Tetsuya Magara

INJECTION OF MAGNETIC ENERGY AND MAGNETIC HELICITY INTO THE SOLAR ATMOSPHERE BY AN EMERGING MAGNETIC FLUX TUBE

We present a detailed investigation of the dynamical behavior of emerging magnetic flux using three-dimensional MHD numerical simulation. A magnetic flux tube with a left-handed twist, initially placed below the photosphere, emerges into the solar atmosphere. This leads to a dynamical expansion of emerging field lines as well as an injection of magnetic energy and magnetic helicity into the atmosphere. The field-aligned distributions of forces and plasma flows show that emerging field lines can be classified as either expanding field lines or undulating field lines. A key parameter determining the type of emerging field line is the aspect ratio of its shape (the ratio of height to footpoint distance). The emergence generates not only vertical but also horizontal flows in the photosphere, both of which contribute to injecting magnetic energy and magnetic helicity. The contributions of vertical flows are dominant at the early phase of flux emergence, while horizontal flows become a dominant contributor later. The emergence starts with a simple dipole structure formed in the photosphere, which is subsequently deformed and fragmented, leading to a quadrupolar magnetic structure.

Dynamics of Emerging Flux Tubes in the Sun

This paper is intended to study the evolution of a magnetic flux tube that rises from the upper convection zone to the solar atmosphere by means of a 2.5-dimensional MHD simulation with the focus on the cross section of the flux tube. A cylindrical flux tube placed horizontally in the convection zone starts rising by magnetic buoyancy. When the top of the tube reaches the photosphere, the cross section of the tube changes from the circular shape to horizontally extended shape, forming a magnetic layer under the contact surface between the tube and the photosphere. As the plasma inside that magnetic layer is squeezed out to both sides of the layer, the contact surface is locally subject to the Rayleigh-Taylor instability because the lighter magnetic layer is overlain by the heavier photospheric layer. The wavelength of the undulating magnetic layer at the contact surface increases as the flattening of the tube proceeds, and after it becomes longer than the critical wavelength for the Rayleigh-Taylor instability, the tube can emerge through the photosphere. The emergence part of the tube starts expanding into the atmosphere if it has a sufficiently strong magnetic pressure compared to the surrounding gas pressure. We find that this expansion process is characterized by a self-similar behavior, that is, both the plasma and the magnetic field have a steady distribution in the expanding area. On the basis of those results, we try to clarify several important features of emerging flux tubes expected from observations. We focus on two solar phenomena, the birth of emerging flux tubes and the formation of filaments, and discuss the physical processes related to these phenomena.

SIGMOID STRUCTURE OF AN EMERGING FLUX TUBE

We present the results from three-dimensional MHD simulations of a magnetic flux tube emerging through the solar photosphere. The simulation is initialized with a straight tube of twisted magnetic field located in the upper convection zone. Buoyancy effects drive an arched segment of the tube upward through the photospheric layer and into the corona. Matter drains from the coronal field, which thereafter undergoes a rapid expansion. The coronal magnetic field formed in this manner exhibits outer poloidal field lines that resemble a potential arcade and inner toroidal field lines that emerge after the tube axis, forming sigmoid structure. The simulations suggest that the neutral-line shear and sigmoidal field arise as a natural by-product of flux emergence.

A Comparison of the Minimum Current Corona to a Magnetohydrodynamic Simulation of Quasi-Static Coronal Evolution

We use two different models to study the evolution of the coronal magnetic field that results from a simple photospheric field evolution. The first, the minimum current corona (MCC), is a self-consistent model for quasi-static evolution that yields an analytic expression approximating the net coronal currents and the free magnetic energy stored by them. For the second model calculation, the nonlinear, time-dependent equations of ideal magnetohydrodynamics are solved numerically subject to line-tied photospheric boundary conditions. In both models high current density concentrations form vertical sheets along the magnetic separator. The time history of the net current carried by these concentrations is quantitatively similar in each of the models. The magnetic energy of the line-tied simulation is significantly greater than that of the MCC, in accordance with the fact that the MCC is a lower bound on energies of all ideal models. The difference in energies can be partially explained from the different magnetic helicity injection in the two models. This study demonstrates that the analytic MCC model accurately predicts the locations of significant equilibrium current accumulations. The study also provides one example in which the energetic contributions of two different MHD constraints, line-tying constraints and flux constraints, may be quantitatively compared. In this example line-tying constraints store at least an order of magnitude more energy than do flux constraints.

A Unified Model of Coronal Mass Ejection-related Type II Radio Bursts

We present a theoretical model for the shock formation that is related to coronal and interplanetary type II radio bursts associated with coronal mass ejections on the basis of the magnetic reconnection model of eruptive solar flares. Coronal type II bursts are usually observed in the metric wavelength range (metric type II bursts), and interplanetary bursts are usually observed in the decametric-hectometric wavelength range (decametric-hectometric bursts). Our research shows that the decametric-hectometric type II radio bursts are produced by the piston-driven fast-mode MHD shock that is formed in front of an eruptive plasmoid (a magnetic island in the two-dimensional sense or a magnetic flux rope in the three-dimensional sense), while the metric radio bursts are produced by the reverse fast-mode MHD shock that is formed through the collision of a strong reconnection jet with the bottom of the plasmoid. This reverse shock apparently moves upward as long as the reconnection jet is sufficiently strong and dies away when the energy release of the reconnection stops or weakens significantly. On the other hand, the piston-driven fast shock continues to exist when the plasmoid moves upward. Our model succeeds in explaining the observational result that the piston-driven fast shock that produces decametric-hectometric type II bursts moves faster and survives longer than the other shock.

Three-Dimensional Evolution of a Magnetic Flux Tube Emerging into the Solar Atmosphere

This review is intended to discuss the evolution of the solar magnetic field emerging from the solar interior into the exterior with a focus on its dynamical behavior. Since emerging magnetic field goes through the dramatically changing environment ranging from a highly dense interior to a tenuous atmosphere, various dynamical processes become involved in the evolution. From a theoretical point of view, numerical simulations have been developing as a useful tool to study dynamical processes related to flux emergence. We first infer the state of magnetic field in the solar interior which is used as the preemergence state of flux-emergence simulaiton. We then show several fundamental physical processes obtained by simulations and discuss how recent theoretical modeling of emerging magnetic field has progressed to explain observations. As a topic of current interest, we also discuss the relation between flux emergence and large-scale solar activity such as coronal mass ejections.