Heyvaerts et al. (1977*) proposed the well-known model of a solar flare driven by magnetic reconnection of an emerging flux and the pre-existing field. Figure 47* shows a schematic illustration from their study. Since then there have been numerous papers on magnetic reconnection between emerging flux and the ambient field, but the essential picture, namely current sheet formation and reconnection between the emerging flux and the pre-existing field, remains unchanged.
The first MHD simulation of magnetic reconnection between the emerging flux and pre-existing field was done by Forbes and Priest (1984). In this paper the emerging flux was driven in from the bottom boundary of the computational domain, which initially consisted of uniform, horizontal magnetic field with opposite direction to the emerging flux. They found that, because the emergence is slower than the Alfvén time-scale but faster than the reconnection time-scale given by the Sweet–Parker reconnection model , where is the Lundquist number, a region of closed loops and a current sheet at the top of the loop are formed. In the later phase reconnection became faster and super-magnetosonic flows (jets) were produced. Thus, the model by Heyvaerts et al. (1977*) shown in Figure 47* was demonstrated by MHD simulation.
Later, Shibata et al. (1992b*) performed 2D MHD simulations of flux emerging into a stratified atmosphere with a pre-existing horizontal field in the model corona. They self-consistently solved the Parker instability of a flux sheet and reproduce similar morphology and dynamics, namely the formation of -shaped loop, its reconnection with pre-existing field and ejection of jets. They also found that multiple plasmoids were formed in the reconnecting current sheet and ejected intermittently. However, due to the limited resolution the reconnection was likely to be numerical.
Interaction of an emerging twisted flux tube with the pre-existing horizontal coronal field was first studied in 3D by Archontis et al. (2004*). In Figure 48* (adopted from their paper), one can recognize the evidence of reconnection between the flux tube and the coronal field in the evolution of the field line connectivities. This probably corresponds to the observation of the formation of coronal loops that connect the newly emerging region and pre-existing flux system (i.e., neighbouring active regions) reported by Longcope et al. (2005).
Following Archontis et al. (2004), the interaction of the emerging twisted flux tube and the horizontal coronal field has been studied in detail (Archontis et al., 2005; Galsgaard et al., 2005; Archontis et al., 2006*; Galsgaard et al., 2007*). It was found that when the coronal field and the two flux systems are nearly anti-parallel, reconnection between them produces high-temperature and high-velocity outflows. However, when the two flux system have more of a parallel orientation, the amount of reconnected flux is limited and no such energetic features appear. Interestingly, despite having different amounts of reconnected flux in the cases with different orientations, the height-time profiles of the apex of the emerging loops look almost identical (Galsgaard et al., 2007) in different cases. The plasmoids (magnetic islands) in the reconnection region found in 2D simulations (Shibata et al., 1992b; Yokoyama and Shibata, 1994) are also found in 3D simulations by Archontis et al. (2006). Due to the three-dimensionality the plasmoids appear as twisted flux tubes.
2D simulations of flux emerging into pre-existing oblique field 13 was first studied by Yokoyama and Shibata (1995*, 1996*), in which they found both hot and cool jets along the oblique field lines as shown in Figure 49*. The hot and cool jets are adjacent to each other, which is consistent with simultaneous observations of X-ray jets and H surges (Canfield et al., 1996).
3D simulations with an emerging twisted flux tube into oblique ambient field was performed by Moreno-Insertis et al. (2008*). Figure 50* shows the 3D topology of the magnetic field. The orange, blue and green lines indicate the field lines in the emerging flux, the pre-existing field, and the reconnected field, respectively. The temperature (red, = 6.5 MK) and (blue) isosurfaces are also shown to visualize the structure of the jet and the reconnecting current sheet. Many results of 2D simulations (Yokoyama and Shibata, 1995, 1996*) are reproduced in 3D simulations. An extension of the work by Moreno-Insertis et al. (2008*) was undertaken by Moreno-Insertis and Galsgaard (2013*), in which they carried out the flux emergence simulation in a larger domain and for longer duration. They found that, after the main jet phase, a number of eruptive events occurred from the same emerging flux region. This will be discussed further in Section 4.2.
The overall picture is thus established, namely that emergence flux into a pre-existing flux system causes reconnection between them, produces plasma heating and dynamic events such as jets. However, it seems there are variety of the acceleration mechanisms of jets. In the next section we discuss the different mechanisms of jet acceleration. Moreover, in cases where the pre-existing flux system has more complicated structure, the emerging flux may trigger the large scale eruption of the pre-existing flux system. In some cases the significant fraction of the emerging flux itself erupts. This topic is discussed in Section 4.
Some observations show that jets recur from the same region (Chae et al., 1999*; Chifor et al., 2008*). The recurrent behavior of reconnection and jets in the MHD simulation of flux emergence was first reported by Murray et al. (2009*). As shown in Figure 51*, reconnection reversal (or oscillatory reconnection) takes place; reconnection occurs in distinct bursts and the inflow and outflow of one burst become the outflow and inflow in the following burst of reconnection, respectively, and this process repeats. The reversal of reconnection occurs because the reconnection outflow cannot escape from the reconnection site and, hence, the gas pressure gradient in the outflow region increases and eventually reverses the direction of the flows. This phenomena has been further investigated in detail by McLaughlin et al. (2012), who confirmed that the mechanism of the oscillatory reconnection is the local imbalance of forces, primarily the gas pressure gradient, between the neighboring flux systems. Archontis et al. (2010) found that essentially the same process also occurs in 3D simulation with a twisted emerging flux tube. Both in 2D and in 3D, the recurrent, oscillatory reconnection gradually becomes weaker and eventually ceases when the system settle down to a new equilibrium. It may also explain observations of the quasi-periodic propagating transverse waves (Liu et al., 2011b).
In the case where the sub-photospheric flux system is much longer than the characteristic scale of the undular mode (scale heights 3000 km), multiple -loops can emerge. Figure 52* shows the result of a 2D MHD simulation of a such case by Isobe et al. (2007b*). The neighbouring loops reconnect and cause heating in the lower atmosphere that may be observed as Ellerman bombs. The reconnection events also remove mass from the field lines and allow the emergence of long field lines. A 3D version of this simulation was presented by Archontis and Hood (2009). This process is also caused when realistic granular convective flows are present in the models (see Section 3.4.3).
Jets, or collimated flows from emerging flux regions have been observed at various wavelengths. H observation of the chromosphere often show dark jets, also called surges (Roy, 1973; Brooks et al., 2007). They appear as dark absorbing feature in H and represent chromospheric () material.
The soft-X-ray observations by Yohkoh revealed numerous X-ray jets (Shibata et al., 1992a; Shimojo et al., 1996), with many of them associated with emerging flux or cancellation events (Shimojo et al., 1998). The typical physical parameters of the jets are: temperature: 3 – 8 MK, density: , and the apparent velocity: 180 – 530 km s–1, comparable or smaller than the sound velocity. In addition to X-ray observations there are also many imaging and spectroscopic EUV observations of coronal jets (e.g., Chae et al., 1999; Chifor et al., 2008*).
Higher resolution observations by Hinode X-ray telescope subsequently revealed two distinct components: a faint and faster component (velocity 800 km s–1), and a bright and slower one similar to those found in Yohkoh observations (Cirtain et al., 2007*). Transverse motion in the jets was also found, suggesting the presence of Alfvén or fast kink-mode waves (Cirtain et al., 2007*; Savcheva et al., 2007). The transverse motion has been also found in chromospheric jets observed in spicules and chromospheric jets (De Pontieu et al., 2007; Nishizuka et al., 2008*; Liu et al., 2011a; Okamoto and De Pontieu, 2011). High-resolution observations from the Solar Optical Telescope onboard Hinode led to the discovery of numerous small-scale jets in the chromosphere (Shibata et al., 2007*; Singh et al., 2012*) whose morphology is similar to X-ray and EUV jets (see Figure 53*).
It is tempting to invoke reconnection outflow as the cause of jets but the answer is not so simple. First of all, 1D numerical simulations and EUV spectroscopic observations indicate that many, though not all, of the soft X-ray jets are not the reconnection outflow itself, but are so-called evaporation jets driven by the gas pressure gradient (Shimojo et al., 2001; Chifor et al., 2008).
Chromospheric evaporation is a process in which the magnetic energy released via magnetic reconnection in the corona is transported to the chromosphere preferentially along the magnetic field either by anisotropic thermal conduction or high-energy particles. Therefore, in order to study the effect of chromospheric evaporation in MHD simulations coronal thermal conduction is necessary (see discussion in Section 3.7.2).
Miyagoshi and Yokoyama (2003*) and Miyagoshi and Yokoyama (2004) performed 2D simulations of emerging flux with pre-existing horizontal coronal field including the anisotropic thermal conduction. Their comparison of simulations with and without thermal conduction demonstrates that thermal conduction is necessary to reproduce high-density evaporation jets. Hot and Alfvénic reconnection outflow was also found in the simulations. The reconnection outflow and the evaporation jet probably correspond to the faint and bright components found by the Hinode/XRT observations (Cirtain et al., 2007).
The acceleration of cool jets is more problematic. It is often naively interpreted that if reconnection occurs in the chromosphere it can launch a jet with chromospheric temperature. Consider the extreme case when all the magnetic energy is used to lift the plasma in the same volume against gravity. The maximum height is given bySingh et al., 2012). This is particularly true when reconnection takes place in the lower chromosphere where is close to unity except in the sunspots. In such a case one needs a mechanism by which the released magnetic energy in the reconnection region is transported upward and subsequently accelerate the plasma where the density is much lower.
Wave propagation and steepening is one such mechanism. Reconnection in the lower atmosphere can generation slow mode wave (Takeuchi and Shibata, 2001) and it is known that as a slow-mode wave propagates upward, its amplitude grows due to the the density contrast, eventually steepening into a shock. The interaction of the shock and the transition region between the chromosphere and the corona can launch the transition region upward, which is observed as a chromospheric jet (Osterbrock, 1961; Shibata and Suematsu, 1982; De Pontieu et al., 2004; Heggland et al., 2009). From their emerging flux simulations with the Bifrost code (which includes radiative transfer, thermal conduction, and changes in ionization state), Martínez-Sykora et al. (2011) reported the occurence of a cool chromospheric jet resulting from the interaction of emerging flux with the overlying arcade field. They identified that reconnection between the emerging flux and ambient field likely occurred in the high- photosphere. As the reconnected field emerged further, however, the Lorentz force accelerated plasma horizontally. Pressed against a neighbouring wall of stronger (i.e., low-), predominantly vertical field, the squeezing of the plasma led to a local enhancement of the gas pressure, which accelerated material upwards along the magnetic field lines. While this may be sufficient to account for the penetration of the chromospheric material into the transition region ( 4 Mm above the normal height, see also Eq. (70*)), the slow-mode wave mechanism likely plays a role in the further evolution of the jet. Takasao et al. (2013*) presented a detailed analyses of the 2D simulation result with similar setup with Yokoyama and Shibata (1996) and found there are three types of acceleration mechanisms of cool jets, as summarized in Figure 55*.
Finally, some recent observations suggest there are other types of coronal jets called blowout jets (Moore et al., 2010*). This type of jet is thought to be a miniature version of large-scale eruptive events such as filament eruptions and CMEs (see Sakajiri et al., 2004, for similar observations in H). The difference from “standard” jets (e.g., Figure 53*) seem to be following: while the standard jets can be more or less regarded as a consequence of direct reconnection between emerging flux and ambient field, the blowout jets are more likely to be a store-and-release process. That is, the free energy and twist is at first stored in a quasi-equilibrium magnetic configuration in the atmosphere, which becomes unstable or loses equilibrium and erupts in a way similar to flares and CMEs. See Shibata and Magara (2011) and Chen (2011) for a review of flare/CME models, and see Archontis and Hood (2013) and Moreno-Insertis and Galsgaard (2013*) for 3D simulations of emerging flux that lead to blowout-type jets. Indeed this type of model may explain the jets that shows significant twisting (or untwisting) motions (Kurokawa et al., 1987; Patsourakos et al., 2008) as demonstrated by 3D simulation by Pariat et al. (2010).
First of all it should be noted that emerging flux can trigger at least small flares (plasma heating) and associated jets, as proposed by Heyvaerts et al. (1977) and already discussed extensively in Section 4.1. This kind of model can be classified as directly driven models, whereas those models in which the emerging flux trigger the eruption of pre-existing flux system larger than the emerging flux itself can be considered as store and release models (Klimchuk, 2001). In this section we cover only the latter.
Observationally, Feynman and Martin (1995) established the picture of the eruption trigger by emerging flux by studying the 53 quiescent filaments. They found that when the emerging flux is oriented favorably for magnetic reconnection with the magnetic field of the filament channel, it is more likely to trigger the eruption (see also Wang and Sheeley Jr, 1999)).
Chen and Shibata (2000*) first demonstrated by 2.5D MHD simulations that emerging flux favorable for reconnection could trigger the eruption of a pre-existing flux rope in the corona, while those not favorable for reconnection could not. Figure 56* schematically illustrates the trigger mechanism of the flux rope in two different cases. In one case (panel a), the emerging flux appears just below the flux rope, which then undergoes reconnection with the pre-existing small loop. The reconnection breaks the mechanical equilibrium of the flux system by reducing the magnetic pressure below the flux rope. The reduced pressure induces the inflows from both sides that carry the magnetic field overlying the flux rope, and reconnection of these field lines brings the flux rope further from mechanical equilibrium. This process is similar to the so-called runaway tether-cutting model (Moore et al., 2001). In the other case (panel b), the emerging flux appears in slightly shifted location and, hence, it undergoes reconnection with the overlying field lines that stabilizes the eruption of the flux rope. As one can see from the figure reconnection weakens the magnetic tension of the overlying field, thus breaking the equilibrium and leading to the eruption of the flux rope. This case is a bit similar to so-called Breakout model (Antiochos et al., 1999) in the sense that the eruption is triggered by the weakening of the tension of the overlying bootstrapping field.
Lin et al. (2001) studied the similar problem with semi-analytic approach and found that the emerging flux does trigger eruption in some cases but the conditions for the eruption trigger is rather complicated and depends also on parameters other than the field orientation, such as the field strength, distance, and area of the emerging flux region. This conclusion is in agreement with the observational study by Zhang et al. (2008). Dubey et al. (2006*) have also carried out a parameter study by 2.5D MHD simulations including the effects of gravity and spherical geometry.
Zuccarello et al. (2008*) and MacTaggart and Hood (2009a*) performed 2.5D simulations of flux emergence into a quadrapole configuration to study whether the emerging flux triggers breakout-type eruption. Despite differences in the initial setup (see the last part of this subsection) the two simulation studies show good agreement: emerging flux did trigger an eruption but it did not lead to the formation of a flux rope which pinches off the central arcade. Comparison of emerging flux and the shearing motion as the trigger for the breakout-type eruption was carried out by Zuccarello et al. (2009*). 2.5D simulations by Leake et al. (2010*) also show the formation of multiple flux ropes due to the reconnection of the flux rope and the pre-existing dipole or quadrapole coronal field. However, much of the magnetic shear and its free energy remains in the lower atmosphere and no large-scale eruption was observed.
In order for an emerging flux to trigger the eruption the pre-existing flux system must have some free energy. MacTaggart (2011*) modeled by 3D simulation the scenario of a flux tube emerging into a potential field arcade, which as expected did not result in eruptions. In order to study the condition for eruption, Kusano et al. (2012*) performed a systematic parameter study of 3D simulations. The models initially have a force-free sheared arcade (as shown in panel (a) of Figure 57*) and in each case an emerging bipole magnetic flux inserted from the bottom boundary on the neutral line. They systematically changed the amount of the shear (angle between the polarity inversion line and the magnetic field) and angle of the emerging bipole to study which combinations triggered eruptions. Figure 57* shows one example of their simulations that successfully produced eruption.
Figure 58* shows a diagram that summarize the simulation results. It is found that when degree, the inserted emerging flux has the reconnection-favorable orientation, and in such case the eruption occurs almost independently from the initial condition. On the other hand, even if the shear is strong and a lot of free magnetic energy is stored ( degree), the non-reconnection-favorable emerging flux ( degree) cannot not trigger the eruption. This diagram is very interesting, though it is not yet clear how universal this behavior. Similar systematic studies should be carried out for different magnetic topologies, in particular with a pre-existing coronal flux rope.
Finally, it should be noted that different numerical treatment of emerging flux are adopted in the literature discussed in this section. Many of them use boundary conditions to insert the emerging flux in the domain (Chen and Shibata, 2000; Dubey et al., 2006; Zuccarello et al., 2008, 2009; Kusano et al., 2012), whereas others solve the buoyant rise of the emerging flux from below the photosphere self-consistently (MacTaggart and Hood, 2009a; MacTaggart, 2011; Leake et al., 2010).
Apart from triggering eruptions, flux emergence can generate self-contained flux ropes which eventually erupt. This approach is more related to the energy storage processes prior to the eruption. The question of whether eruptive flux ropes are formed just prior to eruption or are transported by flux emergence is a question that has attracted considerable attention (Green and Kliem, 2009; Patsourakos et al., 2013).
Even though flux emergence is associated with energy injection, it does not necessary lead to a sufficient build up of free energy nor head down an evolutionary path that leads to an eruptive release of the available free energy. Certain ingredients are needed to induce such behavior. Fan and Gibson (2003*, 2004*) presented 3D simulations of an kink-unstable flux tube inserted from the lower boundary into the pre-existing potential arcade. It was found that the kink instability developed when a sufficient amount of twist is transported in the corona, and consequently S-shaped field lines and current concentration formed.
S-shaped structures in the corona observed in X-ray are called sigmoids and are known to be a good precursor of eruptions (Rust and Kumar, 1996; Canfield et al., 1999). Therefore, the formation of the sigmoidal structures as a result of the emergence of a twisted flux tube have been studied by many authors (Matsumoto et al., 1998; Magara and Longcope, 2001; Fan, 2009a; Archontis et al., 2009; Archontis and Hood, 2012*).
Manchester IV et al. (2004*) first reported the self-consistent 3D simulation of the emergence of a twisted flux tube, which drove shear flows that eventually lead to the formation of a detached coronal flux rope which then ejected from the modeled AR (see Figure 42*). The difference between Fan and Gibson (2003*, 2004) and Manchester IV et al. (2004) is that the scenario studied by the former authors involves the bodily rise of a coherent flux rope (including axial fields and dipped fields beneath the axis) through the photosphere (their bottom boundary) whereas the latter does involve the emergence of the axial fields (nor dipped field lines beneath the axis). The flux rope naturally formed in the latter case from shear flows. The formation of coronal flux ropes by reconnection has been also reported in other simulations of flux emergence (Magara, 2006; Archontis and Török, 2008*; Archontis and Hood, 2010; Leake et al., 2013; MacTaggart and Haynes, 2014). Magara (2007) presented a 3D simulation in which three portions of the initial flux tube emerge at once. He found that the resultant magnetic structure is reminiscent to that of models of filaments.
Archontis and Török (2008) reported that if a magnetic flux tube emerges into a non-magnetized atmosphere, the induced shearing motion and reconnection can form a flux rope in the corona. However, the expanding magnetic field surrounding the flux rope acts as a bootstrapping field that suppresses an eruption. In contrast, if the expanding tube is allowed to reconnect with a pre-existing coronal field, the flux rope is able to erupt with an acceleration profile that is similar to those of observed filament eruptions and CMEs (see also Leake et al., 2014). Archontis and Hood (2012*) further investigated the condition for eruptions by systematically changing the orientation of the ambient field. As shown in Figure 60*, they report that favorable orientations for reconnection increase the likelihood of eruption.
Whether the new coronal flux system formed by emerging flux erupts or not depends on the various parameters of the emerging flux itself as well as the interaction of the emerging flux and the pre-existing magnetic fields. Theoretically, we expect that another important factor that determines the stability of the flux system is the upward gradient of the magnetic field (Kliem and Török, 2006; An and Magara, 2013).
Finally, as briefly mentioned in Section 4.2, Moreno-Insertis and Galsgaard (2013) found in the 3D simulation of a twisted emerging flux with an ambient oblique field that multiple eruptions that look like mini-CMEs from the single emerging flux region. They discuss it as a possible mechanism for so-called blowout jets (Moore et al., 2010). From a simulation of the emergence of a highly twisted flux rope across the lower boundary into a pre-existing coronal arcade field, Chatterjee and Fan (2013) reported the occurence of homologous eruptions. These eruptions lead to a series of three CMEs, one of which catches up with a preceding CME and the two merge in a so-called ‘cannibalistic’ fashion. While each of these two studies is interesting in their own right, together they provide insight regarding the physics that drive eruptions at various scales.