Reconstructing spherical nonlinear force-free field in the solar corona

We present a spherical nonlinear force-free field (NFFF) reconstructing method based on the photospheric vector magnetograms. The importance of this method is its ability to reveal the NFFF configurations, which is necessary for understanding the physical mechanisms of the initiation of the large-scale solar eruptions, such as coronal mass ejections and sympathetic flares. Using smooth continuous functions, the basic NFFF-governing partial differential equations in spherical coordinates reduce to a set of tractable ordinary differential equations. The numerical scheme used in this paper is similar to the recent local nonlinear force-free one developed by Song and coworkers. To illustrate this method, we give two test examples. One is to compute a well-known NFFF analytical solution given by Low & Lou. The other is for two active regions NOAA 10486 and NOAA 10488 observed on 2003 October 29. The results show that the transequatorial magnetic loops are revealed and coincided with some EUV Imaging Telescope loops.