Quantification of the Writhe Number Evolution of Solar Filament Axes

Solar filament eruptions often show complex and dramatic geometric deformation that is highly relevant to the underlying physical mechanism triggering the eruptions. It has been well known that the writhe of filament axes is a key parameter characterizing its global geometric deformation, but a quantitative investigation of the development of writhe during its eruption is still lacking. Here we introduce the Writhe Application Toolkit (WAT) which can be used to characterize accurately the topology of filament axes. This characterization is achieved based on the reconstruction and writhe number computation of three-dimensional paths of the filament axes from dual-perspective observations. We apply this toolkit to four dextral filaments located in the northern hemisphere with a counterclockwise (CCW) rotation during their eruptions. Initially, all these filaments possess a small writhe number (=<0.20) indicating a weak helical deformation of the axes. As the CCW rotation kicks in, their writhe numbers begin to decrease and reach large negative values. Combined with the extended C\u{a}lug\u{a}reanu theorem, the absolute value of twist is deduced to decrease during the rotation. Such a quantitative analysis strongly indicates a consequence of the conversion of twist into writhe for the studied events.