Anisotropy and polarization of solar X-ray bursts

The effects of the Compton back-scattered X-ray flux from the photosphere on the directivity and polarization of flare X-rays between 15 keV and 150 keV are computed. The calculations are made with a thin target model for flares of De Jager-Kundu type with electrons spiralling downward around a vertical magnetic field and for an Isotropie source. The resulting polarization for an isotropic source is not higher than 4%. The resulting directivity of anisotropic sources is greatly reduced, particularly below 70 keV. The results of the statistical studies of the center-limb distribution of solar X-ray bursts are then compatible with the existing measures of polarization. The hypothesis for existence of De JagerKundu type flares is enforced.     

Low-Energy Cutoffs in Electron Spectra of Solar Flares: Statistical Survey

The Reuven Ramaty High Energy Spectroscopic Imager (RHESSI) X-ray data base (February 2002 – May 2006) has been searched to find solar flares with weak thermal components and flat photon spectra. Using a regularized inversion technique, we determine the mean electron flux distribution from count spectra for a selection of events with flat photon spectra in the 15 – 20 keV energy range. Such spectral behavior is expected for photon spectra either affected by photospheric albedo or produced by electron spectra with an absence of electrons in a given energy range (e.g., a low-energy cutoff in the mean electron spectra of nonthemal particles). We have found 18 cases that exhibit a statistically significant local minimum (a dip) in the range of 13 – 19 keV. The positions and spectral indices of events with low-energy cutoff indicate that such features are likely to be the result of photospheric albedo. It is shown that if the isotropic albedo correction is applied, all low-energy cutoffs in the mean electron spectrum are removed, and hence the low-energy cutoffs in the mean electron spectrum of solar flares above ∼ 12 keV cannot be viewed as real features. If low-energy cutoffs exist in the mean electron spectra, their energies should be less than ∼ 12 keV.     

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.     

Hard x-ray and Metric/Decimetric Radio Observations of the 20 February 2002 Solar Flare

The GOES C7.5 flare on 20 February 2002 at 11:07 UT is one of the first solar flares observed by RHESSI at X-ray wavelengths. It was simultaneously observed at metric/decimetric wavelengths by the Nançay radioheliograph (NRH) which provided images of the flare between 450 and 150 MHz. We present a first comparison of the hard X-ray images observed with RHESSI and of the radio emission sites observed by the NRH. This first analysis shows that: (1) there is a close occurrence between the production of the HXR-radiating most energetic electrons and the injection of radio-emitting non-thermal electrons at all heights in the corona, (2) modifications with time in the pattern of the HXR sources above 25 keV and of the decimetric radio sources at 410 MHz are observed occurring on similar time periods, (3) in the late phase of the most energetic HXR peak, a weak radio source is observed at high frequencies, overlying the EUV magnetic loops seen in the vicinity of the X-ray flaring sites above 12 keV. These preliminary results illustrate the potential of combining RHESSI and NRH images for the study of electron acceleration and transport in flares.     

Thick-target processes and white-light flares

Observations indicate that fast electrons in solar flares, which cause the hard X-ray burst and the impulsive microwave burst, lose energy predominantly by collisional processes. This requires a thick-target theory of the emission, for which the electron spectrum inferred from the X-ray spectrum becomes 1.5 powers steeper than in the usual thin-target theory.The low-energy end of this spectrum contains enough energy above about 5 keV to supply the white-light continuum emission occasionally observed in major flares. The penetration of the nonthermal electrons creates long-lived excess ionization which enhances the free-free and free-bound continuum in the heated medium. The emission will occur high above the photosphere at small optical depth in the visible continuum. Thus its spectrum will extend into the infrared and ultraviolet.     

Acceleration and Storage of Energetic Electrons in Magnetic Loops in the Course of Electric Current Oscillations

A mechanism of electron acceleration and storage of energetic particles in solar and stellar coronal magnetic loops, based on oscillations of the electric current, is considered. The magnetic loop is presented as an electric circuit with the electric current generated by convective motions in the photosphere. Eigenoscillations of the electric current in a loop induce an electric field directed along the loop axis. It is shown that the sudden reductions that occur in the course of type IV continuum and pulsating type III observed in various frequency bands (25?–?180 MHz, 110?–?600 MHz, 0.7?–?3.0 GHz) in solar flares provide evidence for acceleration and storage of the energetic electrons in coronal magnetic loops. We estimate the energization rate and the energy of accelerated electrons and present examples of the storage of energetic electrons in loops in the course of flares on the Sun or on ultracool stars. We also discuss the efficiency of the suggested mechanism as compared with the electron acceleration during the five-minute photospheric oscillations and with the acceleration driven by the magnetic Rayleigh–Taylor instability.     

Thermal evolution of flare plasma

The evolution of hot thermal plasma in solar flares is analyzed by a single-temperature model applied to continuum emission in the 5 keV < E ? 13 keV spectral range. The general trend that the thermal plasma observed in soft X-rays is heated by the non-thermal electrons that emit as the hard X-ray bursts is confirmed by the observation of an electron temperature increase at the time interval of hard X-ray spikes and a quantitative comparison between thermal energy content and hard X-ray energy input. Non-thermal electrons of 10 keV < E < 30 keV energy may play an important role in pre- and post-burst phases.     

The Influence of Ion-Acoustic Turbulence on the Electron Acceleration in the Reconnecting Current Sheet

Through solving the single electron equation of motion and the Fokker-Planck equation including the terms of electric field strength and ion-acoustic turbulence, we study the influence of the ion-acoustic wave on the electron acceleration in turbulent reconnecting current sheets. It is shown that the ion-acoustic turbulence which causes plasma heating rather than particle acceleration should be considered. With typical parameter values, the acceleration time scale is around the order of 10^-6 s, the accelerated electrons may have approximately a power-law distribution in the energy range 20 ～100 keV and the spectral index is about 3～10, which is basically consistent with the observed hard X-ray spectra in solar flares.     

Energetic solar electrons in the interplanetary medium

ISEE-3 measurements extending down to 2 keV energy have provided a new perspective on energetic solar electrons in the interplanetary medium. Impulsive solar electron events are observed, on average, several times a day near solar maximum, with 40% detected only below 15 keV. The electron energy spectra have a nearly power-law shape extending smoothly down to 2 keV, indicating that the origin of these events is high in the corona. These coronal flare-like events often produced ³He-rich particle events.In large solar flares which accelerate electrons and ions to relativistic energies, the electron spectrum appears to be modified by a second acceleration which results in a double power-law shape above 10 keV with a break near 100 keV and flattening from 10–100 keV. Large flares result in long-lived (many days) streams of outflowing electrons which dominate the interplanetary fluxes at low energies. Even in the absence of solar activity, significant fluxes of low energy electrons flow out from the Sun.Solar type-III radio bursts are produced by the escaping 2–10² keV electrons through a beam-plasma instability. The detailed ISEE-3 measurements show that electron plasma waves are generated by the bump-on-tail distribution created by the faster electrons running ahead of the slower ones. These plasma waves appear to be converted into radio emission by nonlinear wave-wave interactions.     

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.     

Frequency distributions and correlations of solar X-ray flare parameters

We have determined frequency distributions of flare parameters from over 12000 solar flares recorded with the Hard X-Ray Burst Spectrometer (HXRBS) on the Solar Maximum Mission (SMM) satellite. These parameters include the flare duration, the peak counting rate, the peak hard X-ray flux, the total energy in electrons, and the peak energy flux in electrons (the latter two computed assuming a thick-target flare model). The energies were computed above a threshold energy between 25 and 50 keV. All of the distributions can be represented by power laws above the HXRBS sensitivity threshold. Correlations among these parameters are determined from linear regression fits as well as from the slopes of the frequency distributions. Variations of the frequency distributions were investigated with respect to the solar activity cycle.Theoretical models for the frequency distribution of flare parameters depend on the probability of flaring and the temporal evolution of the flare energy build-up. Our results are consistent with stochastic flaring and exponential energy build-up, with an average build-up time constant that is 0.5 times the mean time between flares. The measured distributions of flares are also consistent with predicted distributions of flares from computer simulations of avalanche models that are governed by the principle of self-organized criticality.     

Energetic Particle Acceleration and Propagation in Strong CME-Less Flares

Flares and coronal mass ejections (CMEs) contribute to the acceleration and propagation of solar energetic particles (SEP) detected in the interplanetary space, but the exact roles of these phenomena are yet to be understood. We examine two types of energetic particle tracers related with 15 CME-less flares that emit bright soft X-ray bursts (GOES X class): radio emission of flare-accelerated electrons and in situ measurements of energetic electrons and protons near 1 AU. The CME-less flares are found to be vigorous accelerators of microwave-emitting electrons, which remain confined in low coronal structures. This is shown by unusually steep low-frequency microwave spectra and by lack of radio emission from the middle and high corona, including dm?–?m wave type IV continua and metre-to-hectometre type III bursts. The confinement of the particles accelerated in CME-less flares agrees with the magnetic field configuration of these events inferred by others. Two events produced isolated metric type II bursts revealing coronal shock waves. None of the seven flares in the western hemisphere was followed by enhanced particle fluxes in the GOES detectors, but one, which was accompanied by a type II burst, caused a weak SEP event detected at SoHO and ACE. Three of the CME-less flares were followed within some hours by SEP-associated flares from the same active region. These SEP-producing events were clearly distinct from the CME-less ones by their association with fast and broad CMEs, dm?–?m wave radio emission, and intense DH type III bursts. We conclude that radio emission at decimetre and longer waves is a reliable indication that flare-accelerated particles have access to the high corona and interplanetary space. The absence of such emission can be used as a signal that no SEP event is to be expected despite the occurrence of a strong soft X-ray burst.     

Great Microwave Bursts and hard X-rays from solar flares

The microwave and hard X-ray characteristics of 13 solar flares that produced microwave fluxes greater than 500 solar flux units have been analyzed. These Great Microwave Bursts were observed in the frequency range from 3 to 35 GHz at Bern, and simultaneous hard X-ray observations were made in the energy range from 30 to 500 keV with the Hard X-Ray Burst Spectrometer on the Solar Maximum Mission spacecraft. The principal aim of this analysis is to determine whether or not the same distribution of energetic electrons can explain both emissions. The temporal and spectral behaviors of the microwaves as a function of frequency and the X-rays as a function of energy were tested for correlations, with results suggesting that optically thick microwave emission, at a frequency near the peak frequency, originates in the same electron population that produces the hard X-rays. The microwave emission at lower frequencies, however, is poorly correlated with emission at the frequency which appears to characterize this common source. A single-temperature and a multitemperature model were tested for consistency with the coincident X-ray and microwave spectra at microwave burst maximum. Four events are inconsistent with both of the models tested, and neither of the models attempts to explain the high-frequency part of the microwave spectrum. A source area derived on the basis of the single-temperature model agrees to within the uncertainties with the observed area of the one burst for which spatially resolved X-ray images are available.Swiss National Science Foundation Fellow from the University of Bern.Also Energy/Environmental Research Group, Incorporated, Tucson, Arizona, and Department of Physics and Astronomy, University of North Carolina, Chapel Hill. Present address: Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland.     

A Study of the Low Energy Cutoff of Nonthermal Electrons in RHESSI Flares

The flattening at the low energy end of the hard X-ray (HXR) photon spectrum of solar flares was generally thought to be due to a cutoff of nonthermal electrons in flares. However, some authors have suggested that inverse Compton scattering (i.e., the albedo effect) or certain other reaction of flare photons with the lower atmosphere can also lead to the flattening. This paper adopts the method of deriving the cutoff proposed by Gan et al. ^[12–14], and makes a statistical analysis on 100 flares observed by the satellite Ramaty High Energy Solar Spectroscopy Imager (RHESSI) in 2002–2005. We found that after the albedo correction, the HXR photon spectra of 18 flares can be fitted with single powerlaw spectra, and those of 80 flares, with double power-law spectra. Besides, 21 flares can be directly interpreted with a single power-law electron spectrum plus a low energy cutoff. The range of the low energy cutoff is 20–50 keV and the mean value is approximately 30 keV. Some other possible interpretations are also investigated.     

Joint Effects of Compton Backscattering and Low-Energy Cutoff on the Flattening of Solar Hard X-Ray Spectra at Lower Energies

Theoretical calculation has shown that the spectrum of the Compton backscattering component in solar hard X-ray flares has a peak around 30 keV for a primary power-law source. Thus the superposition of the Compton backscattering component could cause a photon spectrum received at the Earth to be flattened below the peak energy and steeper above the peak energy. On the other hand, because a thick-target bremsstrahlung photon with a given energy E only could be produced by a nonthermal electron with an energy larger than E, thus if a power-law electron spectrum is cutoff below an energy E _c, then the produced photon spectrum will become flattened below E _c. In this work we present a calculation of the joint effects of the Compton backscattering and the low-energy cutoff on the spectral characteristics of the received solar hard X-ray in the energy range 10–100 keV. The results show that the flattening caused purely by the Compton backscattering could be comparable with that by the low-energy cutoff for hard spectra. So, it is obvious that the joint effects of the low-energy cutoff and the Compton backscattering could result in the received photon spectra to be much more flattened at lower energies. On the other hand, compared to the primary photon spectrum, the received photon spectral index will increase about 0.15 due to the Compton backscattering at higher energy, which seems independent of the primary spectral index.     

X-ray imaging of three flares during the impulsive phase

The impulsive phases of three flares that occurred on April 10, May 21, and November 5, 1980 are discussed. Observations were obtained with the Hard X-ray Imaging Spectrometer (HXIS) and other instruments aboard SMM, and have been supplemented with Hα data and magnetograms. The flares show hard X-ray brightenings (16–30 keV) at widely separated locations that spatially coincide with bright Hα patches. The bulk of the soft X-ray emission (3.5–5.5 keV) originates from in between the hard X-ray brightenings. The latter are located at different sides of the neutral line and start to brighten simultaneously to within the time resolution of HXIS. Concluded is that:

1. The bright hard X-ray patches coincide with the footpoints of loops.
2. The hard X-ray emission from the footpoints is most likely thick target emission from fast electrons moving downward into the dense chromosphere.
3. The density of the loops along which the beam electrons propagate to the footpoints is restricted to a narrow range (10⁹ < n < 2 × 10¹⁰ cm^-3), determined by the instability threshold of the return current and the condition that the mean free path of the fast electrons should be larger than the length of the loop.
4. For the November 5 flare it seems likely that the acceleration source is located at the merging point of two loops near one of the footpoints.

It is found that the total flare energy is always larger than the total energy residing in the beam electrons. However, it is also estimated that at the time of the peak of the impulsive hard X-ray emission a large fraction (at least 20%) of the dissipated flare power has to go into electron acceleration. The explanation of such a high acceleration efficiency remains a major theoretical problem.     

Relative Timing and Spectra of Solar Flare Hard X-ray Sources

Hard X-ray lightcurves, spectrograms, images, and spectra of three medium-sized flares observed by the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) are presented. Imaging spectroscopy of the 20 February 2002, 11:06 UT flare at 10′′ spatial resolution, comparable to the best previous hard X-ray imaging from Yohkoh, shows two footpoints with an ∼ 8 s delay of peak emission between footpoints. Subsequent imaging at le4′′ shows three sources consistent with two separate loops and simultaneous brightening in connected footpoints. Imaging for the simple two footpoint flare of 2 June 2002 also shows simultaneous footpoint brightening. The more complex 17 March 2002 flare shows at least four different sources during the main peak of the event, and it is difficult to clearly demonstrate simultaneous brightening of connected footpoints. Non-thermal power laws are observed down to ∼ 12–13 keV without flattening in all these events, indicating the energy content in energetic electrons may be significantly greater than previously estimated from assumed 25 keV low energy cutoff. Simultaneously brightening footpoints show similar spectra, at least in the three flares investigated. Double-power-law spectra with a relatively sharp break are often observed. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1022469902940     

Hard X-ray bursts from flares behind the solar limb

The determination of the location of the region of origin of hard X-rays is important in evaluating the importance of 10–100 keV electrons in solar flares and in understanding flare particle acceleration. At present only limb-occulted events are available to give some information on the height of X-ray emission. In fifteen months of OSO-7 operation, nine major soft X-ray events had no reported correlated Hα flare. We examine the hard X-ray spectra of eight of these events with good candidate X-ray flare producing active regions making limb transit at the time of the soft X-ray bursts. All eight bursts had significant X-ray emission in the 30–44 keV range, but only one had flux at the 3σ level above 44 keV. The data are consistent with most X-ray emission occurring in the lower chromosphere, but some electron trapping at high altitudes is necessary to explain the small nonthermal fluxes observed.     

Energy of microwave-emitting electrons and hard X-ray/microwave source model in solar flares

We present a new method of estimating the energy of microwave-emitting electrons from the observed rate of increase of the microwave flux relative to the hard X-ray flux measured at various energies during the rising phase of solar flares. A total of 22 flares observed simultaneously in hard X-rays (20–400 keV) and in microwaves (17 GHz) were analyzed in this way and the results are as follows:

1. The observed energy of X-rays which vary in proportion to the 17 GHz emission concentrates mostly below 100 keV with a median energy of 70 keV. Since the mean energy of electrons emitting 70 keV X-rays is ?130 keV or ?180 keV, depending on the assumed hard X-ray emission model (thin-target and thick-target, respectively), this photon energy strongly suggests that the 17 GHz emission comes mostly from electrons with an energy of less than a few hundred keV.
2. Correspondingly, the magnetic field strength in the microwave source is calculated to be 500–1000 G for the thick-target case and 1000–2000 G for the thin-target case. Finally, judging from the values of the source parameters required for the observed microwave fluxes, we conclude that the thick-target model in which precipitating electrons give rise to both X-rays and microwaves is consistent with the observations for at least 16 out of 22 flares examined.

     

A Statistical Study of Microwave Flare Morphologies

This study has been motivated by the detection of a small number of optically thin microwave bursts with maximum emission near the loop top, which is contrary to the prediction of isotropic gyrosynchrotron models. Using Nobeyama Radioheliograph (NoRH) high-spatial-resolution images at 17 and 34 GHz, we study the morphology at the radio peak of 104 flares that occurred relatively close to the limb. Using data from the Nobeyama Polarimeter we were able to determine whether the 17- and 34-GHz emissions came from optically thin or thick sources. We identified single-loop events, taking into account supplementary information from EUV and soft X-ray (SXR) images. We found optically thin emission from the top of the loop in 36% of single-loop events. In agreement with standard models, in this sample 46% and 18% of the events showed optically thin emission from the footpoints and optically thick emission from the entire loop, respectively. The derived percentage of events with gyrosynchrotron emission from isotropic populations of energetic electrons is possibly an upper limit. This point is illustrated by the analysis of an optically thin event that shows footpoint emission during the rise phase and loop-top emission during the decay phase. A model that takes into account both anisotropies in the distribution function of nonthermal electrons and time evolution can reproduce the observed transition from footpoint to loop-top morphology, if electrons with pitch-angle anisotropy are injected near one of the footpoints.