Coronal Flux Rope Research Articles

Influence of Photospheric Magnetic Flux Distribution on Coronal Flux Rope Catastrophe

Previous studies of coronal magnetic flux rope systems indicated that these systems exhibit a catastrophic behavior for background fields with a specific photospheric flux distribution, and that the catastrophic energy threshold exceeds the associated open field energy. In this Letter, we take axisymmetrical bipolar fields in spherical geometry with different flux distributions on the photosphere as the background, and then examine how the flux distribution affects the catastrophic behavior and the energy threshold of a flux rope system. It is found that when the photospheric flux is concentrated too much toward the equator, the flux rope system loses its catastrophic behavior, i.e., that it evolves smoothly with the change of the rope properties. On the other hand, if the flux shifts poleward more than a split monopole field, a catastrophe behavior is recovered, and the catastrophic energy threshold increases in magnitude and percentage relative to the associated open field energy with increasing poleward shift of the flux. As a result, the flux rope erupts upward after catastrophe with a faster acceleration and a larger final speed when the flux is concentrated more toward the solar poles.

Modeling magnetic flux ropes in the solar atmosphere

Coronal flux ropes are highly sheared or twisted magnetic fields overlying polarity inversion lines on the solar photosphere. The formation of such flux ropes is briefly discussed. A coronal flux rope can be stable for many days and then suddenly lose equilibrium and erupt, producing a coronal mass ejection (CME). To understand what causes such eruptions, we need to determine the 3D magnetic structure of observed active regions prior to CMEs. This requires constructing nonlinear force free field models of active regions based on observed photospheric vector fields, Hα filaments, or coronal loop structures. We describe a new method for constructing models containing flux ropes.

Force Balance Analysis of a Coronal Magnetic Flux Rope in Equilibrium or Eruption

Based on a flux rope catastrophe model for coronal mass ejections (CMEs), we calculate the Lorentz forces acting on the rope in equilibrium or eruption in the background field, which is taken to be either a partially open bipolar field or a closed quadrupolar field. The forces, including upward lifting and downward pulling ones, are exerted by the coronal currents inside and outside the rope, as well as the potential field, which has the same normal component distribution on the photosphere as the background field. The resultant of forces vanishes for a rope in equilibrium. For both cases with different background fields, the primary lifting force is provided by the azimuthal current inside the rope and its image below the photosphere. It is mainly balanced by the pulling force produced by the background potential field when the rope is in equilibrium. During an eruption of the rope caused by catastrophe, the two predominant forces mentioned above decrease rapidly with the ascent of the rope. In the meantime, the vertical and/or transverse current sheets and their images, which form and develop along with the rope eruption, contribute additional and significant pulling (or restoring) forces that decelerate the rope. When fast magnetic reconnection takes place across these current sheets, the restoring force provided by the sheets will be greatly reduced, which may play an important role in the dynamics of the rope. The implication of such a conclusion in the acceleration of CMEs is briefly discussed.

Catastrophe of Coronal Flux Rope in Unsheared and Sheared Bipolar Magnetic Fields

This article investigates the catastrophic behavior of a preexisting coronal magnetic flux rope embedded in a dipolar or partially open bipolar background field, which is either unsheared or sheared with a given footpoint displacement of magnetic field lines. It is found that in the unsheared background field the catastrophic energy threshold decreases slightly with increasing extent of opening of the background field and increasing annular flux or decreasing axial flux of the flux rope, varying in the range between 1.08 and 1.1 times the magnetic energy of the corresponding fully open field. As the background field is sheared, on the other hand, catastrophe may be triggered by shear provided that the presheared magnetic energy of the system is high enough. The catastrophic energy threshold is almost invariant but then increases monotonically with the increase of the presheared magnetic energy of the system, and it is bounded above by the energy of the corresponding flux rope system associated with an unsheared background field.

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 ejection geoeffectiveness depending on field orientation and interplanetary coronal mass ejection classification

In this study, we have examined the coronal mass ejection (CME) geoeffectiveness characterized by Dst ≤ −50 nT according to the field orientation (N or S) in a CME source region and its dependence on interplanetary CME (ICME) classification (magnetic clouds or ejecta). We first considered 133 CME‐ICME pairs (1996 to 2001) whose CME source locations are identified by SOHO Large‐Angle Spectrometric Coronograph (SOHO/LASCO) and extreme ultraviolet imaging telescope (SOHO/EIT) data. Then we identified the shapes (S or Inverse‐S) of the X‐ray sigmoids associated with 63 of these CMEs using Yohkoh/Soft X‐Ray Telescope (SXT) data. To determine the field orientation in the sigmoids, we applied the coronal flux rope (CFR) model and the force‐free field (FFF) model to these 63 sigmoids using SOHO/Michelson Doppler Imager (MDI) images. We present the results in contingency tables, classified according to solar field orientation and geomagnetic storm strength/occurrence. We found that (1) the prediction of geomagnetic storms (Dst ≤ −50 nT) based on the CFR model is much better than that on the FFF model, (2) the prediction for magnetic clouds (MCs) is much better than that for ejecta (EJ), which implies that the field orientation of the MCs is well conserved through the heliosphere, and (3) for about 86% of the magnetic clouds, the directions of their leading fields are consistent with those in the CME source regions. Our results support the findings that the southward orientations of the magnetic field in the CME source regions plays an important role in the production of geomagnetic storms.

Models of the Large‐Scale Corona. I. Formation, Evolution, and Liftoff of Magnetic Flux Ropes

The response of the large-scale coronal magnetic field to transport of magnetic flux in the photosphere is investigated. In order to follow the evolution on long timescales, the coronal plasma velocity is assumed to be proportional to the Lorentz force (magnetofriction), causing the coronal field to evolve through a series of nonlinear force-free states. Magnetofrictional simulations are used to study the formation and evolution of coronal flux ropes, highly sheared and/or twisted fields located above polarity inversion lines on the photosphere. As in our earlier studies, the three-dimensional numerical model includes the effects of the solar differential rotation and small-scale convective flows; the latter are described in terms of surface diffusion. The model is extended to include the effects of coronal magnetic diffusion, which limits the degree of twist of coronal flux ropes, and the solar wind, which opens up the field at large height. The interaction of two bipolar magnetic regions is considered. A key element in the formation of flux ropes is the reconnection of magnetic fields associated with photospheric flux cancellation at the polarity inversion lines. Flux ropes are shown to form both above the external inversion line between bipoles (representing type B filaments) and above the internal inversion line of each bipole in a sigmoid shape. It is found that once a flux rope has formed, the coronal field may diverge from equilibrium with the ejection of the flux rope. After the flux rope is ejected, the coronal field once again relaxes down to an equilibrium. This ability to follow the evolution of the coronal fields through eruptions is essential for future full-Sun simulations in which multiple bipoles are evolved for many months or years.

Partially-ejected flux ropes: implications for space weather

The structure and evolution of the sources of solar activity directly affects the nature of space weather disturbances that reach the Earth. We have previously demonstrated that the loss of equilibrium and partial ejection of a coronal magnetic flux rope matches observations of coronal mass ejections (CMEs) and their precursors.In this paper we discuss the significance of such a partially-ejected rope for space weather. We will consider how the evolution and bifurcation of the rope modifies it from its initial, source configuration. In particular, we will consider how reconnections and writhing motions lead to an escaping rope which has an axis rotated counterclockwise from the original rope axis orientation, and which is rooted in transient coronal holes external to the original source region.

Coronal Flux Rope Catastrophe in Octapole Magnetic Fields

As demonstrated by many previous studies, a system consisting of an isolated coronal flux rope and a surrounding background magnetic field exhibits a catastrophic behavior. In particular, if the magnetic field of the system is force-free and axisymmetric in spherical geometry, the magnetic energy at the catastrophic point, referred to as the catastrophic energy threshold, is found to be larger than the corresponding partly or fully open field energy. This paper takes an octapole field as the background and introduces a flux rope within the central arcade of the octapole field. A relaxation method based on time-dependent ideal magnetohydrodynamic (MHD) simulations is used to find axisymmetric force-free field solutions in spherical geometry associated with the flux rope system. With respect to an increase of either the annular flux Φp or the axial flux Φϕ of the rope, the system exhibits a catastrophic behavior as expected, and the catastrophic energy threshold is larger than that of the corresponding partly open field, in which the central arcade is opened up, but the remainder remains closed. For a given octapole field, the energy threshold depends on either Φp or Φϕ at the catastrophic point, and it increases with increasing Φp or decreasing Φϕ. On the other hand, the extent to which the central bipolar component of the octapole field is open also affects the energy threshold. These results differ from those for the bipolar background field case, in which the catastrophic energy threshold is almost independent of the magnetic properties of the flux rope at the catastrophic points and the extent to which the background field is open. The reason for such a difference is briefly discussed.

Confined and Ejective Eruptions of Kink-unstable Flux Ropes

The ideal helical kink instability of a force-free coronal magnetic flux rope, anchored in the photosphere, is studied as a model for solar eruptions. Using the flux rope model of Titov and D?moulin as the initial condition in MHD simulations, both the development of helical shape and the rise profile of a confined (or failed) filament eruption (on 2002 May 27) are reproduced in very good agreement with the observations. By modifying the model such that the magnetic field decreases more rapidly with height above the flux rope, a full (or ejective) eruption of the rope is obtained in very good agreement with the developing helical shape and the exponential-to-linear rise profile of a fast coronal mass ejection (CME) on 2001 May 15. This confirms that the helical kink instability of a twisted magnetic flux rope can be the mechanism of the initiation and the initial driver of solar eruptions. The agreement of the simulations with properties that are characteristic of many eruptions suggests that they are often triggered by the kink instability. The decrease of the overlying field with height is a main factor in deciding whether the instability leads to a confined event or to a CME.

Density Structure of a Preeruption Coronal Flux Rope

A density model is developed for a coronal flux rope with a specified magnetic field configuration in the noninteracting limit, for which transverse pressure forces can be neglected and flows are rapid enough (>1 km s-1) to invalidate a hydrostatic solution. In the coronal portion of the flux rope, we find that the plasma density is depleted on-axis, where the magnetic field lines are least twisted.

Double Catastrophe of Coronal Flux Rope in Quadrupolar Magnetic Field

Using a relaxation method based on time-dependent ideal magnetohydrodynamic simulations, we find 2.5-dimensional force-free field solutions in spherical geometry, which are associated with an isolated flux rope embedded in a quadrupolar background magnetic field. The background field is of Antiochos type, consisting of a dipolar and an octopolar component with a neutral point somewhere in the equatorial plane. The flux rope is characterized by its magnetic fluxes, including the annular flux Φp and the axial magnetic flux Φ, and its geometric features described by the height of the rope axis and the length of the vertical current sheet below the rope. It is found that for a given Φp, the force-free field exhibits a complex catastrophic behavior with respect to increasing Φ. There exist two catastrophic points, and the catastrophic amplitude, measured by the jump in the height of the rope axis, is finite for both catastrophes. As a result, the flux rope may levitate stably in the corona after catastrophe, with a transverse current sheet above and a vertical current sheet below. The magnetic energy threshold for the two successive catastrophes are found to be larger than the corresponding partly open field energy. We argue that it is the transverse current sheet formed above the flux rope that provides a downward Lorentz force on the flux rope and thus keeps the rope levitating stably in the corona.

Coronal flux rope catastrophe in the presence of solar wind

Previous studies of the equilibrium property and catastrophic behavior of coronal magnetic flux ropes assumed that the background field is potential and the background plasma is in static equilibrium. This paper abandons these assumptions and considers the effect of the background solar wind. For simplicity, we take a polytropic process approximation in the energy equation and confine ourselves to axisymmetrical problems in spherical geometry. Steady solutions are obtained by time‐dependent simulations for a system consisting of a magnetostatic helmet streamer astride the equator with a flux rope in it and a steady solar wind outside. The coronal flux rope is characterized by its azimuthal and annular magnetic fluxes and total mass. It is shown that the system possesses a catastrophic behavior. As the azimuthal or annular flux of the rope increases or the total mass in the rope decreases, the flux rope and the helmet streamer expand, the field lines in the outermost part of the streamer are gradually opened, and the originally static plasma there flows outward along the newly opened field lines and joins the solar wind. The magnetic energy of the system increases during this process. We find an energy threshold that is larger than the corresponding open field energy by about 8% if the field in the rope is close to force‐free. The gravity raises the threshold by an amount that approximately equals the magnitude of the excess gravitational energy in the rope. The flux rope sticks to the solar surface in equilibrium if the magnetic energy of the system is below the threshold, whereas it erupts otherwise. In the latter case, the flux rope is gradually accelerated and reaches a velocity that is slightly larger than the background solar wind velocity. We argue that such a catastrophe may serve as a physical mechanism for slow coronal mass ejections. A brief comparison is also made between the present case and the magnetostatic case in the catastrophic behavior of the system.

Coronal Flux Rope Catastrophe in Partly-Open Multipolar Magnetic Field

采用球坐标下二维三分量理想MHD模型,研究部分开放多极背景磁场中日冕磁绳的灾变现象.背景磁场由含3个闭合双极场的冕流和带赤道中性电流片的开放场构成,磁绳位于中心双极场的下方,其特性由环向磁通和轴向磁通表征.对给定的环向磁通,存在轴向磁通的一个临界值;对给定的轴向磁通,也存在环向磁通的一个临界值.在该临界值以下,磁绳附着于太阳表面,系统处于平衡状态;该临界值一旦被超越,磁绳将脱离太阳表面向上喷发,说明部分开放多极背景磁场中的日冕磁绳系统存在灾变现象.本文算例表明,灾变点对应的磁能阈值超过对应部分开放场(中心双极场开放,两侧的双极场仍维持闭合)能量约15%,其超过部分可为日冕物质抛射一类太阳爆发提供能源.

Coronal Magnetohydrodynamic Evolution Driven by Subphotospheric Conditions

We consider the approach to the theory of formation, evolution, and major disruption of coronal twisted flux ropes, in which subphotospheric structures play a crucial role. We set a boundary value problem in the corona in which the boundary conditions at the level are determined by a simple kinematic model describing the rising of a tube throughout the convection zone. In addition to peculiar features like the existence of areas of flux concentration on the lower boundary and the bending of the polarity inversion line, we find that the coronal configuration suffers a transition from arcade to rope topology and (later) a transition from a slow quasi-static evolution to a dynamic nonequilibrium one, both these critical phenomena occurring during the phase of decrease of the net flux. There is a continuous injection of magnetic helicity into the corona, and the magnetic energy remains smaller than that of the corresponding open field. Contrary to what has been observed in some other simulations, the formation of the equilibrium flux rope prior to the disruption is not associated with some reconnection on the photospheric surface. This may possibly suggest the utility of different observational diagnostics.

The Catastrophe of Coronal Magnetic Flux Ropes in CMEs

A brief review is given on the progress made in the study of the catastrophe of coronal magnetic flux ropes with implication in coronal mass ejections (CMEs). Relevant studies have been so far limited to 2.5-D cases, with a flux rope levitating in the corona, either parallel to the photosphere in Cartesian geometry or encircling the Sun like a torus in spherical geometry. The equilibrium properties of the system depend on the features of the flux rope and the surrounding background state. Under certain circumstances, the flux rope exhibits a catastrophic behavior, namely, the rope loses equilibrium and erupts upward upon an infinitesimal variation of any control parameter associated with the background state or the flux rope. The magnetic energy of the system right at the catastrophic point may exceed the corresponding open field energy so that after the background field is opened up by the erupting flux rope, a certain amount of magnetic free energy is left for the heating and acceleration of coronal plasma against gravity. The flux rope model has been used to reveal the common features of CMEs and to simulate typical CME events, proving to be a promising mechanism for the initiation of CMEs. Incidentally, the Aly conjecture on the maximum magnetic energy of force-free fields places a serious constraint on 2.5-D flux models. Nevertheless, current sheets must form during a catastrophe on the Alfven timescale, and magnetic reconnection across the newly formed current sheets may contribute to circumventing such a constraint. In this sense, the catastrophe simply plays a role of driver for the fast magnetic reconnection, and a combination of them is thus responsible for the initiation of CMEs.

Coronal Magnetic Flux Ropes in Quadrupolar Magnetic Fields

Using a 2.5-D, time-dependent ideal MHD model in spherical coordinates, we carry out a numerical study of the equilibrium properties of coronal magnetic flux ropes in a quadrupolar background magnetic field. For such a flux rope system, a catastrophic occurs: the flux rope is detached from the photosphere and jumps to a finite altitude with a vertical current sheet below. There is a transversal current sheet formed above the rope, and the whole system stays in quasi-equilibrium. We argue that the additional Lorentz force provided by the transversal current sheet on the flux rope plays an important role in keeping the system in quasi-equilibrium in the corona. To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Formation of current sheets and sigmoidal structure by the kink instability of a magnetic loop

We study dynamical consequences of the kink instability of a twisted coronal flux rope, using the force-free coronal loop model by Titov & D\'emoulin (1999) as the initial condition in ideal-MHD simulations. When a critical value of the twist is exceeded, the long-wavelength ($m=1$) kink mode develops. Analogous to the well-known cylindrical approximation, a helical current sheet is then formed at the interface with the surrounding medium. In contrast to the cylindrical case, upward-kinking loops form a second, vertical current sheet below the loop apex at the position of the hyperbolic flux tube (generalized X line) in the model. The current density is steepened in both sheets and eventually exceeds the current density in the loop (although the kink perturbation starts to saturate in our simulations without leading to a global eruption). The projection of the field lines that pass through the vertical current sheet shows an S shape whose sense agrees with the typical sense of transient sigmoidal (forward or reverse S-shaped) structures that brighten in soft X rays prior to coronal eruptions. The upward-kinked loop has the opposite S shape, leading to the conclusion that such sigmoids do not generally show the erupting loops themselves but indicate the formation of the vertical current sheet below them that is the central element of the standard flare model.

The Magnetic Helicity Budget of Solar Active Regions and Coronal Mass Ejections

We compute the magnetic helicity injected by transient photospheric horizontal flows in six solar active regions associated with halo coronal mass ejections (CMEs) that produced major geomagnetic storms and magnetic clouds (MCs) at 1 AU. The velocities are computed using the local correlation tracking (LCT) method. Our computations cover time intervals of 1 10-150 hr, and in four active regions the accumulated helicities due to transient flows are factors of 8-12 larger than the accumulated helicities due to differential rotation. As was first pointed out by DCmoulin and Berger, we suggest that the helicity computed with the LCT method yields not only the helicity injected from shearing motions but also the helicity coming from flux emergence. We compare the computed helicities injected into the corona with the helicities carried away by the CMEs using the MC helicity computations as proxies to the CME helicities. If we assume that the length of the MC flux tubes is I = 2 AU, then the total helicities injected into the corona are a factor of 2.94 lower than the total CME helicities. If we use the values of 1 determined by the condition for the initiation of the kink instability in the coronal flux rope or I = 0.5 AU then the total CME helicities and the total helicities injected into the corona are broadly consistent. Our study, at least partially, clears up some of the discrepancies in the helicity budget of active regions because the discrepancies appearing in our paper are much smaller than the ones reported in previous studies. However, they point out the uncertainties in the MC/CME helicity calculations and also the limitations of the LCT method, which underestimates the computed helicities.

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 photosphere, and its magnetic properties, i.e., the annular magnetic flux P and the axial magnetic flux P, are controlled by a single emergence parameter. The whole system 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 P and P: no catastrophe occurs. Moreover, there exists a steep segment in the profiles of the geometrical parameters versus either P or P, and the faster the background field decays with height, the larger both the gradient and the growth amplitude within the steep segment will be.