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…     

Catastrophe of coronal magnetic rope in partly open multipolar magnetic field

Catastrophe of coronal magnetic rope embedded in a partly open multipolar background magnetic field is studied by using a 2-dimensional, 3-component ideal MHD model in spherical coordinates. The background field is composed of three closed bipolar fields of a coronal streamer and an open field with an equatorial current sheet. The magnetic rope lies below the central bipolar field, and it is characterized by its annular and axial magnetic fluxes. For a given annual flux, there is a critical value of the axial flux, and for a given axial flux, there is a critical value of annual flux such that, below the critical value, the magnetic rope is attached to the solar surface and the system stays in equilibrium, but when the critical value is exceeded, the magnetic rope breaks free and erupts upward. This implies that catastrophe can occur in a coronal magnetic rope embedded in a partly open multipolar background magnetic field. Our computation gives a threshold value of magnetic energy that is about 15% greater than the energy of the partly open magnetic field (the central bipolar field open and the fields on either side closed). The excess energy may serve as source for solar explosions such as coronal mass ejections.     

Catastrophe of Coronal Magnetic Flux Ropes Caused by Photospheric Motions

Using a 2.5-D, time-dependent ideal MHD model in Cartesian coordinates, we carried out numerical simulations to investigate the equilibrium and evolution properties of a magnetic configuration that consists of a coronal magnetic flux rope and a partly open photospheric background field, which is equivalent to that produced by a two-patch magnetic source on the photospheric surface. The axial and annular magnetic fluxes of the flux rope are given and fixed. The global magnetic configuration evolves in response to three types of changes of the background field: decreasing of the distance between the two sources, shrinking of the size of each source, and increasing of the shear in the closed component of the background field. As a result, the geometrical parameters of the flux rope, i.e. the height of the rope axis, the half-width of the rope and the length of the vertical current sheet below the rope, change due to the variation of the background field. It is shown that for a given coronal magnetic flux rope in a partly open background field, the variation of the geometrical parameters of the flux rope displays a catastrophic behavior, namely, there exists a critical point for each case, at which an infinitesimal change of the background field leads to a loss of equilibrium, and thus a jump of the flux rope. The implication of such a catastrophe in solar active phenomena is briefly discussed.     

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 Numerical Study of the Response of the Coronal Magnetic Field to Flux Emergence

Large-scale solar eruptions, known as coronal mass ejections (CMEs), are regarded as the main drivers of space weather. The exact trigger mechanism of these violent events is still not completely clear; however, the solar magnetic field indisputably plays a crucial role in the onset of CMEs. The strength and morphology of the solar magnetic field are expected to have a decisive effect on CME properties, such as size and speed. This study aims to investigate the evolution of a magnetic configuration when driven by the emergence of new magnetic flux in order to get a better insight into the onset of CMEs and their magnetic structure. The three-dimensional, time-dependent equations for ideal magnetohydrodynamics are numerically solved on a spherical mesh. New flux emergence in a bipolar active region causes destabilisation of the initial stationary structure, finally resulting in an eruption. The initial magnetic topology is suitable for the ??breakout?? CME scenario to work. Although no magnetic flux rope structure is present in the initial condition, highly twisted magnetic field lines are formed during the evolution of the system as a result of internal reconnection due to the interaction of the active region magnetic field with the ambient field. The magnetic energy built up in the system and the final speed of the CME depend on the strength of the overlying magnetic field, the flux emergence rate, and the total amount of emerged flux. The interaction with the global coronal field makes the eruption a large-scale event, involving distant parts of the solar surface.     

Catastrophe of coronal magnetic flux ropes in partially open magnetic fields

Using a 2.5-D, time-dependent ideal MHD model in Cartesian coordinates, a numerical study is carried out to find equilibrium solutions associated with a magnetic flux rope in the corona. The ambient magnetic field is partially open, consisting of a closed arcade in the center and an open field at the flank. The coronal magnetic flux rope is characterized by its magnetic properties, including the axial and annular magnetic fluxes and the magnetic helicity, and its geometrical features, including the height of the rope axis, the halfwidth of the rope and the length of the vertical current sheet below the rope. It is shown that for a given partially open ambient magnetic field, the dependence of the geometrical features on the magnetic properties displays a catastrophic behavior, namely, there exists a certain critical point, across which an infinitesimal enhancement of the magnetic parameters causes a finite jump of the geometrical parameters for the rope. The amplitude of the jump depends on the extent to which the ambient magnetic field in open, and approaches to zero when the ambient magnetic field becomes completely closed. The implication of such a catastrophe in solar active phenomena is briefly discussed.     

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.     

Coronal mass ejections: Some possibilities for prediction

The onset stage of coronal mass ejections (CMEs) is difficult to observe and is poorly studied. In spite of their practical importance, methods for CME predictions with sufficient lead times are only in the nascent stages of development. The most probable CME mechanism is a catastrophic loss of equilibrium of a large-scale current system in the corona (a flux rope). A twisted magnetic rope is maintained by the tension of field lines of photospheric sources until parameters of the system reach critical values and the equilibrium is lost. Unfortunately, there is low-density plasma (coronal cavity) in most of the rope volume; thus, it is difficult to observe a rope. However, the lower parts of the helical field lines of a rope are fine traps for the dense cold plasma of prominences. Thus, prominences are the best tracers of flux ropes in the corona. The maximal height up to which the rope is in stable equilibrium can be found by analyzing the distribution of the magnetic field generated by photospheric sources in the corona. Comparing this critical height with the actually observed prominence height, one can estimate the probability of the loss of equilibrium by a magnetic rope with a following eruption of prominences and coronal mass ejections.     

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.     

Magnetic field evolution during prominence eruptions and two-ribbon flares

Simple models for the MHD eruption of a solar prominence are presented, in which the prominence is treated as a twisted magnetic flux tube that is being repelled from the solar surface by magnetic pressure forces. The effects of different physical assumptions to deal with this magneto-hydrodynamically complex phenomenon are evaluated, such as holding constant the prominence current, radius, flux or twist or modelling the prominence as a current sheet. Including a background magnetic field allows the prominence to be in equilibrium initially with an Inverse Polarity and then to erupt due to magnetic non-equilibrium when the background magnetic field is too small or the prominence twist is too great. The electric field at the neutral point below the prominence rapidly increases to a maximum value and then declines. Including the effect of gravity also allows an equilibrium with Normal Polarity to exist. Finally, an ideal MHD solution is found which incorporates self-consistently a current sheet below the prominence and which implies that a prominence will still erupt and form a current sheet even if no reconnection occurs. When reconnection is allowed it is, therefore, driven by the eruption.     

Three-Dimensional Evolution of Flux-Rope CMEs and Its Relation to the Local Orientation of the Heliospheric Current Sheet

Flux ropes ejected from the Sun may change their geometrical orientation during their evolution, which directly affects their geoeffectiveness. Therefore, it is crucial to understand how solar flux ropes evolve in the heliosphere to improve our space-weather forecasting tools. We present a follow-up study of the concepts described by Isavnin, Vourlidas, and Kilpua (Solar Phys. 284, 203, 2013). We analyze 14 coronal mass ejections (CMEs), with clear flux-rope signatures, observed during the decay of Solar Cycle 23 and rise of Solar Cycle 24. First, we estimate initial orientations of the flux ropes at the origin using extreme-ultraviolet observations of post-eruption arcades and/or eruptive prominences. Then we reconstruct multi-viewpoint coronagraph observations of the CMEs from ≈?2 to 30 R_⊙ with a three-dimensional geometric representation of a flux rope to determine their geometrical parameters. Finally, we propagate the flux ropes from ≈?30 R_⊙ to 1 AU through MHD-simulated background solar wind while using in-situ measurements at 1 AU of the associated magnetic cloud as a constraint for the propagation technique. This methodology allows us to estimate the flux-rope orientation all the way from the Sun to 1 AU. We find that while the flux-ropes’ deflection occurs predominantly below 30 R_⊙, a significant amount of deflection and rotation happens between 30 R_⊙ and 1 AU. We compare the flux-rope orientation to the local orientation of the heliospheric current sheet (HCS). We find that slow flux ropes tend to align with the streams of slow solar wind in the inner heliosphere. During the solar-cycle minimum the slow solar-wind channel as well as the HCS usually occupy the area in the vicinity of the solar equatorial plane, which in the past led researchers to the hypothesis that flux ropes align with the HCS. Our results show that exceptions from this rule are explained by interaction with the Parker-spiraled background magnetic field, which dominates over the magnetic interaction with the HCS in the inner heliosphere at least during solar-minimum conditions.     

On the maximum energy release in flux-rope models of Eruptive Flares

We determine the photospheric boundary conditions which maximize the magnetic energy released by a loss of ideal-MHD equilibrium in two-dimensional flux-rope models. In these models a loss of equilibrium causes a transition of the flux rope to a lower magnetic energy state at a higher altitude. During the transition a vertical current sheet forms below the flux rope, and reconnection in this current sheet releases additional energy. Here we compute how much energy is released by the loss of equilibrium relative to the total energy release. When the flux-rope radius is small compared to its height, it is possible to obtain general solutions of the Grad-Shafranov equation for a wide range of boundary conditions. Variational principles can then be used to find the particular boundary condition which maximizes the magnetic energy released for a given class of conditions. We apply this procedure to a class of models known as cusp-type catastrophes, and we find that the maximum energy released by the loss of equilibrium is 20.8% of the total energy release for any model in this class. If the additional restriction is imposed that the photospheric magnetic field forms a simple arcade in the absence of coronal currents, then the maximum energy release reduces to 8.6%.     

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.     

Thermal evolution of current sheets and flash phase of solar flares

The physical conditions in a stationary flow of the Petchek type, allowing reconnection between flux emerging from below the solar photosphere and a preexisting magnetic field, are discussed. It is shown that, when rising in the solar atmosphere, the reconnection region has at first a rather low temperature as compared with its environment. Above a certain critical height, however, this low temperature thermal equilibrium often ceases to be possible, and the sheet rapidly heats, seeking a new thermal equilibrium. During this dynamical process, current-driven microinstabilities may be triggered in the current sheet, giving rise to an enhanced resistivity. High energy particles might be produced by the induced electric field developed during the rapid readjustment of MHD flows that results from this change in the transport properties of the plasma.     

A Comparative Study of Coronal Mass Ejections with and Without Magnetic Cloud Structure near the Earth: Are All Interplanetary CMEs Flux Ropes?

An outstanding question concerning interplanetary coronal mass ejections (ICMEs) is whether all ICMEs have a magnetic flux rope structure. We test this question by studying two different ICMEs, one having a magnetic cloud (MC) showing smooth rotation of magnetic field lines and the other not. The two ICMEs are chosen in such a way that their progenitor CMEs are very similar in remote sensing observations. Both CMEs originated from close to the central meridian directly facing the Earth. Both CMEs were associated with a long-lasting post-eruption loop arcade and appeared as an elliptical halo in coronagraph images, indicating a flux rope origin. We conclude that the difference in the in-situ observation is caused by the geometric selection effect, contributed by the deflection of flux ropes in the inner corona and interplanetary space. The first event had its nose pass through the observing spacecraft; thus, the intrinsic flux rope structure of the CME appeared as a magnetic cloud. On the other hand, the second event had the flank of the flux rope intercept the spacecraft, and it thus did not appear as a magnetic cloud. We further argue that a conspicuous long period of weak magnetic field, low plasma temperature, and density in the second event should correspond to the extended leg portion of the embedded magnetic flux rope, thus validating the scenario of the flank-passing. These observations support the idea that all CMEs arriving at the Earth include flux rope drivers.     

灾变理论在太阳物理和天体物理其他研究领域中的应用

叙述和介绍了太阳爆发的磁通量绳灾变理论和模型的发展过程,强调了建立这样的模型所需要的观测基础。讨论了由模型所预言的爆发磁结构的几个重要特征以及观测结果对这种预言的证实。在此模型的基础上,讨论了一个典型的爆发过程中所出现的不同现象及它们之间的相互关系。最后,介绍了作者的一项最新尝试:将太阳爆发的灾变理论和模型应用到对黑洞吸积盘间歇性喷流的理论研究当中,以及研究所取得的初步结果。     

Magnetic Energy of Force-Free Fields with Detached Field Lines

Using an axisymmetrical ideal MHD model in spherical coordinates, we present a numerical study of magnetic configurations characterized by a levitating flux rope embedded in a bipolar background field whose normal field at the solar surface is the same or very close to that of a central dipole. The characteristic plasma β (the ratio between gas pressure and magnetic pressure) is taken to be sosmall (β= 10^-4) that the magnetic field is close to being force-free. The system as a whole is then let evolve quasi-statically with a slow increase of either the annular magnetic flux or the axial magnetic flux of the rope, and the total magneticenergy of the system grows accordingly. It is found that there exists an energy threshold: the flux rope sticks to the solar surface in equilibrium if the magneticenergy of the system is below the threshold, whereas it loses equilibrium if the threshold is exceeded. The energy threshold is found to be larger than that of thecorresponding fully-open magnetic field by a factor of nearly 1.08 irrespective as towhether the background field is completely closed or partly open, or whether the magnetic energy is enhanced by an increase of annular or axial flux of the rope.This gives an example showing that a force-free magnetic field may have an energy larger than the corresponding open field energy if part of the field lines is allowed tobe detached from the solar surface. The implication of such a conclusion in coronal mass ejections is briefly discussed and some comments are made on the maximum energy of force-free magnetic fields.     

The Formation of Large-Scale Current Sheets within Magnetic Clouds

Magnetic clouds are a class of interplanetary coronal mass ejections (CME) predominantly characterised by a smooth rotation in the magnetic field direction, indicative of a magnetic flux rope structure. Many magnetic clouds, however, also contain sharp discontinuities within the smoothly varying magnetic field, suggestive of narrow current sheets. In this study we present observations and modelling of magnetic clouds with strong current sheet signatures close to the centre of the apparent flux rope structure. Using an analytical magnetic flux rope model, we demonstrate how such current sheets can form as a result of a cloud’s kinematic propagation from the Sun to the Earth, without any external forces or influences. This model is shown to match observations of four particular magnetic clouds remarkably well. The model predicts that current sheet intensity increases for increasing CME angular extent and decreasing CME radial expansion speed. Assuming such current sheets facilitate magnetic reconnection, the process of current sheet formation could ultimately lead a single flux rope becoming fragmented into multiple flux ropes. This change in topology has consequences for magnetic clouds as barriers to energetic particle propagation.     

Magnetic flux ropes in the solar corona: structure and evolution toward eruption

Magnetic flux ropes are characterized by coherently twisted magnetic field lines, which are ubiquitous in magnetized plasmas. As the core structure of various eruptive phenomena in the solar atmosphere, flux ropes hold the key to understanding the physical mechanisms of solar eruptions,which impact the heliosphere and planetary atmospheres. The strongest disturbances in the Earth's space environments are often associated with large-scale flux ropes from the Sun colliding with the Earth's magnetosphere, leading to adverse, sometimes catastrophic, space-weather effects. However, it remains elusive as to how a flux rope forms and evolves toward eruption, and how it is structured and embedded in the ambient field. The present paper addresses these important questions by reviewing current understandings of coronal flux ropes from an observer's perspective, with an emphasis on their structures and nascent evolution toward solar eruptions, as achieved by combining observations of both remote sensing and in-situ detection with modeling and simulation. This paper highlights an initiation mechanism for coronal mass ejections(CMEs) in which plasmoids in current sheets coalesce into a 'seed' flux rope whose subsequent evolution into a CME is consistent with the standard model, thereby bridging the gap between microscale and macroscale dynamics.     

MHD Modeling of Coronal Large-Amplitude Waves Related to CME Lift-off

We have employed a two-dimensional magnetohydrodynamic simulation code to study mass motions and large-amplitude coronal waves related to the lift-off of a coronal mass ejection (CME). The eruption of the filament is achieved by an artificial force acting on the plasma inside the flux rope. By varying the magnitude of this force, the reaction of the ambient corona to CMEs with different acceleration profiles can be studied. Our model of the ambient corona is gravitationally stratified with a quadrupolar magnetic field, resulting in an ambient Alfvén speed that increases as a function of height, as typically deduced for the low corona. The results of the simulations show that the erupting flux rope is surrounded by a shock front, which is strongest near the leading edge of the erupting mass, but also shows compression near the solar surface. For rapidly accelerating filaments, the shock front forms already in the low corona. Although the speed of the driver is less than the Alfvén speed near the top of the atmosphere, the shock survives in this region as well, but as a freely propagating wave. The leading edge of the shock becomes strong early enough to drive a metric type II burst in the corona. The speed of the weaker part of the shock front near the surface is lower, corresponding to the magnetosonic speed there. We analyze the (line-of-sight) emission measure of the corona during the simulation and recognize a wave receding from the eruption site, which strongly resembles EIT waves in the low corona. Behind the EIT wave, we clearly recognize a coronal dimming, also observed during CME lift-off. We point out that the morphology of the hot downstream region of the shock would be that of a hot erupting loop, so care has to be taken not to misinterpret soft X-ray imaging observations in this respect. Finally, the geometry of the magnetic field around the erupting mass is analyzed in terms of precipitation of particles accelerated in the eruption complex. Field lines connected to the shock are further away from the photospheric neutral line below the filament than the field lines connected to the current sheet below the flux rope. Thus, if the DC fields in the current sheet accelerate predominantly electrons and the shock accelerates ions, the geometry is consistent with recent observations of gamma rays being emitted further out from the neutral line than hard X-rays.