Looking at field lines in disc around a Kerr black hole...

Magnetic Field Lines in a Black Hole Plasma Disc

 by

Boris Gudiksen & Bjørn Østman

Introduction

Our goal was to create a vizualization of magnetic field lines in a disc around a black hole, and show the disc by either dust or smoke and a black hole. We were not doing this in a rigorous scientific way, so the vizualization is not made to do scientific calculations from, but merely to illustrate how the system looks.
The dataset was given to us by Åke Nordlund, who had simulated it in a cubic box. We then had to make that cubic dataset into part of a disc, and then copy this part of a disc into several pieces that, when combined, would make up a complete disc. This was possible without getting an angular periodic disc, because we only were using field lines, and not isosurfaces for instance.
We hoped to vizualize the plasma disc by using the density data set provided in Åke's original dataset, and then vizualize it through semi-transparent isosurfaces. We have chosen to call it a plasma disc instead of an accretion disc, since there is nothing in this visualization that is accreting, and since the magnetic field lines depend on the disc to consist of ionized particles (a plasma) to be wound up in this way.
It turned out though that the density variations were extremely small, and that the disc would be very hard to make look anything like the real thing, that is what theory predicts, because the data was in this cubic box. The physical reason why there should be a magnetic field in the plasma disc is discussed below in 'Black Holes and Electrodynamics'.

Index

Black Holes and Electromagnetism

  • Black Hole Electrodynamics
  • Accretion Disks
  • Black Hole Magnetosphere
  • Flux Freezing
  • Disc Field Lines

    Exhibitions

  • Inventor
  • WebSpace
  • IDL files

    Conclusion

    The vizualizations are first of all qualitative. The disc and the hole is vizualized to help the viewer understand the surroundings of the magnetic field of the disc, so they are not all quantitatively correct.
    The horizon of the hole (the static limit) is as mentioned just an ellipsoid (ratios 1:1:0.6). This is correct, but since we have not specified the value of the angular momentum of the hole, one cannot deduce anything physical from the vizualization of the hole. We can only say that the specific angular momentum, a/M, must be less than 0.866 (Thorne, Price and McDonald, 1986 - page 96). And the color of the hole is chosen merely so that it can be seen at all. Otherwise it should have been black. And furthermore the hole should have bended the light rays in its vicinity, distorting the image (our disc) behind it.
    The disc is even more qualitative in its vizualization. First of all it is represented only by an isosurface, showing where the border of the disc would lie. And secondly the shape of the disc have been chosen to match a picture in (Thorne, Price and McDonald, 1986 - page 135) and this picture from (Novikov and Frolov 1989). See (Shakura and Sunyaev 1973) for another view.
    We have not considered the internal distances between the horizon of the hole and the disc. Again we have relied on the figures mentioned above.
    The magnetic field has been made out simulations by Åke Nordlund and Axel Brandenburg. They have calculated it in a cubic box 62x63x32 in size, and it was then turned into a slice of a torus by stretching the outer edge. This slice was then copied to form a complete torus, so the field lines are in themselves very realistic.

    References

    Shakura, Sunyaev:'Black Holes in Binary Systems. Observational Appearence', A&A 24,337-355 (1973)
    Blanford, Znajek:'Electromagnetic Extraction of Energy from Kerr Black Holes', Mon. Not. R. astr. Soc., 179, 433-456 (1977).
    Thorne, Price and McDonald:'Black Holes; The Membrane Paradigm', Yale University Press (1986)