Relationship between electric currents,photospheric motions,chromospheric activity,and magnetic field topology

Through coordinated observations made during the Max'91 campaign in June 1989 in Potsdam (magnetograms), Debrecen (white light and H), and Meudon (MSDP), we follow the evolution of the sunspot group in active region NOAA 5555 for 6 days. The topology of the coronal magnetic field is investigated by using a method based on the concept of separatrices - applied previously (Mandriniet al., 1991) to a magnetic region slightly distorted by field-aligned currents. The present active region differs by having significant magnetic shear. We find that the H flare kernels and the main photospheric electric current cells are located close to the intersection of the separatrices with the chromosphere, in a linear force-free field configuration adapted to the observed shear. Sunspot motions, strong currents, isolated polarities, or intersecting separatrices are not in themselves sufficient to produce a flare. A combination of them all is required. This supports the idea that flares are due to magnetic reconnection, when flux tubes with field-aligned currents move towards the separatrix locations.     

The 3-D boundary element formulation of linear force-free magnetic fields with finite energy content in semi-infinite space

In this paper, a formulation describing a force-free magnetic field with constant, either 0 or = 0, with finite energy content in semi-infinite space,z > 0, above the Sun is proposed and solved uniquely by a numerical method: the boundary element method (BEM). The method is effective and convenient in extrapolating the magnetic field above the solar surface, , directly from the measured magnetogram. Meanwhile, no additional data treatment is needed. Based on the existence of such a field, the uniqueness of the solution in the present formulation is proved and some useful properties are obtained. The validity is also demonstrated by its application to the magnetic field computation in the chromosphere from observed magnetogram data. The practical feasibility is thus discussed and further confirmed.     

RECONSTRUCTING THE SOLAR CORONAL MAGNETIC FIELD AS A FORCE-FREE MAGNETIC FIELD

We present some preliminary results on different mathematical problems encountered in attempts to reconstruct the coronal magnetic field, assumed to be in a force-free state, from its values in the photosphere. We discuss the formulations associated with these problems, and some new numerical methods that can be used to get their approximate solutions. Both the linear constant- and the nonlinear cases are considered. We also discuss the possible use of dynamical 3D MHD codes to construct approximate solutions of the equilibrium force-free equations, which are needed for testing numerical extrapolation schemes.     

Calculation of force-free magnetic field with non-constant α

A numerical method is developed for solving the force-free magnetic field equation, × B = B, with spatially-varying . The boundary conditions required are the distribution of B _n (viz. normal component of the field on the photosphere) as well as the value of in the region of positive (or negative) B _n . Examples of calculations are presented for a simple model of a solar bipolar magnetic region. It is found that the field configuration and the energy stored in the field depend crucially on the distribution of . The present method can be applied to a more complex configuration observed on the Sun by making use of actual magnetic field measurements.On leave of absence from Department of Astronomy, University of Tokyo.     

On practical representation of magnetic field

Various manners of determination of a magnetic field are reviewed briefly from the standpoint of practicality and uniqueness. Then a practical representation of magnetic fields in terms of a class of force-free magnetic field is described. The proposed scheme is based on the physical consideration that in the chromosphere and lower corona a quasistatic magnetic field must be nearly force-free and that for the class of force-free magnetic field, i.e., ×B=B with = constant, the magnetic field can be determined uniquely from the observed distribution of the vertical component of a magnetic field. The applicability of the representation is demonstrated by examples and the limitations are discussed.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Vector magnetic field evolution,energy storage,and associated photospheric velocity shear within a flare-productive active region

The evolution of vector photospheric magnetic fields has been studied in concert with photospheric spot motions for a flare-productive active region. Over a three-day period (5–7 April, 1980), sheared photospheric velocity fields inferred from spot motions are compared both with changes in the orientation of transverse magnetic fields and with the flare history of the region. Rapid spot motions and high inferred velocity shear coincide with increased field alignment along the B _L= 0 line and with increased flare activity; a later decrease in velocity shear precedes a more relaxed magnetic configuration and decrease in flare activity. Crude energy estimates show that magnetic reconfiguration produced by the relative velocities of the spots could cause storage of 10³² erg day^–1, while the flares occurring during this time expended 10³¹ erg day^–1.Maps of vertical current density suggest that parallel (as contrasted with antiparallel) currents flow along the stressed magnetic loops. For the active region, a constant-, force-free magnetic field (J = B) at the photosphere is ruled out by the observations.Presently located at NASA/MSFC, Huntsville, Ala. 35812, U.S.A.     

Including stereoscopic information in the reconstruction of coronal magnetic fields

We present a method to include stereoscopic information about the three-dimensional structure of flux tubes into the reconstruction of the coronal magnetic field. Due to the low plasma beta in the corona we can assume a force-free magnetic field, with the current density parallel to the magnetic field lines. Here we use linear force-free fields for simplicity. The method uses the line-of-sight magnetic field on the photosphere as observational input. The value of is determined iteratively by comparing the reconstructed magnetic field with the observed structures. The final configuration is the optimal linear force-free solution constrained by both the photospheric magnetogram and the observed plasma structures. As an example we apply our method to SOHO MDI/EIT data of an active region. In the future it is planned to apply the method to analyse data from the SECCHI instrument aboard the STEREO mission.     

Force-free equilibrium at magnetic neutral points

It is shown that, at neutral points of force-free magnetic fields, the electric current density must vanish. This property is independent of whether the neutral points are isolated or (e.g.) fill lines or surfaces. One implication is the fact that in a cold pressureless plasma the formation of neutral current sheets cannot be adiabatically slow. The field-line topology in the neighbourhood of neutral points is discussed. At neutral points of force-free magnetic fields in general three constant- surfaces, defined by the equation ×B=B, with the same value of intersect orthogonally. If, during a time-development, the magnetic field gradient matrix B _i/x _j becomes singular at a neutral point, the field topology can change qualitatively — in general connected with the merger of two or more neutral points into one and/or the splitting up of one neutral point into several others. This can be interpreted as implying the transition from a quasi-static evolution to a dynamical state in which magnetic energy is released.     

Coronal force-free magnetic field: Source-surface model

Models of the magnetic field in the solar chromosphere and corona are still mainly based on theoretical extrapolations of photospheric measurements. For the practical calculation of the global field, the so-called source-surface model has been introduced, in which the influence of the solar wind is described by the requirement that the field be radial at some exterior (source) surface. Then the assumption that the field is current-free in the volume between the photosphere and this surface allows for its determination from the photospheric measurement. In the present paper a generalization of the source-surface model to force-free fields is proposed. In the generalized model the parameter( = ×B·B/B ²)must be non-constant (or vanish identically) and currents are restricted to regions with closed field lines. A mathematical algorithm for computing the field from boundary data is devised.     

Topology of Magnetic Field and Coronal Heating in Solar Active Regions – II. The Role of Quasi-Separatrix Layers

The photospheric vector magnetic fields, H and soft X-ray images of AR 7321 were simultaneously observed with the Solar Flare Telescope at Mitaka and the Soft X-ray Telescope of Yohkoh on October 26, 1992, when there was no important activity in this region. Taking the observed photospheric vector magnetic fields as the boundary condition, 3D magnetic fields above the photosphere were computed with a new numerical technique. Then quasi-separatrix layers (QSLs), i.e., regions where 3D magnetic reconnection takes place, were determined in the computed 3D magnetic fields. Since Yohkoh data and Mitaka data were obtained in well-arranged time sequences during the day, the evolution of 3D fields, H features and soft X-ray features in this region can be studied in detail. Through a comparison among the 3D magnetic fields, H features and soft X-ray features, the following results have been obtained: (a) H plages are associated with the portions of QSLs in the chromosphere; (b) diffuse coronal features (DCFs) and bright coronal features (BCFs) are morphologically confined by the coronal linkage of the field lines related to the QSLs; (c) BCFs are associated with a part of the magnetic field lines related to the QSLs. These results suggest that as the likely places where energy release may occur by 3D magnetic reconnection, QSLs play an important role in the chromospheric and coronal heating in this active region.