Numerical calculation of force-free magnetic field for solar active regions and its application to prediction of solar flares

Abstract

Investigations on the numerical calculation of the force-free magnetic field for solar active regions and its application, carried out by the author and his collaborators in recent years, is summarized. In this paper, some existing numerical calculations of constant α force-free fields for active regions are evaluated briefly, and the results of applying these to the prediction of solar flares are presented. The main conclusions are: (1) Comparing the existing numerical calculations of constant α force-free fields in active regions, Chiu's expression is relatively superior to the others which are plagued by severe shortcomings. (2) The fact that many phenomena occuring in an active region can be explained naturally by the structure of the magnetic field extrapolated from Chiu's formula suggests that the approximation of constant α force-free fields is an acceptable model for the magnetic field of an active region. (3) Some parameters, such as the force-free factor α and the free energy of magnetic field ΔE, which is defined as the difference between the force-free and potential field energies, are closely related to the occurence rate of solar flares, and hence they could be used as criteria for the prediction of solar flares.