A solar flare triggering mechanism based on the Woltjer-Taylor minimum energy principle

Abstract

The general solution of the Woltjer-Taylor minimum energy state is found in the solar coronal geometry, which is modeled as a rectangular domain. It is shown that the solution bifurcates into two different states when the magnetic helicity integral or the geometrical factor defined as the ration of the height to the width of the domain is satisfactorily increased. Based on this analysis, it is theoretically proposed that a solar flare is a transition process between two different Woltjer-Taylor state, which are generated as a result of the bifurcation. The theory predicts that a solar flare is triggered when the vertical size of the coronal magnetic loop becomes longer than the horizontal size. The topological structure in the coronal magnetic field must be dramatically changed in the transition process. The result implies that in general, magnetic reconnection must be accompanied by a solar flare. The numerical simulation shows that the transition process is dynamically realized as a result of a twisting motion on the photosphere. Based on this theory, disagreements among recent simulation works on the plasmoid formation problem can be consistently explained.