Chaowei Jiang1,2, S. T. Wu2, Xueshang Feng1, & Qiang Hu2
1 SIGMA Weather Group, State Key Laboratory for Space Weather, National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China
2 Center for Space Plasma & Aeronomic Research, The University of Alabama in Huntsville, Huntsville, Alabama 35899, USA
Solar eruptions are explosive release of excess magnetic energy in the solar corona. The most powerful eruptions usually come from solar active regions (ARs). It remains an open question what causes solar eruptions, mainly because a full understanding of the complicated, three-dimensional (3D) coronal magnetic field is still out of reach.
Numerical modelings are often used to study the mechanism for solar eruptions. However, existing models that attempt to characterize the realistic magnetic environment for solar eruptions are mostly restricted to static reconstruction of the nearly force-free coronal magnetic ﬁeld1. The mechanism of eruption can only be investigated tentatively because no dynamics is included. Even a time-sequence of reconstructed magnetic ﬁelds following the coronal evolution does not reﬂect its intrinsic dynamics because these snapshots are treated as being independent of each other. There are models2,3 using the reconstructed coronal ﬁeld immediately preceding the eruption (thus the unstable nature of the ﬁeld is already well developed) as the initial condition for MHD simulation, which prove to be able to reproduce the fast dynamic phase of the erupting ﬁeld. However, these kinds of simulations do not self-consistently show how the pre-eruptive ﬁeld is formed and disrupted, and thus may not be used to identify the true triggering mechanism.
Figure 1 | Comparison of simulated coronal magnetic field of the flux-emerging region with SDO/AIA observations. (a) AIA 304 Å images at different times from the initial emergence to the eruption. (b) Top view of the corresponding magnetic field evolution from our MHD-DARE model. Field lines closed (opening) in the box are colored black (green), while those becoming open during the eruption are colored red. (c) Side view of the magnetic field lines from south. The background shows a cross-section in the 3D volume and its color indicates vertical velocity. (d) Evolution of magnetic squashing degree (Q) on a vertical cross section, suggesting the formation of a coronal-jet-like configuration.
To this end, we have developed a new data-driven 3D MHD AR evolution (MHD-DARE) model. Using the MHD-DARE model, we4 recently presented a self-consistent MHD simulation of the whole process from the formation to initiation of a coronal eruptive ﬁeld in a complex multi-polar active region (NOAA AR 11283, see Fig. 1). The event is characterized by a fast magnetic ﬂux emergence for over 2 days leading to an M-class eruptive ﬂare on the 3rd day (from 2011/09/04 to 2011/09/06). Distinct from those aforementioned works, we start the model from a very stable state when the coronal ﬁeld is still near potential (that is, current-free). Then, a 3-day data sequence of SDO/HMI vector magnetograms are used to drive the coronal magnetic ﬁeld evolution all the way from its initial potential state to eruption. It is found that the modeled magnetic ﬁeld evolves stably over a non-eruptive duration of 2 days and becomes unstable at an instant in good agreement with that of the observed eruption on the 3rd day. Moreover, the continuously evolving coronal ﬁeld presents good morphological similarities with the extreme ultraviolet (EUV) observations.
Figure 2 | Illustration of the jet-like reconnection as the triggering mechanism of the eruption. Left: field lines in black (red) denote magnetic ﬂux before (after) reconnection. Longer arrows denote shearing motion and the resulting expansion of the closed arcade. Shorter arrows indicate the inﬂows and outﬂows at the reconnection site. The bottom surface shows the map of Bz overlaid by white lines showing the trace of separatrices and QSLs (log Q > 5). The vertical cross-section colored by values of J/B shows distinctly a current sheet at the reconnection site. Note that the reconnecting ﬁeld lines are not coplanar, thus the conﬁguration is fully 3D. Right: flow directions at a vertical cross-section at the current sheet (denoted by the dashed box in the left panel). Reconnection inﬂows and outﬂows can be clearly seen.
From the model results, we identified in detail a sequence of processes that leads to the final eruption. First, a small new ﬂux emerged into the core of the multi-polar AR background. By computing the squashing factor (Q), we find a dome-shaped separatrix surface separating the new emerging ﬂux from the pre-existing one. Then, further emergence induced the formation of a jet-like conﬁguration that is favorable for reconnection between the newly emerged short arcade (closed) and the pre-existing ﬂux (longer closed loops or open ones, see Fig. 2 and Ref. 4 for details). Meanwhile, the non-potential ﬂux emergence also continuously injects magnetic free energy/helicity into the system through photospheric shearing motions. Consequently it stresses the field, gradually creating an intense current sheet at the high-Q site. The system becomes unstable once the reconnection starts, as a positive feedback is established between the reconnection and the expansion of the newly emerged arcades. On the other hand, there is no magnetic ﬂux rope fully formed in the model, suggesting that a ﬂux rope, although attracting intense interest recently, is not a must for causing a solar eruption.
In summary, a data-driven MHD model like the one shown here, which is able to realistically simulate the whole process from origin to onset of a solar eruption, can be used as a new way for studying the cause of solar eruptions. Furthermore, utilizing its output to initiate interplanetary CME models between the Sun and the Earth will be a step forward in realistically modeling the space weather conditions5.
 Wiegelmann, T. & Sakurai, T., 2012, LRSP, 9, 5
 Jiang, C. W., Feng, X. S., Wu, S. T. & Hu, Q., 2013, ApJL, 771, L30
 Amari, T., Canou, A., & Aly, J. J., 2014, Nature, 514, 465
 Jiang, C. W., Wu, S. T., Feng, X. S., & Hu, Q., 2016, Nat. Comm., 7, 11522
 Wu, S. T., Y. Zhou, C. Jiang, X. Feng, C.-C. Wu, and Q. Hu., 2016, JGR, 121, 1009