We propose a new model for the initiation of a solar coronal mass ejection (CME). The model agrees with two properties of CMEs and eruptive flares that have proved to be very difficult to explain with previous models: (1) very low-lying magnetic field lines, down to the photospheric neutral line, can open toward infinity during an eruption; and (2) the eruption is driven solely by magnetic free energy stored in a closed, sheared arcade. Consequently, the magnetic energy of the closed state is well above that of the posteruption open state. The key new feature of our model is that CMEs occur in multipolar topologies in which reconnection between a sheared arcade and neighboring flux systems triggers the eruption. In this "magnetic breakout" model, reconnection removes the unsheared field above the low-lying, sheared core flux near the neutral line, thereby allowing this core flux to burst open. We present numerical simulations that demonstrate our model can account for the energy requirements for CMEs. We discuss the implication of the model for CME/flare prediction.

https://iopscience.iop.org/article/10.1086/306563/pdf

A Model for Solar Coronal Mass Ejections

This paper outlines the current understanding of solar flares, mainly focused on magnetohydrodynamic (MHD) processes responsible for producing a flare. Observations show that flares are one of the most explosive phenomena in the atmosphere of the Sun, releasing a huge amount of energy up to about 1032 erg on the timescale of hours. Flares involve the heating of plasma, mass ejection, and particle acceleration that generates high-energy particles. The key physical processes for producing a flare are: the emergence of magnetic field from the solar interior to the solar atmosphere (flux emergence), local enhancement of electric current in the corona (formation of a current sheet), and rapid dissipation of electric current (magnetic reconnection) that causes shock heating, mass ejection, and particle acceleration. The evolution toward the onset of a flare is rather quasi-static when free energy is accumulated in the form of coronal electric current (field-aligned current, more precisely), while the dissipation of coronal current proceeds rapidly, producing various dynamic events that affect lower atmospheres such as the chromosphere and photosphere. Flares manifest such rapid dissipation of coronal current, and their theoretical modeling has been developed in accordance with observations, in which numerical simulations proved to be a strong tool reproducing the time-dependent, nonlinear evolution of a flare. We review the models proposed to explain the physical mechanism of flares, giving an comprehensive explanation of the key processes mentioned above. We start with basic properties of flares, then go into the details of energy build-up, release and transport in flares where magnetic reconnection works as the central engine to produce a flare.

/pdf/solar-flares-magnetohydrodynamic-processes-44l1zcjlip.pdf

Solar Flares: Magnetohydrodynamic Processes

We analyze the physical mechanisms that form a three-dimensional coronal flux rope and later cause its eruption. This is achieved by a zero-β magnetohydrodynamic (MHD) simulation of an initially potential, asymmetric bipolar field, which evolves by means of simultaneous slow magnetic field diffusion and sub-Alfvenic, line-tied shearing motions in the photosphere. As in similar models, flux-cancellation-driven photospheric reconnection in a bald-patch (BP) separatrix transforms the sheared arcades into a slowly rising and stable flux rope. A bifurcation from a BP to a quasi-separatrix layer (QSL) topology occurs later on in the evolution, while the flux rope keeps growing and slowly rising, now due to shear-driven coronal slip-running reconnection, which is of tether-cutting type and takes place in the QSL. As the flux rope reaches the altitude at which the decay index –∂ln B/∂ln z of the potential field exceeds ~3/2, it rapidly accelerates upward, while the overlying arcade eventually develops an inverse tear-drop shape, as observed in coronal mass ejections (CMEs). This transition to eruption is in accordance with the onset criterion of the torus instability. Thus, we find that photospheric flux-cancellation and tether-cutting coronal reconnection do not trigger CMEs in bipolar magnetic fields, but are key pre-eruptive mechanisms for flux ropes to build up and to rise to the critical height above the photosphere at which the torus instability causes the eruption. In order to interpret recent Hinode X-Ray Telescope observations of an erupting sigmoid, we produce simplified synthetic soft X-ray images from the distribution of the electric currents in the simulation. We find that a bright sigmoidal envelope is formed by pairs of -shaped field lines in the pre-eruptive stage. These field lines form through the BP reconnection and merge later on into -shaped loops through the tether-cutting reconnection. During the eruption, the central part of the sigmoid brightens due to the formation of a vertical current layer in the wake of the erupting flux rope. Slip-running reconnection in this layer yields the formation of flare loops. A rapid decrease of currents due to field line expansion, together with the increase of narrow currents in the reconnecting QSL, yields the sigmoid hooks to thin in the early stages of the eruption. Finally, a slightly rotating erupting loop-like feature (ELLF) detaches from the center of the sigmoid. Most of this ELLF is not associated with the erupting flux rope, but with a current shell that develops within expanding field lines above the rope. Only the short, curved end of the ELLF corresponds to a part of the flux rope. We argue that the features found in the simulation are generic for the formation and eruption of soft X-ray sigmoids.

https://iopscience.iop.org/article/10.1088/0004-637X/708/1/314/pdf

Formation of Torus-Unstable Flux Ropes and Electric Currents in Erupting Sigmoids

Nonlinear force-free field (NLFFF) models are thought to be viable tools for investigating the structure, dynamics, and evolution of the coronae of solar active regions. In a series of NLFFF modeling studies, we have found that NLFFF models are successful in application to analytic test cases, and relatively successful when applied to numerically constructed Sun-like test cases, but they are less successful in application to real solar data. Different NLFFF models have been found to have markedly different field line configurations and to provide widely varying estimates of the magnetic free energy in the coronal volume, when applied to solar data. NLFFF models require consistent, force-free vector magnetic boundary data. However, vector magnetogram observations sampling the photosphere, which is dynamic and contains significant Lorentz and buoyancy forces, do not satisfy this requirement, thus creating several major problems for force-free coronal modeling efforts. In this paper, we discuss NLFFF modeling of NOAA Active Region 10953 using Hinode/SOT-SP, Hinode/XRT, STEREO/SECCHI-EUVI, and SOHO/MDI observations, and in the process illustrate three such issues we judge to be critical to the success of NLFFF modeling: (1) vector magnetic field data covering larger areas are needed so that more electric currents associated with the full active regions of interest are measured, (2) the modeling algorithms need a way to accommodate the various uncertainties in the boundary data, and (3) a more realistic physical model is needed to approximate the photosphere-to-corona interface in order to better transform the forced photospheric magnetograms into adequate approximations of nearly force-free fields at the base of the corona. We make recommendations for future modeling efforts to overcome these as yet unsolved problems.

/pdf/a-critical-assessment-of-nonlinear-force-free-field-modeling-6rnd1vrzgu.pdf

A critical assessment of nonlinear force-free field modeling of the solar corona for active region 10953

We compare six algorithms for the computation of nonlinear force-free (NLFF) magnetic fields (including optimization, magnetofrictional, Grad-Rubin based, and Green's function-based methods) by evaluating their performance in blind tests on analytical force-free-field models for which boundary conditions are specified either for the entire surface area of a cubic volume or for an extended lower boundary only. Figures of merit are used to compare the input vector field to the resulting model fields. Based on these merit functions, we argue that all algorithms yield NLFF fields that agree best with the input field in the lower central region of the volume, where the field and electrical currents are strongest and the effects of boundary conditions weakest. The NLFF vector fields in the outer domains of the volume depend sensitively on the details of the specified boundary conditions; best agreement is found if the field outside of the model volume is incorporated as part of the model boundary, either as potential field boundaries on the side and top surfaces, or as a potential field in a skirt around the main volume of interest. For input field (B) and modeled field (b), the best method included in our study yields an average relative vector error En =� |B− b|� /�| B|� of only 0.02 when all sides are specified and 0.14 for the case where only the lower boundary is specified, while

/pdf/nonlinear-force-free-modeling-of-coronal-magnetic-fields-1exgowtuvp.pdf

Nonlinear force-free modeling of coronal magnetic fields part i: a quantitative comparison of methods

The problem under discussion is that of calculating magnetic field configurations in which the Lorentz force j x B is everywhere zero, subject to specified boundary conditions. We choose to represent the magnetic field in terms of Clebsch variables in the form B = grad alpha x grad beta. These variables are constant on any field line so that each field line is labeled by the corresponding values of alpha and beta. When the field is described in this way, the most appropriate choice of boundary conditions is to specify the values of alpha and beta on the bounding surface. We show that such field configurations may be calculated by a magneto-frictional method. We imagine that the field lines move through a stationary medium, and that each element of magnetic field is subject to a frictional force parallel to and opposing the velocity of the field line. This concept leads to an iteration procedure for modifying the variables alpha and beta, that tends asymptotically towards the force-free state. We apply the method first to a simple problem in two rectangular dimensions, and then to a problem of cylindrical symmetry that was previously discussed by Barnes and Sturrock (1972). In one important respect, our new results differ from the earlier results of Barnes and Sturrock, and we conclude that the earlier article was in error.

Force-free magnetic fields - The magneto-frictional method

The problem under discussion is that of calculating magnetic field configurations in which the Lorentz force j x B is everywhere zero, subject to specified boundary conditions. The magnetic field is represented in terms of Clebsch variables in the form B = grad alpha x grad beta. These variables are constant on any field line so that each field line is labeled by the corresponding values of alpha and beta. When the field is described in this way, the most appropriate choice of boundary conditions is to specify the values of alpha and beta on the bounding surface. The author show that such field configurations may be calculated by a magneto-frictional method. They imagine that the field lines move through a stationary medium, and that each element of magnetic field is subject to a frictional force parallel to and opposing the velocity of the field line. This concept leads to an iteration procedure for modifying the variables alpha and beta, that tends asymptotically towards the force-free state. The method is applied first to a simple problem in two rectangular dimensions, and then to a problem of cylindrical symmetry, previously discussed by Barnes and Sturrock (1972). In one important respect, thesemore » new results differ from the earlier results of Barnes and Sturrock, and it is concluded that the earlier article was in error.« less

W. H. Yang

Papers

Force-free magnetic fields - The magneto-frictional method

Force-Free Magnetic Fields,