Twisted Magnetic Flux Rope Research Articles

From kink instability to magnetic reconnection to oscillations in solar flares

We show how some different fundamental plasma processes - the ideal kink instability, magnetic reconnection and magnetohydrodynamic oscillations - can be causally linked. This is shown through reviewing a series of models of energy release in twisted magnetic flux ropes in the solar corona, representing confined solar flares. 3D magnetohydrodynamic simulations demonstrate that fragmented current sheets develop during the nonlinear phase of the ideal kink instability, leading to multiple magnetic reconnections and the release of stored magnetic energy. By coupling these simulations with a test particle code, we can predict the development of populations of non-thermal electrons and ions, as observed in solar flares, and produce synthetic observables for comparison with observations. We also show that magnetic oscillations arise in the reconnecting loop, although there is no oscillatory external driver, and these lead to pulsations in the microwave emission similar to observed flare quasi-periodic pulsations. Oscillations and propagating waves also arise from reconnection when two twisted flux ropes merge, which is modelled utilising 2D magnetohydrodynamic simulations.

Calcium Bright Knots and the Formation of Chromospheric Anemone Jets on the Sun

Space-based observations show that the solar atmosphere from the solar chromosphere to the solar corona is filled with small-scale jets and is linked with small-scale explosions. These jets may be produced by mechanisms similar to those of large-scale flares and such jets may be related to the heating of the corona and chromosphere as well as the acceleration of solar wind. The chromospheric anemone jets on the Sun remain puzzling because their footpoints (or bright knots) have not been well resolved and the formation process of such enigmatic small-scale jets remains unclear. We propose a new model for chromospheric jets using the 3D magnetohydrodynamic simulations, which show that the continuous, upward rising of small-scale twisted magnetic flux ropes in a magnetized solar chromosphere drives small-scale magnetic reconnection and the launching of several small-scale jets during the evolution of the chromospheric anemone jets. Our new, self-consistent, 3D computer modeling of small-scale, but ever-changing flux rope emergence in the magnetized solar atmosphere is fully consistent with observations and provides a universal mechanism for nanoflare and jet formation.

Rapid Rotation of an Erupting Prominence and the Associated Coronal Mass Ejection on 13 May 2013

In this paper, we report the multiwavelength observations of an erupting prominence and the associated coronal mass ejection (CME) on 13 May 2013. The event occurs behind the western limb in the field of view of the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) spacecraft. The prominence is supported by a highly twisted magnetic flux rope and shows rapid rotation in the counterclockwise direction during the rising motion. The rotation of the prominence lasts for ∼ 47 minutes. The average period, angular speed, and linear speed are ∼ 806 sec, ∼ 0.46 rad min−1, and ∼ 355 km s−1, respectively. The total twist angle reaches ∼ 7 $\pi$ , which is considerably larger than the threshold for kink instability. Writhing motion during 17:42 – 17:46 UT is clearly observed by SWAP in 174 Å and Extreme-UltraViolet Imager (EUVI) on board the behind Solar Terrestrial Relations Observatory (STEREO) spacecraft in 304 Å after reaching an apparent height of ∼ 405 Mm. Therefore, the prominence eruption is most probably triggered by kink instability. A pair of conjugate flare ribbons and post-flare loops are created and observed by STA/EUVI. The onset time of writhing motion is consistent with the commencement of the impulsive phase of the related flare. The 3D morphology and positions of the associated CME are derived using the graduated cylindrical shell (GCS) modeling. The kinetic evolution of the reconstructed CME is divided into a slow-rise phase (∼ 330 km s−1) and a fast-rise phase (∼ 1005 km s−1) by the writhing motion. The edge-on angular width of the CME is a constant (60∘), while the face-on angular width increases from 96∘ to 114∘, indicating a lateral expansion. The latitude of the CME source region decreases slightly from ∼ 18∘ to ∼ 13∘, implying an equatorward deflection during propagation.

An Improved Magnetohydrodynamic Simulation of the 2006 December 13 Coronal Mass Ejection of NOAA Active Region 10930

We present a magnetohydrodynamic simulation of the coronal mass ejection on 2006 December 13 in the emerging δ-sunspot NOAA Active Region 10930, improving upon a previous simulation by Fan as follows. (1) Incorporate an ambient solar wind instead of using a static potential magnetic field extrapolation as the initial state. (2) In addition to imposing the emergence of a twisted flux rope, also impose at the lower boundary a random electric field that represents the effect of turbulent convection, which drives field-line braiding and produces resistive and viscous heating in the corona. With the inclusion of this heating, which depends on the magnetic field topology, we are able to model the synthetic soft X-ray images that would be observed by the X-Ray Telescope (XRT) of the Hinode satellite, produced by the simulated coronal magnetic field. We find that the simulated preeruption magnetic field with the buildup of a twisted magnetic flux rope produces synthetic soft X-ray emission that shows qualitatively similar morphology as that observed by the Hinode/XRT for both the ambient coronal loops of the active region and the central inverse S-shaped “sigmoid“ that sharpens just before the onset of the eruption. The synthetic postflare loop brightening also shows similar morphology to that seen in the Hinode/XRT image during the impulsive phase of the eruption. It is found that the kinematics of the erupting flux rope is significantly affected by the open magnetic fields and fast solar wind streams adjacent to the active region.

Prominence fine structures in weakly twisted and highly twisted magnetic flux ropes

Context. Many prominences are supported by magnetic flux ropes. One important question is how we can determine whether the flux rope is weakly twisted or highly twisted. Aims. In this paper, we attempt to decipher whether prominences supported by weakly twisted and highly twisted flux ropes can manifest different features so that we might distinguish the two types of magnetic structures based on their appearance. Methods. We performed pseudo three-dimensional simulations of two magnetic flux ropes with different twists. Results. We find that the resulting two prominences differ in many aspects. The prominence supported by a weakly twisted flux rope is composed mainly of transient threads (∼82.8%), forming high-speed flows inside the prominence, and its horns are evident. Conversely, the prominence supported by a highly twisted flux rope consists mainly of stable quasi-stationary threads (∼60.6%), including longer independently trapped threads and shorter magnetically connected threads. Our simulations also reveal that the prominence spine deviates from the flux rope axis in the vertical direction and from the photospheric polarity inversion line projected on the solar surface, especially for the weakly twisted magnetic flux rope. Conclusions. The two types of prominences differ significantly in appearance. Our results also suggest that a piling-up of short threads in highly twisted flux ropes might account for the vertical-like threads in some prominences.

MHD Simulation of Homologous Eruptions from Solar Active Region 10930 Caused by Sunspot Rotation

The relationship between solar eruption and sunspot rotation has been widely reported, and the underlying mechanism needs to be studied. Here we performed a full 3D MHD simulation using a data-constrained approach to study the mechanism of flare eruptions in active region (AR) NOAA 10930, which is characterized by continuous sunspot rotation and homologous eruptions. We reconstructed the potential magnetic field from the magnetogram of Hinode/SOT as the initial condition and drove the MHD system by applying continuous sunspot rotation at the bottom boundary. The key magnetic structure before the major eruptions and the preformed current sheet were derived, which is responsible for the complex MHD evolution with multiple stages. The major eruptions were triggered directly by fast reconnection in the preformed current sheet above the main polarity inversion line between the two major magnetic polarities of the AR. Furthermore, our simulation shows the homologous eruption successfully. It has reasonable consistency with observations in relative strength, energy release, X-ray and Hα features, and time interval of eruptions. In addition, the rotation angle of the sunspot before the first eruption in the simulation is also close to the observed value. Our simulation offers a scenario different from many previous studies based on ideal instabilities of a twisted magnetic flux rope and shows the importance of sunspot rotation and magnetic reconnection in efficiently producing homologous eruptions by continuous energy injection and impulsive energy release in a recurrent way.

Avalanches of magnetic flux rope in the state of self-organized criticality

ABSTRACT The self-organized criticality (SOC) is a universal theory to explain the ubiquitous power-law size distributions of astrophysical instabilities such as solar eruptions. One way to understand the dynamical processes of an SOC system is through cellular automaton (CA) simulations. Here, we develop a three-dimensional solar CA model that assumes a twisted magnetic flux rope (MFR), in which the avalanche takes place when a local magnetic vector potential exceeds a Gaussian distributed instability criterion, triggered by a global and space-dependent energy driving mechanism. To avoid non-physical released energies, an energy screening mechanism is applied to calculate the avalanche energies of each time-step. Our results show that the statistics of the CA simulated flaring events are comparable to the frequency distributions of observed solar flares originating from an individual active region. Due to the fact of the universality of MFRs, the CA model can be applied to many other astrophysical SOC systems.

Fast plasmoid-mediated reconnection in a solar flare

Magnetic reconnection is a multi-faceted process of energy conversion in astrophysical, space and laboratory plasmas that operates at microscopic scales but has macroscopic drivers and consequences. Solar flares present a key laboratory for its study, leaving imprints of the microscopic physics in radiation spectra and allowing the macroscopic evolution to be imaged, yet a full observational characterization remains elusive. Here we combine high resolution imaging and spectral observations of a confined solar flare at multiple wavelengths with data-constrained magnetohydrodynamic modeling to study the dynamics of the flare plasma from the current sheet to the plasmoid scale. The analysis suggests that the flare resulted from the interaction of a twisted magnetic flux rope surrounding a filament with nearby magnetic loops whose feet are anchored in chromospheric fibrils. Bright cusp-shaped structures represent the region around a reconnecting separator or quasi-separator (hyperbolic flux tube). The fast reconnection, which is relevant for other astrophysical environments, revealed plasmoids in the current sheet and separatrices and associated unresolved turbulent motions.

Multifluid MHD Studies of the Ionospheric Magnetic Flux Ropes at Mars

Abstract We use a multifluid MHD model to study the formation of the small-scale magnetic flux rope (MFR) in the ionosphere of Mars. It is found that a straight flux tube can turn into a twisted MFR during its sinking into the lower ionosphere, caused by the differential compression at different parts of the tube. Further studies show that the MFR is not a force-free structure, in which there is always a pressure gradient force to balance the magnetic force. Moreover, we find that the ionospheric ions inside the MFR can be squeezed out from the two ends of the MFR, with an outflow flux of about 3.5 × 107 cm−2 s−1, which can play an important role for the ion escape from Mars. In addition, we find that both the sinking speed and the ratio of the ion gyroradius to the tube radius can affect the characteristics of MFR. An MFR can be more quickly formed for a larger sinking speed, but it can be also more quickly filled by the ambient ions. Oppositely, the MFR is more difficult to be filled when the ratio of the ion gyroradius to the tube radius is smaller. Once the MFR is filled, the compression is prevented by an outward pressure gradient force, and both the field strength and the rope helicity begin to decrease. Our results can explain the different altitude dependences of MFRs observed at Mars and Venus.

Multiwavelength Observations of the Formation and Eruption of a Complex Filament

Abstract We present an analysis of the formation and eruption of a filament and fast coronal mass ejection associated with a flare that occurred in active region 11429 using observations in the ultraviolet, extreme ultraviolet, X-ray, and radio wavelength bands. Precursor activity began as an interaction between two filaments, F1 and F2, that are identified as having twisted magnetic flux ropes (MFRs). Transient brightenings in all wavelengths are observed as a result of this interaction, likely the result of magnetic reconnection between the two filaments. This interaction results in a reconfiguration of the two filaments into a long overlying filament and a shorter low-lying filament. The upper filament subsequently undergoes a partial confined eruption. Plasma flows originating near the east footpoint of F1 lead to an extension of the upper filament into the filament channel to the west, resulting in a new active region filament (ARF). This new filament begins a slow rise and expansion. During its slowly rising phase, the MFR in which the filament is embedded becomes visible, with both the filament and flux rope rising and expanding simultaneously. The twist of the magnetic rope is determined as four turns. The erupting configuration changes from a twisted arch shape to a reversed γ shape within ∼75 s at the beginning of the fast-rise phase, representing a transformation from twist to writhe. The observations provide a clear example of filament formation via the tether-cutting reconnection of two nearby filaments. A helical kink instability may be the trigger of the ARF eruption.

Intrusion of Magnetic Peninsula toward the Neighboring Opposite-polarity Region That Triggers the Largest Solar Flare in Solar Cycle 24

Abstract The largest X9.3 solar flare in solar cycle 24 and the preceding X2.2 flare occurred on 2017 September 6, in the solar active region NOAA 12673. This study aims to understand the onset mechanism of these flares via analysis of multiple observational data sets from the Hinode and Solar Dynamics Observatory and results from a nonlinear force-free field extrapolation. The most noticeable feature is the intrusion of a major negative-polarity region, appearing similar to a peninsula, oriented northwest into a neighboring opposite-polarity region. We also observe proxies of magnetic reconnection related to the intrusion of the negative peninsula: rapid changes of the magnetic field around the intruding negative peninsula; precursor brightening at the tip of the negative peninsula, including a cusp-shaped brightening that shows a transient but significant downflow (∼100 km s−1) at a leg of the cusp; a dark tube-like structure that appears to be a magnetic flux rope that erupted with the X9.3 flare; and coronal brightening along the dark tube-like structure that appears to represent the electric current generated under the flux rope. Based on these observational features, we propose that (1) the intrusion of the negative peninsula was critical in promoting the push-mode magnetic reconnection that forms and grows a twisted magnetic flux rope that erupted with the X2.2 flare, and (2) the continuing intrusion progressing even beyond the X2.2 flare is further promoted to disrupt the equilibrium that leads the reinforcement of the magnetic flux rope that erupted with the X9.3 flare.

Reconstruction of a Highly Twisted Magnetic Flux Rope for an Inter-active-region X-Class Solar Flare

Solar eruptions are manifestation of explosive release of magnetic energy in the Sun's corona. Large solar eruptions originate mostly within active regions, where strong magnetic fields concentrate on the solar surface. Here we studied the magnetic field structure for an exception, which is a peculiar GOES X1.2 flare accompanied with a very fast coronal mass ejection taking place between two active regions, where the magnetic field is relatively weak. The pre-flare magnetic field is reconstructed from the SDO/HMI vector magnetogram, using a nonlinear force-free field extrapolation method. It is found that prior to the flare, there is a highly twisted magnetic flux rope with magnetic field lines winding over 6 turns, which connects the border of a leading sunspot of one active region and the following polarity of the neighboring active region. The flux rope's configuration is highly consistent with the observed sigmoidal coronal loops and filament channels by SDO/AIA. It resides rather low-lying between the active regions such that the torus instability is not able to be triggered. Thus, it is most likely that, due to the strong magnetic twist, the kink instability of the flux rope triggers the eruption.

How Many Twists Do Solar Coronal Jets Release?

Highly twisted magnetic flux ropes, with finite length, are subject to kink instabilities, and could lead to a number of eruptive phenomena in the solar atmosphere, including flares, coronal mass ejections (CMEs) and coronal jets. The kink instability threshold, which is the maximum twist a kink-stable magnetic flux rope could contain, has been widely studied in analytical models and numerical simulations, but still needs to be examined by observations. In this article, we will study twists released by 30 off-limb rotational solar coronal jets, and compare the observational findings with theoretical kink instability thresholds. We have found that: 1) the number of events with more twist release becomes less; 2) each of the studied jets has released a twist number of at least 1.3 turns (a twist angle of 2.6$\pi$); and 3) the size of a jet is highly related to its twist pitch instead of twist number. Our results suggest that the kink instability threshold in the solar atmosphere should not be a constant. The found lower limit of twist number of 1.3 turns should be merely a necessary but not a sufficient condition for a finite solar magnetic flux rope to become kink unstable.

Flare Energy Release at the Magnetic Field Polarity Inversion Line during the M1.2 Solar Flare of 2015 March 15. I. Onset of Plasma Heating and Electron Acceleration

We present the study of SOL2015-03-15 M1.2 flare, revealing acceleration of electrons and plasma heating in the sheared twisted magnetic structure in the polarity inversion line (PIL). The scope is to make the analysis of nonthermal electrons dynamics and plasma heating in the highly stressed magnetic loops interacting in the PIL by using X-ray, microwave, ultraviolet, and optical observations. It is found that the most probable scenario for the energy release in the PIL is the tether-cutting magnetic reconnection between the low-lying (3 Mm above the photosphere) magnetic loops within a twisted magnetic flux rope. Energetic electrons with the hardest spectrum were appeared at the onset of plasma heating up to the super-hot temperature of 40 MK. These electrons are localized in a thin magnetic channel with width of around 0.5 Mm with high average magnetic field of about 1200 G. The plasma beta in the super-hot region is less than 0.01. The estimated density of accelerated electrons is about 10^9 cm^-3 that is much less than the super-hot plasma density. The energy density flux of non-thermal electrons is estimated up to 3x10^12 ergs cm^-2s^-1 that is much higher than in the currently available radiative hydrodynamic models. These results revealed that one need to develop new self-consisting flare models reproducing 3D magnetic reconnection in the PIL with strong magnetic field, spatial filamentation of energy release, formation of high energy density populations of nonthermal electrons and appearance of the super-hot plasma.

Parametric study on kink instabilities of twisted magnetic flux ropes in the solar atmosphere

Aims. Twisted magnetic flux ropes (MFRs) in the solar atmosphere have been researched extensively because of their close connection to many solar eruptive phenomena, such as flares, filaments, and coronal mass ejections (CMEs). In this work, we performed a set of 3D isothermal magnetohydrodynamic (MHD) numerical simulations, which use analytical twisted MFR models and study dynamical processes parametrically inside and around current-carrying twisted loops. We aim to generalize earlier findings by applying finite plasma β conditions. Methods. Inside the MFR, approximate internal equilibrium is obtained by pressure from gas and toroidal magnetic fields to maintain balance with the poloidal magnetic field. We selected parameter values to isolate best either internal or external kink instability before studying complex evolutions with mixed characteristics. We studied kink instabilities and magnetic reconnection in MFRs with low and high twists. Results. The curvature of MFRs is responsible for a tire tube force due to its internal plasma pressure, which tends to expand the MFR. The curvature effect of toroidal field inside the MFR leads to a downward movement toward the photosphere. We obtain an approximate internal equilibrium using the opposing characteristics of these two forces. A typical external kink instability totally dominates the evolution of MFR with infinite twist turns. Because of line-tied conditions and the curvature, the central MFR region loses its external equilibrium and erupts outward. We emphasize the possible role of two different kink instabilities during the MFR evolution: internal and external kink. The external kink is due to the violation of the Kruskal-Shafranov condition, while the internal kink requires a safety factor q = 1 surface inside the MFR. We show that in mixed scenarios, where both instabilities compete, complex evolutions occur owing to reconnections around and within the MFR. The S-shaped structures in current distributions appear naturally without invoking flux emergence. Magnetic reconfigurations common to eruptive MFRs and flare loop systems are found in our simulations.

Buildup of a highly twisted magnetic flux rope during a solar eruption

The magnetic flux rope is among the most fundamental magnetic configurations in plasma. Although its presence after solar eruptions has been verified by spacecraft measurements near Earth, its formation on the Sun remains elusive, yet is critical to understanding a broad spectrum of phenomena. Here we study the dynamic formation of a magnetic flux rope during a classic two-ribbon flare. Its feet are identified unambiguously with conjugate coronal dimmings completely enclosed by irregular bright rings, which originate and expand outward from the far ends of flare ribbons. The expansion is associated with the rapid ribbon separation during the flare main phase. Counting magnetic flux through the feet and the ribbon-swept area reveals that the rope’s core is more twisted than its average of four turns. It propagates to the Earth as a typical magnetic cloud possessing a similar twist profile obtained by the Grad-Shafranov reconstruction of its three dimensional structure.

Magnetic reconnection during eruptive magnetic flux ropes

Aims. We perform a three-dimensional (3D) high resolution numerical simulation in isothermal magnetohydrodynamics to study the magnetic reconnection process in a current sheet (CS) formed during an eruption of a twisted magnetic flux rope (MFR). Because the twist distribution violates the Kruskal-Shafranov condition, the kink instability occurs, and the MFR is distorted. The centre part of the MFR loses its equilibrium and erupts upward, which leads to the formation of a 3D CS underneath it.Methods. In order to study the magnetic reconnection inside the CS in detail, mesh refinement has been used to reduce the numerical diffusion and we estimate a Lundquist number S = 104 in the vicinity of the CS.Results. The refined mesh allows us to resolve fine structures inside the 3D CS: a bifurcating sheet structure signaling the 3D generalization of Petschek slow shocks, some distorted-cylindrical substructures due to the tearing mode instabilities, and two turbulence regions near the upper and the lower tips of the CS. The topological characteristics of the MFR depend sensitively on the observer’s viewing angle: it presents as a sigmoid structure, an outwardly expanding MFR with helical distortion, or a flare-CS-coronal mass ejection symbiosis as in 2D flux-rope models when observed from the top, the front, or the side.

The global distribution of magnetic helicity in the solar corona (Corrigendum)

By defining an appropriate field line helicity, we apply the powerful concept of magnetic helicity to the problem of global magnetic field evolution in the Sun's corona. As an ideal-magnetohydrodynamic invariant, the field line helicity is a meaningful measure of how magnetic helicity is distributed within the coronal volume. It may be interpreted, for each magnetic field line, as a magnetic flux linking with that field line. Using magneto-frictional simulations, we investigate how field line helicity evolves in the non-potential corona as a result of shearing by large-scale motions on the solar surface. On open magnetic field lines, the helicity injected by the Sun is largely output to the solar wind, provided that the coronal relaxation is sufficiently fast. But on closed magnetic field lines, helicity is able to build up. We find that the field line helicity is non-uniformly distributed, and is highly concentrated in twisted magnetic flux ropes. Eruption of these flux ropes is shown to lead to sudden bursts of helicity output, in contrast to the steady flux along the open magnetic field lines.

The global distribution of magnetic helicity in the solar corona

By defining an appropriate field line helicity, we apply the powerful concept of magnetic helicity to the problem of global magnetic field evolution in the Sun’s corona. As an ideal-magnetohydrodynamic invariant, the field line helicity is a meaningful measure of how magnetic helicity is distributed within the coronal volume. It may be interpreted, for each magnetic field line, as a magnetic flux linking with that field line. Using magneto-frictional simulations, we investigate how field line helicity evolves in the non-potential corona as a result of shearing by large-scale motions on the solar surface. On open magnetic field lines, the helicity injected by the Sun is largely output to the solar wind, provided that the coronal relaxation is sufficiently fast. But on closed magnetic field lines, helicity is able to build up. We find that the field line helicity is non-uniformly distributed, and is highly concentrated in twisted magnetic flux ropes. Eruption of these flux ropes is shown to lead to sudden bursts of helicity output, in contrast to the steady flux along the open magnetic field lines.

Twisted versus braided magnetic flux ropes in coronal geometry

Aims. Sigmoidal structures in the solar corona are commonly associated with magnetic flux ropes whose magnetic field lines are twisted about a mutual axis. Their dynamical evolution is well studied, with sufficient twisting leading to large-scale rotation (writhing) and vertical expansion, possibly leading to ejection. Here, we investigate the behaviour of flux ropes whose field lines have more complex entangled/braided configurations. Our hypothesis is that this internal structure will inhibit the large-scale morphological changes. Additionally, we investigate the influence of the background field within which the rope is embedded. Methods. A technique for generating tubular magnetic fields with arbitrary axial geometry and internal structure, introduced in part I of this study, provides the initial conditions for resistive-MHD simulations. The tubular fields are embedded in a linear force-free background, and we consider various internal structures for the tubular field, including both twisted and braided. These embedded flux ropes are then evolved using a 3D MHD code. Results. Firstly, in a background where twisted flux ropes evolve through the expected non-linear writhing and vertical expansion, we find that flux ropes with sufficiently braided/entangled interiors show no such large-scale changes. Secondly, embedding a twisted flux rope in a background field with a sigmoidal inversion line leads to eventual reversal of the large-scale rotation. Thirdly, in some cases a braided flux rope splits due to reconnection into two twisted flux ropes of opposing chirality – a phenomenon previously observed in cylindrical configurations. Conclusions. Sufficiently complex entanglement of the magnetic field lines within a flux rope can suppress large-scale morphological changes of its axis, with magnetic energy reduced instead through reconnection and expansion. The structure of the background magnetic field can significantly affect the changing morphology of a flux rope.