Unsteady State of the Turbulent Current Sheet of a Flare

The stability of the turbulent current sheet of a flare is analyzed. It is argued that the equilibrium state of the current sheet is extremely unstable relative to certain processes: dissipative tearing instabilities, MHD instabilities of line pinches, overheating of the turbulent plasma, and the threshold dependence of conductivity on the current value. The final state of a flare current sheet must be an extremely inhomogeneous layer containing numerous clusters of bad, turbulent, low-conductivity domains and good, normal ones. The propagation of current in this medium is a percolation process with certain fundamental properties: a threshold regime for current dissipation, which explains the threshold character of the flare phenomenon itself, a universal power-law spectrum of the statistical dependence on flare parameters, and a universal power-law energetic spectrum for the accelerated high-energy particles.     

Prompt particle acceleration around moving X-point magnetic field during impulsive phase of solar flares

We present a model for high-energy solar flares to explain prompt proton and electron acceleration, which occurs around moving X-point magnetic fields during the implosion phase of the current sheet. We derive the electromagnetic fields during the strong implosion of the current sheet, which is driven by the converging flow toward the center of the magnetic arcade. We investigated a test particle motion in the strong electromagnetic fields derived from the MHD equations. It is shown that both protons and electrons can be promptly (within 1 s) accelerated to 70 and 200 MeV, respectively. This acceleration mechanism can be applicable for the impulsive phase of the gradual gamma-ray and proton flares (gradual GR/P flare), which have been called two-ribbon flares.     

Energies of Electrons Accelerated in Turbulent Reconnecting Current Sheets in Solar Flares

Yohkoh observations strongly suggest that electron acceleration in solar flares occurs in magnetic reconnection regions in the corona above the soft X-ray flare loops. Unfortunately, models for particle acceleration in reconnecting current sheets predict electron energy gains in terms of the reconnection electric field and the thickness of the sheet, both of which are extremely difficult to measure. It can be shown, however, that application of Ohm's law in a turbulent current sheet, combined with energy and Maxwell's equations, leads to a formula for the electron energy gain in terms of the flare power output, the magnetic field strength, the plasma density and temperature in the sheet, and its area. Typical flare parameters correspond to electron energies between a few tens of keV and a few MeV. The calculation supports the viewpoint that electrons that generate the continuum gamma-ray and hard X-ray emissions in impulsive solar flares are accelerated in a large-scale turbulent current sheet above the soft X-ray flare loops.     

The gradual and impulsive reconnection and the preheating of solar flares

We discuss the preheating phase of solar flares triggered by emerging magnetic flux. We consider the development of microinstabilities in the diffusion region during the emergence process and we propose four different types of reconnection, by which we explain the preheating, as well as the impulsive phase of flares. We find that during the emergence of new magnetic flux the current sheet will not jump from the initial classical state to a fully turbulent one, but will remain in a marginally turbulent state which may develop either gradually or impulsively depending on the conditions of emergence. As a consequence of this, we find that four cases of reconnection are indeed possible: a week gradual heating, a weak impulsive process, a gradual preheating followed by an impulsive phase, and violent bursty reconnection.The expansion rate of the diffusion region, the duration of the gradual phase, the magnetic energy release, and the energy deposition rate in coronal loops during the gradual phase are derived under simplifying assumptions and applied to X-ray and UV observations of flares from the Solar Maximum Mission.On leave from the Department of Astronomy, Nanjing University, Nanjing, The People's Republic of China.     

The role of flares, CMEs and CME shocks in the generation of solar energetic proton events

We examined solar energetic proton (SEP) events associated with intense H flares. We located these flares on the solar disk and obtained their distribution in heliographic longitude as well as their angular distance distribution with respect to the neutral lines corresponding to the heliospheric current sheet at 2.5R. We found that the SEP-associated H flares tend to occur in active regions at the feet of those helmet streamers which form the heliomagnetic equator and are related to coronal mass ejections (CMEs) and CME shocks. We discuss the possible role of flares, CMEs and CME shocks in generating SEPs.     

Heavy Ion Abundances in Impulsive Solar Flares: Influence of Pre-Acceleration in a Current Sheet

Competition between stochastic energy gains and collisional energy losses is known to lead to preferential acceleration of heavy ions in flare loops. Ion acceleration in a reconnecting current sheet is shown to mitigate the influence of collisional energy losses on stochastic particle acceleration in impulsive solar flares. This effect decreases the sensitivity of the resulting abundance ratios on initial ion charge states. The resulting abundances are determined by the fact that the energy loss rate falls off rapidly with increasing energy. As an example, the expected Fe/O enhancement ratios are computed and shown to be comparable with those observed with ACE SEPICA in several impulsive flares in 1998. One consequence of the model is that the preferential acceleration of heavy ions can occur only when the plasma gas pressure is large enough, m _e/m _p, which may explain the observed correlation between the heavy ion enrichment and selective ³He acceleration in impulsive flares.     

Current sheet models of solar flares

Current sheets have been suggested as the site for flare energy release because they can convert magnetic energy very rapidly into both heat and directed plasma energy. Also they contain electric fields with the potential of accelerating particles to high energies.The basic properties of current sheets are first reviewed. For instance, magnetic flux may be carried into a current sheet and annihilated. An exact solution for such a process in an infinitely long sheet has been found; it describes the annihilation of fields which are inclined at any angle, not just 180°. Moreover, field lines which are expelled from the ends of a current sheet can be described as having been reconnected. The only workable model for fast reconnection in the solar atmosphere, namely Petschek's mechanism, has recently been put on a firm foundation; it gives a reconnection rate which depends on the electrical conductivity but is typically a tenth or a hundredth of the Alfvén speed. A current sheet may be formed when the sources of an initially potential field start to move; a simple analytic technique for finding the position and shape of such a sheet in two dimensions now exists. Finally, a sheet with no transverse magnetic field component is subject to the tearing-mode instability, which rapidly produces a series of loops in the field.The main ways in which current sheets have been used for solar flare models is described. Syrovatskii's mechanism relies on the increase of the electric current density during the formation of a sheet, to a value in excess of the critical value j ^* for the onset of microinstabilities. But Anzer has recently demonstrated that the critical value is most unlikely to be reached during the initial formation process. Sturrock, on the other hand, has advocated the occurrence of the tearing-mode instability in an open streamer-like configuration (which may result from the eruption of a force-free field). But recent observations do not point to that as the relevant configuration. Rather, they suggest that flares are triggered by the emergence of new magnetic flux from below the solar photosphere. This has led Heyvaerts, Priest, and Rust (1976) to propose a new emerging flux model, according to which, as more and more flux emerges, so reconnection occurs, producing some preflare heating. When the current sheet reaches such a height (around the transition region) that its current density exceeds j ^*, then the impulsive phase of the flare is triggered. The main phase is caused by an enhanced level of magnetic energy conversion in a turbulent current sheet. The type of flare depends on the magnetic environment in which the emerging flux finds itself. A surge flare results if the flux appears near a strong unipolar region such as a simple sunspot, whereas a two ribbon flare may be produced by flux emergence near an active region filament, in which case the main phase energy is released from the field that surrounds the filament.     

A circuit model for filament eruptions and two-ribbon flares

We derive a circuit model for solar filament eruptions and two-ribbon flares which reproduces the slow energy build up and eruption of the filament, and the energy dissipation in a current sheet at the top of post-flare loops during the two-ribbon flare. In our model the free magnetic energy is concentrated in a current through the filament, another current through an underlying current sheet, and surface return currents. The magnetic field configuration, generated by these currents and a general photospheric background field, has a topology similar to the field topology derived from observations.We consider two circuits, that of the filament and its return current, and that of the current sheet and its return current. These circuits are inductively coupled and free energy stored in the filament in the pre-flare phase is found to be transferred to the sheet during the impulsive phase, and rapidly dissipated there. A comparable amount of magnetic energy is converted into kinetic energy of the ejected filament. The basic equations of the model are the momentum equations for the filament and the current sheet, and the induction equations for the filament and sheet circuits. The derivation of the equations is an extension of previous models by Kuperus and Raadu, Van Tend and Kuperus, Syrovatskii, and Kaastra. The set of equations is closed in the sense that only the initial conditions and a number of parameters, all related to pre-flare observables, are needed to calculate the evolution of the system. The pre-flare observations we need to determine these parameters, are: (1) a magnetogram, (2) an picture, (3) a measurement of the coronal density in the region, and (4) estimates of the photospheric velocity fields in the region.In the solutions for the evolution of the filament current sheet system we distinghuish 4 phases: (1) a slow energy build up, lasting for almost two days, during which the filament evolves quasi-statically, (2) a metastable state, lasting for about three hours, during which the filament is susceptible to flare triggers, and during which a current sheet emerges, (3) the eruptive phase, with strong acceleration of the filament, during which a large current is induced and dissipated in the current sheet, and energy is injected in the post-flare loops, and finally (4) a post-flare phase, in which the filament acceleration declines and the current sheet vanishes.From further numerical work we derive the following conclusions: (1) The magnetic flux input into the filament circuit has to surpass a certain threshold for an eruption to occur. Below that threshold we find solutions representing quiescent filaments. (2)Flare triggers are neither necessary nor sufficient for an eruption, but may set off the eruption during the metastable state. (3) The model reproduces the increase in shear in the filament prior to the eruption, through adecline of the filament current, in contrast to most models for filament eruptions. (4) The ratio of energy lost as kinetic energy of ejecta to the energy radiated away in the post-flare loops is sensitively dependent on the resistance of the current sheet. (5) Flare prediction is possible with this model, but the potential for triggering during the metastable state complicates the prediction of the exact moment of eruption.Former NAS/NRC Resident Research Associate.ST Systems Corporation.     

The 156-day quasi-periodicity in solar indices

This paper investigates a series of daily solar indices: the sunspot number W (1900–2008), solar flux at 2800 MHz F _10.7 (1947–2008), and a number of X-ray flares N _x (1981–2008). The methods of Fourier and wavelet analysis are used to reveal the so-called 156-day Rieger-type periodicity (RTP). The W index is observed to have a statistically significant RTP amplitude in the neighborhood of the solar maxima in most of the solar cycles under study, except for cycles 14, 15, and 23. The 156-day peak is observed to have its largest power during the declining phase of cycle 16, at the maximum of cycle 21, and during the increasing phase of cycles 20 and 23. Statistically significant RTPs are also observed at the minima of cycles 17, 18 and 19. We conclude that there is no stable dependence between RTP and the solar cycle. The wavelet analysis shows that the pattern of the RTP time dependence for the F _10.7 index is almost identical to that of the W index. The correlation coefficient between the RTP curves is 0.95. The correlation coefficients for the pairs of indices W-N _x and F _10.7-N _x are 0.36 and 0.32, respectively. No time lags are found between the RTP starting points for different indices. Thus, the 156-day quasi-periodicity involves, almost simultaneously, events that occur in active regions of the solar atmosphere at different heights. This paper discusses the possible nature of RTP.     

Electron beams and associated rapid fluctuations in solar flares

Recent observations show that the rapid fluctuations in radio, hard X-ray, and H emissions are closely associated with type III and microwave (or decimetric) bursts during the impulsive and/or preimpulsive phases of solar flares.In order to clarify the physical processes of these observed phenomena, this paper proposes a tentative model of two acceleration regions A (source of type III bursts) and B (source of microwave or decimetric bursts) formed in the neutral sheet and at the top of a flaring loop, respectively; and also suggests that the electron beams streaming from region A and/or region B downward to the chromosphere are responsible for the rapid fluctuations in the different emissions mentioned above during the impulsive and/or pre-impulsive phases of solar flares.     

A theory of filament eruptions before the impulsive phase of solar flares

We present a theory of filament eruption before the impulsive phase of solar flares. We show that the upward motion of the magnetic X-point tracing the filament eruption begins several minutes before the impulsive phase of the flare, where the explosive magnetic reconnection starts at the X-point magnetic field configuration located under the filament. No change occurs in the character of the motion of the X-point during the onset of the explosive magnetic reconnection. The upward speed of the X-point is about 110 km s^-1 at the onset of the impulsive phase. We give an important condition leading to filament eruptions, which relate to the state of the current sheet under the filament, where the magnetic energy can be released.     

The interpretation of the Wilson-Bappu effect

The problem of the physical interpretation of the Wilson-Bappu effect is examined. A postulate is forwarded according to which this effect expresses the dependence of the complete kinetic energyE _t of turbulent motions in the medium generating magnesium emission in the doublet 2800 Mgii on the velocityW ₀ of turbulent motion. One of the consequences of the application of this postulate is the appearance of the relationships (8) and (11) which give the magnitude of the kinetic energyE _t of turbulent motions in the first case (Figure 2) and the magnitude of the mass of emitting mediumM ₀ in the second (Figure 3) depending on the turbulent velocityW ₀ (k). This postulate unit in a common conception all variety of the magnesium emission escaped from a single star as well as from binary systems on the one hand and the magnesium emission generated in chromospheres as well as in intercomponent clouds or streams on the other.     

Particle acceleration in impulsive solar flares

Second-step acceleration of nonrelativistic protons and ions in impulsive solar flares is discussed extending our earlier calculations for relativistic electrons. We derive the relevant particle transport equation, discussing in detail the influence of the particle's effective charge and mass number on the various momentum gain (stochastic acceleration, diffusive shock wave acceleration) and loss (Coulomb interactions, particle escape) processes. Analytical solutions for the ion-momentum spectra in the hard-sphere approximation are given. The inclusion of Coulomb losses modify the particle spectra significantly at kinetic energies smaller than E _B = 0.64( _e /5.0) MeV nucl.^–1 from the well-known Bessel function variation in long-duration flares. For equal injection conditions this modification explains the observed much smaller ion fluxes from impulsive flares at high energies as compared to long-duration flares. We also calculate the ³He/⁴He-isotope variation as a function of momentum in impulsive flares in the hard-sphere approximation and find significant variations near E _m = 0.38(T _e /2 × 10⁶ K) MeV nucl.^–1, where T _e is the electron temperature of the coronal medium.     

Electron surfing acceleration by electrostatic waves in current sheet

The electron surfing acceleration in the current sheet with perpendicular propagating electrostatic waves is studied using analytical theories and test particle simulations. The trapped electron moving with the phase velocity v _p of wave may be accelerated effectively in the outflow direction by force until the electron is de-trapped from the wave potential. A criterion K>0 for the electron surfing acceleration is obtained. The electron will escape from the boundary of current sheet quickly, if this criterion does not hold. The maximum velocity of surfing acceleration is about the same as the electric drift velocity. Superposed longitudinal magnetic field along the wave propagation is favorable for the electron surfing acceleration in the current sheet.      

Non-thermal processes in large solar flares

We analyze particle acceleration processes in large solar flares, using observations of the August, 1972, series of large events. The energetic particle populations are estimated from the hard X-ray and γ-ray emission, and from direct interplanetary particle observations. The collisional energy losses of these particles are computed as a function of height, assuming that the particles are accelerated high in the solar atmosphere and then precipitate down into denser layers. We compare the computed energy input with the flare energy output in radiation, heating, and mass ejection, and find for large proton event flares that:

1. The ～10–10² keV electrons accelerated during the flash phase constitute the bulk of the total flare energy.
2. The flare can be divided into two regions depending on whether the electron energy input goes into radiation or explosive heating. The computed energy input to the radiative quasi-equilibrium region agrees with the observed flare energy output in optical, UV, and EUV radiation.
3. The electron energy input to the explosive heating region can produce evaporation of the upper chromosphere needed to form the soft X-ray flare plasma.
4. Very intense energetic electron fluxes can provide the energy and mass for interplanetary shock wave by heating the atmospheric gas to energies sufficient to escape the solar gravitational and magnetic fields. The threshold for shock formation appears to be ～10³¹ ergs total energy in >20 keV electrons, and all of the shock energy can be supplied by electrons if their spectrum extends down to 5–10 keV.
5. High energy protons are accelerated later than the 10–10² keV electrons and most of them escape to the interplanetary medium. The energetic protons are not a significant contributor to the energization of flare phenomena. The observations are consistent with shock-wave acceleration of the protons and other nuclei, and also of electrons to relativistic energies.
6. The flare white-light continuum emission is consistent with a model of free-bound transitions in a plasma with strong non-thermal ionization produced in the lower solar chromosphere by energetic electrons. The white-light continuum is inconsistent with models of photospheric heating by the energetic particles. A threshold energy of ～5×10³⁰ ergs in >20 keV electrons is required for detectable white-light emission.

The highly efficient electron energization required in these flares suggests that the flare mechanism consists of rapid dissipation of chromospheric and coronal field-aligned or sheet currents, due to the onset of current-driven Buneman anomalous resistivity. Large proton flares then result when the energy input from accelerated electrons is sufficient to form a shock wave.     

Solar flare activity and the structure of the coronal neutral line

In this study we analyse the positions of major flares from 1978 and 1979, with respect to the magnetic structure of the solar corona, as described by a potential field model. We find that major flares exhibit no strong association with the neutral line at the chromospheric level. However, when we calculate the neutral line's position at higher and higher altitudes in the corona, we find that major flares show an increasing tendency to be found close to these high-altitude coronal neutral lines. The correlation between flares and higher-altitude coronal neutral lines reaches a maximum at an altitude of 0.35R , and thereafter decreases as the neutral line is moved out to the source surface at an altitude of 1.50R . This indicates that major flares are strongly associated with coronal structure at the 0.35R level ( 250 000 km) - an altitude surprisingly high in the corona. This reinforces the idea that flares are associated with large-scale coronal magnetic fields and also indicates that the region of coronal magnetic topology important to solar flare processes may be larger than previously thought.     

Models for the motions of flare loops and ribbons

We have found a conformal mapping which is valid for any magnetic boundary condition at the photosphere and which can be used to determine the evolution of an open, two-dimensional magnetic field configuration as it relaxes to a closed one. Solutions obtained with this mapping are in quasi-static equilibrium, and they contain a vertical current sheet and have line-tied boundary conditions. As a specific example, we determine the solution for a boundary condition corresponding to a submerged, two-dimensional dipole below the photosphere. We assume that the outer edges of the hottest X-ray loops correspond to field lines mapping from the outer edges of the H ribbon to the lower tip of the current sheet where field lines reconnect at aY-type neutral line which rises with time. The cooler H loops are assumed to lie along the field lines mapping to the inner edges of the flare ribbons. With this correspondence between the plasma structures and the magnetic field we determine the shrinkage that field lines are observed to undergo as they are disconnected from the neutral line. During the early phase of the flare, we predict that shrinkage inferred from the height of the H and X-ray loops is close to 100% of the loop height. However, the shrinkage should rapidly decrease with time to values on the order of 20% by the late phase. We also predict that the shrinkage in very large loops obeys a universal scaling law which is independent of the boundary condition, provided that the field becomes self-similar (i.e., all field lines have the same shape) at large distances. Specifically, for any self-similar field containing aY-type neutral line, the observed shrinkage at large distances should decrease as (X/X _R)^–2/3, where X is the ribbon width andX _Ris the ribbon separation. Finally, we discuss the relation between the electric field at the neutral line and the motions of the flare loops and ribbons.     

The role of loop footpoints rotation in single loop flares

We consider that single loop flares can be caused by the rotation of loop footpoints. Choosing a typical geometry for this case we find from MHD equations self-consistent expressions and a set equations governing behaviour of all physical quantities. Numerical simulations have revealed that under the determined conditions for the initial azimuthal velocity and current the pinch instability takes place. The most important parameters of the problem are the plasma and the ratio of the initial values of longitudinal and poloidal components of the magnetic field-B ₁. Thus, calculations show that the critical pinch time increases with the increase ofB ₁ and decreases with the increase of plasma . So the most effective flares are probable for the most high loops with strong currents. ForB ₁=10 and =0.01 the critical pinch time is 2.5 s. The critical twist angle for magnetic field depends on the initial one. For low intial twist which corresponds to bigB ₁ the critical one is more less. For exampleB ₁=30 gives 1.8 (when ratio of loop length and radius is 10). Geometrical analysis shows that the present model can explain (for high photospheric rotation) single loop flares taking place on different parts of the loop as on the top of it as closer to one of the footpoints. It depends on the relative rotation momentum of loop footpoints. Subject headings: MHD-Sun:flares.     

Plasma jet and shock formation during current loop coalescence in solar flares

We report on the results of plasma jet and shock formation during the current loop coalescence in solar flares. It is shown by a theoretical model based on the ideal MHD equation that the spiral, two-sided plasma jet can be explosively driven by the plasma rotational motion induced during the two current loop coalescence process. The maximum velocity of the jet can exceed the Alfvén velocity, depending on the plasma (= c _s ² v _A ² ) ratio. The acceleration time getting to the maximum jet velocity is quite short and le than 1 s. The rebound following the plasma collapse driven by magnetic pinch effect can strongly induce super-Alfvénic flow. We present the condition of the shock formation. We briefly discuss the high-energy particle acceleration during the plasma collapse as well as by the shocks.     

1–4 GHz type II-like radio bursts and pinch processes near the transition region

Analyzing 205 radio bursts observed by the Ondejov radiospectrograph in the 1–4 GHz frequency range during 1992 and 1993, we found 6 examples of type II-like radio bursts coinciding with impulsive phases of solar flares. These bursts were interpreted as radio manifestations of MHD (shock) waves generated during impulsive phases of flares in the vicinity of the transition region. Assuming a magnetic-field perturbation origin of these waves, we studied pinch processes in the current sheet near the transition region. In the 2-D MHD numerical model of this current sheet we demonstrated that 2-D pinch processes induced by radiative losses can trigger the impulsive phase of some flares and so generate the observed high-frequency type II-like radio bursts.