As mentioned earlier, in the early years, most of the solar physics community believed that CMEs were shock waves caused by solar flares. Although this belief has since been disproven (refer to Kahler, 1992 and Gosling, 1993 for reviews debunking the “Solar Flare Myth”), some remnants still remain in some circles, particularly those outside the solar physics community. Early mathematical models (and some still in use today) regard solar mass ejections as eruptive solar flares in opposition to the majority of flares which are “confined”. Because the corona is a highly conducting medium, the plasma is essentially “frozen in” to the magnetic field such that for an eruption to occur, the field lines must open up to allow the plasma to escape. But flares and CMEs can have very different properties, not least their spatial scales, and CMEs can occur without flares, so most researchers now consider flares and CMEs to be different aspects of magnetic field reconfiguration on the Sun. For details of CME models in general, see the Living Review by Chen (2011). Here we describe only those models that pertain to material eruption (see, e.g., Aschwanden, 2006 and Forbes et al., 2006 for reviews).
Contemporary models describing the launch and early evolution of CMEs must overcome two major physical obstacles:
While the physical mechanism to launch the CME may vary between models, the overall picture is essentially the same: A magnetic field configuration held in equilibrium is disrupted somehow, causing the system to erupt. The initial configuration typically involves an underlying sheared field often called the core (e.g., Moore and Roumeliotis, 1992) held down by an overlying strapping field. The onset mechanism itself that causes the eruption is actually less important – eventually one will occur. It may take the form of magnetic reconnection or even a simple field reconfiguration could accomplish an equilibrium disruption. The core then erupts beyond the strapping field.
The most recent modeling work in this area (e.g., Rachmeler et al., 2009) has focused on the question of what happens to the strapping field when the CME erupts. Until recently it was accepted that the strapping field must be stretched by the erupting core, which must presumably stretch it out to infinity. This, however, violates the Aly–Sturrock limit meaning it has been difficult to explain physically why a CME would spontaneously move to a more energetic state. This problem has been overcome with the use of 3-D models. In three dimensions, the core can erupt without stretching the strapping field along with it – instead it can simply push the strapping field aside as it erupts. Hence, in 3-D the Aly–Sturrock limit does not pose a problem.
To overcome the first obstacle, that of energy provision, a number of models have emerged. Some, such as the breakout model (e.g., Antiochos et al., 1999; Lynch et al., 2008), involve runaway magnetic reconnection between the erupting core and the strapping field, while others, such as the kink instability (e.g., Török and Kleim, 2003; Török and Kliem, 2005; Fan and Gibson, 2004) involve the twisting of the core field. Figure 29 shows a 3-D diagram of the kink instability, also showing how the strapping field is pushed aside to make way for the erupting core.
After the CME has erupted the magnetic field left behind eventually closes, probably via some form of large-scale magnetic reconnection. The recent models of this process describe the late phase of CMEs reasonably well (cf. Švestka and Cliver, 1992). Kahler and Hundhausen (1992) found that the bright structures following many SMM CMEs are streamers probably newly-formed by reconnection. Observations from Yohkoh and from MLSO of the reformation of a giant helmet streamer also provide strong evidence of reconnection following CMEs (Hiei et al., 1993). As discussed earlier, the white light and spectroscopic evidence for current sheets trailing CMEs also provide support for the reconnection of the surface fields. Reeves and Moats (2010) have examined the relationships among the CME kinematics, thermal energy release and soft X-ray emissions using the Lin and Forbes (2000) loss-of-equilibrium model, finding good correlations among the parameters.
An extensive survey of post-eruptive arcades in SOHO/EIT 195 Å images has shown that every arcade is associated with a LASCO CME (Tripathi et al., 2004). These observations have been interpreted in terms of a basic model of reconnecting magnetic fields behind a magnetic flux rope and over a magnetic arcade (e.g., Lin, 2004), which results in a disconnection of CME fields from the Sun, as shown in Figure 21. This model has been called the CSHKP model to reflect its provenance. The acronym stands for Carmichel, Sturrock, Hirayama, Kopp, and Pneuman, each of whom developed configurations which have now evolved into a “standard” model that continues to be supported by observations and simulations (see Švestka and Cliver, 1992, for the original CSHKP description). Correlations found between inferred magnetic reconnection rates in arcades and the speeds of associated CMEs provide further confirmation of the model (Jing et al., 2005). Radio imaging of the moving and quasi-stationary type IV bursts can provide upper limits to the current sheet length by bracketing the reconnection region (Pick et al., 2005).
Most of the models intended to describe the origin and propulsion of CMEs are not sufficiently developed to compare with observations. Many of them involve force free equilibria which cannot realistically describe the complex evolution of the pressure, magnetic and gravitational forces acting on a magnetically closed coronal structure (e.g., Hundhausen et al., 1994). The class of models which require a thermal or pressure pulse (i.e., flare) as driver no longer seem viable (cf. Dryer, 1994). For instance, such models are not consistent with CMEs that exhibit significant accelerations over large distances. Causes of the evolution of these coronal structures, especially streamer configurations, include the emergence of magnetic flux, the dynamical evolution of arcades (Mikić and Linker, 1994), and the shear of field lines across inversion lines (Wolfson and Low, 1992; Mikić and Linker, 1994). However, no strong consensus has yet emerged.
Models attempting to describe CME evolution at large distances from the Sun can be categorized in order of their increasing complexity. It is important to note that the most complex model does not necessarily indicate the more accurate; sometimes the simpler description can be the most appropriate. We divide models for CME evolution into three categories: 1) A disturbance in the ambient solar wind, 2) an embedded lump of plasma, and 3) an embedded magnetic flux rope. All of these essentially begin with the same foundation, that of a background solar wind into which some form of anomaly is introduced.
The first category, that of a disturbance in the solar wind, is really a derivative of the original idea that CMEs were blast waves from flares. This has since been proven to be a physically incorrect description of CMEs, but nonetheless some of these models have been able to sometimes reproduce well the appearance and propagation characteristics of CMEs. This is probably because at large distances from the Sun the most prominent observable feature is the built-up solar wind material in the sheath, which is governed by the theory of interplanetary shock propagation. The most popular of these models include the Shock Time Of Arrival (STOA) model (Dryer and Smart, 1984), its later version ISPM (Smith and Dryer, 1990), and HAFv2 (Hakamada and Akasofu, 1982; Fry et al., 2001).
The second category, which consists of a lump of material embedded into the solar wind, takes simple and more complex forms, but essentially is based on the assumption that the embedded material responds hydromagnetically to the surrounding solar wind. The simplest description is that of aerodynamic drag, where the CME speed is governed by momentum transfer between it and the solar wind until a kinematic equilibrium is reached. Examples of this include Cargill (2004) and Tappin (2006). A more complex version of this is the ENLIL model (Odstrčil, 2003) which takes into consideration plasma density, CME structure and extrinsic magnetic field as well as the kinematic properties of the CME and solar wind.
The third category treats the CME as a magnetic flux rope which is embedded into the solar wind. These models attempt to include the magnetic interaction between the CME and the interplanetary magnetic field (e.g., Chen, 1996; Manchester IV et al., 2005).
It is important to note that the models discussed above describe the evolution of the CME once it is some distance away from the Sun, i.e., they do not describe the physics of the onset and early evolution. The assumption is that the physics become simplified once the CME has escaped the gravitational and magnetic pressure forces at or near the Sun.
Living Rev. Solar Phys. 9, (2012), 3
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