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 - Toeroek, T. A1 - Leake, J. E. A1 - Titov, Viacheslav S. A1 - Archontis, V. A1 - Mikic, Z. A1 - Linton, M. G. A1 - Dalmasse, K. A1 - Aulanier, Guillaume A1 - Kliem, Bernhard T1 - Distribution of electric currents in solar active regions JF - The astrophysical journal : an international review of spectroscopy and astronomical physics ; Part 2, Letters KW - magnetohydrodynamics (MHD) KW - Sun: corona KW - Sun: coronal mass ejections (CMEs) Y1 - 2014 U6 - https://doi.org/10.1088/2041-8205/782/1/L10 SN - 2041-8205 SN - 2041-8213 VL - 782 IS - 1 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 - TY - JOUR A1 - Liu, Rui A1 - Kliem, Bernhard A1 - Titov, Viacheslav S. A1 - Chen, Jun A1 - Wang, Yuming A1 - Wang, Haimin A1 - Liu, Chang A1 - Xu, Yan A1 - Wiegelmann, Thomas T1 - STRUCTURE, STABILITY, AND EVOLUTION OF MAGNETIC FLUX ROPES FROM THE PERSPECTIVE OF MAGNETIC TWIST JF - The astrophysical journal : an international review of spectroscopy and astronomical physics N2 - We investigate the evolution of NOAA Active Region (AR) 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 ${{ \mathcal T }}_{w}$ for each individual field line. The MFR is moderately twisted ($| {{ \mathcal T }}_{w}| \lt 2$) and has a well-defined boundary of high squashing factor Q. We found that the field line with the extremum $| {{ \mathcal T }}_{w}| $ is a reliable proxy of the rope axis, and that the MFR's peak $| {{ \mathcal 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 in $| {{ \mathcal T }}_{w}| $ has little effect on the AR'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 ${{ \mathcal T }}_{w}$ 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. KW - coronal mass ejections (CMEs) KW - Sun: corona KW - Sun: filaments, pominences KW - Sun: flares KW - Sun: magnetic fields Y1 - 2016 U6 - https://doi.org/10.3847/0004-637X/818/2/148 SN - 0004-637X SN - 1538-4357 VL - 818 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Valori, Gherardo A1 - Kliem, Bernhard A1 - Török, Tibor A1 - Titov, Viacheslav S. T1 - Testing magnetofrictional extrapolation with the Titov-Demoulin model of solar active regions N2 - We examine the nonlinear magnetofrictional extrapolation scheme using the solar active region model by Titov and Demoulin as test field. This model consists of an arched, line-tied current channel held in force-free equilibrium by the potential field of a bipolar flux distribution in the bottom boundary. A modified version with a parabolic current density profile is employed here. We find that the equilibrium is reconstructed with very high accuracy in a representative range of parameter space, using only the vector field in the bottom boundary as input. Structural features formed in the interface between the flux rope and the surrounding arcade - "hyperbolic flux tube" and "bald patch separatrix surface" - are reliably reproduced, as are the flux rope twist and the energy and helicity of the configuration. This demonstrates that force-free fields containing these basic structural elements of solar active regions can be obtained by extrapolation. The influence of the chosen initial condition on the accuracy of reconstruction is also addressed, confirming that the initial field that best matches the external potential field of the model quite naturally leads to the best reconstruction. Extrapolating the magnetogram of a Titov-Demoulin equilibrium in the unstable range of parameter space yields a sequence of two opposing evolutionary phases, which clearly indicate the unstable nature of the configuration: a partial buildup of the flux rope with rising free energy is followed by destruction of the rope, losing most of the free energy. Y1 - 2010 UR - http://www.aanda.org/ U6 - https://doi.org/10.1051/0004-6361/201014416 SN - 0004-6361 ER -