Stochastic acceleration of electrons in solar flares

The generation of lower-hybrid waves by cross-field currents is applied to reconnection processes proposed for solar flares. Recent observations on fragmentation of energy release and acceleration, and on hard X-ray (HXR) spectra are taken into account to develop a model for electron acceleration by resonant stochastic interactions with lower-hybrid turbulence. The continuity of the velocity distribution is solved including collisions and escape from the turbulence region. It describes acceleration as a diffusion process in velocity space. The result indicates two regimes that are determined by the energy of the accelerating electrons which may explain the double power-law often observed in HXR spectra. The model further predicts an anticorrelation between HXR flux and spectral index in agreement with observations.     

Electron acceleration in solar flares

We present observations of an intense solar flare hard X-ray burst on 1980 June 27, made with a balloon-borne array of liquid nitrogen-cooled germanium detectors which provided unprecedented spectral resolution (1 keV FWHM). The hard X-ray spectra throughout the impulsive phase burst fitted well to a double power-law form, and emission from an isothermal 10⁸–10⁹K plasma can be specifically excluded. The temporal variations of the spectrum indicate that the hard X-ray burst is made up of two superposed components: individual spikes lasting 3–15 s, whch have a hard spectrum and a break energy of 30–65 keV; and a slowly varying component characterized by a soft spectrum with a constant low-energy slope and a break energy which increases from 25 keV to 100 keV through the event. The double power-law shape indicates that acceleration by DC electric fields parallel to the magnetic field, similar to that occurring in the Earth's auroral zone, may be the source of the energetic electrons which produce the hard X-ray emission. The total potential drop required for flares is typically 10² kV compared to 10 kV for auroral substorms.     

Particle acceleration in solar flares

Particle acceleration during solar flares is a complex process where the main actors (Direct (D.C.) or turbulent electric fields) are hidden from us. It is easy to construct a successful particle accelertion model if we are allowed to impose on the flaring region arbitrary conditions (e.g., strength and scale length of the D.C. or turbulent electric fields), but then we have not solved the acceleration problem; we have simply re-defined it. We outline in this review three recent observations which indicate that the following physical processes may happen during solar flares: (1) Release of energy in a large number of microflares; (2) short time-scales; (3) small length scales; and (4) coherent radiation and acceleration sources. We propose that these new findings force us to reformulate the acceleration process inside a flaring active region assuming that a large number of reconnection sites will burst almost simultaneously. All the well-known acceleration mechanisms (electric fields, turbulent fields, shock waves, etc.) reviewed briefly here, can be used in a statistical model where each particle is gaining energy through its interaction with many small reconnection sites.     

Electron acceleration in solar flares

We present observations of an intense solar flare hard X-ray burst on 1980 June 27, made with a balloon-borne array of liquid nitrogen-cooled germanium detectors which provided unprecedented spectral resolution (≲1 keV FWHM). The hard X-ray spectra throughout the impulsive phase burst fitted well to a double power-law form, and emission from an isothermal 10⁸–10⁹K plasma can be specifically excluded. The temporal variations of the spectrum indicate that the hard X-ray burst is made up of two superposed components: individual spikes lasting ∼3–15 s, whch have a hard spectrum and a break energy of 30–65 keV; and a slowly varying component characterized by a soft spectrum with a constant low-energy slope and a break energy which increases from 25 keV to ≳100 keV through the event. The double power-law shape indicates that acceleration by DC electric fields parallel to the magnetic field, similar to that occurring in the Earth's auroral zone, may be the source of the energetic electrons which produce the hard X-ray emission. The total potential drop required for flares is typically ∼10² kV compared to ∼10 kV for auroral substorms.

     

Electron acceleration in solar flares

For the period September 1978 to December 1982 we have identified 55 solar flare particle events for which our instruments on board the ISEE-3 (ICE) spacecraft detected electrons above 10 MeV. Combining our data with those from the ULEWAT spectrometer (MPI Garching and University of Maryland) electron spectra in the range from 0.1 to 100 MeV were obtained. The observed spectral shapes can be divided into two classes. The spectra of the one class can be fit by a single power law in rigidity over the entire observed range. The spectra of the other class deviate from a power law, instead exhibiting a steepening at low rigidities and a flattening at high rigidities. Events with power-law spectra are associated with impulsive (<1 hr duration) soft X-ray emission, whereas events with hardening spectra are associated with long-duration (<1 hr) soft X-ray emission. The characteristics of long-duration events are consistent with diffusive shock acceleration taking place high in the corona. Electron spectra of short-duration flares are well reproduced by the distribution functions derived from a model assuming simultaneous second-order Fermi acceleration and Coulomb losses operating in closed flare loops.     

Prompt acceleration of ≳ 30 MeV per nucleon ions in solar flares

Observation of prompt γ-rays in solar flares requires that ions be accelerated to >30 MeV nucl^-1 in ? 2 s. A model for prompt acceleration is developed. The energy release is assumed to occur in a flaring loop with the energy release region being ? 10⁴ km in dimensions and with an Alfvén speed υ _A ? 3 × 10³ km s^-1. The acceleration is assumed to occur in two steps. The second-step acceleration from ? ? _T = 1/2m _p υ_A ² nucl^-1 to ? 30 MeV nucl^-1 is attributed to stochastic acceleration by hydromagnetic turbulence which is found to be fast enough under conditions which are not extreme. Main emphasis is placed on the first step, called preacceleration, to ? _T ? 100 keV nucl^-1. Preacceleration mechanisms which involve accelerating a small fraction of ions from the tail of a Maxwellian distribution are unacceptable because they would lead to enormous abundance anomalies. Preacceleration is attributed either to localized heating of ions to ? 10⁹ K or to acceleration by potential electric fields. The latter mechanism is favoured and some theoretical ideas are outlined based on observations of reconnection in the Earth's magnetotail. Whether energetic ions are prompt, delayed or unobservable depends only on the rate at which the stochastic acceleration proceeds. The second-step acceleration of electrons, invoked to account for a harder microwave component, is predicted to be slower by a factor ? 3 than for ? 30 MeV nucl^-1 ions.     

The acceleration of heavy nuclei in solar flares

The overabundance of heavy nuclei in solar cosmic rays of energy ?10 Me/nucleon (sometimes up to ?30 MeV/nucleon is explained by taking into account the pre-flare ionization states of these nuclei in the region where they are accelerated. A model is proposed which considers two-step accelerations associated with the initial development of solar flares. The first step is closely related to the triggering process of flares, while the second one starts with the development of the explosive phase. Further ionization of medium and heavy nuclei occurs through their interaction with keV electrons accelerated by the first-step acceleration. It is suggested that the role of these electrons is important in producing fully ionized atoms in the acceleration regions.     

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.     

Relativistic electrons from solar flares

Observations of interplanetary relativistic electrons from several solar-flare events monitored through 1964 to mid-1967 are presented. These are the first direct spectral measurements and time histories, made outside the magnetosphere, of solar-flare electrons having relativistic velocities. The 3- to 12-MeV electrons detected have kinetic energies about two orders of magnitude higher than those solar electrons previously studied in space, and measurements of both the time histories and energy spectra for a number of events in the present solar cycle were carried out. These measurements of interplanetary electrons are also directly compared with solar X-ray data and with measurements of related interplanetary solar protons.The time histories of at least four electron events show fits to the typical diffusion picture. A demonstrated similarity between the electron and the medium-energy proton fits for the event of 7 July, in particular, indicates that at these electron energies, but over several orders of magnitude of rigidity, whatever diffusion does take place is very nearly on a velocity, rather than a rigidity or an energy, basis. Diffusion-fit time histories varied as a function of T ₀ also indicate that the electrons in certain flare events originate at times near the X-ray and microwave burst, establishing their likely identity as the same electrons which cause the impulsive radiations. Also, the energy spectra and total numbers of the interplanetary electrons, compared with those of the flare-site electrons calculated from X-ray and microwave measurements, indicate that probably a small fraction of flare electrons escape into interplanetary space.     

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.     

Proton acceleration in flares and magnetohydrodynamic solar activity

The possibility of accelerated protons in solar flares having a sharp change in their spectral index is discussed. The analysis is based on the Tsytovich (1982, 1984, 1987a, b, c) acceleration model by MHD turbulence, which is shown to have different resonant conditions for non-relativistic and relativistic particles. The different resonant condition is shown to result in a sharp change in the accelerated proton spectral index, even in the absence of any peculiarity in the spectra of the MHD turbulence. Time scales for accelerated protons to relativistic energies are also derived, and shown to be consistent with observations. We also show that the threshold energy for electron acceleration by low frequency MHD turbulence is much greater than for proton acceleration. The turbulence therefore preferentially accelerates protons.     

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.     

Propagation and confinement of energetic electrons in solar flares

The propagation, cofinement and total energy of energetic (>25 keV) electrons in solar flares are examined through a brief review of the following hard X-ray measurements: (1) spatially resolved observations obtained by imaging instruments; (2) stereoscopic observations of partially occulted sources providing radial (vertical) spatial resolution; and (3) directivity of the emission measured through stereoscopic observations and the center-to-limb variation of the occurrence frequency of hard X-ray flares. The characteristics of the energetic electrons are found to be quite distinct in impulsive and gradual hard X-ray flares. In impulsive flares the non-thermal electron spectrum seems to extend down to 2 keV indicating that the total energy of non-thermal electrons is much larger than that assumed in the past.     

Propagation and confinement of energetic electrons in solar flares

Solar Physics - The propagation, cofinement and total energy of energetic (>25 keV) electrons in solar flares are examined through a brief review of the following hard X-ray measurements:...     

High energy electrons detected during solar flares

The S 79 experiment on board of the HEOS-A1 European Satellite has been designed to electrons detection whose kinetic energies should be equal or greater than 7.5 MeV. From December 1968 to July 1970, 11 events were observed.Their main characteristics are described in this article. Two different categories of events may be sorted out from these observations. The propagation conditions in the interplanetary space are now discussed to find out a possible interpretation.     

The spectral indices of X-ray and radio producing electrons in solar flares

In the homogeneous model of solar radio burst model, the spectral index of the optically thick part of the spectrum is almost independent of the spectral index of the electron energy, while from the optically thin part, the derived electron index δ_R is far smaller than that derived from the X-ray emission, δ_X. An inhomogeneous model is proposed, in which, by adjusting two parameters within reasonable limits, we can make δ_R, derived from both the optically thick and thin parts, to equal δ_X. The model is exemplified by the 1981 April 27 0800 UT burst.     

Location of the electron acceleration region in solar flares

Observations of impulsive solar flare X-rays 10 keV by the OGO-5 satellite and the measurements of energetic solar electrons made with the Explorer-35 and Explorer-41 (IMP-5) satellites during the period March 1968–September 1969 have been analyzed in order to determine the ion density in the X-ray source region as well as the location of the electron acceleration region in the solar atmosphere. If we assume that the efficiency of escape of the accelerated electrons into interplanetary space is 10^–3, the observations are found to be consistent with the following interpretation: (i) the ion density in the X-ray source region varies from event to event and lies between 10⁹ and 10¹¹ ions cm^–3 for those events in which the impulsive X-ray emission could be detected; (ii) for those events in which no impulsive emission was detected above threshold, the ion density in the X-ray source was < 10⁹ ions cm^–3; (iii) at least in some small solar flares the region where the electrons are accelerated during the flash phase is located in the lower corona.     

The signs of non-periodic acceleration of electrons in solar active regions

The results of observations of type III bursts show that the modulation of the beam of accelerated electrons arises due to a random process with Poisson statistics (noise), but not due to resonant or periodic oscillations.     

Energetic electrons as an energy transport mechanism in solar flares

We review the observations and theory relating to the role of energetic electrons in the solar flare, with particular emphasis on discriminating between thermal and nonthermal origins of these electrons. We discuss diagnostics in hard X-rays, especially those relating to the recent observations of the SMM and HINOTORI satellites. We also briefly address the response of the atmosphere to energy input in the form of high energy electrons, in particular through the diagnostics of both the Fe K feature and optically thin transition region lines such as 0V. Finally, we discuss the relative roles of electron and proton heating in -ray flare events.