Comparisons of solar flare X-ray producing and escaping electrons from ∼ 2 TO 100 keV

Using observations from the ISEE-3 spacecraft, we compare the X-ray producing electrons and escaping electrons from a solar flare on 8 November, 1978. The instantaneous 5 to 75 keV electron spectrum in the X-ray producing region is computed from the observed bremsstrahlung X-ray spectrum. Assuming that energy loss by Coulomb collisions (thick target) is the dominant electron loss process, the accelerated electron spectrum is obtained. The energy spectrum of the escaping electrons observed from 2 to 100 keV differs significantly from the spectra of the X-ray producing electrons and of the accelerated electrons, even when the energy loss which the escaping electrons experienced during their travel from the Sun to the Earth is taken into account. The observations are consistent with a model where the escaping electrons come from an extended X-ray producing region which ranges from the chromosphere to high in the corona. In this model the low energy escaping electrons (2–10 keV) come from the higher part of the extended X-ray source where the overlying column density is low, while the high energy electrons (20–100 keV) come from the entire X-ray source.     

Hard X-ray characteristics of solar flares using electron Monte-Carlo calculations and beamed thick target model

The experimental results of X-ray bursts with spectral characteristics, spatial distribution, fast time variations, polarization, and directivity measurements carried out with Intercosmos, PVO/ISEE-3 spacecrafts, imaging instrument observations of Hard X-ray (HXIS) and Hard X-ray Burst Spectrometers (HXRBS) during solar maximum mission have been reviewed. The observed results about the above characteristics are discussed in detail in terms of non-thermal and thermal models. It is shown that the results can be interpreted in terms of beamed thick-target model in which electrons stream down to the loop footpoints and produce hard X-rays through electron-ion bremsstrahlung.     

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.     

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.     

Thick target X-ray bremsstrahlung from partially ionised targets in solar flares

The effect of partial ionisation of a thick target bremsstrahlung source on the emitted X-ray intensity is analysed. It is shown that a totally ionised target produces an X-ray burst only about one third as intense as that from an unionised target.In the case of a solar flare plasma target, the ionisation decreases with increasing depth in the flare. Thus, in an X-ray flare model in which electrons are continuously accelerated down into the chromosphere, high energy photons are produced with increased efficiency in the deeper layers of the flare plasma with consequent hardening of the X-ray spectrum. As a result, the spectra of nonthermal electrons in flares, inferred from X-ray spectra, are steepened and their total energy correspondingly increased.     

Reverse-current effect in present-day models of solar flares: Theory and high-accuracy observations

We propose an accurate analytical model for the source of hard X-ray emission from a flare in the form of a “thick target” with a reverse current to explain the results of present-day observations of solar flares onboard the GOES, Hinode, RHESSI, and TRACE satellites. The model, one-dimensional in coordinate space and two-dimensional in velocity space, self-consistently takes into account the fact that the beam electrons lose the kinetic energy of their motion along the magnetic field almost without any collisions under the action of the reverse-current electric field. Some of the electrons return from the emission source to the acceleration region without losing the kinetic energy of their transverse motion. Based on the observed hard X-ray bremsstrahlung spectrum, the model allows the injection spectrum of accelerated electrons to be reconstructed with a high accuracy. As an example, we consider the white-light flare of December 6, 2006, which was observed with a high spatial resolution in the optical wavelength range at the main maximum of hard X-ray emission. Within the framework of our model, we show that to explain the hard X-ray spectrum, the flux density of the energy transferred by electrons with energies above 18 keV was ～3 × 10¹³ erg cm^?2 s^?1. This exceeds the habitual values typical of the classical model of a thick target without a reverse current by two orders of magnitude. The electron density in the beam is also very high: ～10¹¹ cm^?3. A more careful consideration of plasma processes in such dense electron beams is needed when the physical parameters of a flare are calculated.     

RHESSI Observations of the Neupert Effect in Three Solar Flares

Previous observations show that in many solar flares there is a causal correlation between the hard X-ray flux and the derivative of the soft X-ray flux. This so-called Neupert effect is indicative of a strong link between the primary energy release to accelerate particles and plasma heating. It suggests a flare model in which the hard X-rays are electron – ion bremsstrahlung produced by energetic electrons as they lose their energy in the lower corona and chromosphere and the soft X-rays are thermal bremsstrahlung from the “chromospheric evaporation” plasma heated by those same electrons. Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) observes in a broad energy band and its high spectral resolution and coverage of the low-energy range allow us to separate the thermal continuum from the nonthermal component, which gives us an opportunity to investigate the Neupert effect. In this paper, we use the parameters derived from RHESSI observations to trace the primary energy release and the plasma response: The hard X-ray flux or spectral hardness is compared with the derivative of plasma thermal energy in three impulsive flares on 10 November 2002 and on 3 and 25 August 2005. High correlations show that the Neupert effect does hold for the two hard X-ray peaks of the 10 November 2002 flare, for the first peaks of the 3 August 2005 flare, and for the beginning period of the 25 August 2005 flare.     

Collective plasma effects and the electron number problem in solar hard X-ray bursts

Due to the relatively high stream densities involved, collective interactions with the ambient plasma are likely to be important for the electrons producing solar hard X-ray bursts. In thick- and thin-target bremsstrahlung models the most relevant process is limitation of the invoked electron beams by ion sound wave generation in the neutralizing reverse current established in the atmosphere. For the thick target model it is shown that typical electron fluxes are near the maximum permitted by stability of the reverse current so that ion-sound wave generation may be the process which limits the electron injection rate. On the other hand the chromospheric reverse current is sufficient to supply the large total number of electrons which have to be accelerated in the corona. For the thin target the low density of the corona severely limits the possible reverse current so that the maximum upward flux of fast electrons is probably much too small to explain X-ray bursts but compatible with observations of interplanetary electrons.A distinct class of model postulates a small number of electrons confined by resonant scattering in a dense coronal slab surrounding a current sheet with continuous stochastic acceleration offsetting collisional losses. The energetic aspects of such a situation described by Hoyng (1975) are developed here by addition of equations describing the slab geometry in terms of electron diffusion by whistler scattering and of the collisional damping of the accelerating Langmuir waves. Solution of these equations results in values for the fieldB(70–350 G), densityn ₀(2–5 × 10¹² cm ^–3), slab dimensions (10¹⁸ km² × 0.3–3 km) and relative Langmuir energy density (10^–3 – 10^–2) required to produce the observed range of bursts. It is pointed out, however, that there may be no real gain in electron number requirements since the fast electrons in the emitting slab would be constantly swept out along with the frozen-in plasma as dissipation proceeds so that a large total number of electrons is still required. It could in fact be that just such a coronal region is the injection mechanism for the thick-target model.On leave from Department of Astronomy, University of Glasgow, Scotland.     

Microwave and hard X-ray bursts from solar flares

We have applied detailed theories of gyro-synchrotron emission and absorption in a magnetoactive plasma, X-ray production by the bremsstrahlung of non-thermal electrons on ambient hydrogen, and electron relaxation in a partially ionized and magnetized gas to the solar flare burst phenomenon. The hard X-ray and microwave bursts are shown to be consistent with a single source of non-thermal electrons, where both emissions arise from electrons with energies < mc ². Further-more, the experimental X-ray and microwave data allow us to deduce the properties of the electron distribution, and the values of the ambient magnetic field, the hydrogen density, and the size of the emitting region. The proposed model, although derived mostly from observations of the 7 July 1966 flare, is shown to be representative of this type of event.NAS-NRC Resident Research Associate.     

Coronal scattering as a source of flare-associated polarized hard X-rays

We consider the scattering of flare-associated X-rays above 1 keV at coronal heights, particularly from regions of enhanced density. This includes a discussion of the polarization of the scattered X-rays. Although the scattered radiation would not be bright by comparison with the total hard X-ray flux from a flare, its detectability would be enhanced for events located a few degrees behind the limb for which the dominant `footpoint' hard X-ray sources are occulted. Thus we predict that major flares occurring beyond the solar limb may be detectable via scattering in density enhancements that happen to be visible above the limb, and that such sources may be strongly polarized. Since thin-target bremsstrahlung will generally greatly exceed the scattered thick-target flux in flare loops themselves, these considerations apply only to coronal structures that do not contain significant populations of non-thermal electrons.     

Directivity of solar hard X-ray bursts

Solar hard X-ray bursts (>10 keV) seem to show a centre-to-limb variation, while softer X-ray bursts show no directivity. This effect of hard X-ray bursts may be due to the directivity of the emission itself. As the cause of the directivity, two possibilities are suggested. One is the inverse Compton effect and the other is the bremsstrahlung from anisotropic electrons.     

Polarization of radiation from a strongly magnetized accretion disk: The asymptotic spectral distribution

We calculate the polarization of the radiation from an optically thick accretion disk with a vertical averaged magnetic field. The polarization arises from the scattering of light by free electrons in a magnetized disk plasma. The Faraday rotation of the polarization plane during the propagation of a photon in a medium with a magnetic field is considered as the main effect. We discuss various models of optically thick accretion disks with a vertical averaged magnetic field. Our main goal is to derive simple asymptotic formulas for the polarization of radiation in the case where the Faraday rotation angle Ψ ≫ 1 at the Thomson optical depth τ = 1. The results of our calculations allow the magnetic field strength in the region of the marginally stable orbit near a black hole to be estimated from polarimetric observations, including X-ray observations expected in the future. Since the polarization spectrum of the radiation strongly depends on the accretion disk model, a realistic physical model of the accretion disk can be determined from data on the polarization of its radiation.     

X-ray and microwave emissions from the July 19, 2012 solar flare: Highly accurate observations and kinetic models

The M7.7 solar flare of July 19, 2012, at 05:58 UT was observed with high spatial, temporal, and spectral resolutions in the hard X-ray and optical ranges. The flare occurred at the solar limb, which allowed us to see the relative positions of the coronal and chromospheric X-ray sources and to determine their spectra. To explain the observations of the coronal source and the chromospheric one unocculted by the solar limb, we apply an accurate analytical model for the kinetic behavior of accelerated electrons in a flare. We interpret the chromospheric hard X-ray source in the thick-target approximation with a reverse current and the coronal one in the thin-target approximation. Our estimates of the slopes of the hard X-ray spectra for both sources are consistent with the observations. However, the calculated intensity of the coronal source is lower than the observed one by several times. Allowance for the acceleration of fast electrons in a collapsing magnetic trap has enabled us to remove this contradiction. As a result of our modeling, we have estimated the flux density of the energy transferred by electrons with energies above 15 keV to be ～5 × 10¹⁰ erg cm^?2 s^?1, which exceeds the values typical of the thick-target model without a reverse current by a factor of ～5. To independently test the model, we have calculated the microwave spectrum in the range 1–50 GHz that corresponds to the available radio observations.     

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.     

Hard X-ray emission in electron-heated solar flares — A comparison of nonthermal and thermal contributions

We calculate the spatial structure of hard X-ray emission during the impulsive phase of electron-heated solar flares. Both direct non-thermal bremsstrahlung and the thermal bremsstrahlung arising from the heated plasma are considered. Our results indicate that the spread of non-thermal emission into the upper parts of the loop, through evaporation of the chromospheric target, may be more important than the appearance of a hot thermal source in the corona. The effects of varying the viewing angle to the flare loop, and of finite-size resolution element, are also considered, and we compare our results with observations from the Solar Maximum Mission Hard X-Ray Imaging Spectrometer. We also contrast the predicted structures with those predicted by other models of flare energy release, and it is found that the electron-heated model provides the most satisfactory agreement with the observations.On leave from: Department of Physics and Astronomy, The University, Glasgow G12 8QQ, Scotland, U.K.Presidential Young Investigator.     

The height distribution of flare hard X-rays in thick and thin target models

The current controversy between thick and thin target models of hard X-ray flares is reviewed and it is concluded that the most promising method of distinguishing them is in terms of the differences in the distribution of the source with height in the solar atmosphere. Quantitative predictions are made of this height distribution for both models and the results discussed in relation to observations of hard X-ray emission from flares behind the limb. It is concluded that the thick target model is as compatible with such events as the thin target whereas the latter is in general much less satisfactory in terms of energy requirements and of flare observations at other wavelengths. Other source models are also briefly considered.     

Hard X-ray emission from the solar corona

This review surveys hard X-ray emissions of non-thermal electrons in the solar corona. These electrons originate in flares and flare-related processes. Hard X-ray emission is the most direct diagnostic of electron presence in the corona, and such observations provide quantitative determinations of the total energy in the non-thermal electrons. The most intense flare emissions are generally observed from the chromosphere at footpoints of magnetic loops. Over the years, however, many observations of hard X-ray and even γ-ray emission directly from the corona have also been reported. These coronal sources are of particular interest as they occur closest to where the electron acceleration is thought to occur. Prior to the actual direct imaging observations, disk occultation was usually required to study coronal sources, resulting in limited physical information. Now RHESSI has given us a systematic view of coronal sources that combines high spatial and spectral resolution with broad energy coverage and high sensitivity. Despite the low density and hence low bremsstrahlung efficiency of the corona, we now detect coronal hard X-ray emissions from sources in all phases of solar flares. Because the physical conditions in such sources may differ substantially from those of the usual “footpoint” emission regions, we take the opportunity to revisit the physics of hard X-radiation and relevant theories of particle acceleration.     

Non-LTE line formation in a magnetic field

Theoretical line contours calculated for fixed values of the line constants and a given model atmosphere show an increase of the Stokes parameters Q, U, and V but a decrease of I if the portion of non-coherent scattering increases. These effects increase from the centre of the solar disk to the limb. The action of scattering may be approximately simulated in LTE contours by increasing the gradient of the source function and fitting in this way theoretical contours to observed ones. There remains, however, the effect of V-reversal near the line core, which is caused by anomalous dispersion and is abnormally increased by scattering.     

Comparison of mm-wave and X-ray diagnostics of flare plasma

To compare mm-wave and X-ray diagnostics of solar flare plasma, five flares observed in 1980–1991 in Metsähovi at 22 and 37 GHz and with GOES, SMM, and GRO are studied. The first impulsive peak of the mm-wave bursts under investigation coincides in time with hard X-ray emission. The second gradual component in mm-wave emission coincides with the maximum of the soft X-ray emission measure. The bremsstrahlung mm-wave radiation from hot chromospheric plasma and gyrosynchrotron radiation driven by common population of superthermal electrons are calculated. It is shown that for mm-wave events with the first peak intensity 100 s.f.u., the thermal bremsstrahlung is more important than the gyrosynchrotron emission. The total energy of fast electrons deduced from the first peak of mm-wave bursts is one to two orders of magnitude less than that determined from the hard X-ray emission in the approximation of a thick-target nonthermal model. That can testify in favour of the hybrid thermal/nonthermal model proposed by Holman and Benka (1992). The emission measure and the energy of evaporated plasma using both mm-wave and soft X-ray data are also determined. For events investigated here the energy of evaporated chromospheric plasma is larger than the total energy of fast electron beams. We have concluded that, for evaporation, additional energy release in the chromosphere is needed. The possibility of such energy release in the framework of an advanced circuit model for solar flares is discussed.