A quantitative MHD study of the relation among arcade shearing, flux rope formation, and eruption due to the tearing instability

The quantitative relationship between the magnetohydrodynamic ( MHD) activity of solar coronal arcade and the magnetic helicity injection, which is caused by shearing motion, has been investigated, using azimuthally symmetric model of MHD simulation. We have calculated several cases in which the width of the shearing region is varied and examined the relationship between the magnetic arcade dynamics and magnetic helicity evolution. As a result, it is found that as the shearing motion is imposed on narrower regions along each side of the magnetic inversion line, the magnetic arcade can be easily destabilized by the resistive tearing mode. However, in this case, even though reconnection driven by the tearing mode produces plasmoids, the plasmoid elevation is almost in proportion to the total amount of magnetic helicity contained in the arcade, and it is too slow to explain the trigger process of coronal mass ejections ( CMEs). On the other hand, in the case where the shearing motion is imposed on the entire region, much larger magnetic helicity injection is required to injected arcade in order to destabilize the system, compared to practical helicity injection measured in the solar corona. The results suggest that it may be difficult to trigger a CME just by the axisymmetric shearing motion and that some other mechanisms should be involved in the triggering process of a CME. The results also imply that the relation between the magnetic helicity and the overlying magnetic flux can be a key parameter for the CME occurrence.