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.     

The eruption of a prominence and coronal mass ejection which drive reconnection

Two possible limiting scenarios are proposed for the production of a coronal mass ejection. In the first the magnetic field around a prominence evolves until it loses equilibrium and erupts, which drives reconnection below the prominence and an eruption of the overlying magnetic arcade. In the second a large-scale magnetic arcade evolves until it loses equilibrium and erupts, thereby causing a prominence to erupt. In general it is likely to be the non-equilibrium of the coupled system which creates the eruption. Furthermore, large quiescent prominences are expected to be centred within the magnetic bubble of a coronal mass ejection whereas when active-region prominences erupt they are likely to be located initially to one side of the bubble.A model is set up for the eruption of a magnetically coupled prominence and coronal mass ejection. This represents a development of the Anzer and Pneuman (1982) model by overcoming two limitations of it, namely that: it is not globally stable initially and so one wonders how it can be set up in a stable way before the eruption; it has reconnection driving the CME whereas recent observations suggest that the reverse may be happening. In our model we assume that magnetic reconnection below the prominence is driven by the eruption and the driver is magnetic non-equilibrium in the coupled prominence-mass ejection system. The prominence is modelled as a twisted flux tube and the mass ejection as an overlying void and magnetic bubble. Two different models of the prominence are considered. In one a globally stable equilibrium becomes unstable when a threshold magnetic flux below the prominence is exceeded and, in the other, equilibrium ceases to exist. In both cases, the prominence and mass-ejection accelerate upwards before reaching constant velocities in a manner that is consistent with observations. It is found that the greater the reconnection that is driven by the eruption, the higher is the final speed.     

Initiation of cmes by magnetic flux emergence

The initiation of solar Coronal Mass Ejections (CMEs) is studied in the framework of numerical magnetohydrodynamics (MHD). The initial CME model includes a magnetic flux rope in spherical, axi-symmetric geometry. The initial configuration consists of a magnetic flux rope embedded in a gravitationally stratified solar atmosphere with a background dipole magnetic field. The flux rope is in equilibrium due to an image current below the photosphere. An emerging flux triggering mechanism is used to make this equilibrium system unstable. When the magnetic flux emerges within the filament below the flux rope, this results in a catastrophic behavior similar to previous models. As a result, the flux rope rises and a current sheet forms below it. It is shown that the magnetic reconnection in the current sheet below the flux rope in combination with the outward curvature forces results in a fast ejection of the flux rope as observed for solar CMEs. We have done a parametric study of the emerging flux rate.     

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。     

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.     

Reconnection of a Kinking Flux Rope Triggering the Ejection of a Microwave and Hard X-Ray Source II. Numerical Modeling

Numerical simulations of the helical (m=1) kink instability of an arched, line-tied flux rope demonstrate that the helical deformation enforces reconnection between the legs of the rope if modes with two helical turns are dominant as a result of high initial twist in the range Φ≳6π. Such a reconnection is complex, involving also the ambient field. In addition to breaking up the original rope, it can form a new, low-lying, less twisted flux rope. The new flux rope is pushed downward by the reconnection outflow, which typically forces it to break as well by reconnecting with the ambient field. The top part of the original rope, largely rooted in the sources of the ambient flux after the break-up, can fully erupt or be halted at low heights, producing a “failed eruption.” The helical current sheet associated with the instability is squeezed between the approaching legs, temporarily forming a double current sheet. The leg – leg reconnection proceeds at a high rate, producing sufficiently strong electric fields that it would be able to accelerate particles. It may also form plasmoids, or plasmoid-like structures, which trap energetic particles and propagate out of the reconnection region up to the top of the erupting flux rope along the helical current sheet. The kinking of a highly twisted flux rope involving leg – leg reconnection can explain key features of an eruptive but partially occulted solar flare on 18 April 2001, which ejected a relatively compact hard X-ray and microwave source and was associated with a fast coronal mass ejection.     

Magnetic reconnection and coronal transients

Every two-ribbon flare observed during the Skylab period produced an observable coronal transient, provided the flare occurred close enough to the limb. The model presented here treats these two events as a combined process. Transients that occur without flares are believed to involve magnetic fields that are too weak to produce significant chromospheric emission. Adopting the hypothesis that the rising flare loop systems observed during two-ribbon flares are exhibiting magnetic reconnection, a model of a coronal transient is proposed which incorporates this reconnection process as the driving force. When two oppositely directed field lines reconnect a lower loop is created rooted to the solar surface (the flare loop) and an upper disconnected loop is produced which is free to rise. The magnetic flux of these upper loops is proposed as the driver for the transient. The force is produced by the increase in magnetic pressure under the filament and transient.A quantitative model is developed which treats the transient configuration in terms of four distinct parts- the transient itself with its magnetic field and material, the region just below the transient but above the filament, the filament with its magnetic field, and the reconnected flux beneath the filament. Two cases are considered - one in which all the prominence material rises with the transient and one in which the material is allowed to fall out of the transient. The rate of rise of the neutral line during the reconnection process is taken from the observations of the rising X-ray flare loop system during the 29 July, 1973 flare. The MHD equations for the system are reduced to four non-linear ordinary coupled differential equations which are solved using parameters believed to be realistic for solar conditions. The calculated velocity profiles, widths, etc., agree quite well with the observed properties of coronal transients as seen in white light. Since major flares are usually associated with a filament eruption about 10–15 min before the flare and since this model associates the transient with the filament eruption, we suspect that the transient is actually initiated some time before the actual flare itself.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

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.     

Giant Meterwave Radio Telescope observations of an M2.8 flare: Insights into the initiation of a flare–coronal mass ejection event

We present the first observations of a solar flare with the GMRT. An M2.8 flare observed at 1060 MHz with the GMRT on 17 November 2001 was associated with a prominence eruption observed at 17 GHz by the Nobeyama radioheliograph and the initiation of a fast partial halo CME observed with the LASCO C2 coronagraph. Towards the start of the eruption, we find evidence for reconnection above the prominence. Subsequently, we find evidence for rapid growth of a vertical current sheet below the erupting arcade, which is accompanied by the flare and prominence eruption.     

Interchange Reconnection Alfvén Wave Generation

Given recent observational results of interchange reconnection processes in the solar corona and the theoretical development of the S-Web model for the slow solar wind, we extend the analysis of the 3D MHD simulation of interchange reconnection by Edmondson et al. (Astrophys. J. 707, 1427, 2009). Specifically, we analyze the consequences of the dynamic streamer-belt jump that corresponds to flux opening by interchange reconnection. Information about the magnetic field restructuring by interchange reconnection is carried throughout the system by Alfvén waves propagating away from the reconnection region, distributing the shear and twist imparted by the driving flows, including shedding the injected stress-energy and accumulated magnetic helicity along newly open fieldlines. We quantify the properties of the reconnection-generated wave activity in the simulation. There is a localized high-frequency component associated with the current sheet/reconnection site and an extended low-frequency component associated with the large-scale torsional Alfvén wave generated from the interchange reconnection field restructuring. The characteristic wavelengths of the torsional Alfvén wave reflect the spatial size of the energized bipolar flux region. Lastly, we discuss avenues of future research by modeling these interchange reconnection-driven waves and investigating their observational signatures.     

Formation of neutral current sheet and loop coronal transients

An eruption of opposite magnetic flux into a bipolar background field is likely to lead to the formation of a natural current sheet between the new emerging field and the background. A numerical study is made on this process, based on the ideal MMD equations, taking into account the interaction between the magnetic field and the coronal plasma. The result shows that a subsonic eruption will give rise to a four region structure; 1) a cool and dense prominence made of the erupting material in the innermost region; 2) a cool and tenuous region further out; 3) a hot and dense loop formed by the concentration of both the erupting material and the coronal material in the neutral current sheet; and 4) a forerunner region outside the loop with density slightly above the background, due to fast magneto-acoustic waves. This structure agrees with the observed features of typical loop coronal transients. Therefore the eruption of opposite magnetic flux into a bipolar background is probably an important mechanism for triggering off such transients.     

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.     

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…     

Implications of solar flare dynamics for reconnection in magnetospheric substorms

From observations of two-ribbon solar flares, we present a new line of evidence that magnetic reconnection is of key importance in magnetospheric substorms. We infer that in substorms reconnection of closed field lines in the near-Earth thinned plasma sheet both initiates and is driven by the overall MHD instability that drives the tailward expulsion of the reconnected closed field (0 loops). The general basis for this inference is the longstanding notion that two-ribbon flares and substorms are essentially similar phenomena, driven by similar processes. We give an array of observed similarities that substantiate this view. More specifically, our inference for substorms is drawn from observations of filament eruptions in two-ribbon flares, from which we conclude that the heart of the overall instability consists of reconnection and eruption of the closed magnetic field in and around the filament. We propose that essentially the same overall instability operates in substorms. Our point is not that the magnetic field configuration or the microphysics in substorms is identical to that in two-ribbon flares, but that the overall instability results from essentially the same combination of reconnection and eruption of closed magnetic field.     

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.     

Magnetic reconnection in the temperature minimum region and prominence formation

Magnetic reconnection at the photospheric boundary is an essential part of some theories for prominence formation. We consider a simple model for reconnection in this region. Parameters of the reconnecting current sheet are expressed in terms of the concentration and temperature of the outside dense and cold plasma, magnetic field intensity, and velocity of convective flows at the photosphere. The reconnection process is shown to be most efficient in a layer several hundred kilometers thick coinciding with the temperature minimum region of the solar atmosphere. The calculated upward flux of matter through the current sheet ( 10¹¹–10¹² g s^–1) is amply sufficient for prominence formation in the upper chromosphere or lower corona.     

Current sheet models of solar flares

Current sheets have been suggested as the site for flare energy release because they can convert magnetic energy very rapidly into both heat and directed plasma energy. Also they contain electric fields with the potential of accelerating particles to high energies.The basic properties of current sheets are first reviewed. For instance, magnetic flux may be carried into a current sheet and annihilated. An exact solution for such a process in an infinitely long sheet has been found; it describes the annihilation of fields which are inclined at any angle, not just 180°. Moreover, field lines which are expelled from the ends of a current sheet can be described as having been reconnected. The only workable model for fast reconnection in the solar atmosphere, namely Petschek's mechanism, has recently been put on a firm foundation; it gives a reconnection rate which depends on the electrical conductivity but is typically a tenth or a hundredth of the Alfvén speed. A current sheet may be formed when the sources of an initially potential field start to move; a simple analytic technique for finding the position and shape of such a sheet in two dimensions now exists. Finally, a sheet with no transverse magnetic field component is subject to the tearing-mode instability, which rapidly produces a series of loops in the field.The main ways in which current sheets have been used for solar flare models is described. Syrovatskii's mechanism relies on the increase of the electric current density during the formation of a sheet, to a value in excess of the critical value j ^* for the onset of microinstabilities. But Anzer has recently demonstrated that the critical value is most unlikely to be reached during the initial formation process. Sturrock, on the other hand, has advocated the occurrence of the tearing-mode instability in an open streamer-like configuration (which may result from the eruption of a force-free field). But recent observations do not point to that as the relevant configuration. Rather, they suggest that flares are triggered by the emergence of new magnetic flux from below the solar photosphere. This has led Heyvaerts, Priest, and Rust (1976) to propose a new emerging flux model, according to which, as more and more flux emerges, so reconnection occurs, producing some preflare heating. When the current sheet reaches such a height (around the transition region) that its current density exceeds j ^*, then the impulsive phase of the flare is triggered. The main phase is caused by an enhanced level of magnetic energy conversion in a turbulent current sheet. The type of flare depends on the magnetic environment in which the emerging flux finds itself. A surge flare results if the flux appears near a strong unipolar region such as a simple sunspot, whereas a two ribbon flare may be produced by flux emergence near an active region filament, in which case the main phase energy is released from the field that surrounds the filament.     

Helical structures around quiescent solar prominences computed from observable magnetic fields

We analyse the magnetic support of solar prominences in two-dimensional linear force-free fields. A line current is added to model a helical configuration, well suited to trap dense plasma in its bottom part. The prominence is modeled as a vertical mass-loaded current sheet in equilibrium between gravity and magnetic forces.We use a finite difference numerical technique which incorporates both vertical photospheric and horizontal prominence magnetic field measurements. The solution of this mixed boundary problem generally presents singularities at both the bottom and top of the model prominence. The removal of the singularities is achieved by superposition of solutions. Together with the line current equilibrium, these three conditions determine the amplitude of the magnetic field in the prominence, the flux below the prominence and the current intensity, for a given height of the line current. A numerical check of accuracy in the removal of singularities, is done by using known analytical solutions in the potential limit.We have investigated both bipolar and quadrupolar photospheric regions. In this mixed boundary problem the polarity of the field component orthogonal to the prominence is mainly fixed by the imposed height of the line current. For bipolar regions above (respectively below) a critical height the configuration is inverse (respectively normal). For quadrupolar regions the polarity is reversed if we refer the prominence polarity to the closest photospheric polarities. We introduce the polarity of the component parallel to the prominence axis with reference to a sheared arcade. Increasing the shear with fixed boundary conditions can increase or decrease the mass supported depending on the configuration.     

The study of magnetic reconnection in solar spicules

This work is devoted to study the magnetic reconnection instability under solar spicule conditions. Numerical study of the resistive tearing instability in a current sheet is presented by considering the magnetohydrodynamic (MHD) framework. To investigate the effect of this instability in a stratified atmosphere of solar spicules, we solve linear and non-ideal MHD equations in the x?z plane. In the linear analysis it is assumed that resistivity is only important within the current sheet, and the exponential growth of energies takes place faster as plasma resistivity increases. We are interested to see the occurrence of magnetic reconnection during the lifetime of a typical solar spicule.     

Breakout and Tether-Cutting Eruption Models Are Both Catastrophic (Sometimes)

We present a simplified analytic model of a quadrupolar magnetic field and flux rope to model coronal mass ejections. The model magnetic field is two-dimensional, force-free and has current only on the axis of the flux rope and within two current sheets. It is a generalization of previous models containing a single current sheet anchored to a bipolar flux distribution. Our new model can undergo quasi-static evolution either due to changes at the boundary or due to magnetic reconnection at either current sheet. We find that all three kinds of evolution can lead to a catastrophe, known as loss of equilibrium. Some equilibria can be driven to catastrophic instability either through reconnection at the lower current sheet, known as tether cutting, or through reconnection at the upper current sheet, known as breakout. Other equilibria can be destabilized through only one and not the other. Still others undergo no instability, but they evolve increasingly rapidly in response to slow steady driving (ideal or reconnective). One key feature of every case is a response to reconnection different from that found in simpler systems. In our two-current-sheet model a reconnection electric field in one current sheet causes the current in that sheet to increase rather than decrease. This suggests the possibility for the microscopic reconnection mechanism to run away.