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Solar flares are observed at all wavelengths from decameter radio waves to gamma-rays at 100 MeV. This review focuses on recent observations in EUV, soft and hard X-rays, white light, and radio waves. Space missions such as RHESSI, Yohkoh, TRACE, and SOHO have enlarged widely the observational base. They have revealed a number of surprises: Coronal sources appear before the hard X-ray emission in chromospheric footpoints, major flare acceleration sites appear to be independent of coronal mass ejections (CMEs), electrons, and ions may be accelerated at different sites, there are at least 3 different magnetic topologies, and basic characteristics vary from small to large flares. Recent progress also includes improved insights into the flare energy partition, on the location(s) of energy release, tests of energy release scenarios and particle acceleration. The interplay of observations with theory is important to deduce the geometry and to disentangle the various processes involved. There is increasing evidence supporting reconnection of magnetic field lines as the basic cause. While this process has become generally accepted as the trigger, it is still controversial how it converts a considerable fraction of the energy into non-thermal particles. Flare-like processes may be responsible for large-scale restructuring of the magnetic field in the corona as well as for its heating. Large flares influence interplanetary space and substantially affect the Earth’s lower ionosphere. While flare scenarios have slowly converged over the past decades, every new observation still reveals major unexpected results, demonstrating that solar flares, after 150 years since their discovery, remain a complex problem of astrophysics including major unsolved questions.
KeywordsFlare Radio Emission Acceleration Region Coronal Source Large Flare
1.1 Detection and definition
Since September 1, 1859, when R.C. Carrington and R. Hodgson observed the first flare in the continuum of white light, the localized, minute-long brightenings on the Sun have remained an enigma. Local flaring of the Sun has been reported at all wavelengths accessible from the ground and from space. Thus the word “flare” is used in solar physics today in a rather ill-defined way, describing a syndrome of apparently related processes at various wavelengths. The problem is even more acute in other languages, such as German and French, denoting flares with the equivalent to “eruption”, which may be confused with Coronal Mass Ejections (CMEs) that often happen simultaneously at the time of large flares. The general use of the term “flare” today often alludes to a “sudden release of magnetic energy by reconnection”. However, one has to bear in mind that such a definition represents a specific, although widely accepted, interpretation of observations. It may be used as a guide for novices to distinguish flares from other plasma physical phenomena in the solar atmosphere also associated with brightenings, such as the expulsion of magnetic flux or dissipation of shock waves. Nevertheless, it is better to define the flare phenomenon observationally as a brightening of any emission across the electromagnetic spectrum occurring at a time scale of minutes. Most manifestations seem to be secondary responses to the original energy release process, converting magnetic energy into particle energy, heat, waves, and motion.
1.2 Brief history of flare observations
1.3 The phases of flares
1.4 The big picture
The flare observations may be ordered in a scenario or a sequence of processes in which the flare energy is released in the corona by reconnecting magnetic fields. The process heats the plasma in the reconnection region to temperatures of tens of millions of degrees Kelvin (MK), but also efficiently accelerates electrons to super-thermal energies peaking below some 20 keV and extending sometimes to several tens of MeV. Reconnection most likely takes place also in the interior of the Sun and the lower solar atmosphere. The impulsiveness of the flare energy release is possibly caused by a sudden change in resistivity by high-frequency (collisionless) wave turbulence and is probably related to the capability of particle acceleration. Both require long collision times, i.e., low density. Not surprisingly, impulsive flare reconnection is generally assumed to take place in the corona, consistent with observations.
1.5 Organization of review
Section 2: Flare signatures in the photosphere, chromosphere, and corona (Coupling atmospheric layers).
Section 3: Where is the flare energy released? (Flare geometry).
Section 4: Into what forms is the energy released? (Energy budget).
Section 5: Which emissions are direct signatures of energy release? (Signatures).
Section 6: How are particles accelerated? (Acceleration processes).
The literature reviewing flare observations spans more than a century. Substantial summaries of flares observations have been published among others recently by Murdin (2001) and Aschwanden (2002), in more specialized fields by Bastian et al. (1998) on radio emissions, Fletcher and Warren (2003) on ultraviolet emissions, Ryan et al. (2000) and Schwenn (2006) on flare effects and energetic flare particles in interplanetary space. Somov (1992), Tajima and Shibata (1997), and Priest and Forbes (2000) have reviewed theory. Older reviews, such as Sturrock (1980) and Švestka (1976) are still worth reading. The Astrophysics Data System lists more than 14,500 articles on the keyword “solar flare”. Any review, including this one, can only focus on a small fraction of the accumulated information. Comments and suggestions are welcome.
2 Energy Release in a Coupled Solar Atmosphere
2.1 Flares and photospheric field configuration
Large-scale shear in the magnetic field can also build up through the slow motion of foot points stretching the length of a loop. This evolution can progress through stable field configurations. Large-scale sheared fields in active regions store huge amounts of free magnetic energy. The emerging flux may then provide the trigger mechanism for impulsive energy release. The energy is unleashed above the photosphere, either in the chromosphere or corona (Moore et al., 2001). The build-up of the unstable configuration for large flares is often well observable in photospheric magnetic fields. The flare leaves, however, few if any observable traces in photospheric magnetograms. Wang et al. (2004) find an increase of the photospheric magnetic field strength during the flare, consistent with the scenario of magnetic flux emerging into the corona. A frequent flare site is the separatrix between different magnetic loop systems (Démoulin et al., 1997) forming a current sheet, or in a cusp-shaped coronal structure (Longcope, 2005). There is also evidence for flares being related to helical magnetic fields (Low, 1996; Pevtsov et al., 1996).
Photospheric observations clearly support the scenario that flare energy originates from free magnetic energy in excess of the potential value (defined by the photospheric boundary) or, equivalently, from electric currents in the corona. For a rapid release, the currents must be concentrated into small regions. Such currents may be inferred observationally in regions with a tangential discontinuity of the magnetic field direction in the system of rising loops near the base of the corona (Solanki et al., 2003).
The flare energy resides in the magnetic field that originated in the interior and is convected to the surface. Not much can be observed of the flare processes until the energy appears in the form of accelerated particles and extremely hot plasma. In the next section we switch from the origin and build-up to the first observable signature after the primary energy release.
2.2 Geometry of hard X-ray emissions
The cross-section of a single electron for producing an X-ray photon of a certain energy is given by the quantum mechanical Bethe-Heitler formalism. The instantaneous emissivity of an electron beam propagating in a plasma is named thin target solution. It does not account for the resulting particle energy change to be considered in further collisions. If the target is deep enough, the incident particle slows down to thermal speed. The total radiation is therefore the integral in time over all emissions starting at the entry into the target until the particle energy is thermalized. If other deceleration processes than Coulomb collisions can be excluded, this is the thick target situation (Brown, 1971). The thick target photon spectrum of an electron beam is flatter (usually called harder) than any thin target it may transverse before, as it includes emission of the decelerating electrons. In an ideal situation including a power-law distribution of electron energies, the power-law index of thin target emission is smaller by 2 than the thick target spectrum.
The emission of hard X-rays with a non-thermal energy distribution was first located by Hoyng et al. (1981) at footpoints of coronal loops. Based on stereoscopic observations, Kane (1983) reported that 95% of the ≳ 150 keV X-ray emission in impulsive flares originates at altitudes ≲ 2500 km, that is at the level of the chromosphere. Brown et al. (1983) concluded that this upper limit in altitude satisfies the collisional thick-target model in which precipitating electrons loose their energy in the dense, cold target. The emission presumably originates from flare-accelerated electrons precipitating into the chromosphere. They follow the field line until they reach a density high enough for collisions and emit bremsstrahlung by scattering and slowing down. Footpoint sources are also occasionally found on Hα flare ribbons some 30,000 km apart, tracing the base of a magnetic arcade (Masuda et al., 2001). The connecting loop are observed in thermal soft X-ray emission, indicating that the density has greatly increased. Densities of more than 1011 cm−3 are frequently reported (e.g., Tsuneta et al., 1997) and agree with the concept of chromospheric evaporation. Up-streaming plasma, presumably heated by precipitating particles and filling up a coronal loop, has been observed in blue shifted lines (Antonucci et al., 1982; Mariska et al., 1993).
The altitude of coronal hard X-ray sources, some 6000–25,000 km, is compatible with observed time delays of hard X-ray peaks emitted at the footpoints (Aschwanden et al., 1995). Low energy photons are emitted later compared to higher energy photons. Delay-time observations scale with the observed lengths of the soft X-ray loop (Aschwanden et al., 1996), consistent with the interpretation of longer propagation times of lower energy electrons. If only time-of-flight effects are assumed, the propagation path would put the acceleration above the loop-top hard X-ray source. The assumption of simultaneous injection puts strong constraints on the timescales involved on the acceleration process (Brown et al., 1998).
The difference in the spectrum of coronal source and footpoints can be taken as a test for the geometry. Measurements by Petrosian et al. (2002) show that the power-law indices differ by about 1 on the average, contrary to expectations. A possible interpretation for a value less than 2 may be a mixture of thick and thin target emissions, overlapping in the observed resolution element. On the other hand, an analysis based on RHESSI data demonstrates the existence of index differences larger than two in 3 out of 9 events (Battaglia and Benz, 2007). This discrepancy requires a more complete physical scenario than ballistic particle motion and will be discussed in the following section.
2.3 Return current
It is unlikely that the fluxes of high-energy electrons and ions precipitating to the chromosphere balance out. Thus a beam current results. In a conducting plasma, a beam current cannot induce appreciable magnetic fields, and in static state the electric charge cannot separate along the field line. Thus a return current builds up to conserve charge and current neutrality (Spicer and Sudan, 1984; van den Oord, 1990; Benz, 2002). The current is most likely driven by a dominant electron flux in the precipitating particles. Thus the return current direction is downward in the loop. It is composed mostly of thermal electrons moving freely upward along field lines.
As the return current consist of thermal particles, collisions play a much bigger role than for the beam particles (see Equation 8). Collisions cause electric resistance. Ohm’s law then requires an electric field in downward direction, slowing down the beam electrons. The return current and its associated electric field are inevitable consequences of the standard flare model.
Return currents solves what has been referred to as the flare particle number problem: as the number of precipitating electrons inferred from hard X-rays is very large, the coronal acceleration region would soon be evacuated if not replenished. If only electrons escape from the acceleration region, the return current keeps its density constant. If also ions escape, the acceleration region is evacuated. This may be avoided by a pressure driven flow of neutral plasma. None of the observational signatures, however, for both neutral flow and return current are fully established, and their existence still needs corroboration.
2.4 Neupert effect
2.5 Standard flare model
Correlation of soft X-ray flux with cumulative hard X-ray flux (Neupert effect)
Hard X-rays (> 25 keV) often originate from sources at the footpoints of the loop emitting soft X-rays.
The coronal hard X-ray source, where reconnection releases energy, is occasionally observed to be above the soft X-ray loop, into which energy was release before and which is still emitting soft X-rays (Masuda et al., 1994).
The energy in accelerated electrons tends to be larger than the thermal energy contained in the soft X-ray source (see discussion in Section 4).
The hard X-ray spectrum of non-thermal electrons in the coronal source is considerably softer than in the footpoints, suggesting that the latter is a thick target. In thick targets the particles lose all their kinetic energy, and their bremsstrahlung emission is the result of all collisions until they come to full stop.
The emission measure of the soft X-ray source greatly increases during the impulsive phase, indicating that chromospheric material is evaporating during this period. Evaporation has been observed directly, first in blue-shifted lines of hot material, later also in soft X-ray images (see following section).
2.6 Evaporation of chromospheric material
The evaporated hot plasma appears to be the source of most of the soft X-ray emission (Silva et al., 1997). Thus, the soft X-ray emitting plasma accumulates a significant fraction of the energy in the precipitating non-thermal electrons. Consequentially, the soft X-ray emission is proportional to the integrated preceding hard X-ray flux. As already noted by Neupert (1968), this may explain the effect named after him. Note that the scenario assumes that the observed soft X-ray plasma is not heated by the primary flare energy release, but is a secondary product when flare energy is transported to the chromosphere. This is an important point to remember in theories assuming that the coronal plasma is heated by flares.
The evaporation scenario predicts a linear relation between instantaneous energy deposition rate by the electron beam and time derivative of the cumulative energy in the thermal plasma, thus a linear relation between hard X-ray flux and derivative of the soft X-ray flux (Figure 12). This is not always the case (Dennis and Zarro, 1993). There are several reasons for this: (i) the spectral index of the hard X-rays changes with time in most flares (Section 5.2), (ii) the flare energy may be preferentially transported by heat conduction (particularly in the pre-flare phase), and (iii) ions may contribute to the energy deposition. Some flares, however, fit extremely well and a time lag in the flare thermal energy of only 3 seconds relative to the energy input as observed in hard X-rays has been reported by Liu et al. (2006).
Evaporation is the result of coupling between corona and chromosphere. Such coupling is expected from the fact that the transition region separating the two layers in the solar atmosphere is relatively small compared to the mean free path length in the corona. The chromosphere is only a few collisions away from the corona even for thermal particles. There must be a constant heat flow through the transition region. In the impulsive phase of a flare, non-thermal particles may well dominate the energy transfer.
The expansion of the heated chromospheric plasma is driven by pressure gradients. Thus “evaporation” is a misnomer, as the phenomenon is no phase transition nor the escape of the fastest particles, but is an MHD process and more like an explosion. Wuelser et al. (1994) report downflowing material in Hα at the location of the flare loop footpoints, suggesting a motion opposite to evaporation in the low chromosphere. The upflowing hot plasma and the downflowing chromospheric plasma have equal momenta, as required by the conservation of momentum in a ballistic explosion. Evaporation due to a flare may thus be understood as a sudden heating in the chromosphere, followed by an expansion that is initially supersonic.
Brosius and Phillips (2004) presented evidence of much more gentle kind of evaporation during the preflare phase of a flare. The maximum velocity in Ca xix was found to be only 65 km s−1. Such gentle evaporation below the coronal sound speed is interpreted by a non-thermal electron flux below 3 × 1010 erg cm−2s−1 (Milligan et al., 2006). Zarro and Lemen (1988) found signatures of gentle evaporation in the post flare phase, and Singh et al. (2005) reported signatures of evaporation also in a non-flaring state of a loop, suggesting thermal conduction of a hot coronal loop as the driver. These observations confirm that the evaporative response of the chromosphere depends sensitively on the flux of incident electrons. Fisher and Hawley (1990) have studied evaporation due to thermal energy input into the corona. Evaporation resulting from non-thermal particle precipitation has been simulated by several groups (Sterling et al., 1993; Hori et al., 1998; Reeves et al., 2007). In general, the results of these simulations agree with observed flare emissions quite well, indicating that the standard model of solar flares is energetically consistent with observations.
2.7 Deviations from standard flare model
There are other indications, that the standard model is not sufficient. In about half of the hard X-ray events, the Neupert behavior is violated in terms of relative timing between soft and hard X-ray emissions (Dennis and Zarro, 1993; McTiernan et al., 1999; Veronig et al., 2002). This is particularly obvious in flares with soft X-rays preceding the hard X-ray emission. Such preheating is well known and cannot be explained by lacking hard X-ray sensitivity (e.g., Benz et al., 1983; Jiang et al., 2006). Also it has been noted by several authors that the plasma in the coronal source at the top is generally hotter than at the footpoints of the loop.
An alternative interpretation to the standard model is that the soft X-ray emitting plasma is not heated exclusively by high-energy electrons, (e.g., Acton et al., 1992; Dennis and Zarro, 1993). A likely amendment to the standard model is that some coronal particles get so little energy during flare energy release that they have frequent enough collisions to approximately retain their Maxwellian velocity distribution. Thus their energization corresponds to heating. In a preflare, the heat of the coronal source may reach the chromosphere by thermal conduction. Depending on the rate of the energy release, other particles may gain so much energy that collisions become infrequent (Equation 8). These particles then are accelerated further, get a non-thermal velocity distribution, and may eventually leave the energy release region.
3 Flare Geometry
3.1 Geometry of the coronal magnetic field
In another also widely proposed geometry, two non-parallel loops meet and reconnect. There are several versions of the cause of interaction. Merging magnetic dipoles (Sweet, 1958), collision of an newly emerging loop with a pre-existing loop, proposed by Heyvaerts et al. (1977), or the breakthrough of the emerging loop through the corona (Antiochos, 1998). In this scenario the geometry is closed, i.e., no magnetic field line leads from the energy release site to interplanetary space. Ejecta leaving the Sun are still possible, but not a necessary ingredient of the model. Thus the two-loop model is often proposed for non-eruptive “compact flares”. The model predicts the existence of 4 footpoints. The number of footpoints in hard X-rays rarely exceeds two. However, radio observations have been presented that complement the number of X-ray footpoints, resulting in the frequent detection of three or more footpoints (Kundu, 1984; Hanaoka, 1996, 1997). Nishio et al. (1997) find that the two loop considerably differ in size and that the smaller loop preferentially emits X-rays. There is also evidence from recent pre-flare EUV observations for multiple-loop interactions (Sui et al., 2006).
One-loop flare models predict the presence of plasmoids in interplanetary space, consisting of hot plasma interwoven with a closed magnetic field (i.e., magnetic field lines that close within the structure). Such plasmoids are characterized by the lack of electron heat flux because their field lines are disconnected from the Sun and have indeed been reported (Gosling et al., 1995). More frequently observed are counterstreaming hot electrons, indicating that the field line is closed, i.e., still connected to the Sun on both sides (Crooker et al., 2004). According to these authors, such features in the electron distribution are frequently observed in magnetic clouds associated with CMEs. Nevertheless, they are not associated with the great number of smaller flares.
Furthermore, there is a well-known association of nearly every large flare with type III radio bursts at meter wavelengths, produced by electron beams escaping from the Sun on open field lines connected to interplanetary space. Benz et al. (2005) report that 33% of all RHESSI hard X-ray flares larger than C5 in GOES class are associated with such bursts. This suggests that in a third of all flares at least one of the four ends of reconnecting field lines is open. As type III bursts represent only a small fraction of the flare energy this may not hold for the major flare energy release site. We note, furthermore, that type III bursts very often occur also in the absence of reported X-ray flares (Kane et al., 1974). The energy release by open and a closed field lines, termed interchange reconnection, has been proposed some time ago (Heyvaerts et al., 1977; Fisk et al., 1999) and applied more recently to in situ observations in a CME (Crooker and Webb, 2006).
In conclusion, there is good evidence for both the one-loop and two-loop scenarios for the geometry of the coronal magnetic field in solar flares. There is no reason to assume that they exclude each other. The combination of both in the same flare, hybrids of a closed loop reconnecting with an open loop, and other scenarios are also conceivable. Thus we do not state a standard geometry for the preflare coronal magnetic field configuration. The magnetic topologies of one loop, interchange and two loop are generally classified as dipolar, tripolar, and quadrupolar, respectively. In addition, 2D and 3D versions can be distinguished (Aschwanden, 2002), and various nullpoint geometries have been proposed (Priest and Forbes, 2000).
3.2 Coronal hard X-ray sources
In the standard flare scenario, where the flare energy is released in the corona and non-thermal particles are accelerated in the corona, coronal X-ray emission showing a power-law photon energy distribution must attract special attention. It is generally assumed that its emission is near or in the acceleration region. This section thus concentrates on flare related X-ray emissions from well above the chromospheric footpoints.
The ordinary corona has a density that is not suggestive of hard X-ray emission. However, such radiation was discovered as soon as it became technically feasible. Frost and Dennis (1971) reported an extremely energetic event from active region behind the limb. Its origin must have been at an altitude of about 45,000 km above the photosphere. The presence of non-thermal electrons in coronal sources has been inferred by the first observers based on the high energy of the detected photons, exceeding 200 keV. Coronal hard X-ray observations have been studied essentially event-by-event beyond the limb (e.g., Kane, 1983) until it became possible to image hard X-rays thanks to the RHESSI satellite (Lin et al., 2002). Krucker et al. (2007) have reviewed the RHESSI results concerning the coronal X-ray sources of flares.
Occasional emission of bremsstrahlung photons by non-thermal electrons in the corona may not be surprising, the observed intensity is. It is so high because of a high density of the background plasma. Estimates of the loop-top density from soft X-rays and EUV lines are typically around 1010 and can reach up to a few times 1012 cm−3 (Tsuneta et al., 1997; Feldman et al., 1994; Veronig and Brown, 2004; Liu et al., 2006; Battaglia and Benz, 2006). The reported temperatures are several ten millions of degree (Lin et al., 1981). The pressure balance of such structures is enigmatic. What is the origin of this thermal loop-top source?
Thermal loop-top sources have first been interpreted in terms of chromospheric evaporation. Thus one may expect them to follow the Neupert behavior where the soft X-rays are proportional to the hard X-ray flux integrated over prehistory. It is then incomprehensible that thermal coronal sources appear before the start of the hard X-ray emission. In fact, the most prominent feature in the preflare phase is the early appearance of a thermal source at the loop-top. The material content (emission measure) in these sources greatly exceeds the normal value in the active region corona. Thus is must have evaporated from the chromosphere. One may speculate that in this early phase the flare energy is not transported by energetic particles, but more gently conducted by thermal particles.
A characteristic of the thermal source is the temperature distribution with loop height. The highest looptops sometimes show Fe xxi emission, suggesting a temperature of 20 MK, while at the same time lower laying loops show emission in the Fe xi and Fe xii lines characteristic for temperatures between 1–3 MK (Warren et al., 1999). The thermal emission must not be confused with the thermal X-ray emission from giant arches observed in the post-flare phase (Švestka, 1984).
Masuda et al. (1994) have reported hard X-ray emission from above the thermal X-ray loop. Historically, this has raised great interest as it seemed to confirm the scenario of reconnection in a current sheet in a vertical cusp-shaped structure above the soft X-ray loops. However, this seems to be rather exceptional. In more recent studies, the large majority of non-thermal sources are cospatial with the thermal source (Battaglia and Benz, 2007). Stereoscopic observations by two spacecraft (Kane, 1983) and recent RHESSI observations find that the non-thermal emission from the corona and the footpoints correlated in time. Even the soft-hard-soft behavior (Section 5.2) has been detected in the coronal source (Battaglia and Benz, 2007). The coronal hard X-ray emission is not always stationary. Upward motions have been reported with velocities of about 1000 km s−1 following the direction of a preceding CME (Hudson et al., 2001).
The coronal source has been observed to emit hard X-rays even in the pre-flare phase before footpoints appear. Even more astonishingly, non-thermal emission at centimeter wavelengths, suggesting the presence of relativistic electrons, has been reported in such sources (Asai et al., 2006).
3.3 Intermediate thin-thick target coronal sources
The observation of Masuda et al. (1994) suggests a model that consists of four basic elements: a particle accelerator above the top of a magnetic loop (consistently imagined at the peak of a cusp), a coronal source visible in SXR and HXR, collision-less propagation of particles along the magnetic loop and HXR-footpoints in the chromosphere. Wheatland and Melrose (1995) developed a simple model that has been used and investigated further (e.g., Metcalf and Alexander, 1999; Fletcher and Martens, 1998). The thermal coronal source acts as an intermediate thin-thick target on electrons depending on energy (thick target for lower energetic electrons, thin target on higher energies). This model is known as intermediate thin-thick target, or ITTT model. The ITTT model features a dense coronal source into which a beam of electrons with a power-law energy distribution is injected. Some high-energy electrons then leave the dense region and precipitate down to the chromosphere. The coronal region acts as a thick target on particles with energy lower than a critical energy E c and as thin target on electrons with energy > E c . This results in a characteristic hard X-ray spectrum showing a broken power-law as well as soft X-ray emission due to collisional heating of the coronal region. The altered electron beam reaches the chromosphere, causing thick target emission in the footpoints of the magnetic loop. Battaglia and Benz (2007) have tested the ITTT model in a series of flares using RHESSI data. The results indicate that such a simple model cannot account for all of the observed relations between the non-thermal spectra of coronal and footpoint sources. Including non-collisional energy loss of the electrons in the flare loop due to an electric field can solve most of the inconsistencies.
The simple ITTT model shows that the standard flare geometry is consistent with current observations. The remaining inconsistencies concern the coronal source. Its non-thermal component was found less bright than the footpoints would predict according the ITTT model (Battaglia and Benz, 2008). A possible remedy is acceleration within the thermal coronal source. Jiang et al. (2006) argue that thermal conductivity in the coronal source is reduced by wave turbulence to interpret the soft X-ray emission. Turbulence would also scatter non-thermal particles or even accelerate them.
It is proper to conclude that the coronal X-ray source is not understood.
3.4 Location of particle acceleration
Accelerated particles precipitate from the acceleration site or are temporarily trapped. On their way spiraling along the magnetic field, they radiate various radio emissions at frequencies depending on the local plasma. As the corona is transparent to radio emission above the plasma frequency, the accelerated particles outline the geometry of the environment of acceleration and/or the actual site of acceleration.
Metric spikes have been found to be associated in some cases with impulsive electron events in the interplanetary medium (Benz et al., 2001). The low energy cut-off of the interplanetary electron distribution defines an upper limit of the density in the acceleration region (Lin et al., 1996). The derived electron density is of the order of 3 × 108 cm−3, consistent with the density in the source of metric spikes, assuming second harmonic plasma emission. The difference between acceleration height in hard X-rays, particle events and coherent radio waves suggests different acceleration processes.
3.5 Energetic ions
3.6 Thermal flare
Flare loop cooling has been investigated by several authors. Radiative cooling and conduction losses have been found to balance approximately (e.g., Jiang et al., 2006). In the late phase, radiative cooling usually dominates, but considerable heat input is frequently observed (e.g., Milligan et al., 2005).
4 Energy Budget
Magnetohydrodynamic models suggest that reconnection releases magnetic energy into ohmic heating and fluid motion in about equal amounts (textbook by Priest and Forbes, 2000). At the level of kinetic plasma theory, ohmic heating may amount to accelerating particles to non-thermal energy distribution. The motion of the reconnection jet may involve waves and shocks, both are also capable of acceleration. Thus a flare releases energy initially into the forms of heat, non-thermal particles, waves, and motion.
In the past, the observed partition of energy in flares into the various forms has often changed with new instrumentation. The most complete estimate of the total flare energy is currently the measured enhancement in total solar irradiance. Woods et al. (2004) determined the total flare irradiance to exceed the soft X-ray emission (< 27 nm) by a factor of 5 in two well observed, large flares. The total irradiance enhancement is dominated by white light and infrared emission (77%). UV and soft X-ray emissions < 200 nm amount to 23%.
Energy budgets as reported by Saint-Hilaire and Benz (2005) for M-class flares and by Emslie et al. (2005) for X-class flares. The non-thermal electron energy strongly depends on the low-energy turn-over of the electron distribution, which may be masked by thermal radiation. Thus the non-thermal electron energy is a lower limit. The total radiated energy includes the contributions of X-rays, UV, and optical emissions.
2002/11/10 M2.6 [erg]
2002/08/22 M7.8 [erg]
2002/04/21 X1.7 [erg]
2002/07/23 X5.1 [erg]
1.9 × 1030
6.5 × 1030
2.0 × 1031
3.2 × 1031
< 4.0 × 1031
7.9 × 1031
Thermal hot plasma
1.4 × 1030
2.6 × 1030
1.2 × 1031
1.0 × 1031
1.6 × 1032
1.6 × 1032
2.0 × 1032
1.0 × 1032
5.0 × 1030
1.6 × 1031
3.2 × 1031
4.1 Non-thermal electron energy
4.2 Thermal energy
4.3 Energy in waves
The process of magnetic energy release reconnects two magnetic field lines and launches two reconnection jets that can be viewed as Alfvénic excursions of two waves. The waves cascade to smaller wavelengths until they resonate with electrons or ion (Miller et al., 1997; Petrosian et al., 2006). Thus waves are essential in the currently most popular view of particle acceleration. Reconnection may be collision-free as found in the terrestrial magnetosphere (Øieroset et al., 2001) and possibly involve effects of electron inertia. For solar conditions, intense turbulence of collision-free waves causing anomalous resistivity may play a role.
Waves of all frequencies from large scale MHD waves to high-frequency waves up to whistler waves have been predicted and observed in magnetospheric reconnection (Deng and Matsumoto, 2001; Øieroset et al., 2001). Waves can propagate energy across magnetic field lines. Low-frequency Alfvén waves produced by coronal reconnection can move through most of the corona having absorption at inhomogeneities. Thus they can transport energy even to the high corona and solar wind.
MHD waves related to flares have been inferred from pulsating radio bursts (Roberts et al., 1983) and were more recently reported in high-temperature EUV emission (Aschwanden et al., 1999) and in X-rays (Foullon et al., 2005; Nakariakov et al., 2006). Schrijver et al. (2002) have shown that most larger flares (classes M and X) trigger loop oscillations. However, the energy deposited in these oscillations is typically six orders of magnitude smaller compared to the flare energy release (Terradas et al., 2007). Furthermore, the oscillations are observed to damp within a few oscillation periods. From the existing observations it is not clear how far the energy of these oscillations propagates into the corona. Nevertheless, it is obvious that the observed oscillations do not significantly contribute to coronal heating.
Current acceleration models are based on wave damping (Section 6). The energy in observed MHD waves originating from flares is in striking contrast to expectation from the assumed role they play in acceleration.
4.4 Other energies
The energy in the non-thermal ions is less known than for electrons. Ramaty et al. (1995) have argued that the fraction of the available flare energy that is contained in accelerated ions above 1 MeV is similar to that of electrons above 20 keV. This conclusion is supported by the observations that the derived non-thermal energy in protons is comparable within an order of magnitude to the non-thermal energy in electrons (e.g., Cliver et al., 1994; Miller et al., 1997). The above observations, however, leave doubtful whether the energy in non-thermal electrons and ions add up to the energy of flares observed in total irradiance (see Table 1).
The possibility remains that some energy propagates from the release site to the chromosphere by means of low energy (non-thermal) particles below the current threshold for X-ray detection or by heat conduction (i.e., thermal particles). This is supported by the observation that in a quarter of the events there is clear evidence for the presence of an additional energy transport mechanism other than non-thermal electron beams (Veronig et al., 2002, 2005). Furthermore, the relative contribution to energy transport by non-thermal electrons is found to decrease with the flare importance and in the late phase of flares.
A further form of energy is the work done by the expansion of the heated flare plasma from chromospheric density to the observed value of the thermal X-ray source. This expansion in volume by a factor of 103 or more, may consume more energy than its heating (Benz and Krucker, 2002). The expansion energy is released when the material cools and rains back to the chromosphere. A fraction is finally radiated away at temperatures below coronal. Other forms of direct energy release, such direct coronal heating are not yet reliably measurable. The uncertainties in these estimates make it difficult to assess the energy partition of flares and their contribution to coronal heating.
4.5 Energy input into the corona
The heating of the corona is a long standing debate and is not the issue here. We may still ask the question of the resulting energy input into the corona based on the new findings on flares. Obviously, large flares occurring in active regions during solar maximum are unlikely candidates. The existence of tiny flares unobservable by current instruments is a questionable hypothesis.
The pertinent question is how much the observed flare-like events contribute to the heating of the corona. The largest nanoflares reported contain energies of a few 1026 erg (Krucker and Benz, 1998). This number refers to the thermal energy in the soft X-rays emitting flare plasma and is identical to the largest individual flare-like events inferred from Fe xi/x, and Fe xii lines. It does not include coronal bright points, locations in the quiet corona where continuous flaring during many hours is observed. The smallest flares reported given by the TRACE instrumental limit is a few 1023 erg (Parnell and Jupp, 2000). The rate of events larger than few 1024 erg and lasting about 15 minutes each, estimated over the whole Sun is 300 per second (Krucker and Benz, 1998). Benz and Krucker (2002) have estimated that the total energy measured in nanoflares in the energy range from 5 × 1024 erg to 5 × 1026 erg observable by EIT/SOHO amounts to about 12% of the radiated energy of the observed coronal area.
This review of flare observations emphasizes that the thermal energy measured at peak soft X-ray or EUV emission is not equivalent to the total flare energy input into the corona. Most of the thermal flare plasma is just the reaction of the chromosphere on a coronal phenomenon. We may thus end this short subchapter by the conclusion that the cause of coronal heating by flares needs more quantitative modeling. Flare heating cannot be quantitatively assessed from observations of one energy receiving channel alone as long as the energy partition of regular flares into waves, direct heating, motion, and particle acceleration is unclear.
5 Signatures of Energy Release
As explained in Section 3, the location of energy release is not well known. Even less understood is its process. Some observational evidence restricting the possible mechanisms is presented in the following.
5.1 Coronal hard X-ray signatures
With higher spectral resolution it became possible to determine also the shape of the photon energy distribution. The coronal hard X-rays have been found to be well represented by a power-law in energy (Emslie et al., 2003; Battaglia and Benz, 2006), similar to what is well known for footpoint sources. The predominant near power-law distribution of accelerated electron energies is a stringent characteristic of the acceleration process, and not the result of propagation.
5.2 Soft-hard-soft behavior in hard X-rays
The hardness of the non-thermal spectrum changes in the course of a flare, starting soft (steep), getting harder at the peak and softening toward the end (Parks and Winckler, 1969; Kane and Anderson, 1970). A few large flares continue to harden after the peak (Frost and Dennis, 1971; Krucker et al., 2005b). These flares have been shown to be particularly well associated with solar energetic particle events (Kiplinger, 1995).
5.3 Radio emissions from the acceleration region
The study of the spatial distribution of the synchrotron emission by mildly relativistic electrons (gyrosynchrotron) has a long history. Both loop-top sources and double sources located close to the conjugate magnetic footpoints were reported (Marsh and Hurford, 1982; Kundu et al., 1982; Kawabata et al., 1983). The comparison with theoretical simulations of the gyrosynchrotron brightness distribution along model magnetic loops (see Bastian et al., 1998, for a review) strongly suggests that the distribution of mildly relativistic electrons along an extended flaring loop must be highly inhomogeneous: accelerated electrons are concentrated in the upper part of the loop (Nindos et al., 2000; Melnikov et al., 2002). Some of the centimeter loop-top emissions were observed in the late phase of flares (e.g., Karlický, 2004). They are not related to the main energy release, but possibly to high-energy X-rays detected late in flares (Krucker, personal communication) and possibly the end stage of the spectral hardening observed in non-thermal X-rays (see Section 5.2). The investigation of the acceleration region using gyrosynchrotron emission has greatly profited from combination with hard X-rays. It may result in the measurement of the magnetic field in loop-tops in future work.
Benz et al. (2007) found some coherent radio emission in all flares larger than C5 class, except near the limb where absorption seems to play a role. While there is good association between coherent radio emission and X-rays, correlation in details of the time profile is less frequent. Thus coherent emissions cannot expected to be reliable tracers of the main flare energy release in general. Emissions at higher frequencies, such as decimetric narrowband spikes, pulsations, and stationary type IV events appear to be more directly related to the acceleration process. The association but loose correlation between HXR and coherent radio emission may be interpreted by multiple reconnection sites connected by common field lines, along which accelerated particles may propagate and serve as a trigger for distant accelerations. Thus coherent radio emissions may be interesting diagnostics in special cases.
Correlation of coherent radio emissions with hard X-rays (or gyrosynchrotron emission) has been reported for spikes and pulsations (Slottje, 1978; Benz and Kane, 1986; Aschwanden et al., 1990; Kliem et al., 2000). If these coherent radiations are emitted at the second harmonic of the plasma frequency — the usual assumption — the density of the source region is in the range from 109 cm−3 to a few times 1010 cm−3. This range is a possible indication for the density in the acceleration region. Although initially interpreted as loss-cone emissions of trapped particles near footpoints, they have been found at high altitudes, consistent with loop-tops (Benz et al., 2002; Khan et al., 2002; Kundu et al., 2006). As the emission mechanism of spikes and pulsations is not well understood, the origin of the radiating high-frequency waves cannot be further investigated.
Best candidates for direct emission from the acceleration region are small clusters of narrowband spikes around 300 MHz, reported to correlate in detail with electron beam emission (type III radio bursts). About 10% of all meter wave type III groups are accompanied with spikes near but slightly above the start frequency (Benz et al., 1982). The spikes are concentrated in the spectrogram on the extrapolation of the type III bursts to higher frequency. More precisely, as suggested by Figure 19, metric spikes are located on the extension of type III trajectories, supporting a model of energy release in or close to the spike sources (Benz et al., 1996). If this is the case, radio observations can approximately locate the acceleration region for the type III electrons and measure the electron density of the acceleration region (Section 3).
Type IV emissions occur late relative to the hard X-ray peak and appear to be connected to some late-phase acceleration (Švestka et al., 1982; Klein et al., 1983). They may be related to delayed electron releases of interplanetary electron events in the corona (Klein et al., 2005).
A major constraint by radio emission on particle acceleration is the fact, that in 15% of larger flares (> C5.0 class) there is no coherent radio emission except some electron beam emitting at very high altitude (Benz et al., 2007). Whether coherent radio emission is necessarily emitted or not, is therefore an observable criterion for the validity of acceleration models. The frequent lack of direct radio emission from the acceleration region suggests that the acceleration is “gentle”, excluding significant deviations from a Maxwellian velocity distribution, such as a monoenergetic beam. The deviations only build up after the non-thermal electrons have traveled some distance and the faster particles have outpaced the slower particles, or after a loss-cone results from magnetic trapping. Gentle acceleration favors acceleration by diffusion in velocity space as predicted by stochastic acceleration (Section 6).
6 Acceleration Processes
A remarkable fraction of the total flare energy released first appears as kinetic particle energy in non-thermal electrons and ions (Section 5). White light observations (Section 4) suggest that in addition to the particles observed in X-rays and gamma-rays particles at lower energies (about 1 keV for electrons) transport energy to the upper chromosphere and transition region. The acceleration process thus is a major issue in flare physics and constitutes the core of the flare enigma. We will briefly review here the major ingredients of the current theories and then present the observational evidence.
The transfer of magnetic energy to kinetic particle energy has been observationally separated into two phases. In the impulsive flare phase, the concept is “bulk energization”, involving an increase of the electron energy by more than two orders of magnitude starting from the coronal thermal energy (some 0.1 keV) within less than 1 s as derived from hard X-ray observations (Kiplinger et al., 1984). The other class of acceleration occurs in a secondary phase, possibly as a result of the first phase such as shock wave initiated by a flare or an associated coronal mass ejection. The second phase may be less productive in particle acceleration, but is more important for solar energetic particles in interplanetary space.
6.1 Electron acceleration theories
The free mobility of charged particles in dilute plasma and the difference in inertia between electrons and ions make it likely that electrons are accelerated in every major impulsive process in the corona. Convertible (free) magnetic energy requires the presence of an electric current and an associated electric field before the flare-like process. Waves of various types from MHD to collisionless are expected to be excited by the flare and are also capable to accelerate particles in resonance. From a plasma physics point of view, acceleration is not surprising; controversial is, however, which process dominates.
stochastic acceleration (e.g., resonant acceleration by waves),
electric field parallel to the magnetic field,
perpendicular and parallel shocks (first and second order Fermi acceleration).
6.2 Comparing theories with observations
High-frequency waves near the plasma frequency can be excluded as drivers for stochastic acceleration. They would couple into radio decimeter waves and be present in every flare. On the other hand, acceleration by Transit-Time Damping is compatible with the frequent lack of radio emission because the frequency of the postulated turbulence is far below the plasma frequency and does not cause radio emission.
Large-scale, stationary electric fields would cause major distortions in velocity space, susceptible to velocity space instabilities and beam driven high-frequency waves observable as radio waves. Such radio emission should correlate well with hard X-ray emission, which is not seen in every flare.
Shock acceleration plays an important role in interplanetary space, which is not the issue here. More directly related to flares are shocks possibly produced by the reconnection process. Radio signatures of such shocks have been reported by Aurass et al. (2002); Mann et al. (2006), but are still disputed and, if confirmed, extremely rare. Nevertheless, slow shocks have been predicted at the interface between inflow and outflow regions of reconnection, as well as fast shocks at the bow of the reconnection outflows. High energies could be readily be achieved (100 MeV ions in < 1s, Ellison and Ramaty, 1985; Tsuneta and Naito, 1998).
The Transit-Time Damping scenario is consistent with present observations, although there is no direct evidence for it. Thus it must be considered as a still unproven hypothesis. In fact, there are other viable scenarios: as an alternative to acceleration by fluctuating magnetic fields (and also to large-scale quasi-electric fields) low-frequency fluctuating electric fields parallel to the magnetic field have been proposed. Such fields may originate from low-frequency and high-amplitude turbulence, such as kinetic Alfvén waves. They accelerate and decelerate electrons, leading to a net diffusion in energy space (Arzner and Vlahos, 2004).
Flares may be considered to result from the loss of equilibrium in magnetic configurations. Although reconnection is a general phenomenon, it occurs in an impulsive way only in the corona, where collisions are rare and thus the plasma is highly conductive. Regular flares must be considered as extreme phenomena of the continuous dynamics of the corona. Radio noise storms (type I bursts) and meter wave type III bursts hint at activity in the high corona that is not yet accessible to other wavelengths and is prone to surprises.
Therefore, flares should not be considered exceptional catastrophes that occur rarely and mostly during solar maximum. Flare-like brightenings, called nanoflares, occur in the quiet corona at a rate of at least a few thousand per second. Is the corona heated by flares? It may well be that the impulsive processes in the coronal plasma related to sudden changes in resistivity are the cause of the corona. We cannot answer this question definitively, however, as long as we do not understand how much energy flares deposit into the corona in the various possible ways. Furthermore, the corona below 20,000 km above the photosphere, including the transition region, is not well explored in flare research. It is also the place where most of the coronal heating occurs. This region will soon become accessible to white light coronagraphs and high-temperature line observations. The future of flare research will also profit from spatial resolution in decimetric radio waves.
Regular flares are not two of a kind, and each flare has individual features. For this reason, it is not surprising that observations at various wavelengths do not correlate in a simple manner as predicted by a simple scenario. The fact, that every flare appears to be different, must be taken as evidence that coronal dynamics has many degrees of freedom. Nevertheless, recent observations in X-rays and EUV allow identifying the magnetic topologies, confirming the general scenario of reconnection. They have shown that various groups of flares exist and have greatly contributed to our ever growing understanding of coronal phenomena.
Flares consist of a series of processes, starting with energy build-up in the corona and ending by restructuring the magnetic configuration and releasing magnetic energy. The processes include reconnection, anomalous resistivity, efficient particle acceleration, particle propagation, coronal and chromospheric heating, evaporation, mass loss, high-frequency waves and MHD oscillations, as well as various emission mechanisms. All these processes are important issues in astrophysics and worth studying for their own. They all have seen significant progress in the past decades and will be addressed by the new observing facilities planned and in construction. A major impact can be expected from simultaneous imaging observations in practically all wavelengths. They will greatly contribute to the growing physical understanding of solar flares in the near future.
The literature often uses the term ‘microwaves’ for frequencies in the range 1–30 GHz, in particular in connection with gyrosynchrotron emission. In the lower wavelength part, microwaves overlap with the decimeter wavelength range. We will thus use strictly the decimal wavelength notation in this review to avoid confusion.
I thank Paolo Grigis and two anonymous referees for a critical and constructive reading of the manuscript. The flare work at ETH Zurich is supported by the Swiss National Science Foundation (grant nr. 200020-113556). This review has made use of NASA’s Astrophysical Data System Bibliographic Services.
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