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Register a new userSlow Rise and Partial Eruption of a Double-Decker Filament. II. Modeling by a Double Flux Rope Equilibrium
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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 (1999) 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 being 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 (Liu et al. 2012). 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.
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Solar filaments often erupt partially. Although how they split remains elusive, the splitting process has the potential of revealing the filament structure and eruption mechanism. Here we investigate the pre-eruption splitting of an apparently single filament and its subsequent partial eruption on 2012 September 27. The evolution is characterized by three stages with distinct dynamics. During the quasi-static stage, the splitting proceeds gradually for about 1.5 hrs, with the upper branch rising at a few kilometers per second and displaying swirling motions about its axis. During the precursor stage that lasts for about 10 min, the upper branch rises at tens of kilometers per second, with a pair of conjugated dimming regions starting to develop at its footpoints; with the swirling motions turning chaotic, the axis of the upper branch whips southward, which drives an arc-shaped EUV front propagating in the similar direction. During the eruption stage, the upper branch erupts with the onset of a C3.7-class two-ribbon flare, while the lower branch remains stable. Judging from the well separated footpoints of the upper branch from those of the lower one, we suggest that the pre-eruption filament processes a double-decker structure composed of two distinct flux bundles, whose formation is associated with gradual magnetic flux cancellations and converging photospheric flows around the polarity inversion line.
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 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 two hours before the eruption, indications for 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.
We present a multiwavelength analysis of two homologous, short lived, impulsive flares of GOES class M1.4 and M7.3, that occurred from a very localized mini-sigmoid region within the active region NOAA 12673 on 2017 September 7. Both flares were associated with initial jet-like plasma ejection which for a brief amount of time moved toward east in a collimated manner before drastically changing direction toward southwest. Non-linear force-free field extrapolation reveals the presence of a compact double-decker flux rope configuration in the mini-sigmoid region prior to the flares. A set of open field lines originating near the active region which were most likely responsible for the anomalous dynamics of the erupted plasma, gave the earliest indication of an emerging coronal hole near the active region. The horizontal field distribution suggests a rapid decay of the field above the active region, implying high proneness of the flux rope system toward eruption. In view of the low coronal double-decker flux ropes and compact extreme ultra-violet (EUV) brightening beneath the filament along with associated photospheric magnetic field changes, our analysis supports the combination of initial tether-cutting reconnection and subsequent torus instability for driving the eruption.
We study an evolving bipolar active region that exhibits flux cancellation at the internal polarity inversion line, the formation of a soft X-ray sigmoid along the inversion line and a coronal mass ejection. The evolution of the photospheric magnetic field is described and used to estimate how much flux is reconnected into the flux rope. About one third of the active region flux cancels at the internal polarity inversion line in the 2.5~days leading up to the eruption. In this period, the coronal structure evolves from a weakly to a highly sheared arcade and then to a sigmoid that crosses the inversion line in the inverse direction. These properties suggest that a flux rope has formed prior to the eruption. The amount of cancellation implies that up to 60% of the active region flux could be in the body of the flux rope. We point out that only part of the cancellation contributes to the flux in the rope if the arcade is only weakly sheared, as in the first part of the evolution. This reduces the estimated flux in the rope to $sim!30%$ or less of the active region flux. We suggest that the remaining discrepancy between our estimate and the limiting value of $sim!10%$ of the active region flux, obtained previously by the flux rope insertion method, results from the incomplete coherence of the flux rope, due to nonuniform cancellation along the polarity inversion line. A hot linear feature is observed in the active region which rises as part of the eruption and then likely traces out field lines close to the axis of the flux rope. The flux cancellation and changing magnetic connections at one end of this feature suggest that the flux rope reaches coherence by reconnection shortly before and early in the impulsive phase of the associated flare. The sigmoid is destroyed in the eruption but reforms within a few hours after a moderate amount of further cancellation has occurred.
We present a detailed analysis of a confined filament eruption and jet associated with a C1.5 class solar flare. Multi-wavelength observations from GONG and SDO reveal the filament forming over several days following the emergence and then partial cancellation of a minority polarity spot within a decaying bipolar active region. The emergence is also associated with the formation of a 3D null point separatrix that surrounds the minority polarity. The filament eruption occurs concurrent with brightenings adjacent to and below the filament, suggestive of breakout and flare reconnection, respectively. The erupting filament material becomes partially transferred into a strong outflow jet (~ 60 km/s) along coronal loops, becoming guided back towards the surface. Utilising high resolution H$alpha$ observations from SST/CRISP, we construct velocity maps of the outflows demonstrating their highly structured but broadly helical nature. We contrast the observations with a 3D MHD simulation of a breakout jet in a closed-field background and find close qualitative agreement. We conclude that the suggested model provides an intuitive mechanism for transferring twist/helicity in confined filament eruptions, thus validating the applicability of the breakout model not only to jets and coronal mass ejections but also to confined eruptions and flares.
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