A Green’s function method for calculating the potential magnetic field in solar active regions in a spherical geometry

Abstract

A Green’s function solution of Laplace’s equation for the potential magnetic field in an external spherical region is found using the derivative of the potential along a selected direction as a boundary condition. A set of programs applying this solution to construct the potential magnetic-field lines in solar active regions based on the photospheric line-of-sight field component has been developed. The method is tested using some model fields, and the optimal step size is found for realistic conditions. The developed software is applied to four real solar active regions, adopting HMI/SDO magnetograms as the boundary conditions. The potential magnetic field in the chromosphere and corona have been reconstructed for the selected regions. The calculated field lines are compared with flux tubes observed by AIA/SDO in the EUV. This comparison is used as a basis to discuss the applicability of a potential field approximation to the magnetic fields in solar active regions.