Several models explain ejection in bipolar system. The so-called mass-loaded model assumes that the drain of plasma from a flux rope reduces the gravitational force, leading to the ejection of a flux rope via enhanced magnetic buoyancy (Low and Hundhausen, 1995; Low, 1996; Wu et al., 1997). The flux-cancellation model shows that the dissipation of magnetic flux at the surface (known as flux cancellation) reduces the magnetic tension force of the overlying field that confines a flux rope so that the upward magnetic pressure dominates at some point of the evolution and an eruption occurs (the configuration has a low beta plasma and magnetic force dominates) (Linker et al., 2003, see Figure 37a). A similar mechanism has been proposed in the so-called the tether-cutting model (Sturrock et al., 1984; Moore et al., 2001, see Figure 37b). If a flux rope is composed of highly twisted field lines, then the kink instability might develop, causing the ejection of it (Sturrock et al., 2001; Fan and Gibson, 2003; Török and Kliem, 2005; Inoue and Kusano, 2006, see Figure 37c). The basic physics related to the kink instability, or more precisely the toroidal magnetic force, has also been studied in early analytical models (Mouschovias and Poland, 1978; Chen, 1989; Vršnak, 1990, see also references therein).
The so-called loss-of-equilibrium model suggests that there is a critical height of a flux rope, beyond which no neighboring equilibrium state exists, so if a flux rope reaches this height, then a dynamic transition inevitably occurs to cause eruption (Forbes and Isenberg, 1991; Amari et al., 2000; Roussev et al., 2003; Lin, 2004; Isenberg and Forbes, 2007, see Figure 37d). In fact, the flux cancellation model mentioned above demonstrates the dynamic process of the loss of equilibrium.
Recently, it has been proposed that the torus instability plays a key role in the ejection of a flux rope (Kliem and Török, 2006). They suggest that the spatial distribution of the magnetic field overlying a flux rope is an important factor in controlling the dynamic state of a flux rope. The loss-of-equilibrium and the torus instability are in fact two different views of the same physical process (Démoulin and Aulanier, 2010).
In multi-polar systems, the following models have been proposed to explain the ejection of a flux rope. In the model called breakout (Antiochos et al., 1999a, Figure 38), a current sheet is first formed at the interface between the inner and overlying flux domains. Magnetic reconnection then occurs at this current sheet, reducing the confining tension force of the overlying field. The inner domain then starts to expand, inside which another current sheet is formed and the second, much more energetic reconnection than the previous one, occurs to produce a flare. As a result of the second reconnection, a flux rope is formed, which eventually erupts into the interplanetary space.
Another model is called the emerging flux trigger model (Chen and Shibata, 2000, Figure 39), in which newly emerging magnetic field interacts with the preexisting field that contains a flux rope. That interaction leads to the formation of a current sheet at the interface between those two fields. Magnetic reconnection then occurs in this current sheet, destabilizing the flux rope, which erupts via the second reconnection that is similar to the one explained in the breakout model. In these two models, the two-step reconnection is a key mechanism for producing a flare and the ejection of a flux rope. This mechanism also works in the helicity annihilation model (Kusano et al., 2004, Figure 40).
Living Rev. Solar Phys. 8, (2011), 6
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