Simulation Study of the Formation Mechanism of Sigmoidal Structure in the Solar Corona

The formation mechanism of sigmoidal structure in the solar coronal magnetic field is studied using the three-dimensional magnetohydrodynamic numerical simulations, based on the so-called reversed-shear flare model recently proposed by Kusano et al. The simulation results clearly indicate that magnetic reconnection driven by the resistive tearing mode instability growing on the magnetic shear inversion layer can cause the spontaneous formation of sigmoidal structure. Furthermore, it is also numerically demonstrated that the formation of the sigmoids can be followed by the explosive energy liberation, if the sigmoids contain sufficient magnetic flux. This implies that the reversed-shear flare model can provide a self-consistent explanation for the formation of sigmoids as well as for the onset of eruption, which is driven by magnetic reconnection above sigmoids. The geometric relationship between the sigmoidal structure and the minimum energy state predicted by J. B. Taylor in 1974 is examined. The result suggests that the sigmoidal formation could be understood as a manifestation of the minimum energy state, which has the excess magnetic helicity compared to the bifurcation criterion of the linear force-free field. The consistency with the observations of magnetic helicity is also discussed.