistent with the \(\cot\chi\)-law, where \(\chi\) is a random quantity uniformly distributed in the interval \([0,\pi/2]\). Our result is suggestive of a unique actual magnetic field strength of the neutron stars along with a random angle between the magnetic and rotational axes and gives insight into the neutron star unification on the geometrical basis.


Pulsar magnetosphere Magnetohydrodynamics Radio pulsars Neutron stars 



The work have used the ATNF Pulsar Catalogue available at The work is funded by the Institute of Radio Astronomy of the National Academy of Sciences of Ukraine.


  1. Aharonian, F.A., Bogovalov, S.V., Khangulyan, D.: Nature 482, 507 (2012) ADSCrossRefGoogle Scholar
  2. Beskin, V.S., Gurevich, A.V., Istomin, I.N.: J. Exp. Theor. Phys. 85, 401 (1983) Google Scholar
  3. Beskin, V.S.: Phys. Usp. 53, 1199 (2010) ADSCrossRefGoogle Scholar
  4. Blandford, R.D., Payne, D.G.: Mon. Not. R. Astron. Soc. 199, 883 (1982) ADSCrossRefGoogle Scholar
  5. Chen, A.Y., Beloborodov, A.M.: (2014). arXiv:1406.7834
  6. Contopoulos, I.: Astron. Astrophys. 442, 579 (2005) ADSCrossRefGoogle Scholar
  7. Contopoulos, I., Kazanas, D., Fendt, C.: Astrophys. J. 511, 351 (1999) ADSCrossRefGoogle Scholar
  8. Goldreich, P., Julian, W.H.: Astrophys. J. 157, 869 (1969) ADSCrossRefGoogle Scholar
  9. Goodwin, S.P., Mestel, J., Mestel, L., Wright, G.A.E.: Mon. Not. R. Astron. Soc. 349, 213 (2004) ADSCrossRefGoogle Scholar
  10. Gralla, S.E., Jacobson, T.: Mon. Not. R. Astron. Soc. 445, 2500 (2014) ADSCrossRefGoogle Scholar
  11. Gruzinov, A.: (2006). arXiv:astro-ph/0604364
  12. Halpern, J.P., Gotthelf, E.V., Camilo, F., Seward, F.D.: Astrophys. J. 665, 1304 (2007) ADSCrossRefGoogle Scholar
  13. Harding, A.K., Contopoulos, I., Kazanas, D.: Astrophys. J. 525, L125 (1999) ADSCrossRefGoogle Scholar
  14. Heyl, J.S.: Magnetars. In: 22nd Texas Symposium on Relativistic Astrophysics, p. 130 (2005) Google Scholar
  15. Kargaltsev, O., Cerutti, B., Lyubarsky, Y., Striani, E.: Space Sci. Rev. 191, 391 (2015) ADSCrossRefGoogle Scholar
  16. Kaspi, V.M., Kramer, M.: ArXiv e-prints (2016). arXiv:1602.07738
  17. Lovelace, R.V.E., Turner, L., Romanova, M.M.: Astrophys. J. 652, 1494 (2006) ADSCrossRefGoogle Scholar
  18. Lyubarskii, Yu.E.: Sov. Astron. 16, 16 (1990) Google Scholar
  19. Manchester, R.N., Hobbs, G.B., Teoh, A., Hobbs, M.: Astrophys. J. 129, 1993 (2005) ADSGoogle Scholar
  20. Mereghetti, S., Pons, J.A., Melatos, A.: Space Sci. Rev. 191, 315 (2015) ADSCrossRefGoogle Scholar
  21. Mestel, L., Shibata, S.: Mon. Not. R. Astron. Soc. 271, 621 (1994) ADSCrossRefGoogle Scholar
  22. Michel, F.C.: Astrophys. J. 180, L133 (1973) ADSCrossRefGoogle Scholar
  23. Michel, F.C.: Theory of Neutron Star Magnetospheres. University of Chicago Press, Chicago (1991). 533 p. Google Scholar
  24. Ogura, J., Kojima, Y.: Prog. Theor. Phys. 109, 619 (2003) ADSCrossRefGoogle Scholar
  25. Okamoto, I.: Mon. Not. R. Astron. Soc. 167, 457 (1974) ADSCrossRefGoogle Scholar
  26. Petrova, S.A.: Astrophys. J. 764, 129 (2013) ADSCrossRefGoogle Scholar
  27. Petrova, S.A.: Astron. Nachr. 335, 246 (2014) ADSCrossRefGoogle Scholar
  28. Philippov, A.A., Spitkovsky, A.: Astrophys. J. 785, L33 (2014) ADSCrossRefGoogle Scholar
  29. Scharlemann, E.T., Wagoner, R.V.: Astrophys. J. 182, 951 (1973) ADSCrossRefGoogle Scholar
  30. Spitkovsky, A.: Astrophys. J. 648, L51 (2006) ADSCrossRefGoogle Scholar
  31. Takamori, Y., Okawa, H., Takamoto, M., Suwa, Y.: Publ. Astron. Soc. Jpn. 66, 25 (2014) ADSCrossRefGoogle Scholar
  32. Tchekhovskoy, A., Spitkovsky, A., Li, J.G.: Mon. Not. R. Astron. Soc. 435, L1 (2013) ADSCrossRefGoogle Scholar
  33. Thompson, C., Duncan, R.C.: Astrophys. J. 473, 322 (1996) ADSCrossRefGoogle Scholar
  34. Thompson, C., Lyutikov, M., Kulkarni, S.R.: Astrophys. J. 574, 332 (2002) ADSCrossRefGoogle Scholar
  35. Tiengo, A., Esposito, P., Mereghetti, S., Turolla, R., Nobili, L., Gastaldello, F., Gotz, D., Israel, G.L., Rea, N., Stella, L., Zane, S., Bignami, G.F.: Nature 500(7462), 312 (2013) ADSCrossRefGoogle Scholar
  36. Uzdensky, D.A.: Astrophys. J. 598, 446 (2003) ADSCrossRefGoogle Scholar
  37. Vigano, D., Pons, J.A.: Mon. Not. R. Astron. Soc. 425, 2487 (2012) ADSCrossRefGoogle Scholar
  38. Yuki, S., Shibata, S.: Publ. Astron. Soc. Jpn. 64, 43 (2012) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Radio Astronomy of the NAS of UkraineKharkivUkraine

Personalised recommendations