Solar Flares: Magnetohydrodynamic Processes
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- Shibata, K. & Magara, T. Living Rev. Sol. Phys. (2011) 8: 6. doi:10.12942/lrsp-2011-6
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This paper outlines the current understanding of solar flares, mainly focused on magnetohydrodynamic (MHD) processes responsible for producing a flare. Observations show that flares are one of the most explosive phenomena in the atmosphere of the Sun, releasing a huge amount of energy up to about 1032 erg on the timescale of hours. Flares involve the heating of plasma, mass ejection, and particle acceleration that generates high-energy particles. The key physical processes for producing a flare are: the emergence of magnetic field from the solar interior to the solar atmosphere (flux emergence), local enhancement of electric current in the corona (formation of a current sheet), and rapid dissipation of electric current (magnetic reconnection) that causes shock heating, mass ejection, and particle acceleration. The evolution toward the onset of a flare is rather quasi-static when free energy is accumulated in the form of coronal electric current (field-aligned current, more precisely), while the dissipation of coronal current proceeds rapidly, producing various dynamic events that affect lower atmospheres such as the chromosphere and photosphere. Flares manifest such rapid dissipation of coronal current, and their theoretical modeling has been developed in accordance with observations, in which numerical simulations proved to be a strong tool reproducing the time-dependent, nonlinear evolution of a flare. We review the models proposed to explain the physical mechanism of flares, giving an comprehensive explanation of the key processes mentioned above. We start with basic properties of flares, then go into the details of energy build-up, release and transport in flares where magnetic reconnection works as the central engine to produce a flare.
Solar flares are explosive phenomena observed in the solar atmosphere filled with magnetized plasma. The energy released during a flare is about 1028 - 1032 erg, and it takes various forms such as radiative energy, kinetic bulk energy, thermal and nonthermal energy. Because of their magnificent behavior, flares have been one of the most attractive scientific targets of the solar physics since they were first observed in the 19th century. The spatial size of a flare depends on individual events; in the smallest event the height of a flaring loop is less than 104 km, whereas it reaches 105 km in the largest event (see Section 2). The size also affects the duration of a flare (103 – 104 s) and the amount of energy released during a flare mentioned above.
Flares are observed in a wide range of electromagnetic waves such as radio, visible light, X-rays, and gamma rays (see Section 5). Emissions in these wavelengths come from the atmospheric layers extending from the chromosphere to the corona. In the extreme case, even the photosphere responds to a big flare, observed as white-light brightenings. Also a flare produces high-energy particles which travel through the interplanetary space, sometimes having a severe impact on the environment of the Earth (see Section 7).
Historically, flares were discovered in white light (Carrington, 1859; Hodgson, 1859). Later, spectroheliographs developed and an Hα filter was invented, flares can be observed in Hα. An Hα monochromatic image of a flare often shows beautiful two ribbons of bright patches, and the distance between these ribbons increases with time (e.g., Švestka, 1976; Zirin, 1988). For a long time flares were considered as chromospheric phenomena observed in Hα. However, the discovery of coronal radio and X-ray emissions from a flaring site has revealed that flares are actually coronal phenomena.
Here we show a brief history about the naming of “CSHKP”. In the 1980s, this model was called the “Kopp-Pneuman model” in the United States. Shibata (1991) proposed to change the name from Kopp-Pneuman model to “SHKP model”, by respecting the pioneering works by Sturrock and Hirayama. Soon after, Sturrock himself proposed to add “C” in front of “SHKP” in his 1992 proceedings (Sturrock, 1992), noting another pioneering work by Carmichael. Švestka and Cliver (1992) also use the term “CSHKP model” in the same proceedings book.
The CSHKP model has been improved significantly since Kopp and Pneuman (1976), especially because the theory of magnetic reconnection has been developed, which is summarized in a nice review paper by Priest and Forbes (2002). Kopp and Pneuman (1976) considered that open field lines reconnect to form a closed loop, then the upflows of the solar wind along the reconnected field lines collide each other to generate a shock inside the closed loop, thereby heating coronal plasma up to the typical temperature of a flare. However, Cargill and Priest (1982) later pointed out that it is important to consider the slow MHD shocks suggested by Petschek (1964). Forbes and Priest (1984) noted that a fast MHD shock (termination shock) is also formed above the reconnected loop when a reconnection jet collides with this loop. Furthermore, Forbes and Malherbe (1986) showed that the slow MHD shock could be dissociated to an isothermal slow shock and a conduction front in the case of flares. Those features mentioned above have been reproduced by recent MHD simulations (Yokoyama and Shibata, 1997, 1998, 2001), which are discussed in Section 5.
As we mentioned, the theory of magnetic reconnection is not completed yet, not only in solar plasma but also in laboratory and magnetospheric plasma. This is why many anti-reconnection models of a flare have been proposed (e.g., Alfvén and Carlqvist, 1967; Akasofu, 1984; Melrose, 1997; Uchida and Shibata, 1988, etc.). However, recent space missions such as Yohkoh (1991 – 2001), SOHO (SOlar Heliospheric Observatory; 1995 -), TRACE (Transition Region and Coronal Explorer; 1998 -), RHESSI (Ramaty High Energy Solar Spectroscopic Imager; 2002 -), and Hinode (2006 -) have provided a huge amount of observational results suggesting that the magnetic reconnection occurs during a flare (e.g., Shibata, 1999). These observational results supporting the reconnection model of a flare are summarized in Section 3.
The magnetic field providing the energy source of a flare originally comes below the solar surface (Zwaan, 1985), after traveling across the convection zone. While it travels across this region, the magnetic field is surrounded by a high-pressure plasma doing convective motions (e.g., Parker, 1979), so the magnetic field may take the form of a thin flux tube with some twist (Fan, 2009). When such a flux tube emerges into the surface, the background gas pressure decreases abruptly, so the magnetic field expand rapidly. The emerging magnetic field eventually fills a large volume up in the solar atmosphere and forms a magnetic structure there. The magnetic field loses the magnetic energy originally stored in the flux tube through this process, although part of magnetic energy remains in the magnetic structure as field-aligned electric current which does not produce the Lorentz force. The field-aligned current is therefore stored as free energy unless it is dissipated. The field-aligned current also introduces distortion into the magnetic structure (Sakurai, 1979), which is observed as a sheared arcade and/or twisted flux rope. The formation of distorted magnetic structure is important for understanding the state that leads to the onset of a flare, and we discuss this topic in Section 3.
It has been known that there are events preceding the onset of a flare. These are called ‘precursors’, and one of the prominent precursors is a newly emerging bipolar region at the surface, which may interact with preexisting magnetic field in the corona and produce a flare (Rust, 1968; Martres et al., 1968; Zirin, 1974; Heyvaerts et al., 1977; Martin et al., 1982; Feynman and Martin, 1995). Another well-known precursor is the activation, or eruption of a filament. A filament is composed of a relatively cool plasma with T ∼ 104 K, floated in the corona that is occupied by a much hotter plasma with T ≥ 106 K. The activation of a filament suggests that some destabilization proceeds in a magnetic structure containing a filament. Since a filament is formed in a low-beta coronal region (magnetic pressure is dominant compared to gas pressure), the main forces causing such destabilization are the gradient force of magnetic pressure, magnetic tension force, and gravitational force. It is therefore important to know how these three forces keep balance during the pre-eruptive phase of a filament, and under what condition the balance is lost to cause the eruption of a filament. This issue is related to the onset of a flare and discussed in (Section 3).
Since the corona is filled with a highly conductive medium, dissipating electric current there is usually inefficient. This, on the other hand, indicates that the magnetic energy tends to be stored in the corona without any easy, continuous dissipation of electric current. An important question then arises regarding how to release the magnetic energy in the corona (otherwise tremendous amount of magnetic energy would be accumulated in the corona). One of the possible scenarios is that the magnetic energy is released via the dissipation of electric current in a thin, sheet-like region where the current density is enhanced, which is called current sheet. This is accompanied by the reconnection of magnetic field that converts the magnetic energy to not only thermal but also kinetic energy of plasma jets (high-energy particles are produced as well; selected particles are accelerated by electromagnetic force). The magnetic reconnection changes the configuration of magnetic field (field line topology) in a magnetic structure, destroying force balance to drive a global evolution of the structure. It has been suggested that a number of current sheets are spontaneously formed in the corona (Parker, 1994; Longcope, 2005; Low, 2006). Magnetic reconnection is a process of converting energies and changing topologies, so the coronal field can relax via successive reconnections to a lower energy state, avoiding a monotonous increase of the magnetic energy in the corona. We discuss the formation of a current sheet followed by rapid energy release by magnetic reconnection in Section 4.
The energy released by magnetic reconnection is immediately transported from the site of reconnection via radiation, thermal conduction, high-energy particles, and plasma blobs (Priest and Forbes, 2002). The configuration of magnetic field significantly influences this energy transport. Part of the released energy is transported downward along magnetic field lines via thermal conduction and high-energy particles, heating chromospheric plasma. This produces not only Hα ribbons shown in Figure 1, but also hard X-ray (HXR) kernels in some energetic flares. The gas pressure of the heated chromospheric plasma increases, which drives the upflow of a plasma into the corona against gravitational force (chromospheric evaporation), filling a magnetic loop with hot plasma. This loop is observed in soft X-ray, so it is called a soft X-ray (SXR) loop. Another part of the released energy is transported upward as an ejecting plasma blob called plasmoid. During this phase selected particles are accelerated to become nonthermal energetic particles (Ramaty and Murphy, 1987). Those processes mentioned above are highly dynamic and complex, so numerical simulations are quite useful and indispensable for a better modeling of time-dependent, nonlinear energy transporting processes. In Section 5, we show the result obtained from such numerical simulations and explain key issues of energy transport during a flare.
A flare is often associated with other dynamic phenomena on the Sun. As we mentioned, the activation of a filament is one of those flare-associated phenomena. Sometimes a flare is part of a large-scale eruption known as a coronal mass ejection (CME), which carries a tremendous amount of plasma (up to 1016 g) to the interplanetary space. In a typical CME, a large magnetic loop with the size of the solar radius moves away from the Sun at 30 – 2500 km s-1 (Yashiro et al., 2004), which forms a shock wave at the front of the erupting loop. Regarding the modeling of CME, there are several concise and comprehensive reviews (Forbes, 2000; Klimchuk, 2001; Gibson et al., 2006; Mikić and Lee, 2006; Forbes et al., 2006; Chen, 2011). The physical relationship between a flare and CME has intensively been investigated (Gosling, 1997).
Observational features and phenomenological models
LDE flares, Impulsive flares, Giant arcade, Transient brightenings, X-ray jets, and models focused on their phenomenological aspects
Flux emergence, Force-free fields, Preflare structure, Magnetic helicity
Magnetic reconnection, Current-sheet formation, Flux-rope eruption
Radiation, Mass ejection, Shock heating, Particle acceleration, Wave propagation, Chromospheric evaporation
Application of solar flare model to stellar flares
Summary of physical processes for producing a flare
2 Observational Features and Phenomenological Models
2.1 Long-durational-event (LDE) flares
Tsuneta et al. (1992a) derived the following features of this LDE flare. These are now recognized as the common properties of LDE flares: The temperature distribution is somewhat chaotic in the early phase when the flare started, while in the late phase the temperature is systematically higher near the edge of the cusp-shaped loop (Veronig et al., 2006, and references therein). This can be explained by the radiative cooling efficiently working at inner central part of the loop (Forbes and Malherbe, 1991; Vršnak et al., 2006).
The cusp-shaped loop is also observed in many other flares (e.g., Tsuneta, 1997), even in somewhat indistinct observations done during the pre-Yohkoh era (MacCombie and Rust, 1979; Hanaoka et al., 1986).
2.2 Giant-arcade formation associated with filament eruption (or coronal mass ejection)
Outside the cusp-shaped structure the soft X-ray intensity often decreases with time, which is called dimming (Tsuneta, 1996; Sterling and Hudson, 1997; Harra and Sterling, 2001). Tsuneta (1996) attributed dimming to the inflow driven by reconnection that carries a large amount of plasma surrounding a current sheet into the sheet, thereby decreasing the gas density outside the current sheet (see also Shiota et al., 2005). Although usual dimmings associated with CMEs are attributed to stretching /opening of field lines by eruption (e.g., Sterling and Hudson, 1997; Harra and Sterling, 2001), there is a possibility that some of them are caused by the evacuation via the inflow into reconnection region like above (e.g., Shiota et al., 2005).
2.3 Impulsive flares
Those flares called impulsive flares show simple loop structure in soft X-ray, and they do not have a cusp-shaped structure, as found by Skylab before Yohkoh. Because of their apparent shape, impulsive flares are also called compact flares or confined flares (Pallavicini et al., 1977). Historically, it was considered that these flares were produced via energy release inside the loop observed in soft X-ray (Alfvén and Carlqvist, 1967; Spicer, 1977; Uchida and Shibata, 1988). Obviously, this is different from the energy release outside the loop, suggested by the CSHKP model for LDE flares, in which the energy release site is a current sheet formed above the soft X-ray (SXR) loop (see Figure 42).
The velocity is 50 – 400 km s-1.
The size is 4 – 10 × 104 km.
The soft X-ray intensity is 10-4 – 10-2 of the peak intensity of a soft X-ray loop.
The ejection of a plasmoid starts almost simultaneously at the beginning of the impulsive phase during which hard X-ray intensity takes a peak value. This relation also holds true in the case of multiple ejection where multiple impulsive phases exist (e.g., Oct. 4, 1992 flare).
A small soft X-ray bright point appears during the impulsive phase of a flare (Shibata et al., 1995), about a few 104 km away from a soft X-ray loop. It is suggested that this bright point corresponds to one of the footpoints of an erupting flux rope forming a plasmoid in three-dimensonal space.
Recently, Shimizu et al. (2008) made an analysis of fifteen impulsive flares to examine the correlation among the rise velocity of a soft X-ray loop and the ejection velocity of a plasmoid. The main conclusion is that there is a positive correlation between these two velocities (the ejection velocity is an order larger than the rise velocity), suggesting that the CSHKP model can be applied even for these impulsive flares. This further suggests that the plasmoid-induced-reconnection may play a key role in flares (see Section 4.1.6).
2.4 Transient brightenings and X-ray jets
Two sided-loop jet: When emerging field interacts with the preexisting field that extends horizontally, jets are produced in the horizontal direction toward both sides of an emerging flux region.
Anemone-type jet: When a newly emerging flux region appears in a unipolar region such as coronal holes, vertical jets are generated via the interaction of emerging field and the preexisting field that extends vertically. This forms an anemone-like loop structure in three-dimensional space (see the bottom panel of Figure 31).
2.5 Unified model for flares, microflares, and jets
Characteristics of flares and flare-like phenomena.
hot cusp loop
HXR loop-top source
Comparison of scales and associated mass ejection.
size (L) (104 km)
time scale (t) (s)
0.5 – 4
60 – 600
1026 – 1029
1 – 10
60 – 3 × 103
1029 – 1032
X-ray/Hα filament eruption
10 – 40
3 × 103 – 105
1030 – 1032
X-ray/Hα filament eruption
large scale arcade formation
30 – 100
104 – 2 × 105
1029 – 1032
X-ray/Hα filament eruption
Comparison of physical quantities.
VA (km s-1)
tA = L/VA (s)
12 – 120
6 – 300
2 × 109
30 – 103
3 × 108
25 – 500
Unified view of flares and flare-like phenomena.
mass ejections (cool)
mass ejections (hot)
Hα filament eruptions
Hα filament eruptions
X-ray plasmoid ejections/CMEs
X-ray plasmoid ejections
transient brightenings (microflares)
facular points (nanoflares?)
2.6 Avalanche model and non-reconnection models
Observations revealed several interesting statistical properties of flares. First, the occurrence rate of flares decreases with the total energy from microflares to largest flares, following a power law (e.g., Lin et al., 1984; Dennis, 1985; Shimizu, 1995), as presented in Equation (4). The fact that the index of power-law is less than 2 suggests that microflares alone are insufficient to support the energy for coronal heating (Hudson, 1991), though the exact value of the power-law index is still controversial, especially for small events such as nanoflares (e.g., see Aschwanden, 2004). Even so, an universal power law seems to hold true for flares of various sizes suggests that there is a common physical mechanism operating in these different-scale flares.
It is well known that the occurrence rate of earthquakes and the avalanches of a sandhill against their magnitude also show power law-like distributions, and these phenomena can now be understood in terms of self-organized criticality (Bak et al., 1987). Lu and Hamilton (1991) proposed that the coronal magnetic field is in a self-organized critical state, and solar flare represents the avalanche of many small reconnection events, which is analogous to the avalanche in the sandpile model. They successfully explained the observed power-law distribution of the occurrence rate of flares. Although there is a big gap between the avalanche model for a group of events and the magnetohydrodynamic model focused on an individual event, the avalanche model is still useful for understanding the process of energy release in the system of the solar atmosphere. If you want to know the recent development of the avalanche model, see the review by Charbonneau et al. (2001).
There have also been proposed several models for flares where magnetic reconnection is not assumed. One of them is found at the Alfvén’s current disruption model (Alfvén and Carlqvist, 1967). The other models are proposed by Akasofu (1984), Uchida and Shibata (1988), Melrose (1997), and so on. Many of these models assume energy release inside a flaring loop, thus they are not consistent with those observations provided by Yohkoh, such as loop-top hard X-ray source and plasmoid ejection above a soft X-ray loop.
3 Energy Build-up
The evolution of a flare basically starts with the emergence of magnetic field into the surface (flux emergence), which carries magnetic energy from the interior to the atmosphere. Part of this magnetic energy is immediately released when emerging magnetic field expands to form a magnetic structure on the Sun. The electric current crossing the magnetic field (cross-field current) generate the Lorentz force, so it drives expansion. The electric current flowing along magnetic field (Field-aligned current), on the other hand, does not generate the Lorentz force, so the field-aligned current is not used during an expanding process. In addition to that, the field-aligned current is not easy to dissipate in a highly conductive medium such as the solar corona, so it is stored there as free energy that becomes the energy source of flares and flare-associated phenomena.
3.1 Emergence of magnetic field (flux emergence)
In this section we start with the morphology of flux emergence, then explain the dynamic nature of flux emergence and the characteristics of magnetic structures formed via flux emergence.
Morphologically speaking, the field-aligned current introduces distortion to a magnetic structure where magnetic field lines tend to be aligned with the so-called polarity inversion line defined as the boundary between positive and negative polarity regions on the surface. When there is no field-aligned current, and when the inversion line is nearly straight, field lines overlie the inversion line transversely, forming a potential field without any free energy. The configuration of magnetic field therefore indicates whether field-aligned current (or free energy) exist or not in a magnetic structure (it is not generally true that field lines overlie the inversion line transversely in a potential field; for example, if the inversion line is bent, the angle between field lines and the inversion line deviates significantly from 90°, while there are cases with field lines locally almost parallel to the inversion line in quadrupolar configurations).
The evolution of EFRs observed on the Sun provides the key information on the subsurface structure of emerging magnetic field. As we mentioned in the introduction, it has been suggested that the magnetic field is confined to form thin flux tubes in the convection zone. The swirling motions of convective plasma in helical turbulence might add some twist to these flux tubes (Longcope et al., 1998), and the twisted field lines naturally generate the field-aligned current. Also flux tubes might be twisted enough to keep their coherence when they rise through the convection zone (Emonet and Moreno-Insertis, 1998; Cheung et al., 2006; Fan, 2008). An idealized model of such a twisted flux tube is the so-called Gold-Hoyle flux tube (Gold and Hoyle, 1960), in which field lines are uniformly twisted while the current density takes the highest value at the axis of the flux tube and decreases toward the boundary of the flux tube. Assuming that such a twisted flux tube emerges into the surface, part of the flux tube with less field-aligned current first appears and forms a potential field-like structure, which is reminiscent of an AFS observed on the surface. As emergence proceeds, inner central part of the flux tube that contains strong field-aligned current appears, forming a sheared arcade. This thought experiment presents a scenario of forming a sheared magnetic structure with free energy in the corona. The dynamic process suggested by this scenario will be discussed in the succeeding sections.
Similar two-dimensional simulations have been performed by Nozawa et al. (1992) to study the effect of convection on flux emergence. Shibata et al. (1990a) studied the convective collapse (Parker, 1978; Spruit and Zweibel, 1979) that occurs at photospheric footpoints of emerged loops, showing that the field strength becomes a kilo Gauss at the footpoints. The interaction of emerging and preexisting coronal fields has also been investigated by Yokoyama and Shibata (1996), which is further developed by Miyagoshi and Yokoyama (2004) where thermal conduction is taken into account.
The emergence in a flux-tube configuration is significantly different from the emergence in a flux-sheet configuration. In a flux-tube configuration field lines have different geometric shapes depending on their locations inside the flux tube, and this causes the difference in evolution among these field lines. To see how different it is, we should know the relation between the dynamic nature and geometrical shape of emerging field lines, which is demonstrated below.
3.1.3 Latest progress
Continuously increasing computational power enables to investigate flux emergence in the three dimension. Fan (2001) simulated the pattern of surface flows driven by the emergence of a twisted flux tube and compared it with observations. Abbett and Fisher (2003) present an integrated simulation where a subsurface convection model and a coronal model are combined. They have confirmed that emerging magnetic field tends to be relaxed to a force-free field state in the chromosphere and corona. Nozawa (2005), Murray et al. (2006) and Murray and Hood (2007, 2008) have done an extended survey of flux emergence by changing the subsurface configuration of magnetic field.
One of the issues related to flux emergence is the behavior of the axis of an emerging flux tube. It can be expected that the emergence of the axis becomes easy when the axis is strongly bent and has an Ω shape because the mass drains efficiently along the axis, thereby enhancing buoyancy. This conjecture has been confirmed by a series of works: in Magara (2001) which keeps a straight axis in the horizontal direction (2.5-dimensional simulation), the axis does not emerge (see Figure 14a), while when a flux tube is assumed to have a curved axis, the axis emerges. In fact, the emergence of the axis proceeds more efficiently when a curved (convex-up) flux tube is initially assumed (Hood et al., 2009; MacTaggart and Hood, 2009). Archontis et al. (2004, 2005, 2007), Isobe et al. (2005, 2006), and Galsgaard et al. (2005, 2007) have studied the interaction of emerging and pre-existing fields in various three-dimensional configurations (see Section 4.3). A series of works done by Manchester (Manchester IV, 2001; Manchester IV et al., 2004; Manchester IV, 2007) have shown the origin of shear flows observed on the surface (see Section 4.3). Recently, studies taking realistic factors into account such as radiation, thermal conduction, viscosity and partial ionization, have enabled to make a detailed comparison between simulations and observations (Leake and Arber, 2006; Cheung et al., 2007, 2008; Abbett, 2007; Hansteen et al., 2007).
3.2 Magnetic structure
Flux emergence is an essential process by which a magnetic structure containing free energy is formed on the Sun. It is still difficult to grasp the whole magnetic structure formed on the Sun observationally, while parts of the structure can be deduced from observed objects such as filament (or equivalently prominence which is observed on the limb of the Sun) and sigmoid that shows ‘S’ or ‘inverse-S’ shape in soft X-rays (Pevtsov et al., 1995; Rust and Kumar, 1996; Canfield et al., 1999). Modeling of these objects is therefore a key to the understanding of the magnetic structure related to flares.
We here try to understand the nature of such magnetic structure by referring to filament/prominence and sigmoid, both of which are observed before the onset of a flare (precursor), where an emphasis is put on their formation processes. We also explain how to reconstruct invisible magnetic structure using surface magnetic field which is observed. Force-free-field modeling is one of the possible methods of reconstruction. We also explain a famous conjecture on the energy state of force-free field, which is known as Aly-Sturrock conjecture.
3.2.1 Filament (Prominence)
Observations have revealed various structural features of filament (Martin, 1990, 1998; Schmieder et al., 2006; Rust and Kumar, 1994). A filament tends to form around the polarity inversion line separating opposite polarity regions (main polarity regions), forming a filament channel. Along the inversion line is observed the main body of a filament, which is called ‘spine’. There are also small weak-flux regions distributed in a filament channel (Martin, 1998; Chae et al., 2001), and these regions, which are called parasitic or satellite polarity regions compared to the main polarity regions, contribute to forming secondary structure such as filament feet called ‘barbs’. An important result about parasitic polarity regions is that these regions have the opposite polarity to the nearby main polarity region (Martin et al., 1994), and field lines connecting to parasitic polarity regions are suggested to have dipped structure (Aulanier and Démoulin, 1998; Aulanier et al., 1998; López Ariste et al., 2006).
There is also known a hemispheric chirality rule of filaments: ‘dextral’ filaments tend to appear in the northern hemisphere where the magnetic field with left-handed twist is preferentially observed, while ‘sinistral’ filaments are frequently observed in the southern hemisphere where the right-handed twist is dominant (Rust and Kumar, 1994; Martin, 1998; Pevtsov et al., 2003).
Although there are some observations suggesting that a filament is formed via the emergence of a twisted flux tube (Lites, 2005; Okamoto et al., 2008), it should be mentioned that a number of filaments are formed away from emerging active regions. These filaments form along the polarity inversion line of decaying active regions, in between active regions, and even in the polar regions (polar crown filaments).
Recently, the dynamic nature of filament/prominence has well been captured with advanced observing tools, which provides the detailed information on plasma motions in a filament/prominence (Berger et al., 2008; Okamoto et al., 2007). The modeling focused on the dynamic nature of filament/ prominence has also been reported (Antiochos et al., 1999b; Karpen and Antiochos, 2008).
Sigmoid is observed as either S or inverse S-shaped structure with soft X-ray enhancement in the corona, and it has been known as the precursor of a big cusp-shaped flare (Tsuneta et al., 1992a) or coronal mass ejection (CME) (Canfield et al., 1999; Sterling and Hudson, 1997). Recently, using the soft X-ray observations by Hinode, McKenzie and Canfield (2008) found that sigmoid is not a single loop but consists of many loops.
Gibson et al. (2002) use linear force-free field modeling to analyze an observed sigmoid. Pevtsov (2002) shows an interesting result on the spatial relationship between a filament and a sigmoid. Régnier and Amari (2004) use nonlinear force-free field modeling to study a global magnetic structure containing a filament, sigmoid, and a large Ω-loop overlying the filament and sigmoid. They explain that the filament and sigmoid are composed of the loops that have a smaller aspect ratio of height to footpoint separation than the overlying Ω-loop. This result suggests that a filament and sigmoid are located at inner central part of a magnetic structure formed through the emergence of a twisted flux tube, as we discussed in Section 3.1.2.
It is not clear whether sigmoid is just a thin current layer formed at the interface between two magnetic flux domains such as overlying and emerging fields, or it is more like a volumetric structure occupied by field lines with strong field-aligned current flowing on them. Three-dimensional modeling focused on the magnetic structure of an observed sigmoid such as force-free field modeling (see the next section) could provide useful information to clarify this issue.
3.2.3 Force-free field
Force-free field provides a method to reconstruct coronal magnetic field from surface magnetic field, the latter of which is easier to observe than the former. By using this method, Nakagawa et al. (1971) studied the magnetic structure of an isolated sunspot. Similarly, Sheeley Jr and Harvey (1975) construct a magnetic configuration formed by discrete flux sources at the surface. The helical nature of force-free field has been investigated by Sakurai (1979). By considering a series of force-free states, Barnes and Sturrock (1972), Low and Nakagawa (1975), and Low (1977) investigated the characteristics of evolving magnetic structure.
Recent developments are found in the attempt to combine force-free field modeling and the observation of surface magnetic field. Wheatland et al. (2000) introduce an optimization method to calculate force-free field, and according to this method Wiegelmann et al. (2000) calculate a force-free field based on observed surface magnetic field. Wiegelmann and Neukirch (2006) extended this method to calculate a magnetohydrostatic state. Régnier and Priest (2007) estimated difference among energy states of nonlinear force-free, linear force-free, and potential field in several active regions. A good review on various methods to calculate force-free field is given by Wiegelmann (2008). Very recently, Valori et al. (2010) have done two important steps in coronal field modeling. First, they show that it is possible to compute the coronal field even when it is significantly twisted (more than one turn), which was not obvious from previous studies. Second, they relate the specific behavior of the extrapolated field to its MHD evolution when the test field is out of equilibrium.
3.2.4 Aly-Sturrock conjecture
Full opening of field lines is not required (creating a current sheet of finite length) (Aly, 1991).
Resistive processes introduce a new factor that the conjecture does not assume, that is, the resistivity allows the formation of a twisted flux tube in a highly sheared arcade. This process prevents from forming a long current sheet by increasing the magnetic energy monotonically during a preflare state. At some point of preflare phase, the flux rope becomes unstable and is launched away, creating a current sheet of finite length below an ejecting flux rope to produce a flare. Then, a CME-like event occurs without opening fully bipolar field (arcade). This actually describes “Full opening of field lines is not required” (Mikić and Linker, 1994).
Cylindrically axisymmetric force-free field formed on a spherical surface gives a configuration whose energy state is not bounded by the energy limit suggested by the conjecture (Lynden-Bell and Boily, 1994).
Non-force-free field effects (e.g., gas pressure and gravitational force) unbound the energy limit suggested by the conjecture (Sturrock, 1991).
Regarding the energetics of force-free fields, Kusano et al. (1995) demonstrate a difference between two energy states of linear force-free fields that have the same magnetic helicity (see Section 3.3). They present an energy-bifurcation theory in which a vertically elongated magnetic arcade tends to be reduced to a state in which a twisted flux rope exists.
3.3 Magnetic helicity
The relative magnetic helicity quantitatively describes how much a magnetic structure is sheared compared to a (shearless) potential field. In a right-handed coordinate system the relative magnetic helicity takes a positive (negative) value when a magnetic structure is sheared in a right-handed (left-handed) way, while it take zero in the case of a potential field. Hereafter, we simply use the magnetic helicity to express the relative magnetic helicity.
Deriving observationally how much magnetic helicity is injected into the atmosphere has widely been done, which is a key to the understanding of the relationship between helicity evolution and the occurrence of active phenomena including flares (Chae, 2001; Moon et al., 2002; Nindos and Zhang, 2002; Kusano et al., 2002; Démoulin and Berger, 2003; Yang et al., 2004; Pariat et al., 2005; Jeong and Chae, 2007; Magara and Tsuneta, 2008). These studies are important in that we can derive the characteristics of helicity evolution and use it to predict the occurrence of active phenomena on the Sun. A recent review by Démoulin and Pariat (2009) is worth reading for those who are interested in this subject.
4 Energy Release
We here focus on magnetic reconnection, the central engine that enables the rapid release of the magnetic energy accumulated via the energy build-up process mentioned in the previous section. We first explain the basic physics of magnetic reconnection, and then discuss theoretical models which demonstrate how magnetic reconnection works to produce flares and flare-associated phenomena.
4.1 Magnetic reconnection
A finite value of resistivity causes the so-called Ohmic dissipation of electric current (cross-field current), which is especially efficient in a region where an intensive electric current flows, called current sheet. When the dissipation causes the topological change of magnetic field, the magnetic field is then reduced to a state that has lower energy than before. This is called magnetic reconnection. Through this process the magnetic energy stored inside and outside a current sheet is converted to kinetic and thermal energy. Magnetic reconnection is also accompanied by the generation of strong electric field around a current sheet (convective electric field), which could accelerate charged particles. The concept of magnetic reconnection is simple, although its physics is deep and wide, so we here suggest one of the textbooks that provide a comprehensive explanation of this really complicated process (Priest and Forbes, 2000). In the following, we briefly explain the basics of magnetic reconnection, focusing on its time scale in the environment of the solar corona.
4.1.1 Basic models of magnetic reconnection
4.1.2 Sweet-Parker model
4.1.3 Petschek model
4.1.4 Locally enhanced resistivity
The evolution leading to the steady state assumed in the Petschek model has widely been investigated with the help of numerical simulations. Here we discuss two types of reconnection: (i) driven-type reconnection (Sato and Hayashi, 1979), and (ii) spontaneous-type reconnection (Ugai and Tsuda, 1977). In the driven-type reconnection, fast reconnection is achieved by an external object that drives an inflow toward a current sheet. Sato and Hayashi (1979) performed two-dimensional MHD simulations in which an inflow is driven as boundary condition, showing that the Petschek-type reconnection occurs when the resistivity is locally enhanced in a current sheet. Biskamp (1986) also followed the concept of the driven-type reconnection, but the result shows that when a uniform resistivity is assumed the Petschek-type reconnection does not arise, instead the Sweet-Parker-type reconnection occurs.
For the spontaneous-type reconnection, resistivity is locally enhanced inside a current sheet via some microscale instabilities attributed to the nature of a current sheet, then an inflow spontaneously arises without any external sources, which draws plasma toward a current sheet. In this case the nature of a current sheet is the primary factor causing fast reconnection. Ugai and Tsuda (1977) performed two-dimensional MHD simulations of the spontaneous-type reconnection, and successfully reproduced the Petschek-type reconnection by locally enhancing resistivity inside a current sheet. Their result was later confirmed by Scholer (1989) showing that fast reconnection is closely related to the local enhancement of resistivity. Yokoyama and Shibata (1994) presented a result on the role of locally enhanced resistivity in the Petschek-type reconnection.
In either driven or spontaneous case, the local enhancement of resistivity seems an essential process, by which the Petschek-type reconnection occurs (Kulsrud, 2001; Uzdensky and Kulsrud, 2000). Also there is an issue about the origin of the external source assumed in the driven-type reconnection. This is crucial when we apply the driven-type reconnection to space plasma because we should identify the object that drives an inflow in a free space occupied by space plasma. In the case of laboratory plasma, we may easily identify such external objects outside a current sheet.
Very recently, it was shown that the classical Petschek-type solution with fast stationary magnetic reconnection is possible with a spatially uniform resistivity (Baty et al., 2009a,b) when a non-uniform viscosity distribution is assumed, which gives a new insight into the relation between the distribution of resistivity and the speed of reconnection. Also the self-similarity aspect of Petschek-type reconnection has been investigated (Nitta, 2010, and references therein).
4.1.5 Tearing instability and fractal reconnection
Following the discussion presented above, we then focus on how the resistivity is locally enhanced in a current sheet. Firstly, it should be noticed that even if the resistivity is uniformly distributed in a current sheet, the sheet is subject to the tearing instability (Furth et al., 1963; Steinolfson and van Hoven, 1984; Horton and Tajima, 1988), which eventually introduces nonuniformity into the current sheet where a series of magnetic islands are formed.
These magnetic islands tend to coalesce together to make a large magnetic island, and during this coalescencing process the magnetic energy is efficiently converted to kinetic energy (Bhattacharjee et al., 1983; Sakai and Ohsawa, 1987; Tajima et al., 1987). Nonsteady reconnection associated with multiple magnetic islands (Choe and Cheng, 2000) often causes impulsive bursty reconnection (Priest, 1985). Recently, Karlický and Bárta (2007) and Bárta et al. (2008) performed a series of simulations where tearing process is incorporated into the evolution of a flare.
If the thickness of a current sheet is reduced to microscales such as the ion’s Larmor radius or ion’s inertial length, kinetic processes such as the decoupling of ions and electrons as well as the interaction of waves and charged particles become important. These kinetic processes might enhance the resistivity significantly over the Spitzer resistivity based on collisions among particles (Spitzer, 1962). The coupling between macroscopic (MHD) and microscopic (kinetic) processes is important during magnetic reconnection, which has intensively been investigated by theory, simulation, and laboratory (Treumann and Baumjohann, 1997; Biskamp et al., 1995; Horiuchi and Sato, 1999; Yamada et al., 2000; Birn et al., 2001; Shay et al., 2001; Bhattacharjee et al., 2003; Drake et al., 2003; Hanasz and Lesch, 2003; Heitsch and Zweibel, 2003; Rogers et al., 2003; Ji et al., 2004; Craig and Watson, 2005).
4.1.6 Plasmoid-induced reconnection
It has been speculated that the speed of magnetic reconnection is related to the behavior of magnetic island, i.e., plasmoid formed in a current sheet (Shibata, 1999). While staying in a current sheet, a plasmoid significantly reduces the speed of reconnection by inhibiting an inflow accompanied by magnetic flux from entering a current sheet. When a plasmoid moves out of a current sheet, substantial amount of magnetic flux can come into the sheet, thereby triggering magnetic reconnection. This facilitates the ejection of a plasmoid via strong reconnection outflow (reconnection jet), which in turn enables new magnetic flux to continuously enter the current sheet. The positive feedback between plasmoid ejection and inflow enhancement contributes to producing fast reconnection, and eventually a plasmoid is ejected at about the Alfvén velocity. The whole process is named as plasmoid-induced reconnection by Shibata (1999). Recently, a detailed relation between plasmoid velocity and reconnection rate has been investigated by performing a series of numerical simulations (Nishida et al., 2009).
4.2 Current-sheet formation
a current sheet is formed at the interface between different flux domains interacting each other. Multiple flux domains might be formed via the emergence of a partially split flux tube (Figure 25).
a current sheet is formed inside a single flux domain where sheared magnetic field develops (development of magnetic shear)
4.2.1 Interaction of flux domains
Those works mentioned above are basically focused on the local dynamics produced by interacting flux domains, while it is also important to investigate the global magnetic configuration of multiple flux domains observed in real active regions. In particular, such a global approach permits to understand where current sheets are able to form, so where they locate flare ribbons/loops and how they evolve. It also permits a detailed comparison between modeling and observations (Aulanier et al., 2006; Masson et al., 2009, and references therein).
The so-called Minimum Current Corona (MCC) estimates the free energy stored in those multiple flux domains (see Longcope, 2005, for details). The original MCC assumes a configuration in which the magnetic field is in a potential state inside each flux domain, while it allows nonzero electric current flowing at the interface between flux domains. This gives a minimum excess of magnetic energy over the potential field energy in multiple flux domains. The MCC tells where current sheets form and how much electric current flows, so it can be used to investigate where flares might occur and how much energy will be released (Longcope, 1998). Later MCC was extended to enable the magnetic field to deviate from a potential state inside each flux domain (Longcope and Magara, 2004). While the MCC assumes a current sheet of infinitesimal thickness, there is also a model using a current sheet of finite thickness, which is called the quasi-separatrix layer (QSL) (Priest and Démoulin, 1995; Démoulin et al., 1996). Longcope (2005) is one of the comprehensive reviews on magnetic topology on the Sun.
4.2.2 Development of magnetic shear in single flux domain
Manchester IV et al. (2004) show that a twisted flux tube forms a flux rope above the surface, which tends to keep floating in the corona (the rising velocity of the flux rope decreases toward zero with time). This suggests that a mechanism to eject a flux rope from the corona to the interplanetary space is needed.
4.3 Modeling of energy-release processes
The ejection of a flux rope to the interplanetary space has widely been investigated using various kinds of models. Coronal mass ejections (CMEs) are one of the direct manifestation of this ejection. Since the ejection occurs in the corona with low plasma beta, the main forces exerting on a flux rope are the gravitational force, gradient force of magnetic pressure, and magnetic tension force. Losing a balance among them causes the ejection of a flux rope.
4.3.1 Bipolar system (single flux domain)
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).
4.3.2 Multi-polar system (two-step reconnection)
5 Energy Transport
The energy released by magnetic reconnection is transported in various ways, such as radiation, thermal conduction, mass ejection, wave propagation, and generation of high energy particles. The energy transporting process affects the solar atmosphere significantly, making the main phase of a flare rich with dynamic events such as shock formation, jet and plasmoid ejection, chromospheric evaporation, and acceleration of charged particles. In this section we explain these dynamic processes observed in a postflare phase.
An HXR source is formed at the chromospheric footpoint of a loop observed in soft X-rays (SXR loop), which is called HXR footpoint source. High-energy electrons generated by magnetic reconnection in the corona are supposed to stream downward along an SXR loop, heating chromospheric plasma to form an HXR footpoint source there. These high-energy electrons also produce microwave emissions intermittently via gyro-synchrotron radiation while streaming downward along an SXR loop. Another type of HXR sources is formed above the top of an SXR loop, which is called HXR loop-top source (Masuda et al., 1994). The HXR loop-top source may be formed by a downward high-speed flow (jet) which has been produced by magnetic reconnection and collides with the top of an SXR loop. The collapsing trap effect may be occurring during this phase near the top of the SXR loop (Somov and Kosugi, 1997; Karlický and Kosugi, 2004; Veronig et al., 2006). Soft X-ray emissions start to increase gradually during the preflare phase of a flare, suggesting that plasma heating already occurs before the onset of a flare. During the impulsive phase, the intensity of soft X-ray emissions increases rapidly and the time derivative of the soft X-ray intensity rise corresponds to the time variation of hard X-ray emissions, which is known as Neupert effect (Neupert, 1968). The main contribution to producing these soft X-ray emissions comes from a loop filled with hot plasma whose temperature is about T ≥ 107 K. This plasma originally comes from the chromosphere via evaporation driven by the thermal conduction (and high-energy electrons in part) emanating from a super-hot region formed in the corona (around the region where magnetic reconnection occurs). The thermal conduction also continuously heats the evaporated plasma and tries to keep its coronal temperature (eventually the evaporated plasma reduces its temperature by radiative cooling and forms Hα loops).
During the impulsive phase, bright kernels are observed in Hα at the footpoints of an SXR loop. This also indicates the heating of chromospheric plasma by thermal conduction and high-energy electrons. It has often been argued that explosive evaporation in the impulsive phase is primarily due to electron beams, causing Neupert effect, whereas the gentle evaporation in the gradual phase is due to conduction (e.g., Veronig et al., 2010, and references therein). When a group of SXR loops appear almost simultaneously and form an arcade, the Hα kernels are observed as two ribbons distributed along the polarity inversion line (called Hα ribbons, see Figure 1). In an extremely energetic case, high-energy electrons can penetrate the chromosphere and heat the photosphere, causing the enhancement of white-light emissions (white-light flare).
Hα emissions are also observed during the gradual phase of a flare. In this case the main contribution comes from a loop filled with cool plasma with T ∼ 104 K (Hα loop). An Hα loop starts to appear when an SXR loop experiences sufficient cooling via radiation and now is observed in Hα. As magnetic reconnection proceeds in the corona, a newly reconnected field line successively piles up on a preexisting SXR loop, so the apparent height of an observed SXR loop increases with time. In accordance with this, the distance between the two H.. ribbons observed at both footpoints of an Hα loop also increases with time (see Figure 1). The postflare loops are seen on the disc in emission in Hα only if they are dense enough (say n > 1012 cm-3; Švestka, 1976) which happens only in very powerful flares, so this is a rather rare phenomenon.
5.2 Mass ejection
5.2.1 Reconnection jet
5.2.2 Plasmoid ejection
Figure 43a shows a result from a two-dimensional MHD simulation, in which magnetic reconnection produces an ejecting magnetic island (two-dimensional counterpart of a plasmoid). The time variation of the convective electric field defined by Equation (16) is also plotted at this panel. Figure 43b shows the height-time relations of an observed plasmoid as well as hard X-ray intensity (Ohyama and Shibata, 1997). When comparing these simulation and observation, we assume that the time variation of the convective electric field is closely related to the time variation of hard X-ray emissions because the electric field can accelerate particles which contribute to producing hard X-ray emissions. The comparison suggests that the plasmoid ejection drives fast magnetic reconnection. More detailed investigations of plasmoid ejection are given by Choe and Cheng (2000), where multiple ejection of plasmoids and associated HXR bursts are discussed (see Figure 43c).
5.3 Shock formation and heating
5.3.1 Slow shock
It should be noted that the conduction could be strongly reduced due to a large difference in the magnetic field strength in inflow and outflow region, as well as due to thermal flux saturation and the flow/field geometry (for details see Vršnak et al., 2006, and references therein).
5.3.2 Chromospheric evaporation
Nagai (1980) first performed a one-dimensional hydrodynamic simulation of chromospheric evaporation. Since then, similar one-dimensional hydrodynamic simulations have been performed extensively (Somov et al., 1981; Nagai and Emslie, 1984; Peres et al., 1987; MacNeice et al., 1984; Mariska et al., 1989; Fisher and Hawley, 1990; Gan et al., 1991), which qualitatively explained the blue shift of Bragg Crystal Spectrometer (BCS) lines observed by Yohkoh as well as the red shift of Hα line observed during the impulsive phase of a flare (Ichimoto and Kurokawa, 1984). Investigations into the quantitative agreement between one-dimensional models and observations are still in progress. Later, pseudo two-dimensional models have been developed, reported by several authors (Hori et al., 1997; Warren et al., 2003). Yokoyama and Shibata (1998) performed a two-dimensional MHD simulation reproducing the chromospheric evaporation driven by thermal conduction (see the bottom panels in Figure 44). By combining magnetic reconnection, thermal conduction and radiative cooling, they derived a scaling law about the temperature observed in a loop filled with evaporated plasma, as shown in Equation (38). Later, Shibata and Yokoyama (1999) applied this scaling law to stellar flares (see Section 6).
5.3.3 Fast shock
5.4 Wave propagation
The so-called EIT wave gives another type of waves associated with a flare, which was discovered by the EUV Imaging Telescope (EIT) aboard SOHO as a transient wave-like phenomenon with enhanced coronal emissions (Moses et al., 1997; Thompson et al., 1998). The mechanism for producing an EIT wave has been investigated by Delannée and Aulanier (1999), Wang (2000), and Wu et al. (2001). Chen et al. (2002) presents an integrated model of EIT and Moreton waves in which these two waves are subproducts of an expanding magnetic loop responsible for a CME.
5.5 Particle acceleration
Particle acceleration associated with a flare has intensively been investigated (Ramaty and Murphy, 1987; Miller et al., 1997; Tsuneta and Naito, 1998; Aschwanden, 2002). Detailed processes of particle acceleration are beyond the scope of MHD, where the kinetic process involving charged particles become important. A typical length scale characterizing the kinetic process is the ion Larmor radius or ion inertial length, both of which are of the order meter in the corona. This is much smaller than the typical size of a flare, making it difficult to incorporate particle acceleration into the model developed for the global structure and overall evolution of a flare.
High-energy electrons produced by strong convective electric field could contribute to forming foot-point as well as loop-top HXR sources, as illustrated in Figure 42. Some of the high-energy electrons are not trapped near the Sun; instead they travel outward through the corona along open field lines. These electrons drive the plasma oscillation in the corona, which is observed as the type III radio bursts.
In some big flares (GOES X-class flares), solar neutron events (SNE) can be observed on the ground of the Earth. The neutrons are produced by the interaction of relativistic ions accelerated at the flare site and atomic nuclei (Watanabe et al., 2006). It is to be noted that when a large amount of electrons are accelerated simultaneously to produce a strong electron beam, a return current (a reverse current) may be generated around the electron beam to cause atmospheric heating. The effect of the return current have been studied by many authors (e.g., Karlický, 2008).
6 Application to Stellar Flares
It is well known that stellar flares and coronae have many similarities to solar flares and corona (e.g., Haisch, 1989; Güdel, 2002). Not only light curves of stellar flare emissions (in radio, Hα, visible continuum, and X-rays) but also quantitative nature of flares such as time scale, plasma temperature, density, and magnetic field strength are all similar, though the distribution of temperature and total energy of stellar flares is much broader (T ∼ 107 – 108 K, total energy 1029 – 1037 erg) than those of solar flares (T ∼ 1 – 3 × 107 K, total energy ∼ 1029 – 1032 erg).
It is believed that stellar flares are produced by the same mechanism, magnetic reconnection, as solar flares. However, why do some of stellar flares show very high temperature and extremely large total energy? Recent observations of young stars by X-ray satellites ASCA and ROSAT have revealed that young stars such as protostars and T-Tauri stars frequently produce superhot flares with temperature of 108 K (Koyama et al., 1996; Tsuboi et al., 1998; Imanishi et al., 2001, see Feigelson and Montmerle, 1999 for a review). Time variation of X-ray intensity is similar to that of solar flares, while the total energy released by those stellar flares amounts to 1036 – 1037 erg, much larger than those of solar flares. Can these protostellar flares be explained on the basis of magnetic reconnection?
Figure 46 shows the observed correlation between the emission measure of solar and stellar flares and their temperatures. It also shows the theoretical relation between the emission measure and temperature given by the Equation (43) is plotted as solid lines for three cases of B = 15, 50, 150 G in the case of n0 = 109 cm-3. Figure 46 shows that the observed correlation line corresponds to the line of constant magnetic field strength within 30 – 150 G, and indeed the coronal magnetic field strength is estimated to be about 40 – 300 G for solar and stellar flares. Similarly, if we eliminate the magnetic field strength (B) from the Equations (43) and (46), we can plot the relation between the emission measure and temperature for constant loop length, which is also shown in Figure 46 as dash-dotted lines. We can see that the length of a solar microflaring loop is 108 – 109 cm, and the length of a solar flaring loop is 109 – 1010 cm. These are fully consistent with observations.
It is interesting to see that the length of a stellar flaring loop is 1010 – 1012 cm, much larger than the length of a solar flaring loop. This is consistent with observations that average field strength at the surface of young stars is very strong, which is of order kilo Gauss (e.g., Johns-Krull et al., 1999), indicating that the size of a coronal loop with strong magnetic field (≫ 100 G) is much larger than that in the Sun.
The size of a flaring loop in young stars is estimated to be comparable to or even larger than the solar radius (∼ 7 × 1010 cm). It should be noted here that the range of radius for these young stars is from 1 to 4 solar radii (e.g., Johns-Krull et al., 1999).
Consequently, we found the reason why some of stellar flares, especially young star flares, show very high temperature and extremely large total energy, which is because the size of these flares is much larger than that of solar flares. If the length of a flaring loop is larger, the flare temperature increases in proportion to L2/7 even if the magnetic field is the same, because the conduction cooling (κ0T7/2/L2) become less efficient for a longer loop. The total energy is simply determined by the total magnetic energy contained in the corona in a normal state, ∼ L3B2/(8π), which explains the observations very well, although only a fraction of this energy is available as we mentioned before (Equation (1)).
Why can such a large coronal loop with strong magnetic field exist? Why is the filling factor of strong magnetic fields large (near unity) in young stars? One possibility is that the protostar is just born, keeping primordial magnetic field whose origin is in interstellar medium. The other possibility is that the strong magnetic field with large filling factor is created by the dynamo action. Since young stars rotate rapidly (more than 30 km s-1 which is much faster than the solar rotation, ∼ 2 km s-1), the dynamo action would be stronger. It is also expected that there is an accretion disk (planet-forming disk) around a young star, so that strong interaction would occur between the central stellar core and the surrounding disk, which may lead to magnetic reconnection. This interacting process has been treated by Hayashi et al. (1996), who performed 2.5-dimensional MHD simulations for the interaction of an accretion disk and stellar magnetosphere (dipole magnetic field). They have shown that vigous magnetic reconnection associated with mass ejection occurs. The reconnection releases a huge amount of magnetic energy up to the order 1036 erg (about 104 times more energetic than solar flares) stored in a sheared loop with a size of L ∼ 1011 cm.
7 Concluding Remarks
As we have seen in the previous sections, the main process responsible for producing a flare is the dissipation of electric current in the corona. The magnetic energy stored by coronal field is first released, followed by various dynamic events such as mass ejection and wave propagation. It should be noticed that the low density in the corona makes these accompanying events so dynamic, which is why we feel that flares are dynamic phenomena as well.
Since the electric conductivity is generally high in the corona, the dissipation of electric current there is only efficient in a current sheet where a large amount of electric current flows. The high electric conductivity of the corona therefore contributes to locally concentrating electric current (this means to amplify free magnetic energy), which in fact makes the dissipation of electric current explosive. This gives an explosive character to a flare, which is quite different from the dissipation of electric current in a resistive medium (conductivity is low) where electric current is dissipated easily and less dynamically without amplifying free magnetic energy.
Finally, we should mention that the solar activity including flares potentially has a significant impact on the Earth. This research field investigating the Sun-Earth environment has been developing as the space weather. Flares can produce high-energy particles and CMEs, which sometimes damage telecommunications and power supplies on the Earth. A big flare known as a proton flare produces high-energy protons (> 10 MeV), and these high-energy particles travel through the interplanetary space to the Earth, having a huge impact on the polar region of the Earth (polar cap absorption, PCA). Predicting the occurrence of flares therefore becomes of great importance nowadays when human activity extends to the space. This requires the detailed investigations into the mechanism of such magnetically driven solar activity, and the nature of magnetic field transported via flux emergence into the solar atmosphere is a key to a better understanding of the Sun-Earth system.
The authors would like to thank the following people for allowing them to use their original figures in this review paper: T. Amari, S. K. Antiochos, V. Archontis, A. Asai, H. Carmichael, P. F. Chen, G. S. Choe, Y. Fan, T. G. Forbes, K. Galsgaard, E. Hiei, T. Hirayama, H. Isobe, S. R. Kane, R. A. Kopp, H. Kurokawa, K. Kusano, J. A. Linker, B.C. Low, W. B. Manchester, S. Masuda, A. McAllister, Z. Mikić, R. L. Moore, F. Moreno-Insertis, N. Narukage, M. Ohyama, E. Pariat, M. Shimojo, P. A. Sturrock, T. Tajima, T. Yokoyama, S. Tsuneta, and A. A. van Ballegooijen.
All figures from the Astrophysical Journal reproduced by permission of the AAS; from Astronomy and Astrophysics reproduced with permission from ESO; from Journal of Geophysical Research reproduced with permission from AGU; from Nature reprinted by permission from Macmillan Publishers Ltd.; from Physics of Plasmas reprinted with permission from AIP; from Publications of the Astronomical Society of Japan reproduced with permission from ASJ; from Solar Physics, Space Science Reviews, and Astrophysics and Space Science reproduced with kind permission from Springer Science+Business Media B.V.
This work was supported by the Grant-in-Aid for the Global COE Program ‘The Next Generation of Physics, Spun from Universality and Emergence’ from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan. One of the authors (T.M.) was also financially supported by Basic Science Research Program (2010-0009258, PI: T. Magara) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology, as well as the World Class University (WCU) program through the NRF (R31-10016).