Marion Weinzierl¹ and Anthony R. Yeates^1
1 Department of Mathematical Sciences, Durham University, Durham, DH1 3LE, UK

Driving coronal simulations by magnetic maps derived from real observations poses certain challenges which have to be overcome in order to provide the foundations for improved, reliable space weather forecasts.

Non-potential solar coronal magnetic field simulations using the magnetofrictional method (see, ref. 1 and references therein) have demonstrated to be a practical alternative to global magnetohydrodynamic (MHD) methods in extensive computational coronal studies. At the same time they give a better approximation to the physical processes in the corona than the potential-field source-surface (PFSS) extrapolation which is used in operational space weather forecasting codes.

We show² how to drive global non-potential coronal simulations solely from routinely available line-of-sight magnetic maps of the solar surface. “Photospheric driving” means that the evolution of the real solar magnetic field (with events such as the emergence of new active regions or structural changes) is observed at the photosphere and then imposed as inner boundary condition in the coronal simulation. We compute this boundary condition by an enhanced method based on ref. 3 (and references therein), using a sequence of maps from the Air Force Data-Assimilative Photospheric Flux Transport (ADAPT) model⁴. ADAPT uses a photospheric flux transport model based on that of ref. 5, together with data assimilation techniques (in this case, ensemble least squares) from the Los Alamos National Laboratory (LANL) framework. In practice this means: the magnetic flux is evolved with the flux transport model, and once per day new observational data from the Earth side of the Sun is integrated. However, despite sophisticated data assimilation, there remains the problem that structural changes that happen at the far-side can only be integrated when they rotate into view. This creates a time discontinuity in the map sequence. The sequence of maps used here runs from 2014 November 1, 00:00 UT to 2014 December 23, 22:00 UT (1270 hours).

Figure 1 | Integrated quantities in the non-potential simulation. The top panel shows the total unsigned magnetic flux through the photosphere, the second panel shows the total unsigned open magnetic flux (i.e., through the outer boundary), the third panel shows the total magnetic energy, and the fourth panel shows the averaged electric current |j| in the volume — this current would be neglected in a PFSS model.

The effect of this time discontinuity on our simulation is demonstrated in Fig. 1: When a big active region (AR12209, previously AR12192) that has changed its structure on the far-side comes back into view, a large flux rope eruption takes place in the simulation. This is visible as a large peak in the open flux and is also shown in Fig. 2. Everything settles back down, until the region comes around again about 27 days later (as AR12237). During the assimilation of the new region, the free energy in the simulation increases, and then decays back to a slightly higher level than before. This might be due to the assimilation method in ADAPT and the corresponding electric field we chose. In the real evolution of the region, the same amount of free energy may not have been generated.

Figure 2 | Example magnetic field lines (with random colors for identification) of AR12209 when it appears on the east limb in the ADAPT simulation. In book-reading order: Hour 340, 352, 364, 376, 388, 400. The newly-assimilated region contains less magnetic flux than before, leading to disconnection of many coronal magnetic field lines and their subsequent eruption.

Inspecting observational data for AR12192/12209 we find that in fact no such eruption took place, at least not while the region was on the visible disk. Instead, the region is known to have produced many, often large, flares but no significant CMEs, which is quite unusual and has not yet been explained completely (see April nugget and references therein). As the flux rope eruption in our simulation is associated with a sudden rearrangement of the magnetic field lines due to newly assimilated data, a smoother transition for structural changes which appear at the far-side, which is planned to be available in future ADAPT maps, might change this behavior.

References

[1] Yeates, A. R., 2014, SoPh, 289, 631
[2] Weinzierl, M., Yeates, A. R., Mackay, D. H., Henney, C. J., & Arge., C. N., 2016, in preparation
[3] Fisher, G. H., Welsch, B. T., Abbett, W. P., & Bercik, D. J., 2010, ApJ, 715, 242
[4] Arge, C. N., Henney, C. J., Koller, J., et al., 2010, AIPC, 1216, 343
[5] Worden, J., & Harvey, J., 2000, SoPh, 195, 247