Structure, Stability, and Evolution of Magnetic Flux Ropes From the Perspective of Magnetic Twist

Abstract

We investigate the evolution of NOAA Active Region 11817 during 2013 August 10-12, when it developed a complex field configuration and produced four confined, followed by two eruptive, flares. These C-and-above flares are all associated with a magnetic flux rope (MFR) located along the major polarity inversion line, where shearing and converging photospheric flows are present. Aided by the nonlinear force-free field modeling, we identify the MFR through mapping magnetic connectivities and computing the twist number T w for each individual field line. The MFR is moderately twisted (|T w | < 2) and has a well-defined boundary of high squashing factor Q. We found that the field line with the extremum |T w | is a reliable proxy of the rope axis, and that the MFR's peak |T w | temporarily increases within half an hour before each flare while it decreases after the flare peak for both confined and eruptive flares. This pre-flare increase 9 Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany -2 -in |T w | has little effect on the active region's free magnetic energy or any other parameters derived for the whole region, due to its moderate amount and the MFR's relatively small volume, while its decrease after flares is clearly associated with the stepwise decrease in the whole region's free magnetic energy due to the flare. We suggest that T w may serve as a useful parameter in forewarning the onset of eruption, and therefore, the consequent space weather effects. The helical kink instability is identified as the prime candidate onset mechanism for the considered flares.

High-resolution observations of flare precursors in the low solar atmosphere

“…A "weighted optimization" method 47,48 is then applied to derive the NLFFF, from which magnetic field lines are computed. Physical properties of field lines, such as the magnetic twist, can be further deduced 49 .…”

The Causes of Quasi-homologous CMEs

“…A magnetic flux rope, characterized by magnetic fields twisted about a common axis, may become unstable and act as a driver for an eruption (e.g., Amari et al 1999;Török & Kliem 2005).Aflux rope can be identified using a combination of topological measures deduced from the employed NLFF models, e.g., in the form of the twist number T w and the squashing factor Q (Liu et al 2016b). T w gives the number of turns by which two infinitely approaching field lines, i.e., two neighboring field lines whose separation could be arbitrarily small, wind around each other, and it is computed by where α is the force-free parameter, dl is the length increment along a magnetic field line, and L is the length of the field line (Berger & Prior 2006;Liu et al 2016b).…”

Flux Rope Formation Due to Shearing and Zipper Reconnection

“…However, we would also emphasise that a direct comparison between values of t w and the twist given by the angle of footpoint rotation relative to axis footpoints, even in relatively simple cases, can be complex and potentially misleading (as shown in Appendix A, and discussed further in e.g. Liu et al (2016)). …”

“…This is the definition used by Hood and Priest (1979) when analysing the kink instability. The link between this definition of twist and the integral expression t w (which is the value of the force-free parameter, α, times the length of the field line) is often unclear (see the detailed theoretical comparison in Appendix C of Liu et al, 2016, and the discussion therein). We practically demonstrate how these two quantities are linked in the simple case of a straight cylindrical, force-free loop, which allows the two expressions to be evaluated analytically and directly compared.…”