  Solar flares and coronal mass ejections (CMEs), the most catastrophic
eruptions in our solar system, have been known to affect terrestrial
environments and infrastructure. However, because their triggering mechanism is
still not sufficiently understood, our capacity to predict the occurrence of
solar eruptions and to forecast space weather is substantially hindered. Even
though various models have been proposed to determine the onset of solar
eruptions, the types of magnetic structures capable of triggering these
eruptions are still unclear. In this study, we solved this problem by
systematically surveying the nonlinear dynamics caused by a wide variety of
magnetic structures in terms of three-dimensional magnetohydrodynamic
simulations. As a result, we determined that two different types of small
magnetic structures favor the onset of solar eruptions. These structures, which
should appear near the magnetic polarity inversion line (PIL), include magnetic
fluxes reversed to the potential component or the nonpotential component of
major field on the PIL. In addition, we analyzed two large flares, the X-class
flare on December 13, 2006 and the M-class flare on February 13, 2011, using
imaging data provided by the Hinode satellite, and we demonstrated that they
conform to the simulation predictions. These results suggest that forecasting
of solar eruptions is possible with sophisticated observation of a solar
magnetic field, although the lead time must be limited by the time scale of
changes in the small magnetic structures.
