TY - JOUR A1 - Kliem, Bernhard A1 - Toeroek, Tibor A1 - Titov, Viacheslav S. A1 - Lionello, Roberto A1 - Linker, Jon A. A1 - Liu, Rui A1 - Liu, Chang A1 - Wang, Haimin T1 - Slow rise and partial eruption of a double-decker filament. II. A double flux rope model JF - The astrophysical journal : an international review of spectroscopy and astronomical physics N2 - Force-free equilibria containing two vertically arranged magnetic flux ropes of like chirality and current direction are considered as a model for split filaments/prominences and filament-sigmoid systems. Such equilibria are constructed analytically through an extension of the methods developed in Titov & Demoulin and numerically through an evolutionary sequence including shear flows, flux emergence, and flux cancellation in the photospheric boundary. It is demonstrated that the analytical equilibria are stable if an external toroidal (shear) field component exceeding a threshold value is included. If this component decreases sufficiently, then both flux ropes turn unstable for conditions typical of solar active regions, with the lower rope typically becoming unstable first. Either both flux ropes erupt upward, or only the upper rope erupts while the lower rope reconnects with the ambient flux low in the corona and is destroyed. However, for shear field strengths staying somewhat above the threshold value, the configuration also admits evolutions which lead to partial eruptions with only the upper flux rope becoming unstable and the lower one remaining in place. This can be triggered by a transfer of flux and current from the lower to the upper rope, as suggested by the observations of a split filament in Paper I. It can also result from tether-cutting reconnection with the ambient flux at the X-type structure between the flux ropes, which similarly influences their stability properties in opposite ways. This is demonstrated for the numerically constructed equilibrium. KW - instabilities KW - magnetohydrodynamics (MHD) KW - Sun: coronal mass ejections (CMEs) KW - Sun: filaments, prominences KW - Sun: flares Y1 - 2014 U6 - https://doi.org/10.1088/0004-637X/792/2/107 SN - 0004-637X SN - 1538-4357 VL - 792 IS - 2 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Liu, Rui A1 - Kliem, Bernhard A1 - Toeroek, Tibor A1 - Liu, Chang A1 - Titov, Viacheslav S. A1 - Lionello, Roberto A1 - Linker, Jon A. A1 - Wang, Haimin T1 - Slow rise and partial eruption of a double-decker filament. I. observations and interpretation JF - The astrophysical journal : an international review of spectroscopy and astronomical physics N2 - We study an active-region dextral filament that was composed of two branches separated in height by about 13 Mm, as inferred from three-dimensional reconstruction by combining SDO and STEREO-B observations. This "double-decker" configuration sustained for days before the upper branch erupted with a GOES-class M1.0 flare on 2010 August 7. Analyzing this evolution, we obtain the following main results. (1) During the hours before the eruption, filament threads within the lower branch were observed to intermittently brighten up, lift upward, and then merge with the upper branch. The merging process contributed magnetic flux and current to the upper branch, resulting in its quasi-static ascent. (2) This transfer might serve as the key mechanism for the upper branch to lose equilibrium by reaching the limiting flux that can be stably held down by the overlying field or by reaching the threshold of the torus instability. (3) The erupting branch first straightened from a reverse S shape that followed the polarity inversion line and then writhed into a forward S shape. This shows a transfer of left-handed helicity in a sequence of writhe-twist-writhe. The fact that the initial writhe is converted into the twist of the flux rope excludes the helical kink instability as the trigger process of the eruption, but supports the occurrence of the instability in the main phase, which is indeed indicated by the very strong writhing motion. (4) A hard X-ray sigmoid, likely of coronal origin, formed in the gap between the two original filament branches in the impulsive phase of the associated flare. This supports a model of transient sigmoids forming in the vertical flare current sheet. (5) Left-handed magnetic helicity is inferred for both branches of the dextral filament. (6) Two types of force-free magnetic configurations are compatible with the data, a double flux rope equilibrium and a single flux rope situated above a loop arcade. KW - Sun: coronal mass ejections (CMEs) KW - Sun: filaments, prominences KW - Sun: flares Y1 - 2012 U6 - https://doi.org/10.1088/0004-637X/756/1/59 SN - 0004-637X VL - 756 IS - 1 PB - IOP Publ. Ltd. CY - Bristol ER -