Coronal Magnetic Flux Rope Equilibria and Magnetic Helicity

1 INTRODUCTIONObservations show that the magnetic helicity of solar magnetic structures has a predominantsign in each hemisphere of the Sun, positive in the southern hemisphere and negative in thenorthern, regardless of the solar cycle (Rust, 1994). The magnetic helicity is strictly conservedin the frame of ideal MHD (WOltjer, 1958), and approximately conserved in the presence ofresistive dissipation and magnetic reconnection in a highly conductive plajsma (Taylor, 1974;Berger, 1984; H…     

Flux-Rope Twist in Eruptive Flares and CMEs: Due to Zipper and Main-Phase Reconnection

The nature of three-dimensional reconnection when a twisted flux tube erupts during an eruptive flare or coronal mass ejection is considered. The reconnection has two phases: first of all, 3D “zipper reconnection” propagates along the initial coronal arcade, parallel to the polarity inversion line (PIL); then subsequent quasi-2D “main-phase reconnection” in the low corona around a flux rope during its eruption produces coronal loops and chromospheric ribbons that propagate away from the PIL in a direction normal to it. One scenario starts with a sheared arcade: the zipper reconnection creates a twisted flux rope of roughly one turn (\(2\pi \) radians of twist), and then main-phase reconnection builds up the bulk of the erupting flux rope with a relatively uniform twist of a few turns. A second scenario starts with a pre-existing flux rope under the arcade. Here the zipper phase can create a core with many turns that depend on the ratio of the magnetic fluxes in the newly formed flare ribbons and the new flux rope. Main phase reconnection then adds a layer of roughly uniform twist to the twisted central core. Both phases and scenarios are modeled in a simple way that assumes the initial magnetic flux is fragmented along the PIL. The model uses conservation of magnetic helicity and flux, together with equipartition of magnetic helicity, to deduce the twist of the erupting flux rope in terms the geometry of the initial configuration. Interplanetary observations show some flux ropes have a fairly uniform twist, which could be produced when the zipper phase and any pre-existing flux rope possess small or moderate twist (up to one or two turns). Other interplanetary flux ropes have highly twisted cores (up to five turns), which could be produced when there is a pre-existing flux rope and an active zipper phase that creates substantial extra twist.     

Formation of Transient Coronal Holes during the Eruption of a Quiescent Filament and its Overlying Sigmoid

By using Hα, He I 10830, EUV and soft X-ray (SXR) data, we examined a filament eruption that occurred on a quiet-sun region near the center of the solar disk on 2006 January 12, which disturbed a sigmoid overlying the filament channel observed by the GOES-12 SXR Imager (SXI), and led to the eruption of the sigmoid. The event was associated with a partial halo coronal mass ejection (CME) observed by the Large Angle and Spectrometric Coronagraphs (LASCO) on board the Solar and Heliospheric Observatory (SOHO), and resulted in the formation of two flare-like ribbons, post-eruption coronal loops, and two transient coronal holes (TCHs), but there were no significantly recorded GOES or Hα flares corresponding to the eruption. The two TCHs were dominated by opposite magnetic polarities and were located on the two ends of the eruptive sigmoid. They showed similar locations and shapes in He Ⅰ 10830, EUV and SXR observations. During the early eruption phase, brightenings first appeared on the locations of the two subsequent TCHs, which could be clearly identified on He Ⅰ 10830, EUV and SXR images. This eruption could be explained by the magnetic flux rope model, and the two TCHs were likely to be the feet of the flux rope.     

Determining the Intrinsic CME Flux Rope Type Using Remote-sensing Solar Disk Observations

A key aim in space weather research is to be able to use remote-sensing observations of the solar atmosphere to extend the lead time of predicting the geoeffectiveness of a coronal mass ejection (CME). In order to achieve this, the magnetic structure of the CME as it leaves the Sun must be known. In this article we address this issue by developing a method to determine the intrinsic flux rope type of a CME solely from solar disk observations. We use several well-known proxies for the magnetic helicity sign, the axis orientation, and the axial magnetic field direction to predict the magnetic structure of the interplanetary flux rope. We present two case studies: the 2 June 2011 and the 14 June 2012 CMEs. Both of these events erupted from an active region, and despite having clear in situ counterparts, their eruption characteristics were relatively complex. The first event was associated with an active region filament that erupted in two stages, while for the other event the eruption originated from a relatively high coronal altitude and the source region did not feature a filament. Our magnetic helicity sign proxies include the analysis of magnetic tongues, soft X-ray and/or extreme-ultraviolet sigmoids, coronal arcade skew, filament emission and absorption threads, and filament rotation. Since the inclination of the post-eruption arcades was not clear, we use the tilt of the polarity inversion line to determine the flux rope axis orientation and coronal dimmings to determine the flux rope footpoints, and therefore, the direction of the axial magnetic field. The comparison of the estimated intrinsic flux rope structure to in situ observations at the Lagrangian point L1 indicated a good agreement with the predictions. Our results highlight the flux rope type determination techniques that are particularly useful for active region eruptions, where most geoeffective CMEs originate.     

Damped Oscillations of Coronal Loops

A mechanism of damped oscillations of a coronal loop is investigated. The loop is treated as a thin toroidal flux rope with two stationary photospheric footpoints, carrying both toroidal and poloidal currents. The forces and the flux-rope dynamics are described within the framework of ideal magnetohydrodynamics (MHD). The main features of the theory are the following: i) Oscillatory motions are determined by the Lorentz force that acts on curved current-carrying plasma structures and ii) damping is caused by drag that provides the momentum coupling between the flux rope and the ambient coronal plasma. The oscillation is restricted to the vertical plane of the flux rope. The initial equilibrium flux rope is set into oscillation by a pulse of upflow of the ambient plasma. The theory is applied to two events of oscillating loops observed by the Transition Region and Coronal Explorer (TRACE). It is shown that the Lorentz force and drag with a reasonable value of the coupling coefficient (c _d ) and without anomalous dissipation are able to accurately account for the observed damped oscillations. The analysis shows that the variations in the observed intensity can be explained by the minor radial expansion and contraction. For the two events, the values of the drag coefficient consistent with the observed damping times are in the range c _d ≈2 – 5, with specific values being dependent on parameters such as the loop density, ambient magnetic field, and the loop geometry. This range is consistent with a previous MHD simulation study and with values used to reproduce the observed trajectories of coronal mass ejections (CMEs).     

A New Model for Propagating Parts of EIT Waves: A Current Shell in a CME

EIT waves are observed in EUV as bright fronts. Some of these bright fronts propagate across the solar disk. EIT waves are all associated with a flare and a CME and are commonly interpreted as fast-mode magnetosonic waves. Propagating EIT waves could also be the direct signature of the gradual opening of magnetic field lines during a CME. We quantitatively addressed this alternative interpretation. Using two independent 3D MHD codes, we performed nondimensional numerical simulations of a slowly rotating magnetic bipole, which progressively result in the formation of a twisted magnetic flux tube and its fast expansion, as during a CME. We analyse the origins, the development, and the observability in EUV of the narrow electric currents sheets that appear in the simulations. Both codes give similar results, which we confront with two well-known SOHO/EIT observations of propagating EIT waves (7 April and 12 May 1997), by scaling the vertical magnetic field components of the simulated bipole to the line of sight magnetic field observed by SOHO/MDI and the sign of helicity to the orientation of the soft X-ray sigmoids observed by Yohkoh/SXT. A large-scale and narrow current shell appears around the twisted flux tube in the dynamic phase of its expansion. This current shell is formed by the return currents of the system, which separate the twisted flux tube from the surrounding fields. It intensifies as the flux tube accelerates and it is co-spatial with weak plasma compression. The current density integrated over the altitude has the shape of an ellipse, which expands and rotates when viewed from above, reproducing the generic properties of propagating EIT waves. The timing, orientation, and location of bright and faint patches observed in the two EIT waves are remarkably well reproduced. We conjecture that propagating EIT waves are the observational signature of Joule heating in electric current shells, which separate expanding flux tubes from their surrounding fields during CMEs or plasma compression inside this current shell. We also conjecture that the bright edges of halo CMEs show the plasma compression in these current shells.     

Hα Dimming Associated With the Eruption of a Coronal Sigmoid in the Quiet Sun

We report on the occurrence of Hα dimming associated with a sigmoid eruption in a quiet-sun region on 14 August 2001. The coronal sigmoid in soft X-ray images from the Yohkoh Soft X-ray Telescope was located over an Hα filament channel. Its eruption was accompanied by a flare of GOES X-ray class C2.3 and possibly associated with a halo coronal mass ejection (CME) observed with the Large Angle and Spectroscopic Coronagraphs (LASCO) on board the Solar and Heliospheric Observatory (SOHO). During the eruption, coronal bipolar double dimming took place at the regions with opposite magnetic polarities around the two sigmoid ends, but the underlying chromospheric channel did not show observable changes corresponding to the coronal eruption. Different from the erupting coronal sigmoid itself, however, the coronal dimming had a detectable chromosphere counterpart, i.e., Hα dimming. By regarding the sigmoid as a coronal sign for a flux rope, these observations are explained in the framework of the flux rope model of CMEs. The flux rope is possibly deeply rooted in the chromosphere, and the coronal and Hα dimming regions mark its evacuated feet, through which the material is possibly fed to the halo CME.     

Soft X-ray Solar Activities Associated with Interplanetary Magnetic Flux Ropes

We studied the soft X-ray solar events that could be associated with the interplanetary magnetic flux ropes observed by the WIND satellite during 1995 through 1998. The timings of the launches of the magnetic flux ropes from the Sun were estimated using flux rope speeds derived by the fitting of a cylindrical model. In the reasonable time window, soft X-ray solar signatures were found in approximately 70% of the flux ropes. Parameters (e.g., axis direction, strength of magnetic field, radius, and helicity) of the magnetic flux ropes obtained by the model fitting were compared with the characteristics of the corresponding soft X-ray events observed by Yohkoh. According to the result of the comparison, the magnetic flux ropes with strong magnetic fields or high speeds were observed in association with higher soft X-ray solar activities.     

Are CME-Related Dimmings Always a Simple Signature of Interplanetary Magnetic Cloud Footpoints?

Coronal dimmings are often present on both sides of erupting magnetic configurations. It has been suggested that dimmings mark the location of the footpoints of ejected flux ropes and, thus, their magnetic flux can be used as a proxy for the flux involved in the ejection. If so, this quantity can be compared to the flux in the associated interplanetary magnetic cloud to find clues about the origin of the ejected flux rope. In the context of this physical interpretation, we analyze the event, flare, and coronal mass ejection (CME) that occurred in active region 10486 on 28 October 2003. The CME on this day is associated with large-scale dimmings, located on either side of the main flaring region. We combine SOHO/Extreme Ultraviolet Imaging Telescope data and Michelson Doppler Imager magnetic maps to identify and measure the flux in the dimming regions. We model the associated cloud and compute its magnetic flux using in situ observations from the Magnetometer Instrument and the Solar Wind Electron Proton Alpha Monitor aboard the Advance Composition Explorer. We find that the magnetic fluxes of the dimmings and magnetic cloud are incompatible, in contrast to what has been found in previous studies. We conclude that, in certain cases, especially in large-scale events and eruptions that occur in regions that are not isolated from other flux concentrations, the interpretation of dimmings requires a deeper analysis of the global magnetic configuration, since at least a fraction of the dimmed regions is formed by reconnection between the erupting field and the surrounding magnetic structures.     

Observation of Interactions and Eruptions of Two Filaments

We present new observations of the interactions of two close, but distinct, Hα filaments and their successive eruptions on 5 November 1998. The magnetic fields of the filaments are both of the sinistral type. The interactions between the two filaments were initiated mainly by an active filament of one of them. Before the filament eruptions, two dark plasma ejections and chromospheric brightenings were observed. They indicate that possible magnetic reconnection had occurred between the two filaments. During the first filament eruption, salient dark mass motions transferring from the left erupting filament into the right one were observed. The right filament erupted 40 minutes later. This second filament eruption may have been the result of a loss of stability owing to the sudden mass injection from the left filament. Based on the Hα observations, we have created a sketch for understanding the interactions between two filaments and accompanying activities. The traditional theory of filament merger requires that the filaments share the same filament channel and that the reconnection occurs between the two heads, as simulated by DeVore, Antiochos, and Aulanier (Astrophys. J. 629, 1122, 2005; 646, 1349, 2006). Our interpretation is that the external bodily magnetic reconnection between flux ropes of the same chirality is another possible way for two filament bodies to coalesce. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.     

Solar Cycle Variation of Magnetic Flux Ropes in a Quasi-Static Coronal Evolution Model

The structure of electric current and magnetic helicity in the solar corona is closely linked to solar activity over the 11-year cycle, yet is poorly understood. As an alternative to traditional current-free “potential-field” extrapolations, we investigate a model for the global coronal magnetic field which is non-potential and time-dependent, following the build-up and transport of magnetic helicity due to flux emergence and large-scale photospheric motions. This helicity concentrates into twisted magnetic flux ropes, which may lose equilibrium and be ejected. Here, we consider how the magnetic structure predicted by this model – in particular the flux ropes – varies over the solar activity cycle, based on photospheric input data from six periods of cycle 23. The number of flux ropes doubles from minimum to maximum, following the total length of photospheric polarity inversion lines. However, the number of flux rope ejections increases by a factor of eight, following the emergence rate of active regions. This is broadly consistent with the observed cycle modulation of coronal mass ejections, although the actual rate of ejections in the simulation is about a fifth of the rate of observed events. The model predicts that, even at minimum, differential rotation will produce sheared, non-potential, magnetic structure at all latitudes.     

On-Disc Observations of Flux Rope Formation Prior to Its Eruption

Coronal mass ejections (CMEs) are one of the primary manifestations of solar activity and can drive severe space weather effects. Therefore, it is vital to work towards being able to predict their occurrence. However, many aspects of CME formation and eruption remain unclear, including whether magnetic flux ropes are present before the onset of eruption and the key mechanisms that cause CMEs to occur. In this work, the pre-eruptive coronal configuration of an active region that produced an interplanetary CME with a clear magnetic flux rope structure at 1 AU is studied. A forward-S sigmoid appears in extreme-ultraviolet (EUV) data two hours before the onset of the eruption (SOL2012-06-14), which is interpreted as a signature of a right-handed flux rope that formed prior to the eruption. Flare ribbons and EUV dimmings are used to infer the locations of the flux rope footpoints. These locations, together with observations of the global magnetic flux distribution, indicate that an interaction between newly emerged magnetic flux and pre-existing sunspot field in the days prior to the eruption may have enabled the coronal flux rope to form via tether-cutting-like reconnection. Composition analysis suggests that the flux rope had a coronal plasma composition, supporting our interpretation that the flux rope formed via magnetic reconnection in the corona. Once formed, the flux rope remained stable for two hours before erupting as a CME.     

中尺度磁绳结构的行星际观测

由磁绳结构主导、平均尺度约二、三十个小时的行星际磁云是日冕物质抛射在行星际膨胀、传播的体现。最近，Moldwin等人报道在太阳风中还观测到一些尺度在几十分钟的小尺度磁绳结构，并认为太阳风中的磁绳结构在尺度分布上可能具有双峰特征，在全面检视了WIND卫星(1995年-2000年)和ACE卫星(1998年-2000年)的观测资料后，发现了在行星际太阳风中一些尺度为几个小时的中尺度磁绳结构，利用初步整理的其中28个中尺度磁绳结构事件，认为太阳风中的磁绳结构在尺度分布上可能是连续的，这对行星际太阳风中磁绳结构物理起源的研究可能提出重要的物理限制。     

Coronal Flux Rope Equilibria in Closed Magnetic Fields

Using a 2.5-dimensional ideal MHD model in Cartesian coordinates,we investigate the equilibrium properties of coronal magnetic flux ropes in background magnetic fields that are completely closed.The background fields are produced by a dipole,a quadrupole,and an octapole,respectively,located below the photosphere at the same depth.A magnetic flux rope is then launched from below the photo-sphere,and its magnetic properties,i.e,the annular magnetic fluxφp and the axial magnetic fluxφz,are controlled by a single emergence parameter.The whole sys-tem eventually evolves into equilibrium,and the resultant flux rope is characterized by three geometrical parameters:the height of the rope axis,the half-width of the rope,and the length of the vertical current sheet below the rope.It is found that the geometrical parameters increase monotonically and continuously with increasing φp and φz:no catastrophe occurs.Moreover,there exists a steep segment in the profiles of the geometrical parameters versus either φp or φz,and the faster the background field decays with height,the larger both the gradient and the growth amplitude within the steep segment will be.     

A statistical study of flux ropes in the Martian magnetosphere

Using minimum variance analysis of the circular mapping data from the Mars Global Surveyor (MGS) spacecraft during four selected weeks of observation, we identify 360 magnetic field structures in the Martian topside ionosphere with characteristic signatures of flux ropes. Physical parameters including size, peak field strength, helicity, orientation, and external conditions at the time of each observation are compiled for the events in each population. We observe that Martian flux ropes typically have a peak field amplitude of ∼15 nT and a diameter of ∼80–100 km assuming they are stationary. Flux ropes tend to be aligned approximately parallel to the planetary surface, and perpendicular to the direction from which the solar wind flows. They are more frequently observed during times of low solar wind pressure, but do not show a clear preference for a particular Interplanetary Magnetic Field (IMF) draping direction. Flux rope characteristics of peak field amplitude, diameter, and helicity vary with solar zenith angle. Amplitudes tend to be higher during periods of high solar wind pressure. The events are sorted into three populations based on the location at which they were observed, possibly corresponding to distinct formation mechanisms. Flux ropes observed in eclipse tend to have smaller peak amplitudes and are larger than those observed in sunlight, and are less likely to be oriented parallel to the planetary surface. Proximity to crustal fields does not appear to influence the characteristics of flux ropes observed at the 400 km spacecraft altitude. The frequent observation of flux rope structures near Mars in a variety of locations suggests that the low-altitude plasma environment is quite dynamic, with magnetic shear playing a prominent role in determining magnetic field structure near the planet.     

Catastrophic Behavior of Multiple Coronal Flux Rope System

A major solar active event called Bastille Day Event occurred in AR 9077 on July 14, 2000. Simultaneous occurrence of a filament eruption, a flare and a coronal mass ejection was observed in this event. Previous analyses of this event show that before the event, there existed an activation and eruption of a huge trans-equatorial filament, which might play a crucial role in triggering the Bastille Day event. This implies that independent flux systems are closely related to and affect each other, which has encouraged us to investigate the catastrophic behavior of a multiple coronal flux rope system with the use of a 2.5-D time-dependent MHD model. A force-free field that contains three separate coronal flux ropes is taken to be the initial state. Starting from this state, we increase either the annular or the axial flux of a certain flux rope to examine the catastrophic behavior of the system in two regimes, the ideal MHD regime and the resistive MHD regime. It is found that a catastrophe occurs if the flux exceeds a certain critical value, or the magnetic energy of the system exceeds a certain threshold: the rope of interest breaks away from the base and escapes to infinity, leaving a current sheet below. Moreover, the destiny of the remainder flux ropes relies on whether reconnection takes place across the current sheet. In the ideal MHD regime, i.e., in the absence of reconnection, these ropes remain to be attached to the base in equilibrium, whereas in the resistive MHD regime they abruptly erupt upward during reconnection and escape to infinity. Reconnection causes the field lines to close back to the base and thus changes the background field outside the attached flux ropes in such a way that the constraint on these ropes is substantially relaxed and the corresponding catastrophic energy threshold is reduced accordingly, leading to a catastrophic eruption of these ropes. Since magnetic reconnection is generally inevitable when a current sheet forms and develops through an eruption of one flux rope, the eruption of this flux rope must lead to an eruption of the others. This provides an example to demonstrate the interaction between several independent magnetic flux systems in different regions, as implied by the Bastille Day event, and may serve as a possible mechanism for sympathetic events occurring on the Sun.     

Progressive Transformation of a Flux Rope to an ICME

The solar wind conditions at one astronomical unit (AU) can be strongly disturbed by interplanetary coronal mass ejections (ICMEs). A subset, called magnetic clouds (MCs), is formed by twisted flux ropes that transport an important amount of magnetic flux and helicity, which is released in CMEs. At 1 AU from the Sun, the magnetic structure of MCs is generally modeled by neglecting their expansion during the spacecraft crossing. However, in some cases, MCs present a significant expansion. We present here an analysis of the huge and significantly expanding MC observed by the Wind spacecraft during 9 – 10 November 2004. This MC was embedded in an ICME. After determining an approximate orientation for the flux rope using the minimum variance method, we obtain a precise orientation of the cloud axis by relating its front and rear magnetic discontinuities using a direct method. This method takes into account the conservation of the azimuthal magnetic flux between the inbound and outbound branches and is valid for a finite impact parameter (i.e., not necessarily a small distance between the spacecraft trajectory and the cloud axis). The MC is also studied using dynamic models with isotropic expansion. We have found (6.2±1.5)×10²⁰ Mx for the axial flux and (78±18)×10²⁰ Mx for the azimuthal flux. Moreover, using the direct method, we find that the ICME is formed by a flux rope (MC) followed by an extended coherent magnetic region. These observations are interpreted by considering the existence of a previously larger flux rope, which partially reconnected with its environment in the front. We estimate that the reconnection process started close to the Sun. These findings imply that the ejected flux rope is progressively peeled by reconnection and transformed to the observed ICME (with a remnant flux rope in the front part).     

Numerical simulations of fast and slow coronal mass ejections

Solar coronal mass ejections (CMEs) show a large variety in their kinematic properties. CMEs originating in active regions and accompanied by strong flares are usually faster and accelerated more impulsively than CMEs associated with filament eruptions outside active regions and weak flares. It has been proposed more than two decades ago that there are two separate types of CMEs, fast (impulsive) CMEs and slow (gradual) CMEs. However, this concept may not be valid, since the large data sets acquired in recent years do not show two distinct peaks in the CME velocity distribution and reveal that both fast and slow CMEs can be accompanied by both weak and strong flares. We present numerical simulations which confirm our earlier analytical result that a flux‐rope CME model permits describing fast and slow CMEs in a unified manner. We consider a force‐free coronal magnetic flux rope embedded in the potential field of model bipolar and quadrupolar active regions. The eruption is driven by the torus instability which occurs if the field overlying the flux rope decreases sufficiently rapidly with height. The acceleration profile depends on the steepness of this field decrease, corresponding to fast CMEs for rapid decrease, as is typical of active regions, and to slow CMEs for gentle decrease, as is typical of the quiet Sun. Complex (quadrupolar) active regions lead to the fastest CMEs. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Helicity of solar active regions from a dynamo model

We calculate helicities of solar active regions based on the idea that poloidal flux lines get wrapped around a toroidal flux tube rising through the convection zone, thereby giving rise to the helicity. We use our solar dynamo model based on the Babcock-Leighton α-effect to study how helicity varies with latitude and time.     

Comparison of Helicity Signs in Interplanetary CMEs and Their Solar Source Regions

If all coronal mass ejections (CMEs) have flux ropes, then the CMEs should keep their helicity signs from the Sun to the Earth according to the helicity conservation principle. This study presents an attempt to answer the question from the Coordinated Data Analysis Workshop (CDAW), “Do all CMEs have flux ropes?”, by using a qualitative helicity sign comparison between interplanetary CMEs (ICMEs) and their CME source regions. For this, we select 34 CME–ICME pairs whose source active regions (ARs) have continuous SOHO/MDI magnetogram data covering more than 24 hr without data gap during the passage of the ARs near the solar disk center. The helicity signs in the ARs are determined by estimation of cumulative magnetic helicity injected through the photosphere in the entire source ARs. The helicity signs in the ICMEs are estimated by applying the cylinder model developed by Marubashi (Adv. Space. Res., 26, 55, 2000) to 16 second resolution magnetic field data from the MAG instrument onboard the ACE spacecraft. It is found that 30 out of 34 events (88 %) are helicity sign-consistent events, while four events (12 %) are sign-inconsistent. Through a detailed investigation of the source ARs of the four sign-inconsistent events, we find that those events can be explained by the local helicity sign opposite to that of the entire AR helicity (28 July 2000 ICME), incorrectly reported solar source region in the CDAW list (20 May 2005 ICME), or the helicity sign of the pre-existing coronal magnetic field (13 October 2000 and 20 November 2003 ICMEs). We conclude that the helicity signs of the ICMEs are quite consistent with those of the injected helicities in the AR regions from where the CMEs erupted.