Computation of the Potential Magnetic Field in Solar Active Regions

摘要

The Green's function solution of the Laplace equation for potential magnetic field in an external spherical region is found for special boundary conditions, namely, the derivatives of the potential along the selected direction. The set of programs which incorporates this solution to build potential magnetic field lines in solar active regions with the use of the photospheric line-of-sight field component is developed. The correctness of the method is testified with some model fields, and the optimal step size is found. 78 real solar active regions are analyzed and sets of potential magnetic field lines are calculated inside them with the use of the HMI/SDO and MDI/SOHO line-of-sight magnetograms as boundary conditions. The computed field lines are compared with flux tubes seen by the AIA/SDO and TRACE in the EUV range in each active region in an arbitrarily chosen time moment. It is found that the potential approximation is valid (applicable) only in 18 out of 78 cases, and thus is not very reliable. Also we try to find some correlations between applicability of the potential approximation for the selected regions and its McIntosh or Hale classes, and flare activity. No strong correlations are found.