EDP Sciences
Free access
Issue
A&A
Volume 413, Number 3, January III 2004
Page(s) L27 - L30
Section Letters
DOI http://dx.doi.org/10.1051/0004-6361:20031691


A&A 413, L27-L30 (2004)
DOI: 10.1051/0004-6361:20031691

Letter

Ideal kink instability of a magnetic loop equilibrium

T. Török1, 2, B. Kliem1 and V. S. Titov3

1  Astrophysikalisches Institut Potsdam, 14482 Potsdam, Germany
2  School of Mathematics and Statistics, University of St Andrews, St Andrews, Fife KY16 9SS, UK
3  Theoretische Physik IV, Ruhr-Universität Bochum, 44780 Bochum, Germany

(Received 25 September 2003 / Accepted 3 November 2003 )

Abstract
The force-free coronal loop model by Titov & Démoulin (1999) is found to be unstable with respect to the ideal kink mode, which suggests this instability as a mechanism for the initiation of flares. The long-wavelength ( m = 1) mode grows for average twists $\Phi\ga3.5\pi$ (at a loop aspect ratio of  $\approx$5). The threshold of instability increases with increasing major loop radius, primarily because the aspect ratio then also increases. Numerically obtained equilibria at subcritical twist are very close to the approximate analytical equilibrium; they do not show indications of sigmoidal shape. The growth of kink perturbations is eventually slowed down by the surrounding potential field, which varies only slowly with radius in the model. With this field a global eruption is not obtained in the ideal MHD limit. Kink perturbations with a rising loop apex lead to the formation of a vertical current sheet below the apex, which does not occur in the cylindrical approximation.


Key words: instabilities -- magnetic fields -- MHD -- Sun: activity -- Sun: corona -- stars: coronae

Offprint request: T. Török, ttoeroek@aip.de




© ESO 2004