Particle acceleration in impulsive solar flares

A model for second-step electron acceleration in impulsive solar flares is presented. We have extended the theory of stochastic particle acceleration to include Coulomb energy losses which become important at low coronal heights. This inclusion successfully explains the observed steepening of interplanetary electron spectra below 3 MeV following impulsive solar flares taking place at low coronal heights. It also explains the observed spectral differences of relativistic electrons in long-duration and impulsive flares.     

Prompt proton and electron acceleration to relativistic energies in solar flares

As a possible mechanism for particle acceleration in the impulsive phase of solar flares, a new particle acceleration mechanism in shock waves is proposed; a collisionless fast magnetosonic shock wave can promptly accelerate protons and electrons to relativistic energies, which was found by theory and relativistic particle simulation. The simultaneous acceleration of protons and electrons takes place in a rather strong magnetic field such that _{ce pe} . For a weak magnetic field ( _{ce pe} ), strong acceleration occurs to protons only. Resonant protons gain relativistic energies within the order of the ion cyclotron period (much less than 1 s for solar plasma parameters). The electron acceleration time is shorter than the ion-cyclotron period.     

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.     

Excitation of whistler waves driven by an electron temperature anisotropy

A 3-D particle simulation of excitation of whistler waves driven by an electron temperature anisotropy (T > T ) is presented. Results show that whistler waves can have appreciable growth driven by the anisotropy. The maximum intensity of the excited whistler waves increases as a quadratic function of the anisotropy. Due to the presence of a threshold, one needs a relatively large electron temperature anisotropy above threshold to generate large-amplitude whistler waves. The average amplitude of turbulence in the context of whistler waves is up to as large as about 1% of the ambient magnetic field when T /T . The total energy density of the whistler turbulence is adequate for production of relativistic electrons in solar flares through stochastic acceleration.     

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.     

Shock versus stochastic acceleration of impulsive solar flare protons

The two major candidates for proton acceleration in impulsive -ray producing flares, shock and stochastic acceleration, are considered in light of recent observations of mass motions and turbulence in flares. Starting with the basic problem of energies required, energy storage and the currents which must be involved, it is concluded that the primary energy release must occur close to the temperature minimum region. It is shown that energy can propagate upwards in the form of fast magnetosonic waves which become evanescent in the transition region, converting a large fraction of their energy to mass motions and turbulence. Present observations are mostly of rather coarse (7000 km) spatial resolution and it is quite possible that significantly higher velocities than those observed were present. Using the results of recent simulations of parallel shocks and the well tested theory of Lee (1983) for parallel shock acceleration in the interplanetary medium, it is shown that shock acceleration is a viable candidate at velocities slightly higher than present observations. It is also shown that shocks must be driven by a mass of material which would be visible in coronal lines such as Caxix for them to be energetically important in proton acceleration.Stochastic acceleration is examined using the hypothesis that there is an equipartition of energy between observed turbulence and magnetic field fluctuations. It is shown that this is a viable acceleration mechanism within a large range of presently observed turbulence provided that the above equipartition hypothesis is valid and the turbulent elements are of small scale (1–200 km). Since turbulence is observed in many flares without any evidence of -rays, one of the above conditions must not be satisfied in general. It is concluded that although present observations favor stochastic acceleration, no definitive conclusion can be made without higher spatial resolution observations and additional theoretical work.     

Second-stage acceleration in a limb-occulted flare

We analyze hard and soft X-ray, microwave and meter wave radio, interplanetary particle, and optical data for the complex energetic solar event of 22 July 1972. The flare responsible for the observed phenomena most likely occurred 20° beyond the NW limb of the Sun, corresponding to an occultation height of 45 000 km. A group of type III radio bursts at meter wavelengths appeared to mark the impulsive phase of the flare, but no impulsive hard X-ray or microwave burst was observed. These impulsive-phase phenomena were apparently occulted by the solar disk as was the soft X-ray source that invariably accompanies an H flare. Nevertheless essentially all of the characteristic phenomena associated with second-stage acceleration in flares - type II radio burst, gradual second stage hard X-ray burst, meter wave flare continuum (FC II), extended microwave continuum, energetic electrons and ions in the interplanetary medium - were observed. The spectrum of the escaping electrons observed near Earth was approximately the same as that of the solar population and extended to well above 1 MeV.Our analysis of the data leads to the following results: (1) All characteristics are consistent with a hard X-ray source density n _i 10⁸ cm^–3 and magnetic field strength 10 G. (2) The second-stage acceleration was a physically distinct phenomenon which occurred for tens of minutes following the impulsive phase. (3) The acceleration occurred continuously throughout the event and was spatially widespread. (4) The accelerating agent was very likely the shock wave associated with the type II burst. (5) The emission mechanism for the meter-wave flare continuum source may have been plasma-wave conversion, rather than gyrosynchrotron emission.     

Particle acceleration and the decay of soft X-ray non-thermal line broadening in solar flares

The relationship between the production of -ray emitting particles and non-thermal soft X-ray line broadening is investigated. A model of particle acceleration via the stochastic interaction with MHD turbulence is assumed and the time development of the wave energy density derived under the condition of energy conservation between waves and particles. The inferred numbers and energy distribution of accelerated protons for four -ray flares are used to define the wave energy density and its temporal development. The presence of Alfvén wave turbulence is considered as the source of the non-thermal motions in the ambient plasma. These motions are observed as excess widths in the soft X-ray line emission from these events. The decay of the waves via the particle acceleration process is compared with the observed decays of this non-thermal line broadening. Our results show that both the -ray emission and excess soft X-ray line widths in these flares can be explained by the single physical phenomenon of Alfvén wave turbulence.     

THE AMOUNT OF LITHIUM PRODUCED DURING IMPULSIVE FLARES

Recent observations have provided much real information about the acceleration of particles in solar flares. High-reliability data about accelerated particles have been obtained for an impulsive phase of some flares of the activity cycle XXII. Therefore, it seems reasonable to re-estimate the amount of Li atoms produced in the upper photospheric layers by – reactions. A value of 5 × 10 29 nuclei during the largest impulsive solar events has been found from calculations for the thick-target model. This agrees with observations of the line of lithium. In conclusion, the probability of enhanced Li absorption observed after large impulsive flares in the sunspot penumbra is discussed.     

Coronal Shocks of November 1997 Revisited: The Cme–Type II Timing Problem

We re-examine observations bearing on the origin of metric type II bursts for six impulsive solar events in November 1997. Previous analyses of these events indicated that the metric type IIs were due to flares (either blast waves or ejecta). Our point of departure was the study of Zhang et al. (2001) based on the Large Angle and Spectrometric Coronagraphs C1 instrument (occulting disk at 1.1 R₀) that identified the rapid acceleration phase of coronal mass ejections (CMEs) with the rise phase of soft X-ray light curves of associated flares. We find that the inferred onset of rapid CME acceleration in each of the six cases occurred 1–3 min before the onset of metric type II emission, in contrast to the results of previous studies for certain of these events that obtained CME launch times 25–45 min earlier than type II onset. The removal of the CME-metric type II timing discrepancy in these events and, more generally, the identification of the onset of the rapid acceleration phase of CMEs with the flare impulsive phase undercuts a significant argument against CMEs as metric type II shock drivers. In general, the six events exhibited: (1) ample evidence of dynamic behavior [soft X-ray ejecta, extreme ultra-violet imaging telescope (EIT) dimming onsets, and wave initiation (observed variously in H, EUV, and soft X-rays)] during the inferred fast acceleration phases of the CMEs, consistent with the cataclysmic disruption of the low solar atmosphere one would expect to be associated with a CME; and (2) an organic relationship between EIT dimmings (generally taken to be source regions of CMEs) and EIT waves (which are highly associated with metric type II bursts) indicative of a CME-driver scenario. Our analysis indicates that the broad (90 to halo) CMEs observed in the outer LASCO coronagraphs for these impulsive events began life as relatively small-scale structures, with angular spans of 15 in the low corona. A review of on-going work bearing on other aspects (than timing) of the question of the origin of metric type II bursts (CME association; connectivity of metric and decametric-hectometric type II shocks; spatial relationship between CMEs and metric shocks) leads to the conclusion that CMEs remain a strong candidate to be the principal/sole driver of metric type II shocks vis-à-vis flare blast waves/ejecta.     

Alfvén turbulence and the time dependence of non-thermal line broadening in flares

Alfvén wave turbulence is considered as the source of the non-thermal line broadenings observed in soft X-rays in solar flares. The waves are assumed to lose energy to particle acceleration and the temporal development for the case of Fermi acceleration,W(k)k ^–2, is investigated. The decay of the wave energy density is compared to that of the non-thermal velocity for the event of 1980 June 29. The wave energy densities required to explain the degree of non-thermal broadening and its temporal characteristics are consistent with those typically inferred from-ray observations. A relationship between the degree of non-thermal broadening and-ray fluxes is predicted. In general, the larger the-ray flux the shorter the time scales for the decay of the wave energy.     

Formation of coronal MHD shock waves – II. The Pressure Pulse Mechanism

The ignition of coronal shock waves by flares is investigated. It is assumed that an explosive expansion of the source region caused by impulsive heating generates a fast-mode MHD blast wave which subsequently transforms into a shock wave. The solutions of 1-D MHD equations for the flaring region and for the external region are matched at their boundary. The obtained results show under what conditions flares can ignite shock waves that excite the metric type II bursts. The heat input rate per unit mass has to be sufficiently high and the preflare value of the plasma parameter in the flaring region has to be larger than ₀ ^crit. The critical values depend on the flare dimensions and impulsiveness. Larger and more impulsive flares are more effective in generating type II bursts. Shock waves of a higher Mach number require a higher preflare value of and a more powerful heating per unit mass. The results demonstrate why only a small fraction of flares is associated with type II bursts and why the association rate increases with the flare importance.     

On a new class of impulsive flares with no nuclear γ-ray line emission

The new class of -ray spectra from impulsive flares without nuclear -ray lines is compared with bremsstrahlung spectra of energetic electrons undergoing stochastic acceleration, Coulomb and synchrotron losses. The remarkable agreement of both the produced -spectra from the precipitated electrons and the electron spectra measured in the interplanetary space leads to the conclusion that seed population and acceleration process are identical for both classes of electrons. A new estimate of the electron bremsstrahlung contribution in -spectra of impulsive solar flares seems to be necessary.     

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.     

Noise-Storm Continua: Power Estimates for Electron Acceleration

We use a generic stochastic acceleration formalism to examine the power L_in (erg s^-1) input to non-thermal electrons that cause noise-storm continuum emission. The analytical approach includes the derivation of the Greens function for a general second-order Fermi process, and its application to obtain the particular solution for the non-thermal electron distribution resulting from the acceleration of a Maxwellian source in the corona. We compare L_in with the power L_out observed in noise-storm radiation. Using typical values for the various parameters, we find that L_in 10²³–10²⁶ erg s^-1, yielding an efficiency estimate L_out/L_in in the range 10^-10 10^-6 for this non-thermal acceleration/radiation process. These results reflect the efficiency of the overall process, starting from electron acceleration and culminating in the observed noise-storm emission.     

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.     

Ca X line ratios in solar flares

Theoretical Ca X electron temperature sensitive emission line ratios, derived using electron excitation rates interpolated from accurateR-matrix calculations, are presented forR ₁ =I(419.74 )/I(574.02 ,),R ₂ =I(411.65 )/I(574.02 ),R ₃ =I(419.74 )/I(557.75 ), andR ₄ =I(411.65 )/I(557.75 ). A comparison of these with observational data for three solar flares, obtained by the Naval Research Laboratory's S082A slitless spectrograph on boardSkylab, reveals good agreement between theory and observation forR ₁ andR ₃ in one event, which provides limited support for the accuracy of the atomic data adopted in the analysis. However, in the other flares the observed values ofR ₁ –R ₄ are much larger than the theoretical high-temperature limits, which is probably due to blending of the 419.74 line with Civ 419.71 , and 411.65 with possibly Ciii 411.70 .     

Magnetic fields and flares in the region CMP 20 September 1963

The position of bright knots of 30 flares at their very beginning relative to the high-resolution isogauss maps of the longitudinal component (H ) and maps of the transverse component (H ) of magnetic field are considered for seven days during the passage of the active and large spot group in Sept. 1963 (see Table I and maps on Figures 1–8).The flare bright knots occur simultaneously in regions of opposite magnetic polarity, and the majority of these knots are adjacent to neutral line H = 0, although not coinciding precisely with this line (Figure 9). Lenticular form of flare knots and the motions of bright material of flares is restrained by transversal field H . Also flares are closely associated (83%) with so-called bifurcated regions, where specific crossing of transverse components takes place (Figures 4–5). There is well-expressed (80%) coincidence of flare knots with the strongest (positive or negative) electric currents as determined from the relation j = c/4 rot H. The relation of results obtained to some existing theories of flares is briefly discussed.U.S. Nat. Acad. of Science - U.S.S.R. Acad. Nauk. Exchange Scientist Program; now at CSIRO Division of Physics, Australia.     

Characteristics of electron and high-energy proton flares

High-energy proton (E _p > 55 MeV) and electron (E _e > 50 keV) events were observed by University of Iowa experiments on the satellites Explorer 33 and 35. The solar X-ray (2–12 Å) flares associated with the energetic proton events were found to have in general higher peak fluxes, considerably longer decay times (t) and smaller rise to decay time ratios (r) than the X-ray flares associated with the electron events. The most common decay times and rise to decay time ratios are: 80 t 100 min, 0.1 r 0.2 for the proton X-ray flares and t 20 min, 0.3 r 0.7 for the electron ones.     

Electric fields in the solar atmosphere: A review

Macroscopic electric fields in the solar atmosphere have received much less attention than magnetic fields, although they must play a role of comparable importance in plasma heating, and in charged particle acceleration and transport. We review various remote sensing techniques that have been developed, whose sensitivity is now 5–10 V cm ^–1 for measurement of the electric field component transverse to the line-of-sight. Our review of the processes most likely to produce observable fields in the solar atmosphere indicates that quasi-static, macroscopic values of E (the electric field component parallel to the magnetic vector) well above this detection threshold are predicted by the discharge model of flares, by models of return currents associated with flare particle beams, and by models of neutral sheets associated with two-ribbon flares and post-flare loops. In addition, both E and E components may be detectable in time dependent electric fields associated with MHD and plasma waves, and with plasma turbulence. The emission measures and time-scales associated with these electrified plasma volumes are as highly uncertain as our present understanding of the volumes, plasma conditions and processes involved in the liberation of flare energy. Observations of electric field vector intensities, orientations, time-behaviour and spatial distribution at the presently attained electric field sensitivity levels could provide new, direct information of great interest in the electrodynamics of solar magnetic structures.