Temporal Sequences of Static Magnetic Fields Used to Find the Dynamic Processes with Less Ad Hoc Assumptions

As the spatial and temporal resolution of solar observation has been enhanced, a data-driven simulation is quite widely attempted. To simulate the dynamics of the solar corona, the time-dependent boundary conditions must be derived from a time sequence of vector magnetograms. A temporal change of the vector magnetogram is caused by a certain plasma motion, which is not necessarily horizontal, but also vertical. Sometimes the tangential (2D) velocity field at the bottom boundary is acceptably well estimated by footpoint tracking methods. However, the magnetograms usually show magnetic flux changes implying vertical transport of fluxes. The 3D velocity field at the boundary plane is much more difficult to estimate than the 2D field and thus requires many ad hoc assumptions. The dynamic processes we want to find heavily depend on these assumptions. In contrast to dynamic simulations, a sequence of static magnetic fields can tell little on the transient dynamic processes. However, the construction of static magnetic fields as snapshots demands far less ad hoc assumptions than the dynamic simulation. Particularly, a transient change showing up in a dynamic simulation may not take place with a milder driving condition. However, a change showing up between two static solutions must be manifested in dynamic simulations in any case. As an example, we present the sequence of force-free fields constructed for AR 11974, which produced to M class flares and a halo CME. Although overall field connectivity is very complex, we can pinpoint the field connectivity change responsible for each eruptive process from the sequence static fields constructed by our new force-free field method.