As a large-scale eruptive phenomenon, CMEs often reveal thermal or nonthermal signatures during the initiation process just prior to the eruption, i.e., precursors. The CME precursors are very useful since they can be used to predict the occurrence of a CME, as well as to constrain or construct the CME triggering mechanisms (see Gopalswamy et al., 2006, for a review). Before reviewing the triggering mechanisms proposed so far, we have an overview of the possible precursor phenomena that precede CMEs in observations.
The imaging and spectroscopic observations of the CME source region are crucial to find out precursors and to understand how CMEs are initiated. The precursors for CMEs found in the past decades can be summarized as follows:
With the Solar Maximum Mission (SMM) satellite observations, Hundhausen (1993) found that most CMEs arise from pre-existing helmet streamers, with the streamers being increasing in brightness and size for days before final eruption. Therefore, the streamer swelling can be used to predict the eruption of CMEs, mainly the limb events. Different from the following precursors, the streamer swelling is the direct imaging of the CME initiation.
A phenomenon intimately linked to the streamer swelling is the slow rise of prominences (Filippov and Koutchmy, 2008).
Feynman and Martin (1995) analyzed 53 quiescent filaments, and found that 17 out of 22 filaments that were associated with emerging bipolar magnetic flux erupted and only 5 out of 31 filaments that were not associated with emerging flux erupted. More importantly, they found that in all cases when the emerging flux was oriented favorably for magnetic reconnection, the filaments were observed to erupt. Two examples of new flux emerging inside and outside the filament channel are depicted in Figure 7, which shows the photospheric magnetograms for the two events. Generally, the new flux emergence begins a few days before the filament eruption and typically is still occurring at the time of eruption. It is noted that new magnetic flux emerges all the time and everywhere, especially those weak fields. However, the filament eruption-associated emerging bipolar field has a similar amount of magnetic flux as that of the original filament channel (Feynman and Martin, 1995). Wang and Sheeley Jr (1999) confirmed such a correlation (see also Srivastava et al., 2000; Nitta and Hudson, 2001; Zhang et al., 2001b). Further statistical studies showed that 68% of the filament eruptions during 1999 to 2003 (Jing et al., 2004) and 91% of halo CMEs during 1997 to 2005 (Zhang et al., 2008) are associated with magnetic flux emergence. Caution should be taken that these later statistical studies did not consider the polarity orientation and the total flux of the emerging field as done by Feynman and Martin (1995).
Roy and Tang (1975) studied six flares and found that SXR bursts often accompany the preflare expansion of the filaments. Such a phenomenon was studied by several researchers (Pallavicini et al., 1975; Rust et al., 1975; Webb et al., 1976). As an extension, Simnett and Harrison (1985) studied the relation between the preflare activity and CMEs, and found that there is usually a weak SXR enhancement 15 – 30 min prior to the linearly extrapolated onset time of the CMEs, which was called SXR precursors for CMEs. As an example, Figure 8 shows an SXR enhancement 20 min before the CME-related flare. Caution should be taken that there are many SXR brightenings over the Sun, and high-cadence SXR imaging observations are needed to distinguish whether any pre-CME brightening is spatially and physically related to the CME.
It was found that the radio noise storm continuum emissions, sometimes called type I radio bursts, are associated with the SXR brightenings (Raulin and Klein, 1994; Krucker et al., 1995; Crosby et al., 1996), with the former lasting for a longer time. Evidence was revealed to show that the radio noise storms are related to the initiation of CMEs in a statistical study (Lantos et al., 1981). Ramesh and Sundaram (2001) also found that CMEs often erupted after significant metric noise storm continuum emissions, which are located under the angular span of the associated CMEs. As shown by Figure 9, Wen et al. (2007) found that the noise storm sources are within the CME dimming regions. It is believed that the commencement of the radio noise storm is due to the magnetic restructuring during CME initiations. Waves, e.g., Alfvén waves, induced by the changing magnetic field, slightly accelerate electrons, which then emit radio radiations. On the other hand, the rapid decay of the pre-existing metric radio storms, e.g., above sunspots, might also be related to CMEs (Chertok et al., 2001). However, it is noted that the corona is always in a dynamic state, with radio noise storms happening frequently. Many of them might not be associated with CME initiations.
Combining the radio and white-light coronagraph observations, Jackson et al. (1978) found that generally 5 – 10 hours before the first appearance of a CME in the coronagraph field of view (), type III radio bursts appeared intensively, with the occurrence rate being 2.5 times higher than normal, as seen from Figure 10. It is also shown that the faster the CME is, the shorter the interval between the CME appearance and the intense type III radio burst group is. It was revealed that these type III bursts, which are earlier than the main type III burst in the flare impulsive phase, are generally located within 20° around the central position angle of the CMEs. Jackson et al. (1978), as well as Kundu et al. (1987), proposed that the type III radio burst precursor is linked to the CME initiation, resulting from small-scale magnetic reconnection. Klein et al. (1997) clearly showed that the radio burst group-associated magnetic reconnection precedes the ensuing eruption of a large-scale structure.
Martin (1980) pointed out that among many preflare precursors, the most typical one is the filament darkening and widening, as illustrated by Figure 11. Generally a flare would occur 1 hour after the appearance of such features (Bruzek, 1951). Since the filament/flare eruptions are the key ingredients of major CMEs, the filament darkening and widening can also be considered as CME precursors.
Owing to ubiquitous perturbations in the corona, prominences often oscillate, even in the quiescent state. Generally, the oscillations last 1 – 3 times the corresponding period, decaying rapidly. After analyzing the spectroscopic data of a prominence eruption event, Chen et al. (2008) found that before the final eruption, the prominence was oscillating for 4 hours, which was almost 12 times the corresponding oscillation period, as shown by the alternating red/blue shifts along the dashed line in the panel (a) of Figure 12. They proposed that this kind of long-term oscillation might be a precursor for a CME, since any triggering process, as a kind of perturbation, can drive the prominence to oscillate. For example, panels (b) and (c) of Figure 12 illustrate how the emerging flux would drive the prominence to oscillate as it triggers the prominence to erupt. They revealed from one event that the oscillating velocity is 10 km s–1, and the spatial displacement is about 2 arcsec, which requires further high-resolution imaging observations to find more events.
With the Heliospheric Imagers on board the Solar TErrestrial RElations Observatory (STEREO) satellite, Harrison et al. (2009) identified narrow rays comprised of a series of outward-propagating plasma blobs apparently forming near the edge of the streamer belt prior to many CME eruptions. They suggest that these blobs result from the interchange reconnection between the streamer and the neighboring magnetic field, which removes the downward magnetic tension force holding the streamer static. Therefore, they call this phenomenon as pre-CME fuse.
Among the above-mentioned precursors, only the emerging flux appears well before the onset of CMEs, whereas others are the signatures associated with the initiation of the CME. It should be noted that none of the precursors is a necessary or sufficient condition for CME eruptions. For instance, many CMEs are not triggered by emerging flux (e.g., Démoulin et al., 2002; van Driel-Gesztelyi et al., 2003). On the other hand, Zhang et al. (2008) pointed out that new magnetic flux frequently emerged in active regions, during which no any eruption happened. Tappin (1991) found that it is also often to have SXR brightenings without any ensuing main flare (nor CME). Therefore, when we try to construct an empirical model for CME forecast, it is important to combine some or all of the above-mentioned precursors together in order to increase the success rate. It is noticed that some of the triggers, e.g., the emerging flux, are only the external cause for the CME eruptions, whereas the magnetic complexity of the CME progenitor is the internal cause.
As the magnetic field, which is generated at the base of the convection zone, emerges into the corona, it starts a ceaseless journey. On one hand, new magnetic flux continues to emerge from the subsurface into the corona, colliding with the pre-existing field and producing electric current layers or even current sheets in the highly conducting coronal plasma. On the other hand, photospheric motions with various length scales, e.g., the differential rotation, supergranular, mesogranular, and granular convections, persistently drag the footpoints of all the magnetic field lines to move in both organized and random ways, building up a highly stressed coronal magnetic field (Forbes, 2000). As a result, Poynting flux is continually injected into the corona, and the magnetic energy is thus accumulated gradually. It is generally accepted that the required energy for powering a strong CME comes from the coronal magnetic field, which is in an equilibrium state before it is initiated to erupt. From the mechanical equilibrium point of view, the CME progenitor sustains its equilibrium as the downward magnetic tension force balances the upward magnetic pressure force. Either the decrease of the tension force or the increase of the upward magnetic pressure force would cause the CME progenitor to seek an equilibrium at a higher altitude, and a CME might be then initiated.
Probably in the following two cases the accumulated energy could be suddenly released to host an eruption: (1) the CME progenitor reaches a metastable state (Sturrock et al., 2001); (2) the CME progenitor reaches a state close to the loss of equilibrium or instability (Forbes, 2000). In the first case, the CME progenitor is stable to small perturbations, and a proper trigger with significant observable features is necessary for the eruption, whereas in the second case, any further change of the instability-related parameter in the magnetic field, e.g., the magnetic twist, would directly trigger the eruption.
In the past decades, several triggering mechanisms have been proposed either conceptually or through MHD analysis and/or simulations, as described as follows. However, caveats should be taken that at the present stage, photospheric motions in models and in reality still do not match, and only observational data-driven MHD simulations can provide a quantitative understanding of the eruptive processes involved in CMEs, which is actually under development (Wu et al., 2006). It will also be seen that some of the following models are almost the same in nature, with their emphasis on different aspects of the same triggering process.
Moore and LaBonte (1980) analyzed the filament eruption event on 1973 July 29, and found that:
(a) the magnetic field is strongly sheared near the magnetic neutral line;
(b) the filament eruption and the two-ribbon flare were preceded by precursor activities in the form of small H brightenings and mass motion along the neutral line;
(c) H precursor brightening and the initial brightening of the flare are both located in the vicinity of the steepest magnetic field gradient.
Piecing these features together, they proposed the tether-cutting mechanism: as depicted by Figure 13, a filament is supported somehow, e.g., on dips, by magnetic field (not plotted in the figure) that is nearly aligned with the magnetic inversion line (dashed). Just around the filament, the magnetic field is still strongly sheared, e.g., the field lines AB and CD, which probably correspond to the associated SXR sigmoid. These strongly-sheared core field is overlaid by less-sheared envelope magnetic arcade. Before the filament erupts, all the field lines around the filament, except those holding the filament threads, are almost in a force-free state, i.e., the downward magnetic tension force is balanced by an outward magnetic pressure force. As the magnetic shear increases, the negative leg of the field line AB is close to be antiparallel to the positive leg of the field line CD, forming a strong current sheet in between (left panel of Figure 13). Owing to micro-scale instability-driven anomalous resistivity or many other non-ideal effects (such as the Hall effect, electron inertia, and so on), magnetic reconnection commences. As a result of the reconnection, the line-tied field lines AB and CD, which are like tethers constraining the filament, are cut from being tied to the photosphere, forming a long field line AD and a short loop CB (middle panel). Such a reconnection would also produce the observed H brightenings and mass motions along the magnetic inversion line. Following the reconnection outflow, the long loop AD expands upward, and the small loop CB shrinks down or even submerges down (Wang, 2006).
This process can be easily understood, since after reconnection, the loop AD is concave-upward near the reconnection site, which imposes an upward magnetic tension force on the loop, and the short loop CB is concave-downward, which imposes a downward tension force on the loop. As the localized reconnection goes on, the core field near AD pulls up the filament to rise, by which all the overlying envelope magnetic field are stretched up, forming an elongated current sheet above the magnetic neutral line (right panel of Figure 13). Such a tether-cutting process until now (from the left to the middle panels of Figure 13) can be regarded as the triggering phase of the whole CME eruption. Such a process results in the magnetic configuration required in the CSHKP model, and the magnetic reconnection of the newly-formed current sheet speeds up the filament eruption to form a CME, and produces a two-ribbon flare near the solar surface at the same time.
A similar mechanism was proposed by van Ballegooijen and Martens (1989), who pointed out that the magnetic flux cancellation near the neutral line of a sheared magnetic arcade would produce helical magnetic field lines, i.e., a flux rope, that can support a filament, and that further cancellation can result in the eruption of the previously-formed filament, as depicted by Figure 14 and numerically simulated by Amari et al. (2003b). The flux cancellation model is the same as the tether-cutting model in nature. The difference, if any, is that the flux cancellation model might emphasize a more gradual evolution of magnetic reconnection in the photosphere, while tether-cutting is a relatively more impulsive process occurring in the low corona. Besides, the flux cancellation also allows the flux rope to grow and its axis to rise. A current sheet might be formed as the flux rope rises, creating the required magnetic configuration for the CSHKP model. The flux cancellation would also increase the twist of the core field, which might also drive an ideal MHD eruption (see Section 4.1 for the discussions about ideal MHD eruptions).
The tether-cutting model, however, does not tell how the strongly sheared core field is formed. From the observational point of view, shearing motions may be one effective way to increase the magnetic shear near the polarity inversion line (PIL). Therefore, in the next item, we describe a similar model, i.e., the CME initiation by localized shearing motions.
The shearing motion is indeed one important way for the corona to build up free energy (Low, 1977). A lot of observations also revealed that many CME source regions experienced strong shearing motions before eruption (e.g., Deng et al., 2001). Therefore, it is not surprising that the shearing motion was proposed to be a trigger mechanism for CMEs (e.g., Aly, 1990). The shearing motion localized near the PIL would produce a strongly-sheared core field, which is covered by a less-sheared envelope field. Thus, this model well explains the required magnetic configuration in the tether-cutting model. In this sense, these two mechanisms are the same in nature.
As illustrated by Barnes and Sturrock (1972), the coronal arcades inflate as the shearing motion is imposed at the bottom boundary. It was conjectured by Klimchuk (1990) that the shearing of simple arcade configurations always results in an inflation of the entire field. The 2.5-dimensional MHD simulations performed by Mikić and Linker (1994) in the spherical coordinates indicate that subject to the localized shearing motion, the magnetic field expands outward in a process that stretches the field lines and produces a tangential discontinuity, i.e., a strong current sheet, above the PIL. Therefore, the shearing motions can be regarded as a triggering mechanism since it paves the way for the potential eruption of the arcade. Once resistivity is excited in the current sheet, magnetic reconnection sets in, and leads to an impulsive release of magnetic energy along with the ejection of a plasmoid. The effects of the shearing profile and background solar wind models on the triggering were numerically studied by Jacobs et al. (2006) with 2.5D MHD simulations in the axisymmetric coordinates. It is shown that (1) a faster shearing velocity leads to a faster eruption; (2) a wider shearing region facilitates the formation of a flux rope; (3) the evolution is dependent on the chosen solar wind model.
It is important to note that some of the plasma shearing motions in observations might not the the driver of the magnetic shear, they might be the result of magnetic flux emergence, as found in MHD simulations (Manchester IV et al., 2004).
Different from the above numerical models where the magnetic shear increases monotonically, Kusano et al. (2004) found that the injection of the reversal magnetic shear at the bottom boundary can also trigger the CME eruption, via a series of two different kinds of magnetic reconnection.
It is noted that, in most numerical simulations the evolution of the photospheric field is too fast compared to the very gradual accumulation of the magnetic energy in the solar atmosphere. This is true for the simulations mentioned above, as well as below.
In order to circumvent the Aly–Sturrock constraint (Aly, 1991; Sturrock, 1991, see discussions in Section 4.1), Antiochos et al. (1999) proposed the so-called magnetic breakout model, as shown in Figure 15. The essence is that the initial magnetic configuration consists of a quadrupolar topology, with a null point being above the central flux system. As the central flux system experiences shear motions, it expands upward, pressing the X-type null point to form a current layer. If gas pressure and resistivity are ignored, the current layer collapses to be an infinitely thin current sheet, which hinders the upward motion of the central flux system; If gas pressure and resistivity are considered, the current sheet would undergo magnetic reconnection owing to anomalous resistivity or other non-ideal effects. Such a reconnection process removes the constraint of the higher magnetic loops, triggering the eruption of the core field (thick lines). They demonstrated that the final state with the central flux system being fully open possesses a total magnetic energy less than that of the initial state, suggesting that partial opening of a closed magnetic configuration is energetically feasible.
As the central flux system rises, a current sheet forms underneath, whose reconnection leads to the drastic formation and eruption of a flux rope. The MHD simulation results of such an eruption process were compared with the CME features in observations (Lynch et al., 2004). Many other numerical models can be classified to this magnetic breakout model, e.g., Archontis and Török (2008) and MacTaggart and Hood (2009).
Note that the essence of this model is that part of the central flux system reconnects with the overlying background magnetic field, by which the constraint over the sheared core field is removed gradually like an onion-peeling process. Such a model can be regarded to be physically the same as the tether-cutting mechanism, and it can be considered as the external tether cutting. It is expected to have SXR bright loops on both sides of the sheared core field and reverse type III radio bursts that are produced by the reconnection-accelerated electrons which, however, might be too weak to be observed. Many authors compared the observed CME initiations with the breakout model (e.g., Sterling and Moore, 2004). The first evidence supporting the breakout model was presented by Aulanier et al. (2000), who found a null point above the source region in the extrapolated coronal magnetic field. Another indirect evidence supporting the quadrupolar configuration in the magnetic breakout model is that many quiescent prominences are located on the magnetic neutral lines between bipolar regions (Tang, 1987). From statistical point of view, Li and Luhmann (2006) conducted a statistical study, showing that the CME source regions with quadrupolar background magnetic field, which is crucial for the breakout model, are 3 times less than those with bipolar field. Similarly, Ugarte-Urra et al. (2007) found that the initiation of 7 out of 26 CME events in their study can be interpreted in terms of the breakout model.
By checking the variations of the magnetograms before CME eruptions, Feynman and Martin (1995) found that many CMEs are preceded by emerging flux that possesses polarity orientation favorable for magnetic reconnection between the emerging flux and the pre-existing coronal field either inside or outside the filament channel. Motivated by such a correlation, Chen and Shibata (2000) proposed an emerging flux triggering mechanism for CMEs, as illustrated by Figure 16: when the reconnection-favorable emerging flux appears inside the filament channel as seen in panel (a), it cancels the small magnetic loops near the PIL below the flux rope. Thereby, the magnetic pressure decreases locally. Plasmas on both sides of the PIL, which are initially in equilibrium, are driven to move convergently along with the frozen-in anti-parallel magnetic field under the pressure gradient. As a result, a current sheet forms below the flux rope, and the flux rope is also triggered to move upward slightly. When the reconnection-favorable emerging flux appears outside the filament channel (say, on the right side, as illustrated by panel b), it reconnects with the large-scale magnetic loops that cover the flux rope. The right leg of the large-scale magnetic loop, which is initially rooted very close to the PIL, is re-connected to the right side of the emerging flux, which becomes further from the PIL. The magnetic tension force from the kinked field line pulls up the magnetic loop (the larger thick black line) to move upward, with the flux rope following immediately. As the plasma is evacuated below the flux rope, the X-type null point collapses to form a current sheet.
In both cases, the core field, i.e., the flux rope here, is initiated to move up, with a current sheet forming below, by which a magnetic configuration required for the CSHKP model is formed. The later evolution can well fit into the CSHKP model, i.e., on one hand, the reconnection at the current sheet leads to the formation of a cusp-shaped two-ribbon flare below; on the other hand, the Lorentz force along the upward reconnection jet accelerates the jet and the flux rope system above, as seen from Figures 17 and 18, which show the evolutions of the magnetic field (lines), temperature (color), and velocity (arrows). Note that even though the flux rope in the initial conditions of their simulations is located slightly above the critical height for the torus instability, where , the flux rope was found to be ideally stable without the flux emergence. This implies the difference between MHD evolutions and the circuit analysis of the torus instability. With the plasma chosen in Chen and Shibata (2000), the flux rope erupts with a velocity of 400 km s–1. If the plasma is reduced, the eruption becomes faster.
In this model, the onset of the CME is triggered by the localized reconnection between the emerging magnetic flux and the pre-existing coronal field. Such a reconnection, which was originally proposed by Heyvaerts et al. (1977) to explain impulsive solar flares, would produce SXR bright points/jets (and H surges), which correspond to the SXR precursors well before the main flare as mentioned by Simnett and Harrison (1985). Recent observations indicate that such a localized reconnection would also drive the filament and surrounding magnetic loop to oscillate, which in turn modulates the localized reconnection to be intermittent (Chen et al., 2008). Therefore, it will be interesting to investigate how the CME precursors (2) – (5), and (7) mentioned in Section 3.4.1 can be understood along with the emerging flux trigger mechanism. What can be speculated is as follows: As the reconnection-favorable magnetic flux emerges, it reconnects with the coronal field. The coronal magnetic field is rearranged, and the filament loses its equilibrium. The coronal magnetic loops and the filament oscillate due to the kinked field lines, which may in turn modulate the magnetic reconnection to proceed in a repetitive way (Nakariakov et al., 2006; McLaughlin et al., 2009). The magnetic rearrangement would induce MHD waves, which then slightly accelerate electrons to emit radio noise storms. The repetitive localized reconnection generates SXR brightenings, and accelerates nonthermal electrons, producing a series of type III radio bursts when the background magnetic field happens to be open. A noticeable feature of the localized reconnection in the triggering phase of the CME is that the magnetic reconnection progresses in a repetitive manner, rather than continually.
A similar model was investigated by Archontis and Hood (2008), who simulated the emergence of two twisted flux tubes. They found that the interaction and reconnection between the magnetic fields of the two tubes lead to multiple formation and eruption of flux ropes.
As mentioned in Section 3.4.1, many CMEs were found to be associated with emerging flux. However, it should be kept in mind that some of these CMEs might be triggered by other mechanisms rather than the emerging flux, and the association might be just a coincidence. A parameter survey of this model was conducted by Xu et al. (2008), who showed that whether a new emerging flux can trigger a CME depends on several parameters of the emerging flux: its polarity orientation, its total flux, and its distance to the PIL. Image synthesis was composed by Shiota et al. (2005) in order to compare with Yohkoh SXR images, which indicates that the Y-shaped ejecting structure observed in some CME/giant arcade events corresponds to slow and fast shocks associated with magnetic reconnection. Such a model was also extended from 2D Cartesian coordinates to 3D spherical coordinates (Dubey et al., 2006).
Noticing that a curved current loop has a “toroidal force”, Chen (1989) extended the previously studied stability analysis of a current loop into the nonlinear phase in order to study its dynamic evolution. As shown in the left panel of Figure 19, the line-tied current-carrying loop, e.g., a flux rope holding a prominence at its bottom, is characterized by the major radius , the minor radius , a toroidal current , and describing how the flux rope closes below the photosphere. With some simplifications, Chen (1989) derived the total force exerted on a toroidal section of the flux rope. According to the Newton’s second law, and the plasma in the section is approximated as a particle, the motion of the plasma section is then established. It is found that with some parameters, the flux rope is unstable to radial perturbations, and may expand subsonically for extended periods of time; with some other parameters, the flux rope can expand and then reach a new equilibrium. He also found that if the flux rope carries a relatively large current, a fast eruption can be formed. For example, an initial loop with 20 G expands at 1200 km s–1, releasing magnetic energy of the order of 1032 ergs in tens of minutes.
Considering that a prominence is generally stable for weeks before its eruption, Chen (1996) proposed that an initial stable flux rope, as new poloidal flux is injected somehow, is accelerated and becomes eruptive. As an example, the right panel of Figure 19 shows the early evolution of the velocity of the flux rope in one case. It is noted that the energy release in this model mainly comes from the injected energy. In this sense, this model is different from other storage-and-release models discussed in this subsection.
Such a flux injecting and triggering processes have not been testified by MHD simulations, which should be quite different from the approximated particle dynamics. The flux injection triggering mechanism was sometimes criticized in the sense that the flux injection process would induce too large surface motions that have not been observed (e.g., Forbes, 2000; Schuck, 2010). However, it is interesting to see that an instability exists in the flux rope due to the “toroidal force”, as indicated by the equilibrium analysis of the system (Chen, 1989), which might serve as a trigger mechanism. This was called “torus instability”, inherited from laboratory plasmas (Kliem and Török, 2006, see Item 6 below).
Since the time scale of the coronal magnetic energy accumulation is very long, whereas flare and filament eruptions commence in a very short time scale, Gold and Hoyle (1960), even early in the 1960s, proposed that the trigger of the energy release should be related to some kind of instability. Along this line of thought, various instability/catastrophe mechanisms have been developed (see Forbes, 2000, for a review). The basic idea is: as the coronal magnetic field, subject to the photospheric motions and flux emergence, keeps evolving in a quasi-statical way (both ideally and non-ideally), it might reach a critical stage where the equilibrium is unstable (i.e., instability) or no nearby equilibrium state exists anymore (i.e., loss of equilibrium). The pre-CME structure is then at an unstable equilibrium and starts to erupt in the corona where perturbations are ubiquitous.
(a) Kink instability: Sakurai (1976) numerically analyzed the development of the kink instability of a twisted flux tube, as revealed by Figure 20. He pointed out that the kink instability can explain the observed height-time profile of an erupting filament. Hood and Priest (1979) further considered the line-tying effect of the photosphere on the kink instability of the twisted flux tubes, and found that there is a critical twist, above which the flux tube is unstable. In their analysis, the critical twist ranges from to (see also Mikić et al., 1990). However, these authors did not consider the effect of the external magnetic field overlying the twisted flux tube, which would stabilize the flux tube. Such an effect was studied in the MHD numerical simulations of Török and Kliem (2005) and Inoue and Kusano (2006). According to Török and Kliem (2005), if the overlying magnetic arcade decays gently with height, the kink instability would be suppressed after initial development, producing the so-called “failed eruption” found by Ji et al. (2003), and if the overlying magnetic field decays rapidly, the kink instability would lead to an ejective CME. According to Inoue and Kusano (2006), the short axis of the flux rope would also suppress the kink instability. Besides, as pointed by Baty (2001), the classical critical twist for the onset of the kink instability is applicable only for flux ropes with the radius much larger than the axis pitch length. For a general case, it is the local pitch angle that determines the instability.
(b) Torus instability: A current ring is unstable against expansion if the external potential field decays sufficiently fast, e.g., (Bateman, 1978), which was extended to study the dynamics of the flux rope in CMEs (Chen, 1989), and was called torus instability by Kliem and Török (2006), though these early works are based on circuit models, rather than solving full MHD equations.
With 3D MHD simulations, Fan and Gibson (2007) studied the emergence of a flux rope from the subsurface into the magnetized corona. As illustrated by Figure 21, when the background magnetic field declines slowly with height, a strongly-twisted flux tube emerging out of the solar surface may rupture through the arcade field via kink instability (top panels); whereas when the background magnetic field declines rapidly with height, a weakly-twisted flux tube, whose twist is below the threshold for kink instability, still erupts with little writhing like a planary outward expansion. They interpret the latter case as the “torus instability”.
It is pointed out here that in their simulations the flux rope is transported kinematically into the simulation box by changing the boundary conditions. Besides, reconnection due to numerical resistivity exists, which would have affected the dynamics of the system, and makes it not straightforward to distinguish ideal MHD instability from resistive instability. The observational result that the extrapolated magnetic field for the torus instability eruption events does not show a systematic rapid decay with height, as presented by Liu (2008), suggests that more factors should be considered.
It is noted in passing that, in several simulations works (e.g., Amari et al., 2004; Manchester IV et al., 2004; Fan and Gibson, 2007; Archontis and Hood, 2008), the flux rope erupts soon after it emerges out of the solar surface. This is slightly different from other “storage-and-release” models, and might explain the CMEs associated with the emergence of a new active region.
(c) Catastrophe: As demonstrated by MHD numerical simulations (e.g., Török and Kliem, 2005), the often used linear instability analysis has the limitation of saying nothing about the nonlinear development (Priest, 2007). One of the earliest efforts was to seek for the possibility of catastrophe of the magnetic system. Following van Tend and Kuperus (1978), Priest and Forbes (1990) constructed a model to study the equilibrium of a line current filament in the background coronal magnetic field. It was found that as the filament current or twist increases to a critical value, catastrophe takes place. In the ensuing researches on the catastrophic solutions, the measurable quantities, in place of the electric current in the filament, were adopted as the changing parameter. These models can further be divided into two branches, depending whether the triggering process is a resistive or an ideal process, as described separately in the following paragraphs.
As reconnection proceeds below the flux rope in the aforementioned tether-cutting reconnection or flux cancellation model, the flux rope would definitely rise. However, it does not mean that an eruption can be triggered. For example, with zero- MHD simulations, Aulanier et al. (2010) stated that the tether-cutting reconnection below the flux rope does not trigger the eruption of the flux rope, it just pushes the flux rope to rise. It is the torus instability that triggers the onset of the eruption. Alternatively, the 2D analytical solution by Forbes and Isenberg (1991) indicates that as flux cancellation continues near the magnetic neutral line, the flux rope embedded in a bipolar field initially rises smoothly (see Figure 22a-d). However, at a critical point, the flux rope presents a catastrophic behavior, i.e., the flux rope has the potential to jump from a lower altitude (panel e) to a higher altitude (panel f) from the energy point of view, with the flux distribution at the surface unchanged. The energy release in this transition is trivial (the fraction of the magnetic energy released in the transition depends on the background magnetic field, as shown by Forbes et al., 1994), so it might be insufficient to power an eruption. However, the higher state contains a current sheet, whose reconnection would result in the rapid eruption of the filament. Therefore, the flux cancellation-induced transition works as an efficient triggering mechanism for CMEs. On the other side, the trivial energy release associated with the catastrophe is based on 2D models. In the 3D case, more magnetic energy release is expected since the newly-formed current sheet can be localized in a finite volume.
It is mentioned here that such a catastrophe behavior, i.e., the transition from a null-point (at x = y = 0) to a current sheet in Figure 22, reminds us of the X-point instability found by Dungey (1953). Interestingly, Démoulin and Aulanier (2010) found that the critical conditions for the catastrophe also satisfy the instability criterion.
The decay of the background magnetic field is another way to trigger the CME progenitor to deviate from the equilibrium state. The decay of the photospheric magnetic field is often due to the magnetic diffusion that can lead to the formation, as well as the eruption, of flux ropes (Mackay and van Ballegooijen, 2006). The inward diffusion toward the PIL has the effect as the flux cancellation process, and the outward diffusion results in the weakening of the background field. With analytical solutions, Isenberg et al. (1993) found that before decreases to 0.8136, where describes the strength of the background magnetic field, the flux rope has only one equilibrium state. However, at = 0.8136, there exist two equilibrium states, i.e., a higher energy state and a lower-energy state with a current sheet below the flux rope, which means that the flux rope can transit catastrophically. Lin et al. (1998) extended this work so that the effect of the large-scale curvature of the flux rope is considered. It is found that unlike previous results, flux ropes with large radii are more likely to erupt than ones with small radii. The triggering model due to the decay of the background magnetic field might account for why the peak CME occurrence rate is delayed by 6 – 12 months with respect to the peak Sunspot number (see Section 2), since the background magnetic field becomes weaker and weaker during the declining phase of the solar cycle.
The increase of the upward magnetic pressure, which can push the CME progenitor to expand, can be realized by either converging motions or the shearing motions. With MHD simulations, Inhester et al. (1992) found that in addition to the shearing motions, the convergent motions can effectively facilitate the formation of a current sheet above the PIL of the magnetic arcade, which would then become resistive unstable. Analytically, Forbes and Priest (1995) found that even without flux cancellation, a flux rope system subject to the photospheric converging motion would also experience a catastrophic behavior. When the half distance of the dipole decreases from 4 to > 0.97, the flux rope always possesses only one equilibrium state. However, at = 0.97, the flux rope has two equilibrium states, i.e., a higher energystate and a lower energy state with a current sheet below the flux rope. Similar to the background magnetic field decay, such a catastrophe can serve as a nice trigger mechanism for CMEs. It is noticed in Forbes and Priest (1995) that as the background magnetic charges get closer, the flux rope decreases in altitude before the catastrophe appears. However, the 3D MHD numerical simulations by Amari et al. (2003a) indicate that as the converging motion is imposed at the bottom boundary, the flux rope always goes up. The difference is due to the fact that in the analytical study of Forbes and Priest (1995), for any point along the vertical axis, the background field from the two “magnetic charges” increases first (and decreases later). In order to realize a force balance, the line current and its image current should be put closer first (and further away later). One thing has to be kept in mind here: when deriving equilibrium state series subject to changing parameters in the analytical solutions, the frozen-in effect in the ideal MHD might be violated. It is also seen from their comparison that the catastrophe existing in the analytical study is not present in the MHD simulations. It might be due to that there is a “toroidal force” in the 3D flux rope (not existing in the 2D model), which excites the “torus instability” (Török and Kliem, 2007). It also reminds us of the warning that the searching for “loss of equilibrium” solution needs to consider global constraints (Klimchuk and Sturrock, 1989), including the frozen-in effect as mentioned above.
It is interesting to see that, for a system with a flux rope embedded in a bipolar magnetic field, a diversity of changes of the background magnetic field would trigger the catastrophic initiation of the flux rope eruption. As an example, Figure 23 shows the evolution of the loss of equilibrium of the flux rope driven by shearing motions. With the zero plasma and inertialess approximation, Lin et al. (2001) analytically studied the response of the flux rope system to the emerging flux as numerically solved by Chen and Shibata (2000). They found that there are also catastrophic behaviors in the triggering process. However, different from the MHD numerical simulations, the parameter regime in favor of the CME eruptions becomes complicated.
Considering the complexity of the solar atmosphere, such as the unceasing convective motions and magnetic flux emergence, probably several triggering factors may take effect collaboratively. For example, with 3D MHD simulations, Amari et al. (2000) studied the initiation of CMEs associated with both shearing motions and flux emergence. As shown by Figure 24, after the shearing motion and the opposite-polarity emerging flux are imposed at the bottom boundary, an initially simple magnetic arcade (upper-left panel) evolves into a twisted flux rope overlaid by an almost potential arcade (upper-right panel). If the magnetic flux of the emerging field is small, the flux rope rises to reach a neighboring equilibrium state. However, if the emerging flux is large enough, the whole system cannot find any equilibrium state, and begins to erupt (bottom panels).
Besides the above-mentioned triggering models, there are some other mechanisms that have not been investigated extensively and quantitatively.
(a) Mass drainage: It is generally assumed that filaments are supported by the Lorentz force against gravity. If a part of filament material drains down to the chromosphere, the filament would lose its equilibrium under the excess Lorentz force (or called magnetic buoyancy, see Tandberg-Hanssen, 1974; Low, 2001). Such a process was studied by Fan and Low (2003) and Wu et al. (2004), and was identified in some eruption events (e.g., Zhou et al., 2006).
(b) Sympathetic effect: Moreton waves and/or EIT waves generated by some CME events might trigger the oscillation (Eto et al., 2002; Okamoto et al., 2004) or even the eruption (Ballester, 2006) of a remote filament (such a speculation is worth detailed modelings); The reconnection inflow below an erupting CME may also induce the loss of equilibrium of a neighboring filament, as shown by Figure 25 (see Cheng et al., 2005, for details). In addition, the primary CME pushes aside the background magnetic field, which can also induce the loss of equilibrium of a neighboring filament (Ding et al., 2006).
(c) Solar wind: As illustrated by Figure 26, the CME source region with a closed magnetic configuration is often bounded by open magnetic field, where solar wind is accelerated from being nearly static to several hundred km s–1. It is possible that the CME source region might be pulled up by the solar wind with the drag force (Forbes et al., 2006) or the pressure gradient (X. Moussas, 2008, private communication). The latter might be called Bernoulli effect, which claims that along a streamline, the higher the velocity the lower the pressure. Note that the dragging effect of the solar wind is significant only when the flux tube extends to a height where the plasma is around unity.
After introducing the triggering mechanisms of CMEs, let us come back to the topic on the CME progenitors. For the slow CMEs that might be accelerated by the solar wind, the energy source is attributed to the solar wind, and the requirement for the CME progenitor is probably that its plasma should be big enough so that the line-tied magnetic field cannot restrain the plasma in the closed field. For the eruptive events, the energy source is attributed to the magnetic energy stored in the progenitor beforehand. The most important question is, then, what physical parameters can well describe the state that the progenitor is ready to be triggered to erupt as a CME.
For the first four triggering processes, such as tether-cutting or flux emergence, the progenitor is not necessarily close to an unstable state, e.g., it might be at a metastable state (Sturrock et al., 2001) (a metastable state means that the system is stable against small perturbations, but it can transit to a lower energy state with a sufficiently large perturbation). During the triggering process, significant changes can be found in observations, such as brightenings or evolving magnetic features. The problem is what parameters can characterize the progenitor that has the potential to erupt.
For the instability and catastrophe-related triggering processes, the progenitor should be close to but still have not reached the criteria of the instability. Therefore, future research might be focused on the quantitative determination of the criteria of the related instabilities based on the real observational data, especially the vector magnetograms and the extrapolated coronal magnetic field.
Based on multiwavelength observations, especially the photospheric vector magnetograms, researchers tried to find out some empirical measures that can well represent the nonpotentiality of CME-productive regions. For instance, Falconer et al. (2002) found that three measures are well correlated with the CME productivity: , the length of strong-shear, strong-field main neutral line; , the net electric current arching from one polarity to the other; and , a flux-normalized measure of the field twist.
From the theoretical point view, magnetic free energy is a parameter directly related to the nonpotentiality of the pre-CME metastable state. However, it is not rare to see that the magnetic free energy is increasing after one CME due to the Poynting flux through the solar surface, without any ensuing eruptions for hours (e.g., Jing et al., 2009). In this sense, the combinative study on the internal cause, e.g., the free energy, and the external cause, e.g., a suitable trigger, becomes crucial. Magnetic helicity, which is an almost conservative quantity even in a resistive process (Berger, 1984), could be a better parameter. The coronal electric current helicity, as well as the magnetic helicity, is cyclic invariant (Seehafer, 1990), therefore, CMEs are the main process to remove the otherwise accumulating helicity in active regions (Rust, 1994; Low, 1996). (The interchange reconnection between the closed and the open fields is another way.) Zhang et al. (2006) conjectured that for a given boundary condition, there may exist an upper bound on the magnetic helicity, which changes with the boundary conditions (Zhang and Flyer, 2008). According to the conjecture, any further pumping of magnetic helicity (or evolving boundary conditions) into the magnetic system at the threshold would lead to the eruption of a CME. As a support from observations, Nindos and Andrews (2004) found that in a statistical sense the preflare value of (the force-free factor) and coronal helicity of the active regions producing big flares that do not have associated CMEs are smaller than those producing CME-associated big flares. On the other hand, Phillips et al. (2005) argued that CME eruptions occur at a fixed amount of free energy in the corona, no matter the magnetic helicity is large or zero. Also a little surprisingly, the CME eruption may be triggered by a process along with the injection of magnetic helicity that has an opposite sign to the source active region, as demonstrated by Kusano et al. (2002) and Wang et al. (2004). Therefore, the role of magnetic helicity in triggering CMEs remains a controversial problem (see Démoulin, 2007, for a review).
Anyway, we are far from being able to predict where and when a CME is going to erupt.
Living Rev. Solar Phys. 8, (2011), 1
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