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.     

A dominant role for protons at the onset of solar flares

The energetics of the onset of the impulsive phase of solar flares are examined on the premise that a single acceleration mechanism is operating in the corona. From considerations of recent observations of plasma turbulence and upflows, and nuclear gamma-rays it is concluded that a model where the bulk of the energy resides in a non-thermal electron beam with a low energy cut-off at 20–25 keV is incompatible with many of the observations. Conversely, a model where the bulk of the energy resides in non-thermal protons is consistent with the majority, if not all, of the observations. It is suggested that the bulk of the energy in the impulsive phase is initially transferred to 10²–10³ keV protons. Acceleration by a series of small shocks is an energy transfer mechanism which gives particles increments in velocity rather than energy and would naturally favour protons over electrons. An important consequence of this result is that the hard X-ray burst must be thermal. At this time the precise mechanism for thermal X-ray production is unclear; however recent theoretical plasma physics results have indicated promising avenues of research in this context.     

Particle acceleration in flares

Particle acceleration is intrinsic to the primary energy release in the impulsive phase of solar flares, and we cannot understand flares without understanding acceleration. New observations in soft and hard X-rays, -rays and coherent radio emissions are presented, suggesting flare fragmentation in time and space. X-ray and radio measurements exhibit at least five different time scales in flares. In addition, some new observations of delayed acceleration signatures are also presented. The theory of acceleration by parallel electric fields is used to model the spectral shape and evolution of hard X-rays. The possibility of the appearance of double layers is further investigated.Report of Team 3, Flares 22 Workshop, Ottawa, May 25–28, 1993.     

Multi-spacecraft observations of particle events and interplanetary shocks during November/December 1982

We present a sample of solar energetic particle events observed between November 18 and December 31, 1982 by the HELIOS 1, the VENERA 13, and IMP 8 spacecraft. During the entire time period all three spacecraft were magnetically connected to the western hemisphere of the Sun with varying radial and angular distances from the flares. Eleven proton events, all of them associated with interplanetary shocks, were observed by the three spacecraft. These events are visible in the low-energy (about 4 MeV) as well as the high-energy (30 MeV) protons. In the largest events protons were observed up to energies of about 100 MeV. The shocks were rather fast and in some cases extended to more than 90% east of the flare site. Assuming a symmetrical configuration, this would correspond to a total angular extent of some interplanetary shocks of about 180%. In addition, due to the use of three spacecraft at different locations we find some indication for the shape of the shock front: the shocks are fastest close to the flare normal and are slower at the eastern flank. For particle acceleration we find that close to the flare normal the shock is most effective in accelerating energetic particles. This efficiency decreases for observers connected to the eastern flank of the shock. In this case, the efficiency of shock acceleration for high-energy protons decreases faster than for low-energy protons. Observation of the time-intensity profiles combined with variations of the anisotropy and of the steepness of the proton spectrum allows one in general to define two components of an event which we term solar and interplanetary. We attempt to describe the results in terms of a radially variable efficiency of shock acceleration. Under the assumption that the shock is responsible not only for the interplanetary, but also for the solar component, we find evidence for a very efficient particle acceleration while the shock is still close to the Sun, e.g., in the corona. In addition, we discuss this series of strong flares and interplanetary shocks as a possible source for the formation of a superevent.     

On proton and electron acceleration by shock waves during large solar flares

The data on optical, X-ray and gamma emission from proton flares, as well as direct observations of flare-associated phenomena, show energetic proton acceleration in the corona rather than in the flare region. In the present paper, the acceleration of protons and accompanying relativistic electrons is accounted for by a shock wave arising during the development of a large flare. We deal with a regular acceleration mechanism due to multiple reflection of resonance protons and fast electrons from a collisionless shock wave front which serves as a moving mirror. The height of the most effective acceleration in the solar corona is determined. The accelerated particle energy and density are estimated. It is shown in particular that a transverse collisionless shock wave may produce the required flux of protons with energy of 10 MeV and of relativistic electrons of 1–10 MeV.The proposed scheme may also serve as an injection mechanism when the protons are accelerated up to relativistic energies by other methods.     

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.     

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.     

Shock surfing acceleration

Analytical and numerical analysis identify shock surfing acceleration as an ideal pre-energization mechanism for the slow pick-up ions at quasiperpendicular shocks. After gaining sufficient energy by shock surfing, pick-up ions undergo diffusive acceleration to reach their observed energies. Energetic ions upstream of the cometary bow shock, acceleration of solar energetic particles by magnetosonic waves in corona, ion enhancement in interplanetary shocks, generation of anomalous cosmic rays from interstellar pick-up ions at the termination shock are some of the cases where shock surfing acceleration apply. Inclusion of the lower-hybrid wave turbulence into the laminar model of shock surfing can explain the preferential acceleration of heavier particles as observed by Voyager at the termination shock. At relativistic energies, unlimited acceleration of ions is theoretically possible; because for sufficiently strong shocks main limitation of the mechanism, caused by the escape of accelerated particles downstream of the shock during acceleration no longer exists.     

The relativistic quasilinear theory of particle acceleration by hydromagnetic turbulence

The quasilinear theory of acceleration of relativistic particles by hydromagnetic turbulence is treated in the adiabatic limit of small gyration radius. The theory is based on the relativistic Vlasov equation; however, a given pitch-angle scattering rate by microturbulence is postulated and is added to this equation. The resulting acceleration is found to be given by a diffusion coefficient in total momentum, which is proportional to the spectrum of turbulence with a rate coefficient . is a frequency that represents the efficiency of each wave component of the turbulence in producing acceleration. It is given as an integral over the solution of a differential equation in pitch angle. is evaluated in various limiting cases and is shown to lead to familiar forms of acceleration, such as Fermi acceleration and magnetic pumping. Thus, a comprehensive theory of these forms of heating is achieved.     

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.     

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.     

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.     

Particle acceleration during the explosive phase of a solar flare

Starting with the quasi-linear equation of the distribution function of particles in a regular electric field, a combined diffusion coefficient in the momentum space conbining the effects of the regular field and a turbulent field is obtained and a combined mechanism of acceleration by the regular and turbulent fields in the neutral sheet of solar proton flares is proposed. It is shown by calculation that conditions in solar proton flares are such that the charged particles can be effectively accelerated to tens of MeV, even ~1 GeV. It is shown that the combined acceleration by a regular electric field and ion-acoustic turbulence pumps the protons and other heavy ions into ranges of energy where they can be accelerated by Langmuir turbulence. By considering the combined acceleration by Langmuir turbulence and the regular electric field, the observed spectrum of energetic protons and the power-law spectrum of energetic electrons can be reproduced.     

Field-Guided Proton Acceleration at Reconnecting x-Points in Flares

An explicitly energy-conserving full orbit code CUEBIT, developed originally to describe energetic particle effects in laboratory fusion experiments, has been applied to the problem of proton acceleration in solar flares. The model fields are obtained from solutions of the linearised MHD equations for reconnecting modes at an X-type neutral point, with the additional ingredient of a longitudinal magnetic field component. To accelerate protons to the highest observed energies on flare timescales, it is necessary to invoke anomalous resistivity in the MHD solution. It is shown that the addition of a longitudinal field component greatly increases the efficiency of ion acceleration, essentially because it greatly reduces the magnitude of drift motions away from the vicinity of the X-point, where the accelerating component of the electric field is largest. Using plasma parameters consistent with flare observations, we obtain proton distributions extending up to -ray-emitting energies (>1 MeV). In some cases the energy distributions exhibit a bump-on-tail in the MeV range. In general, the shape of the distribution is sensitive to the model parameters.     

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.     

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.     

Particle acceleration,X-rays,and gamma-rays from winds

The instability of the line-driven winds of hot stars leads to the formation of strong shocks. These shocks not only emit thermal X-rays, but also accelerate a small fraction of the thermal electrons and ions to relativistic energies. Synchrotron radiation from these energetic particles can account for the non-thermal radio emission observed from some hot stars, and can also explain the hard X-rays detected in theEinstein X-ray spectra. Our calculations indicate that the-ray emission from non-thermal particles should be detectable by GRO. The detection (or non-detection) of these emissions over a wide energy range, from the radio to-rays, should provide a great deal of information on the structure of the unstable winds and the physics of particle acceleration by shocks.     

Particle propagation effects on solar flare X- and γ-ray time profiles

Much of the evidence for second stage particle acceleration in solar flares lies in the temporal variation of solar X- and -ray emissions. However, the solar flare X- and -ray burst time-intensity profiles are governed not only by the production or acceleration of electrons and protons but by the propagation of these particles in the solar atmosphere. The effects of particle propagation on X-ray and -ray time profiles are illustrated and compared through the use of three models with the result that a variety of particle propagation schemes reproduce effects commonly associated with second stage acceleration. The first model is that of a closed uniform density trap. The other two models employ particle diffusion from a trap to denser regions of the solar atmosphere to produce the high energy radiation. These calculations show that delayed peaking of the photon flux with respect to particle production and reduction in the impulsiveness of the high energy emission is to be expected, effects commonly associated with second stage acceleration. Thus, well understood physical processes are capable of producing so-called time delays in the high energy emission independent of any delays produced by additional particle acceleration processes. Diagnostic differences between these models are also discussed.     

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.     

Structure and stationarity of quasi-perpendicular shocks: Numerical simulations

This paper presents an overview of numerical simulation studies of fast collisionless shocks and compares these simulation results with observations of the Earth's bow shock and theoretical works. Especially, we review the structure and stationarity of the supercritical quasi-perpendicular shocks. In situ observations indicate that these shocks are generally quasi-stationary whereas full particle simulations as well as hybrid simulations often present a strong nonstationary behavior, a shock self-reformation. The simulation results, along with theoretical and observational works, suggest that the classical models of the quasi-stationary structure generated by reflected protons or by dispersive whistlers are not generally applicable for the supercritical quasi-perpendicular shocks and other phenomena are to be included into the model to ensure the observed quasi-stationarity: The role of a small scale turbulence and shock ripples is investigated. The downstream turbulence and the electron dynamics in the quasi-perpendicular shocks are also discussed.