College of Science, George Mason University
Magnetohydrodynamics (MHD) simulation can numerically reproduce three-dimensional structures of the coronal magnetic field and plasma. In this simulation strategy, the whole-Sun synoptic map data of the line-of-sight (LoS) magnetogram observation have been used to specify the solar-surface boundary values in the simulation and to determine the initial potential field. An advance of this simulation approach, like the capability of reproducing highly nonpotential magnetic features, can be achieved by using the three-component vector magnetic-field data from the polarimetry observations. For the global coronal models, three-component vector synoptic maps from the SDO/HMI are available at the JSOC database.
Recently, we developed a new MHD simulation model for the global corona. In this model (hereafter called E-driven model), the simulated corona can be driven with electric field, whose curl fully matches the temporal variations of the full three-component magnetic field on the photosphere as observed[3,4]. By driving the simulated global solar corona with the curl of electric field, the divergence-free condition of the magnetic field can be preserved and the boundary values of the magnetic field can evolve as specified. As a natural consequence, we can obtain the nonpotential coronal magnetic features matching the solar-surface observations. In our E-driven simulation model, a set of special boundary treatments is needed for properly handling the horizontal (latitudinal and longitudinal) components of the specified boundary magnetic field.
Figure 1| (Time-relaxed states of the solar corona at CR2106, as an example. Panel (a) shows the (quasi-)steady state from the conventional method. Panel (d) is from the “full” E-driven simulation. Panels (b) and (c) are those obtained with the boundary treatment with the switching. The blue (red) colors on the sphere in each panel indicate the positive (negative) radial component of the boundary magnetic field. The boundary radial component is identical among the four panels. The cyan-white-orange colors on the field lines indicates the twist (or chirality) of the magnetic field, cyan for positive and orange for negative. The sign of chirality is found mostly unchanged along the relaxed-state magnetic field line.
Figure 1 demonstrates the results from the time-relaxation simulations (i.e. data-constraint simulations) with our E-driven model: Panels (a) and (d) show the two extreme cases: (a) the conventional simulation where only the boundary radial component is specified all over the boundary sphere; and (d) the “full” E-driven simulation where all three components of the simulated boundary magnetic field are enforced to match the given vector-magnetic-field data map. In the intermediate two cases (b) and (c), the plasma beta and the plasma velocity (as a proxy of whether the region is within the closed-field stagnant streamer or in the open-field coronal hole) are used to determine whether all three components of the simulated boundary magnetic field will follow the observation or only the radial component will. Figure 2 shows the scatter plots of the simulated boundary values and the observation-based map.
Figure 2| Scatter plots of the simulated and specified boundary magnetic-field components: In the case shown in Panel (d) of Figure 1, as designed, the scatter points are well aligned along the diagonal line, with minor scatters due to the errors in the numerical spatial differencing. The latitudinal and longitudinal components of the potential field, shown in Panel (a), are nearly of no correlation with observation. Panels (b) and (c) have large scatters in these two horizontal components around zero values, as designed.
Figure 3 shows an example of long-term, full E-driven simulations. This full data-driven simulation can simulate a long-term evolution of the solar corona by giving the time-series vector-magnetic-field data. Several highly nonpotential features are obtained, although many of them do not have any counterparts in the actual corona.
Figure 3| Panels (a) and (b) are the snapshots of the simulated coronal field lines derived through the full E-driven simulation model, at 2 and 4 Carrington Rotation periods from the time-relaxed state at CR2106 (shown in Panel (d) of Figure 1).
The E-driven model can introduce the observed (or observation-based) three-component vector magnetic field data to MHD simulation, straightforwardly and accurately within the discretization errors. This is a new capability realized with the E-driven boundary treatments. The switching for handling the horizontal components of the boundary magnetic field is a key part to reproduce the potential-like features and nonpotential ones simultaneously. Improvements for the numerical boundary treatment and the input data preprocess are in progress, to obtain better agreements with the actual coronal observations.
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