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-emptive 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 ∼6π for the majority of filaments prior to their eruption.
Highlights
The m = 1 kink mode or helical kink instability is a current-driven, ideal magnetohydrodynamic (MHD) instability
Such writhing is often observed in erupting filaments or prominences in the solar corona (Figure 1), which has led to the suggestion that the KI can trigger filament eruptions and coronal mass ejections (CMEs) (e.g., Sakurai 1976; Sturrock et al 2001; Torok & Kliem 2005; Fan 2005)
We studied the conversion of twist into writhe in a simulation series of the KI in the GH model, considering initial flux rope twists in the range 3.0 π ≤ Φ0 ≤ 10.6 π
Summary
The instability lowers the magnetic energy of the flux rope by reducing the bending of field lines, which leads to a characteristic helical deformation (writhe) of the rope axis Such writhing is often observed in erupting filaments or prominences in the solar corona (Figure 1), which has led to the suggestion that the KI can trigger filament eruptions and CMEs (e.g., Sakurai 1976; Sturrock et al 2001; Torok & Kliem 2005; Fan 2005). MHD simulations of kink-unstable flux ropes have been employed to model coronal loop heating and bright-point emission (Galsgaard & Nordlund 1997; Haynes & Arber 2007), soft X-ray sigmoids (Kliem et al 2004), energy release in compact flares (Gerrard & Hood 2003), microwave sources in eruptive flares (Kliem et al 2010), and rise profiles, rotation, and writhing of erupting filaments and CMEs (Torok & Kliem 2005; Williams et al 2005; Fan 2005; Kliem et al 2012). Twist estimates from the writhe can only be obtained in retrospect, they may facilitate systematic studies of this possibly critical parameter for CME initiation and may be useful for comparison with other means of estimation
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