The Evolution of Writhe in Kink-Unstable Flux Ropes and Erupting Filaments

Abstract

The helical kink instability of a twisted magnetic flux tube has been suggested as a trigger mechanism for solar filament eruptions and coronal mass ejections (CMEs). In order to investigate if estimations of the pre-eruptive twist can be obtained from observations of writhe in such events, we quantitatively analyze the conversion of twist into writhe in the course of the instability, using numerical simulations. We consider the line tied, cylindrically symmetric Gold-Hoyle flux rope model and measure the writhe using the formulae by Berger and Prior which express the quantity as a single integral in space. We find that the amount of twist converted into writhe does not simply scale with the initial flux rope twist, but depends mainly on the growth rates of the instability eigenmodes of higher longitudinal order than the basic mode. The saturation levels of the writhe, as well as the shapes of the kinked flux ropes, are very similar for considerable ranges of initial flux rope twists, which essentially precludes estimations of pre-eruptive twist from measurements of writhe. However, our simulations suggest an upper twist limit of $\sim 6\pi$ for the majority of filaments prior to their eruption.

16 pages, 4 figures, to appear in Plasma Physics and Controlled Fusion

References in corpus (4)

• Ideal kink instability of a magnetic loop equilibrium
• Formation of current sheets and sigmoidal structure by the kink instability of a magnetic loop
• 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

Cited by in corpus (8)

• Prominence and Filament Eruptions Observed by the Solar Dynamics Observatory: Statistical Properties, Kinematics, and Online Catalog
• Decoding the Pre-Eruptive Magnetic Field Configurations of Coronal Mass Ejections
• Origin of Quasi-Periodic Pulsation at the Base of Kink Unstable Jet
• Untwisting and Disintegration of a Solar Filament Associated with Photospheric Flux Cancellation
• Observational signatures of a kink-unstable coronal flux rope using Hinode/EIS
• Formation and Eruption of Hot Channels during an M6.5 Class Solar Flare
• Evolution of an arched magnetized laboratory plasma in a sheared magnetic field
• Observations of Photospheric Vortical Motions During the Early Stage of Filament Eruption