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Magnetic Pinching of Hyperbolic Flux Tubes: I. Basic Estimations  

Vyacheslav S Titov   Submitted: 2002-10-16 08:58

The concept of hyperbolic flux tubes (HFTs) is a generalization of the concept of separator field lines for coronal magnetic fields with a trivial magnetic topology. An effective mechanism of a current layer formation in HFTs is proposed. This mechanism is called magnetic pinching and it is caused by large-scale shearing motions applied to the photospheric feet of HFTs in a way as if trying to twist the HFT. It is shown that in the middle of an HFT such motions produce a hyperbolic flow that causes an exponentially fast growth of the current density in a thin force-free current layer. The magnetic energy associated with the current layer that is built up over a few hours is sufficient for a large flare. Other implications of HFT pinching for solar flares are discussed as well.

Authors: V.S. Titov, K. Galsgaard and T. Neukirch

Publication Status: to appear in Astrophys. J. 582, No 2, 2003
Last Modified: 2002-10-16 08:58
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Quasi-separatrix layers: refined theory and its application to solar flares  

Vyacheslav S Titov   Submitted: 2000-04-13 10:01

Although analysis of observational data indicates that the quasi-separatrix layers (QSLs) have to play an important role in magnetic configurations of solar flares, the corresponding theory is at an initial stage so far. In particular, there is still a need in a proper definition of QSL. This problem is analyzed here on the basis of geometrical properties of the mapping produced by the field lines which connect positive and negative magnetic polarities of active regions. It is proved that in generic cases this mapping locally stretches and compresses the corresponding displacements of the field-line footpoints, so that such stretching and compressing occur at each point along some fixed and mutually perpendicular directions. This fact enables us to get a remarkably clear and concise definition of QSL as a volume filled by coronal field lines for which the ratio of stretching and compressing coefficients is anomalously large. The new definition is also compared with the ones previously introduced by other authors, in particular, by Démoulin et al. and Schindler et al. The theory is applied to flare events of so called sigmoid-type by using a model of a twisted force-free configuration as proposed by Titov and Démoulin (A&A, v. 351, p.707-720 (1999)). It is shown that such a configuration contains QSL even if genuine separatrix surfaces are absent. To identify the QSL is very important for understanding the mechanism of magnetic energy release in this type of flares. Also we demonstrate that the magnetic field under study has a Hamiltonian structure, which makes it possible in this case to reveal a geometrical reason for the appearance of QSL.

Authors: Titov, V. S., Démoulin, P., Hornig, G.

Publication Status: published in ESA SP Series: SP-448, p. 715-722 (1999)
Last Modified: 2000-04-13 10:01
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Basic topology of twisted magnetic configurations in solar flares  

Vyacheslav S Titov   Submitted: 2000-04-13 09:05

It is accepted now that flare-like phenomena are the result of reconnection of topologically complex magnetic fields. Observations show that such fields are often characterized by a twisted structure. This is modeled here using a force-free flux tube whose arc-like body is embedded into an external potential magnetic field. We study how the topological structure of this configuration evolves when the flux tube emerges quasi-statically from below the photosphere to a certain height in the corona, where the tube becomes unstable and its eruption has to occur. During this evolution below the flux tube there appears a separator field line, along which two separatrix surfaces intersect. This separator is of generalized type because there are no magnetic nulls in the configuration. Both the separator and the separatrices are topological features, where the connectivity of magnetic field lines suffers a jump. We propose that the eruption of the flux tube has to stimulate the formation of strong current layers, in which the free magnetic energy of configuration is released in the form of a flare. The model predicts the formation of hot loops of two kinds during the reconnection phase: the long loops which make nearly one turn around the twisted flux tube, and short sheared loops below. The proposed model provides important clues to the mechanism of solar flares in twisted configurat- configurations.

Authors: Titov, V. S., Démoulin, P.

Publication Status: published in A&A, v.351, p.707-720 (1999)
Last Modified: 2000-04-13 09:05
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Magnetic Pinching of Hyperbolic Flux Tubes: I. Basic Estimations
Quasi-separatrix layers: refined theory and its application to solar flares
Basic topology of twisted magnetic configurations in solar flares

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