Skip to main content
Log in

The magnetic-field structure in a stationary accretion disk

  • Published:
Astronomy Reports Aims and scope Submit manuscript

Abstract

The magnetic-field structure in regions of stationary, planar accretion disks around active galactic nuclei where general-relativistic effects can be neglected (from 10 to 200 gravitational radii) is considered. It is assumed that the magnetic field in the outer edges of the disk, which forms in the magnetosphere of the central black hole during the creation of the relativisitic jets, corresponds to the field of a magnetic dipole perpendicular to the plane of the disk. In this case, the azimuthal field component B φ in the disk arises due to the presence of the radial field B ρ and the azimuthal velocity component U φ . The value of the magnetic field at the inner radius of the disk is taken to correspond to the solution of the induction equation in a diffusion approximation. Numerical solutions of the induction equation are given for a number of cases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. I. Shakura and R. A. Sunyaev, Astron. Astrophys. 24, 337 (1973).

    ADS  Google Scholar 

  2. P. Ghosh and F. K. Lamb, Astrophys. J. 223, L83 (1978).

    Article  ADS  Google Scholar 

  3. J. Guilet and G. I. Ogilvie, Mon. Not. R. Astron. Soc. 441, 852 (2014).

    Article  ADS  Google Scholar 

  4. A. E. Dudorov and S. A. Khaibrakhmanov, Astrophys. Space. Sci. 352, 103 (2014).

    Article  ADS  Google Scholar 

  5. V. I. Pariev, E. G. Blackman, and S. A. Boldyrev, Astron. Astrophys. 407, 403 (2003).

    Article  ADS  Google Scholar 

  6. S. Okuzumi, T. Takeuchi, and T. Muto, Astrophys. J. 785, 127 (2014).

    Article  ADS  Google Scholar 

  7. G. I. Ogilvie and M. Livio, Astrophys. J. 553, 158 (2001).

    Article  ADS  Google Scholar 

  8. X. Cao and H. C. Spruit, Astrophys. J. 765, 149 (2013).

    Article  ADS  Google Scholar 

  9. S. H. Lubow, J. C. Papaloizou, and J. E. Pringle, Mon. Not. R. Astron. Soc. 267, 235 (1994).

    Article  ADS  Google Scholar 

  10. D.-X. Wang, R.-Y. Ma, and W.-H. Lei, Astrophys. J. 595, 109 (2003).

    Article  ADS  Google Scholar 

  11. A. G. Zhilkin, D. V. Bisikalo, and A. A. Boyarchuk, Phys. Usp. 55, 115 (2012).

    Article  ADS  Google Scholar 

  12. G. S. Bisnovatyi-Kogan and R. V. E. Lovelace, Astrophys. J. 750, 109 (2012).

    Article  ADS  Google Scholar 

  13. R. D. Blandford and R. L. Znajek, Mon. Not. R. Astron. Soc. 179, 143 (1977).

    Article  Google Scholar 

  14. D. A. MacDonald, Mon. Not. R. Astron. Soc. 211, 313 (1984).

    Article  ADS  Google Scholar 

  15. F. Krauze and K.-H. Rädler, Mean Field Electrodynamics and Dynamo Theory (Pergamon, Oxford, 1980; Mir,Moscow, 1984).

    Google Scholar 

  16. N. A. Silant’ev, J. Exp. Theor. Phys. 85, 712 (1997).

    Article  ADS  Google Scholar 

  17. N. A. Silant’ev, ov. Phys. JETP 74, 650 (1992).

    Google Scholar 

  18. M. Yu. Piotrovich, Yu. N. Gnedin, S. D. Buliga, and T. M. Natsvlishvili, Astron. Lett. 40, 459 (2014).

    Article  ADS  Google Scholar 

  19. V. L. Afanasiev, N. V. Borisov, Yu. N. Gnedin, T. M. Natsvlishvili, M. Yu. Piotrovich, and S. D. Buliga, Astron. Lett. 37, 302 (2011).

    Article  ADS  Google Scholar 

  20. G. C. Murphy and M. E. Pessah, arXiv:1410.6196 [astro-ph.SR] (2014).

  21. G. Bateman and A. Erdelyi, Tables of Integral Transforms (McGraw-Hill, New York, 1954).

    Google Scholar 

  22. V. A. Ditkin and A. P. Prudnikov, Integral Transforms and Operational Calculus (Vysshaya Shkola,Moscow, 1965; Pergamon, Oxford, 1965).

    MATH  Google Scholar 

  23. A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics (Nauka, Moscow, 1977) [in Russian].

    MATH  Google Scholar 

  24. G. Barton, Elements of Green’s Functions and Propagation (Clarendon, Oxford, 1991).

    Google Scholar 

  25. H. Li, J. M. Finn, R. V. E. Lovelace, and S. A. Colgate, Astrophys. J. 533, 1023 (2000).

    Article  ADS  Google Scholar 

  26. O. Kaburaki, Mon. Not. R. Astron. Soc. 229, 165 (1987).

    Article  ADS  Google Scholar 

  27. R. V. E. Lovelace, H. Li, S. A. Colgate, and A. F. Nelson, Astrophys. J. 513, 805 (1999).

    Article  ADS  Google Scholar 

  28. L. Collatz, Functional Analysis and Numerical Mathematics (Academic, New York, 1966; Mir, Moscow, 1969).

    Google Scholar 

  29. V. I. Pariev and S. A. Colgate, Astrophys. J. 658, 114 (2007).

    Article  ADS  Google Scholar 

  30. N. A. Silant’ev, M. Yu. Piotrovich, Yu. N. Gnedin, and T. M. Natsvlishvili, Astron. Astrophys. 507, 171 (2009).

    Article  ADS  Google Scholar 

  31. N. A. Silant’ev, Yu. N. Gnedin, M. Yu. Piotrovich, S. D. Buliga, and T. M. Natsvlishvili, Astron. Rep. 58, 63 (2014).

    Article  ADS  Google Scholar 

  32. S. D. Buliga, Yu. N. Gnedin, T. M. Natsvlishvili, M. Yu. Piotrovich, and N. A. Silant’ev, Astron. Lett. 40, 185 (2014).

    Article  ADS  Google Scholar 

  33. V. V. Sobolev, Uch. Zap. Leningr. Univ. 116, 1 (1949).

    Google Scholar 

  34. S. Chandrasekhar, Radiative Transfer (Clarendon, Oxford, 1950).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Yu. Piotrovich.

Additional information

Original Russian Text © M.Yu. Piotrovich, N.A. Silant’ev, Yu.N. Gnedin, T.M. Natsvlishvili, S.D. Buliga, 2016, published in Astronomicheskii Zhurnal, 2016, Vol. 93, No. 5, pp. 463–473.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Piotrovich, M.Y., Silant’ev, N.A., Gnedin, Y.N. et al. The magnetic-field structure in a stationary accretion disk. Astron. Rep. 60, 486–497 (2016). https://doi.org/10.1134/S1063772916040090

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063772916040090

Keywords

Navigation