Catastrophe versus instability for the eruption of a toroidal solar magnetic flux rope

Abstract

The onset of a solar eruption is formulated here as either a magnetic catastrophe or as an instability. Both start with the same equation of force balance governing the underlying equilibria. Using a toroidal flux rope in an external bipolar or quadrupolar field as a model for the current-carrying flux, we demonstrate the occurrence of a fold catastrophe by loss of equilibrium for several representative evolutionary sequences in the stable domain of parameter space. We verify that this catastrophe and the torus instability occur at the same point; they are thus equivalent descriptions for the onset condition of solar eruptions.

V2: update to conform to the published article; new choice for internal inductance of torus; updated Fig. 2; new Figs. 3, 5, and 8

References in corpus (7)

• Torus instability
• Ideal kink instability of a magnetic loop equilibrium
• Photospheric flux cancellation and associated flux rope formation and eruption
• Numerical simulations of fast and slow coronal mass ejections
• Observations and modeling of the early acceleration phase of erupting filaments involved in coronal mass ejections
• A Magnetohydrodynamic Model for the Formation of Episodic Jets
• Flux Rope Formation Preceding Coronal Mass Ejection Onset

Cited by in corpus (10)

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• The eruption of a small-scale emerging flux rope as the driver of an M-class flare and a coronal mass ejection
• Are complex magnetic field structures responsible for the confined X-class flares in super active region 12192?
• Downward catastrophe of solar magnetic flux ropes
• Influence of photospheric magnetic conditions on the catastrophic behaviors of flux ropes in active regions
• Upward and downward catastrophes of coronal magnetic flux ropes in quadrupolar magnetic fields