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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 similar to 6 pi for the majority of filaments prior to their eruption.
Arch filament systems occur in active sunspot groups, where a fibril structure connects areas of opposite magnetic polarity, in contrast to active region filaments that follow the polarity inversion line. We used the GREGOR Infrared Spectrograph (GRIS) to obtain the full Stokes vector in the spectral lines SiI lambda 1082.7 nm, He I lambda 1083.0 nm, and Ca I lambda 1083.9 nm. We focus on the near-infrared calcium line to investigate the photospheric magnetic field and velocities, and use the line core intensities and velocities of the helium line to study the chromospheric plasma. The individual fibrils of the arch filament system connect the sunspot with patches of magnetic polarity opposite to that of the spot. These patches do not necessarily coincide with pores, where the magnetic field is strongest. Instead, areas are preferred not far from the polarity inversion line. These areas exhibit photospheric downflows of moderate velocity, but significantly higher downflows of up to 30 km s(-1) in the chromospheric helium line. Our findings can be explained with new emerging flux where the matter flows downward along the field lines of rising flux tubes, in agreement with earlier results. (C) 2016 WILEY-VCH Verlag GmbH& Co. KGaA, Weinheim