The discovery of such an unexpected and spectacular wave sparked a lot of interests as well as debates among the community (see Chen, 2008; Wills-Davey and Attrill, 2009; Warmuth, 2010; Gallagher and Long, 2010, for reviews). The modelings of EIT waves are important in the sense that: (1) they may provide crucial clues for the understanding of CMEs (Chen, 2009a); (2) they may be used to diagnose the coronal magnetic topology (Attrill et al., 2006; Zhang et al., 2007); and (3) they can be used in coronal seismology to diagnose the magnetic field (Warmuth and Mann, 2005; Ballai, 2007; Chen, 2009b). Several models have been proposed so far, and the debates are mainly focused on two issues: (1) What drives the EIT waves: flare or CME? (2) What is the nature of EIT waves? While there is a converging consensus that EIT waves are physically linked to CMEs rather than flares (Biesecker et al., 2002; Cliver et al., 2005; Chen, 2006), the nature of EIT waves is still under hot debate. Here we briefly introduce several models, and more details can be found in the reviews by Wills-Davey and Attrill (2009) and Gallagher and Long (2010).
Since “EIT waves” propagate across the magnetic field lines, with a velocity sometimes larger than the sound speed in the corona, and are associated with density enhancement, they are unlikely to be slow-mode MHD waves or Alfvén waves. Therefore, they were immediately considered to be fast-mode magnetoacoustic waves in the corona (e.g., Wang, 2000; Wu et al., 2001; Vršnak et al., 2002; Warmuth et al., 2004; Grechnev et al., 2008; Pomoell et al., 2008; Temmer et al., 2009; Schmidt and Ofman, 2010), being regarded as the coronal counterpart of the H Moreton waves (Moreton and Ramsey, 1960; Uchida, 1968). Figure 39 shows the observation of the EIT wave event on 1997 May 12 (upper panels) and the MHD simulation result of the fast-mode wave (lower panels), which are claimed to match very well (Wu et al., 2001). Several groups came to the same conclusion from the observational point of view (e.g., Veronig et al., 2008; Patsourakos et al., 2009; Kienreich et al., 2009; Veronig et al., 2010).
However, it is difficult fot the fast-mode wave model to explain the following features of “EIT waves” (e.g., see Wills-Davey et al., 2007; Chen, 2008, for details): (1) the “EIT wave” velocity is significantly smaller than those of Moreton waves. The latter are generally believed to be due to fast-mode waves in the corona (Uchida, 1968; Eto et al., 2002); (2) The velocities of “EIT wave” have no any correlation with those of type II radio bursts (Klassen et al., 2000). The latter are also well established to be due to fast-mode shock waves in the corona; (3) The “EIT wave” fronts may stop when they meet with magnetic separatrices (Delannée and Aulanier, 1999; Delannée et al., 2007; Delannée, 2009); (4) The “EIT wave” velocity may be below 100 km s–1 (e.g., the Figure 3 of Long et al., 2008; Zhukov et al., 2009), which is even smaller than the sound speed in the corona. Some of these strange features provoked Delannée and Aulanier (1999) and Delannée (2000) to question the fast-mode wave model for the first time.
In 2D MHD numerical simulations, Chen et al. (2002; 2005b; 2005c; 2006b) identified the “EIT wave” to be the density-enhanced boundary of the dimming region (the dimming is indicated by the blue region in the upper panels of Figure 40), which is located well behind the fast-mode piston-driven shock waves (the red front in the upper panels of Figure 40) during CME eruptions. They proposed that “EIT waves” are apparently-moving density enhancements, which are actually produced by successive stretching of the closed field lines overlying the erupting flux rope, rather than being real waves. The model is illustrated in the bottom panels of Figure 40: as the flux rope erupts, the overlying field lines will be pushed to stretch up successively by the erupting flux rope, and for each field line, the stretching starts from the top, and is then transferred to the footpoints, where the stretched field line compresses the plasma to form a bright front. That is to say, the stretching starts from point A and then propagates to point C with the local fast-mode wave speed. At the same time, the stretching propagates from point A to point B and then to point D with the local fast-mode wave speed. Therefore, the apparent speed for the EIT wave to propagate from point C to point D is , with , where is the Alfvén speed, and is the fast-mode wave speed perpendicular to the field line, and the last two integrals are along the field line shown in Figure 40 (see Chen et al., 2002, 2005c, for details). If the field lines are semi-circles, is found to be about one-third of the fast-mode wave speed. When the EIT wave encounters another active region (to the right of point D in Figure 40) or an open field (in both cases there is a magnetic separatrix), no stretching can be transferred into the closed region or the open field, and the EIT wave stops near the magnetic separatrix, as demonstrated by Chen et al. (2005c). The model can account for the main characteristics of “EIT waves”, such as their low velocity, their diffuse fronts, and the stationarity near magnetic separatrices. The model also predicts that there should be two EUV waves, one is the coronal counterpart of Moreton wave, which has a sharp front, and the other is the diffuse “EIT wave”. The model found support in observations (e.g., Harra and Sterling, 2003) and in 3D MHD simulations (Downs et al., 2011).
Noticing that the EIT wave fronts rotate apparently in the same direction as the erupting filament, Attrill et al. (2007) also claimed that EIT waves should be related to the magnetic rearrangement. As shown in Figure 41, they proposed a successive reconnection model, i.e., EIT wave fronts are the footprint of the CME frontal loop, which is formed due to successive magnetic reconnection between the expanding core field lines and the small-scale opposite polarity loops.
The successive reconnection model was criticized by Delannée (2009), who demonstrated that the extrapolated potential field for the famous EIT wave event on 1997 May 12 does not fix into the model illustrated in Figure 41. The discrepancy can be reconciled if we accept that reconnection can happen occasionally during the CME expansion, but not always. This is consistent with the recent 3D MHD simulations by Cohen et al. (2009). They proposed that along with the CME eruption the “EIT wave” front consists of two wave components. The bright non-wave component is produced by the CME expansion (or called field line stretching in Chen et al., 2002), which is facilitated by magnetic reconnection (Attrill et al., 2007). The weak wave component is initially attached to the bright component, and then becomes detached after the CME ceases lateral expansion.
Through 3D MHD simulations, Delannée et al. (2008) found that as a flux tube erupts, an electric current shell is formed by the return currents of the system, which separate the twisted flux tube from the surrounding fields, as shown in Figure 42. Slightly different from their early idea of magnetic rearrangement (Delannée and Aulanier, 1999), they claim that this current shell corresponds to the “EIT waves”. They also revealed that the current shell rotates, similar to the apparent rotation of the EIT wave fronts found by Podladchikova and Berghmans (2005). They also emphasized the role of Joule heating in the current shell in explaining the EIT wave brightening, which was criticized by Wills-Davey and Attrill (2009).
Noticing that EIT waves generally keep single-pulse fronts and that the EIT wave velocity is sometime smaller than the sound speed in the corona, Wills-Davey et al. (2007) speculated that the EIT waves might be best explained as a soliton-like phenomenon, say, a slow-mode solitary wave. They stated that a solitary wave model can also explain other properties of the EIT waves, such as their stable morphology, the nonlinearity of their density perturbations, the lack of a single representative velocity, and their independence of Moreton waves. There is no modeling of such an idea.
Wang et al. (2009) performed 2D MHD numerical simulations of a flux rope eruption, where they found that behind the piston-driven shock appear velocity vortices and slow-mode shock waves. They interpret the vortices and the slow-mode shock wave as the EIT waves, which are 40% as fast as the Moreton waves.
Living Rev. Solar Phys. 8, (2011), 1
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