Topology of Magnetic Field and Coronal Heating in Solar Active Regions

Force-free magnetic fields can be computed by making use of a new numerical technique, in which the fields are represented by a boundary integral equation based on a specific Green's function. Vector magnetic fields observed on the photospheric surface can be taken as the boundary conditions of this equation. In this numerical computation, the following two points are emphasized: (1) A new method for data reduction is proposed, for removing uncertainties in boundary data and determining the parameter in this Green's function, which is important for solving the boundary integral equation. In this method, the transverse components of the observed boundary field are calibrated with a linear force-free field model without changing their azimuth. (2) The computed 3-D fields satisfy the divergence-free and force-free conditions with high precision. The alignment of these field lines is mostly in agreement with structures in Hα and Yohkoh soft X-ray images. Since the boundary data are calibrated with a linear force-free field model, the computed 3-D magnetic field can be regarded as a quasi-linear force-free field approximation. The reconstruction of 3-D magnetic field in active region NOAA 7321 was taken as an example to quantitatively exhibit the capability of our new numerical technique.