Energetic electrons in impulsive solar flares: Radio diagnostics

Radio emissions during and outside solar flares are tracers of energetic electrons from the bottom of the corona to the interplanetary space. This review focusses on impulsive flares, where joint analyses of radio, hard X-ray and γ-ray observations proved to be powerful probes of the properties of accelerated electrons and of the sites in the corona where they are accelerated. Evidence of electron acceleration and transport in the corona from microwave imaging and decimetre wave spectroscopy is reviewed and compared, and recent work on the interpretation of microwave spectra in terms of energetic electron spectra is discussed. The two directions for future instrumentation are the extension to shorter wavelengths, with the aim of probing relativistic electrons, and solar dedicated spectral imaging from centimetric to metric waves to provide a unified view of the acceleration signatures that stem so far from different instruments with either spectroscopic or imaging capabilities.     

Collapsing magnetic trap as accelerator of electrons in solar flares

A collapsing trap in the cusp topology of solar flares is simulated using a 2D MHD model. Then in this collapsing trap trajectories of test electrons and their acceleration are studied in detail. In the model we use the test particle technique with the guiding centre approximation including also collisional losses and scattering of test electrons. Computing the X-ray emission of the accelerated electrons it is shown that the acceleration process in the collapsing trap easily explains the formation of observed loop-top X-ray sources.     

Energy content of accelerated electrons and ions in intense solar flares

The energy content of nonthermal particles in solar flares is shared between accelerated electrons and ions. It isimportant for understanding the particle acceleration mechanism in solar flares. Yohkoh observed a few intense flares which produced both strong gamma-ray lines and electron bremsstrahlung continuum. We analyze energy spectra of X-class solar flares on October 27, 1991(X6.1), November 6, 1997 (X9.4), July 14, 2000 (X5.7) and November 24, 2000 (X2.3). The accelerated electron and proton spectra are derived from a spectral analysis of their high-energy photon emission and the energy contents in >1 MeV electrons and >10 MeV protons are estimated to be 6×l0²⁸ – 4×10³⁰ and 2×10²⁸ – 5×10²⁹ erg, respectively. We study the flare to flare variation in the energy content of >1 MeV electrons and >10 MeV protons for the four Yohkoh gamma-ray flares. Ratios of >1 MeV electron energy content to >10 MeV proton energy content are roughly within an order of magnitude.     

Power-law spectra of energetic electrons in solar flares from the maximum entropy and dimensional considerations

The maximum entropy formalism and dimensional analysis are used to derive a power-law spectrum of accelerated electrons in impulsive solar flares, where the particles can contain a significant fraction of the total flare energy. Entropy considerations are used to derive a power-law spectrum for a particle distribution characterised by its order of magnitude of energy. The derivation extends an earlier one-dimensional argument to the case of an isotropic three-dimensional particle distribution. Dimensional arguments employ the idea that the spectrum should reflect a balance between the processes of energy input into the corona and energy dissipation in solar flares. The governing parameters are suggested on theoretical grounds and shown to be consistent with solar flare observations. The flare electron flux, differential in the non-relativistic electron kinetic energy E, is predicted to scale as $E^{-3}$. This scaling is in agreement with RHESSI measurements of the hard X-ray flux that is generated by deka-keV electrons, accelerated in intense solar flares.     

The Neupert effect and new RHESSI measures of thetotal energy in electrons accelerated in solar flares

It is believed that a large fraction of the total energy released in a solar flare goes initially into acceleratedelectrons. These electrons generate the observed hard X-ray bremsstrahlung as they lose most of their energy by coulomb collisions in the lower corona and chromosphere. Results from the Solar Maximum Mission showed that there may be even more energy in accelerated electrons with energies above 25 keV than in the soft X-ray emitting thermal plasma. If this is the case, it is difficult to understand why the Neupert Effect — the empirical result that for many flares the time integral of the hard X-ray emission closely matches the temporal variation of the soft X-ray emission — is not more clearly observed in many flares. From recent studies, it appears that the fraction of the released energy going into accelerated electrons is lower, on average, for smaller flares than for larger flares. Also, from relative timing differences, about 25% of all flares are inconsistent with the Neupert Effect. The Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) is uniquely capable of investigating the Neupert Effec since it covers soft X-rays down to 3 keV (when both attenuators are out of the field of view) and hard X-rays with keV energy resolution, arcsecond-class angular resolution, and sub-second time resolution. When combined with the anticipated observations from the Soft X-ray Imager on the next GOES satellite, these observations will provide us with the ability to track the Neupert Effect in space and time and learn more about the relation between plasma heating and particle acceleration. The early results from RHESSI show that the electron spectrum extends down to as low as 10 keV in many flares, thus increasing the total energy estimates of the accelerated electrons by an order of magnitude or more compared with the SMM values. This combined with the possible effects of filling factors smaller than unity for the soft X-ray plasma suggest that there is significantly more energy in nonthermal electrons than in the soft X-ray emitting plasma in many flares.     

Energy transfer in solar flares

We review the recent advances in the field of energy transfer and dissipation in solar flares. New observations and theoretical results have been obtained during the SMY and discussed in several workshops. Important new results have been provided by imaging hard X-ray and radio observations, high resolution spectra in the soft X-ray range, polarization measurements and combined optical, gamma- and X-ray data. We summarize results on the following topics: a) interpretation of hard X-ray bursts; b) heating and cooling of X-ray flare plasmas; c) chromospheric heating and evaporation; d) white-light flares. An overall picture of the importance of transfer processes is given, together with prospects for development of future research topics.     

Modeling large solar flares

The basic ideas to model the large solar flares are reviewed and illustrated. Some fundamental properties of potential and non-potential fields in the solar atmosphere are recalled. In particular, we consider a classification of the non-potential fields or, more exactly, related electric currents, including reconnecting current layers. The so-called ‘rainbow reconnection’ model is presented with its properties and predictions. This model allows us to understand main features of large flares in terms of reconnection. We assume that in the two-ribbon flares, like the Bastille-day flare, the magnetic separatrices are involved in a large-scale shear photospheric flow in the presence of reconnecting current layers generated by a converging flow.     

Proton versus electron heating in solar flares

Proton and electron heating of a flaring atmosphere is compared in a kinetic approach for the particles ejected from a non-neutral reconnecting current sheet (RCS) located above the top of reconnected flaring loops in a two-ribbon flare. Two kinds of high-energy particles are considered: particles accelerated by a super-Dreicer electric field and those ejected from the reconnection region as neutral outflows, or separatrix jets. The beam electrons are assumed to deposit their energy in Coulomb collisions and Ohmic heating of the ambient plasma particles by the electric field induced by the precipitating beams. The protons are assumed to deposit their energy in generation of kinetic Alfvén waves (KAWs), which, in turn, dissipate due to Cherenkov resonant scattering on the ambient plasma electrons. The beam electrons are found to provide a fast (within a few tenth of a second) heating of the atmosphere that is well spread in depth from the corona to the lower chromosphere. The protons are shown to precipitate to the lower atmosphere much slower (up to few seconds for beam and up to 10–20 s for slow jets). Slow jet protons provide heating of the two compact regions: the first located at the top of a flaring loop just below the RCS, and the second one appearing at the transition region (TR) and upper chromosphere; fast beam protons deposit their energy in the TR and chromosphere only.     

Asymmetric X-ray line broadening in solar flares

The symmetry and time development of X-ray spectral lines are examined for many flares using Yohkoh Bragg Crystal Spectrometer (BCS) observations. We examine the degree of line blueshift and asymmetric broadening as a function of flare impulsiveness. The results of the analysis present a consistent observational picture for the 16 flares that were studied. The blueshift of the total flare spectrum increases with increasing fractional rate of change of flux. This result supports models that predict stronger heating in flares results in more blueshifted plasma. It also suggests that most flares will exhibit very weak or no blueshifts if the peak fractional energy release rate remains relatively low. This will be the case if stationary plasma builds up quickly by early ‘gentle’ evaporation or rapid slowing of moving plasma, even when most of the hot plasma is generated by explosive chromospheric evaporation.     

First-order Fermi shock acceleration in solar flares

First order Fermi shock acceleration of electrons, protons and alpha particles is compared to observations of energetic particle events. For each event, a unique shock compression ratio produces spectra in good agreement with observation. The simple model predicts that the acceleration time to a given energy will be approximately equal for electrons and protons and, for reasonable solar parameters, can be less than 1 second to ～ 100 MeV.     

Reconnection during substorms and solar flares

The patterns of reconnection in the Earth magnetotail and in the solar corona above the active region are presented. The electric field and field-aligned currents (FAC) generation in the current sheet are discussed.     

Ionospheric heating due to solar flares as measured by SROSS-C2 satellite

The data on thermal fluctuations of the topside ionosphere have been measured by Retarding Potential Analyser (RPA) payload aboard the SROSS-C2 satellite over the Indian region for half of the solar cycle (1995–2000). The data on solar flare has been obtained from National Geophysical Data Center (NGDC) Boulder, Colorado (USA) and other solar indices (solar radio flux and sunspot number) were download from NGDC website. The ionospheric electron and ion temperatures show a consistent enhancement during the solar flares. The enhancement in the electron temperature is 28–92% and for ion temperature it is 18–39% compared to the normal day’s average temperature. The enhancement of ionospheric temperatures due to solar flares is correlated with the variation of sunspot and solar radio flux (F10.7cm). All the events studied in the present paper fall in the category of subflare with almost same intensity. The ionospheric electron and ion temperatures enhancement have been compared with the IRI model values.     

Energy input in solar flares and coronal explosions

A coronal explosion is a density wave observed in X-ray images of solar flares. The wave occurs at the end of the impulsive phase, which is the time at which the flare's thermal energy content has reached its maximum value. It starts in a small area from where it spreads out, mainly into one hemisphere, with velocities that tend to rapidly decrease with time, and which are between ～ 10³ and a few tens of km s^?1. We interpret them as magneto-hydrodynamic waves that (mainly) move downward from the low corona into denser regions.     

Differential emission measure distributions in X-ray solar flares

X-ray spectrometer RESIK has observed spectra in the four wavelength bands from 3.3 Å to 6.1 Å. This spectral range contains many emission lines of H- and He-like ions for Si, S, Ar and K. These lines are formed in plasma of coronal temperatures (T > 3 MK). Analysis of their intensities allows studying differential emission measure distributions (DEM) in temperature range roughly between 3 MK and 30 MK. The aim of present study was to check whether any relationship exists between the character of DEM distribution, the event phase and the X-ray flare class. To do this we have calculated and analyzed the DEM distributions for a set of flares belonging to different GOES classes from the range B5.6–X1. The DEM distributions have been calculated using “Withbroe–Sylwester” multiplicative, maximum likelihood iterative algorithm. As the input data we have used absolute fluxes observed by RESIK in several spectral bands (lines + continuum). Respective emission functions have been calculated using the CHIANTI v. 5.2 atomic data package.     

Turbulence,complexity, and solar flares

The issue of predicting solar flares is one of the most fundamental in physics, addressing issues of plasma physics, high-energy physics, and modelling of complex systems. It also poses societal consequences, with our ever-increasing need for accurate space weather forecasts. Solar flares arise naturally as a competition between an input (flux emergence and rearrangement) in the photosphere and an output (electrical current build up and resistive dissipation) in the corona. Although initially localised, this redistribution affects neighbouring regions and an avalanche occurs resulting in large scale eruptions of plasma, particles, and magnetic field. As flares are powered from the stressed field rooted in the photosphere, a study of the photospheric magnetic complexity can be used to both predict activity and understand the physics of the magnetic field. The magnetic energy spectrum and multifractal spectrum are highlighted as two possible approaches to this.     

Ionospheric effects of the solar flares as deduced from global GPS network data

Results derived from analysing the ionospheric response to faint and bright solar flares are presented. The analysis used novel technology of a global detection of ionospheric effects from solar flares as developed by the authors (Afraimovich, 2000a; Afraimovich, 2000b), on the basis of phase measurements of the total electron content (TEC) in the ionosphere using an international GPS network. The essence of the method is that use is made of appropriate filtering and a coherent processing of variations in the TEC which is determined from GPS data, simultaneously for the entire set of visible GPS satellites at all stations used in the analysis. This technique is useful for identifying the ionospheric response to faint solar flares (of X-ray class C) when the variation amplitude of the TEC response to separate line-on-sight (LOS) is comparable to the level of background fluctuations. The dependence of the TEC variation response amplitude on the flare location on the Sun is investigated.     

The magnetohydrodynamic development of two-ribbon flares or a five-finger theory for solar flares

A semi-analytical model for the electrodynamic development of two-ribbon flares is presented. A current filament above a bipolar active region starts rising according to the model of Van Tend and Kuperus. Due to this motion large induced electric fields arise at a magnetic neutral line far below the filament, resulting in and associated with magnetic reconnection and the formation of a current sheet. The interaction of this current sheet with the original current filament, the background magnetic field and the boundary layer of the photosphere determine the further electrodynamic development of the flare. The model predicts the energy release, the time of maximum, the height of the energy source and other quantities reasonably well.     

Magnetic reconnection in solar flares and corresponding radio bursts

The 2D MHD model of the flare magnetic reconnection shows that a reconnection activity, changes of the magnetic field topology and generation of waves are connected. It is found that after the phase of a quasi-stationary reconnection in the extended current sheet above the flare arcade the tearing mode instability produces the plasmoids which then can interact and generate MHD waves. Results of particle-in-cell simulations of the tearing processes, which accelerate electrons, are mentioned. Then all these processes are discussed from the point of view of possible radio emissions. While shocks can contribute to the type II radio burst, the superthermal electrons trapped in plasmoids can generate so called drifting pulsating structures. Furthermore, regions with the MHD turbulence may manifest themselves as the lace or dm-spike bursts.     

The role of magnetic field shear in solar flares

We present observational results and their physical implications garnered from the deliberations of the FBS Magnetic Shear Study Group on magnetic field shear in relation to flares. The observed character of magnetic shear and its involvement in the buildup and release of flare energy are reviewed and illustrated with emphasis on recent results from the Marshall Space Flight Center vector magnetograph. It is pointed out that the magnetic field in active regions can become sheared by several processes, including shear flow in the photosphere, flux emergence, magnetic reconnection, and flux submergence. Modeling studies of the buildup of stored magnetic energy by shearing are reported which show ample energy storage for flares. Observational evidence is presented that flares are triggered when the field shear reaches a critical degree, in qualitative agreement with some theoretical analyses of sheared force-free fields. Finally, a scenario is outlined for the class of flares resulting from large-scale magnetic shear; the overall instability driving the energy release results from positive feedback between reconnection and eruption of the sheared field.     

Investigation of impulsive soft X-ray brightening in solar flares

Four multi-loops or arcade flares showing strong impulsive soft X-ray brightenings on Yohkoh/SXT frames have been selected. By inspection of light curves of individual pixels, the areas of brightening have been localised. Evidences that non-thermal electron beams easily penetrate through whole flaring structures have been found. In some footpoints of the flaring structures during the impulsive phase the evidence of the chromospheric evaporation driven by non-thermal electron beams has been detected. The velocities of the upflowing plasma have been estimated. Derived values are in a wide range among 220 and 750 km/s. The SXT images of the investigated flares have been compared with the Yohkoh/HXT images. Generally good spatial and temporal coincidence between soft and hard X-ray emission from footpoints of flaring structures during the impulsive phase have been found but some exceptions occur. An explanation of the reported exceptions based on the magnetic field configuration has been proposed.