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.     

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.     

The shock-reprocessing model of electron acceleration in impulsive solar flares

We propose a new two-stage model for acceleration of electrons in solar flares. In the first stage, electrons are accelerated stochastically in a post-reconnection turbulent downflow. The second stage is the reprocessing of a subset of these electrons as they pass through a weakly compressive fast shock above the apex of the closed flare loop on their way to the chromosphere. We call this the 'shock-reprocessing' model. The model reproduces the sign and magnitude of the energy-dependent arrival time delays for both the pulsed and smooth component of impulsive solar flare X-rays, but requires either enhanced cooling or the presence of a loop-top trap to explain the concavity of the observed time delay energy relation for the smooth component. The model also predicts an emission site above the loop-top, as seen in the Masuda flare. The loop-top source distinguishes the shock-reprocessing model from previous models. The model makes testable predictions for the energy dependence of footpoint pulse strengths and the location and spectrum of the loop-top emission, and can account for the observed soft-hard-soft trend in the spectral evolution of footpoint emission. The model also highlights the concept that magnetic reconnection provides an environment which permits multiple acceleration processes. Which combination of processes operates within a particular flare may depend on the initial conditions that determine, for example, whether the reconnection downflow is turbulent or laminar. The shock-reprocessing model comprises one such combination.     

Energetics and morphology of powerful impulsive solar flares

We have studied the energetics of two impulsive solar flares of X-ray class X1.7 by assuming the electrons accelerated in several episodes of energy release to be the main source of plasma heating and reached conclusions about their morphology. The time profiles of the flare plasma temperature, emission measure, and their derivatives, and the intensity of nonthermal X-ray emission are compared; images of the X-ray sources and magnetograms of the flare region at key instants of time have been constructed. Based on a spectral analysis of the hard X-ray emission from RHESSI data and GOES observations of the soft X-ray emission, we have estimated the spatially integrated kinetic power of nonthermal electrons and the change in flare-plasma internal energy by taking into account the heat losses through thermal conduction and radiation and determined the parameters needed for thermal balance. We have established that the electrons accelerated at the beginning of the events with a relatively soft spectrum directly heat up the coronal part of the flare loops, with the increase in emission measure and hard X-ray emission from the chromosphere being negligible. The succeeding episodes of electron acceleration with a harder spectrum have virtually no effect on the temperature rise, but they lead to an increase in emission measure and hard X-ray emission from the footpoints of the flare loops.     

Solar energetic particle events from solar flares with weak impulsive phases of microwave emission

In some solar energetic particle events relatively intense proton fluxes are accompanied by disproportionately weak intensity of-burst. A possible reason for such a situation is discussed in this paper. We use the idea that the dynamics of particles in flare loops strongly influences the efficiency of their escape into interplanetary space. It is proposed that in events with weak impulsive phase flare loops are large sized and stretched high into the corona, the magnetic field is weak, and the level of excited turbulence is rather low. All this leads to the weak diffusion of protons into the loss cone, a large lifetime of a particle in the loop ( 10³ s) and, hence, to the relatively high efficiency of their escape into interplanetary space.     

The role of non-thermal electrons in the hydrogen and calcium lines of stellar flares

There is observational evidence showing that stellar and solar flares occur with a similar circumstance, although the former are usually much more energetic. It is expected that the bombardment by high-energy electrons is one of the chief heating processes of the flaring atmosphere. In this paper we study how a precipitating electron beam can influence the line profiles of Ly α , H α , Ca  ii K and λ 8542. We use a model atmosphere of a dMe star and make non-LTE computations taking into account the non-thermal collisional rates owing to the electron beam. The results show that the four lines can be enhanced to different extents. The relative enhancement increases with increasing formation height of the lines. Varying the energy flux of the electron beam has different effects on the four lines. The wings of Ly α and H α become increasingly broad with the beam flux; change of the Ca  ii K and λ 8542 lines, however, is most significant in the line centre. Varying the electron energy (i.e. the low-energy cut-off for a power-law beam) has a great influence on the Ly α line, but little on the H α and Ca  ii lines. An electron beam of higher energy precipitates deeper, thus producing less enhancement of the Ly α line. The Ly α /H α flux ratio is thus sensitive to the electron energy.     

Gyrosynchrotron emission of solar flares

The current status of our knowledge on the theory of radio emission from mildly relativistic electrons and its application in the interpretation of solar radio bursts are reviewed. The recent high spatial resolution microwave observations have given important information about the geometry of the emitting region and have helped in the computation of better inhomogeneous models that reproduce qualitatively several observational characteristics of the emission. The limitations of the observations and the theory (particularly the effect of mode coupling on the observed polarisation) are pointed out and the potential of the gyrosynchrotron process as a diagnostic of the physical conditions is discussed. This will help us to obtain quantitative information about the changes of the magnetic field and the acceleration of particles in solar flares.Proceedings of the Workshop on Radio Continua during Solar Flares, held at Duino (Trieste), Italy, 27–31 May, 1985.     

Behavior of transition-region lines during impulsive solar flares

We describe briefly the Ultraviolet Spectrometer and Polarimeter on the Solar Maximum Mission and discuss data pertaining to the emissions observed in lines originating in the transition-region plasma, particularly during impulsive flares. The data pertain to lines from the following ions: SiII, CIV, OIV, SiIV, OV, and FeXXI.     

Role of non-thermal electrons on the generation of X-ray and EUV lines in solar flares

The energy and angular distributions of electrons have been studied by combining small angle scatterings using analytical treatment with large angle collisions using Monte Caroo calculations as a function of column density for initially power-law electron distributions and incidence angles of 0, 30, and 60°. Using these distributions the X-ray and EUV line flux as a function of column density has been computed. The flux increases with increase in column density. At the initial column densities the contribution of non-thermal electrons for the production of line flux is negligible. However, it becomes significant at intermediate column densities at which the electron energy and angular distributions have non-Maxwellian nature. X-ray and EUV flux have also been calculated as a function of electron spectral index at a fixed column density. It falls steeply with increase in spectral index. The calculated flux is compared with the observations.     

Kernel heating and ablation in the impulsive phase of two solar flares

At the very start of the impulsive phase of two solar flares the temperature derived from medium-energy ( 16 keV) X-ray countrates was observed to rise abruptly, by several times 10⁷ K above the temperature derived from low-energy X-ray ( 7 keV) countrates. The difference between the two temperatures relaxed to zero thereafter, quasi-exponentially, with a characteristic time of 1.5 min. This differential temperature variation appears to mimique the differences between the ionic kinetic and the electron temperatures derived from spectral observations (Figures 1 and 2).These observations are explained in a quantitatively supported model of the flare kernel (Figure 4) in which the kernel is heated by electron beams from above. The low-energy electrons are stopped above the kernel and only the medium and high energy electrons penetrate down to the top of the chromosphere, causing heating of the chromospheric gas to about 50 MK, and ablation (evaporation), leading to the abrupt formation of a superhot flare kernel and a likely superhot dome above it (Figure 4), through which gas rises up and spreads out convectively, while cooling down in approximately the same time (45 s). The heating process lasts only for a few minutes. The difference between the Doppler temperature and the electron temperature derived from line intensity ratios or from low energy countrate ratios is ascribed to truncation of the tail of the electron energy distribution in the kernel. The kernel is about 2500 km deep; H emission is radiated by a thin layer at its basis.     

Hard X-ray emission processes in solar flares

Solar hard X-ray emission is one of the most direct diagnostics of accelerated particles during solar flares. In this review, the current understanding of hard X-ray emission processes is discussed: first the different emission mechanisms (in particular inverse Compton radiation, energetic ion or electron bremsstrahlung) are presented and the plausibility of each of these mechanisms is discussed. Then, different types of hard X-ray models (thermal or non-thermal, homogeneous or inhomogeneous emission regions) are presented together with the comparison of their predictions with X-ray observations (spectral, spatial and temporal informations - directivity and polarization).Proceedings of the Second CESRA Workshop on Particle Acceleration and Trapping in Solar Flares, held at Aubigny-sur-Nère (France), 23–26 June, 1986.     

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.     

Sub-terahertz emission from solar flares: The plasma mechanism of chromospheric emission

We consider the plasma mechanism of sub-terahertz emission from solar flares and determine the conditions for its realization in the solar atmosphere. The source is assumed to be localized at the chromospheric footpoints of coronal magnetic loops, where the electron density should reach n ≈ 10¹⁵ cm^?3. This requires chromospheric heating at heights h ? 500 km to coronal temperatures, which provides a high degree of ionization needed for Langmuir frequencies ν _p ≈ 200–400 GHz and reduces the bremsstrahlung absorption of the sub-THz emission as it escapes from the source. The plasma wave excitation threshold for electron-ion collisions imposes a constraint on the lower density limit for energetic electrons in the source, n ₁ > 4 × 10⁹ cm^?3. The generation of emission at the plasma frequency harmonic ν ≈ 2ν _p rather than the fundamental tone turns out to be preferred. We show that the electron acceleration and plasma heating in the sub-THz emission source can be realized when the ballooning mode of the flute instability develops at the chromospheric footpoints of a flare loop. The flute instability leads to the penetration of external chromospheric plasma into the loop and causes the generation of an inductive electric field that efficiently accelerates the electrons and heats the chromosphere in situ. We show that the ultraviolet radiation from the heated chromosphere emerging in this case does not exceed the level observed during flares.     

A Clarification on the invariable point in the power-law energy spectra of non-thermal electrons of solar flares

The invariable point of non-thermal electrons was proposed two years ago, based on analyzing the two intense gamma-ray line flares observed with the X2 detector on GRS/SMM. Due to too strong hard X-ray flux in those two flares, the influence of pile-up effect might not be fully excluded. In this paper, we check the invariable point by using some medium hard X-ray events observed with HXRBS/SMM and BATSE/CGRO. It is found that the invariable point could indeed appear in some weaker hard X-ray events, in which the pile-up effect cannot play a role. Further refinement should be based on the observations with a high energy resolution. This revised version was published online in July 2006 with corrections to the Cover Date.     

Soft X-ray line profiles in the impulsive phase of electron-heated solar flares

We have measured the motion of facular points and granules in the same region near a decaying sunspot. It is found that both features move away across the moat surrounding the sunspot. The mean speed of facular points is larger than that of granules: 0.65 km s^–1 and 0.4 km s^–1, respectively. These results are consistent with previous measurements of the speed of bright network features and moving magnetic fields, as well as of non-magnetic photospherical material. They support models in which a decaying sunspot is at the center of a supergranule, whose horizontal motions sweep out granules and magnetic flux tubes associated to the facular points. It is also found that granules are dragged by supergranular motions away of the moat.Contributions from the Kwasan and Hida Observatories, University of Kyoto.A part of this work was done while one of the authors (R.M.) was staying at the Kwasan and Hida Observatories, University of Kyoto, Japan, as a JSPS research fellow.     

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.     

On the polarization of the emission of X-ray solar flares

X-ray polarization measurements at three flares occurred in October 1969 were performed by means of a Thomson scattering type instrument installed on board the satellite Intercosmos-1. The polarization (P) at the wavelength of about 0,8 Å was detected at the rising phase and at the second maximum of intensity. The obtained averaged value of P for all three flares is 0.4 ± 0.2 at confidence level 0.9.     

OSO-8 observations of the impulsive phase of solar flares in the transition-zone and corona

Several solar flares have been observed from their onset in C IV 1548.2 and 1–8 Å X-rays using instruments aboard OSO-8. In addition, microwave and H flare patrol data have been obtained for this study. The impulsive brightening in C IV is frequently accompanied by redshifts, interpreted as downflows, of the order of 80 km s^-1. The maximum soft X-ray intensity usually arrives several minutes after the maximum C IV intensity. The most energetic C IV event studied shows a small blueshift just before reaching maximum intensity, and estimates of the mass flux associated with this upflow through the transition-zone are consistent with the increase of mass in the coronal loops as observed in soft X-rays. This event had no observable microwave burst, suggesting that electron beams did not play a major role in the chromospheric and transition-zone excitation. Lastly, our observations suggest that the frequent occurrence of violent dynamical processes at the onset of the flare are associated with the initial energy release mechanism.Currently at High Altitude Observatory, National Center for Atmospheric Research, P.O. Box 3000, Boulder, Colo. 80307, U.S.A.     

Study of hard X-ray characteristics of solar flares - support for non-thermal processes

The spatial and angular distributions and also the energy spectrum of hard X-rays from solar flares have been studied in terms of the energy and angular distributions of the accelerated electron beam. The incident electron distributions as functions of column density have been computed by combining the analytical treatment of small-angle scattering with the Monte-Carlo calculations for large angle scattering. To start with monoenergetic electrons at 0°, 30°, and 60° incidence angles have been taken. Using the Bethe-Heitler total cross section and the Sauter differential cross section along with the calculated electron distributions, the bremsstrahlung flux and its angular distribution for different photon energies > 10 keV have been studied as function of column density. The shape of the calculated curves agrees with the observations of PVO/ISEE-3 lending support to the beamed thick-target model for X-ray generation with continuous injection.Physics Department, Vishwa Bharti Institution, Rainawari, Srinagar, India.