TY - JOUR A1 - Kliem, Bernhard A1 - Lin, J. A1 - Forbes, T. G. A1 - Priest, E. R. A1 - Toeroek, T. T1 - Catastrophe versus instability for the eruption of a toroadal solar magnetic flux JF - The astrophysical journal : an international review of spectroscopy and astronomical physics N2 - The onset of a solar eruption is formulated here as either a magnetic catastrophe or as an instability. Both start with the same equation of force balance governing the underlying equilibria. Using a toroidal flux rope in an external bipolar or quadrupolar field as a model for the current-carrying flux, we demonstrate the occurrence of a fold catastrophe by loss of equilibrium for several representative evolutionary sequences in the stable domain of parameter space. We verify that this catastrophe and the torus instability occur at the same point; they are thus equivalent descriptions for the onset condition of solar eruptions. KW - magnetohydrodynamics (MHD) KW - Sun: corona KW - Sun: coronal mass ejections (CMEs) KW - Sun: filaments, prominences KW - Sun: flares KW - Sun: magnetic fields Y1 - 2014 U6 - https://doi.org/10.1088/0004-637X/789/1/46 SN - 0004-637X SN - 1538-4357 VL - 789 IS - 1 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Cheng, X. A1 - Ding, M. D. A1 - Zhang, J. A1 - Sun, X. D. A1 - Guo, Y. A1 - Wang, Yi-Ming A1 - Kliem, Bernhard A1 - Deng, Y. Y. T1 - Formation of a double-decker magnetic flux rope in the sigmoidal solar active region 11520 JF - The astrophysical journal : an international review of spectroscopy and astronomical physics N2 - In this paper, we address the formation of a magnetic flux rope (MFR) that erupted on 2012 July 12 and caused a strong geomagnetic storm event on July 15. Through analyzing the long-term evolution of the associated active region observed by the Atmospheric Imaging Assembly and the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, it is found that the twisted field of an MFR, indicated by a continuous S-shaped sigmoid, is built up from two groups of sheared arcades near the main polarity inversion line a half day before the eruption. The temperature within the twisted field and sheared arcades is higher than that of the ambient volume, suggesting that magnetic reconnection most likely works there. The driver behind the reconnection is attributed to shearing and converging motions at magnetic footpoints with velocities in the range of 0.1-0.6 km s(-1). The rotation of the preceding sunspot also contributes to the MFR buildup. Extrapolated three-dimensional non-linear force-free field structures further reveal the locations of the reconnection to be in a bald-patch region and in a hyperbolic flux tube. About 2 hr before the eruption, indications of a second MFR in the form of an S-shaped hot channel are seen. It lies above the original MFR that continuously exists and includes a filament. The whole structure thus makes up a stable double-decker MFR system for hours prior to the eruption. Eventually, after entering the domain of instability, the high-lying MFR impulsively erupts to generate a fast coronal mass ejection and X-class flare; while the low-lying MFR remains behind and continuously maintains the sigmoidicity of the active region. KW - Sun: corona KW - Sun: coronal mass ejections (CMEs) KW - Sun: filaments, prominences KW - Sun: magnetic fields Y1 - 2014 U6 - https://doi.org/10.1088/0004-637X/789/2/93 SN - 0004-637X SN - 1538-4357 VL - 789 IS - 2 PB - IOP Publ. Ltd. CY - Bristol ER - 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 -