Thermal electrons runaway from a hot plasma during a flare in the reverse-current model and their X-ray bremsstrahlung

The behaviour of the thermal electrons escaping from a hot plasma to a cold one during a solar flare is investigated. We suppose that the direct current of fast electrons is compensated by the reverse current of the thermal electrons in ambient plasma. It is shown that the direct current strength is determined only by the regular energy losses due to Coulomb collisions. The reverse-current electric field and the distribution function of fast electrons are found in the form of an approximate analytical solution to the self-consistent kinetic problem of the dynamics of a beam of escaping thermal electrons and its associated reverse current.The reverse-current electric field in solar flares leads to a significant reduction of the convective heat flux carried by fast electrons escaping from the high-temperature plasma to the cold one. The spectrum and polarization of hard X-ray bremsstrahlung, and its spatial distribution along flare loops are calculated and can be used for diagnostics of flare plasmas and escaping electrons.Send offprint requests to B. V. Somov.     

Interpretation of time characteristics of solar X-ray bursts referring to associated microwave bursts

It has been controversial whether the flare-associated hard X-ray bursts are thermal emission or non-thermal emission. Another controversial point is whether or not the associated microwave impulsive burst originates from the common electrons emitting the hard X-ray burst.It is shown in this paper that both the thermal and non-thermal bremsstrahlung should be taken into account in the quantitative explanation of the time characteristics of the hard X-ray bursts observed so far in the photon energy range of 10–150 keV. It is emphasized that the non-thermal electrons emitting the hard X-rays and those emitting the microwave impulsive burst are not common. The model is as follows, which is also consistent with the radio observations.At the explosive phase of the flare a hot coronal condensation is made, its temperature is generally 10⁷ to 10⁸K, the number density is about 10¹⁰ cm^–3 and the total volume is of the order of 10²⁹ cm³. A small fraction, 10^–3–10^–4, of the thermal electrons is accelerated to have power law distribution. Both the non-thermal and thermal electrons in the sporadic condensation contribute to the X-ray bursts above 10 keV as the bremsstrahlung. Fast decay of the harder X-rays (say, above 20 keV) for a few minutes is attributed to the decay of non-thermal electrons due to collisions with thermal electrons in the hot condensation. Slower decay of the softer X-rays including around 10 keV is attributed to the contribution of thermal component.The summary of this paper was presented at the Symposium on Solar Flares and Space Research, COSPAR, Tokyo, May, 1968.     

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.     

Evidence for or against a common origin of hard X-rays and microwaves from solar flares

The problem of whether hard X-rays and microwaves are emitted from the same electrons in common or closely separated sources is reviewed on direct and indirect observational evidence. Detailed analyses of time structure and peak flux suggest that hard X-rays and microwaves are emitted from nearly co-spatial sources due to electrons streaming down to the chromosphere. However this model has not been confirmed yet by direct imaging observations.     

Evidence for or against a common origin of hard X-rays and microwaves from solar flares

The problem of whether hard X-rays and microwaves are emitted from the same electrons in common or closely separated sources is reviewed on direct and indirect observational evidence. Detailed analyses of time structure and peak flux suggest that hard X-rays and microwaves are emitted from nearly co-spatial sources due to electrons streaming down to the chromosphere. However this model has not been confirmed yet by direct imaging observations.

     

Chromospheric heating by electron and proton bombardment in the solar flare of June 7, 1980

Using observations of both hard X-rays and γ-rays in the large solar flare on June 7, 1980, we infer the amount of chromospheric heating due to bombardment both by non-thermal electrons and by protons, respectively. If a thick-target model for the X-ray bremsstrahlung is adopted, then proton heating is shown to be important only in the lower chromosphere; however, if the hard X-rays are substantially thermal in origin, then proton heating may play an important or indeed dominant role in determining the structure of the entire flaring chromosphere.     

Dynamics of electron beams in a coronal loop and the hard X-ray burst

A numerical simulation has been made for the dynamics of non-thermal electrons (> 10keV) injected with spatial, temporal and velocity distributions into a model coronal loop. The time variations of the spatial intensity distribution and the spectrum for the expected hard X-rays are computed for many models in order to find the important physical parameters for those characteristics.The most important one is the column density of plasma, CD, along the loop. If CD is smaller than 10²⁰ cm^–2, the expected X-rays behave like the solar impulsive hard X-ray bursts, that is the spatial maximum of X-rays shifts to the top of the loop in the later phase of the burst accompanying a spectral softening. On the other hand, if CD is greater than this value, quasi-steady decay appears in the later phase. In this case the intensity distribution of X-rays above about 20 keV along the loop shows a broad maximum away from the loop top giving an extended spatial distribution of hard X-rays, and spectral hardness is kept constant. These characteristics are similar to the solar gradual hard X-ray bursts (the so-called extended burst which is not a hot thermal gradual burst).     

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.     

On the origin of solar flare X-rays

The origin of X-ray solar bursts is investigated on the basis of the theoretical model developed by Syrovatskii. According to this model (i) one of the most important manifestations of flares is the acceleration of charged particles (mainly of electrons) to subrelativistic and relativistic energies, and (ii) the two flare phases: stationary (soft) and nonstationary (hard) should be distinguished. The first phase is accompanied by the generation of the soft (2–8 Å) thermal X-rays and the second one by the generation of hard thermal and nonthermal X-rays in the 10 keV range. The thermal X-rays arise in both phases due to the heating of the ambient gas by accelerated particles. The possible mechanisms of non-thermal X-rays are investigated. Simple models of the emitting region are considered, taking into account the simultaneous observations in different regions of the electromagnetic spectrum.     

Spectral development of a solar X-ray burst observed on OSO-7

The UCSD solar X-ray instrument on the OSO-7 satellite observes X-ray bursts in the 2–300 keV range with 10.24 s time resolution. Spectra obtained from the proportional counter and scintillation counter are analyzed for the event of November 16, 1971, at 0519 UT in terms of thermal (exponential spectrum) and non-thermal (power law) components. The energy content of the approximately 20 × 10⁶K thermal plasma increased with the 60 s duration hard X-ray burst which entirely preceded the 5 keV soft X-ray maximum. If the hard X-rays arise by thick target bremsstrahlung, the nonthermal electrons above 10 keV have sufficient energy to heat the thermally emitting plasma. In the thin target case the collisional energy transfer from non-thermal electrons suffices if the power law electron spectrum is extrapolated below 10 keV, or if the ambient plasma density exceeds 4 × 10¹⁰ cm^–3.Formerly at UCSD.     

Spectral evolution of microwaves and hard X-rays in the 1989 March 18 flare and its interpretation

We analyze the time variation of microwave spectra and hard X-ray spectra of 1989 March 18, which are obtained from the Solar Array at the Owens Valley Radio Observatory (OVRO) and the Hard X-Ray Burst Spectrometer (HXRBS) on the Solar Maximum Mission (SMM), respectively. From this observation, it is noted that the hard X-ray spectra gradually soften over 50–200 keV on-and-after the maximum phase while the microwaves at 1–15 GHz show neither a change in spectral shape nor as rapid a decay as hard X-rays. This leads to decoupling of hard X-rays from the microwaves in the decay phase away from their good correlation seen in the initial rise phase. To interpret this observation, we adopt a view that microwave-emitting particles and hard X-ray particles are physically separated in an inhomogeneous magnetic loop, but linked via interactions with the Whistler waves generated during flares. From this viewpoint, it is argued that the observed decoupling of microwaves from hard X-rays may be due to the different ability of each source region to maintain high energy electrons in response to the Whistler waves passing through the entire loop. To demonstrate this possibility, we solve a Fokker-Planck equation that describes evolution of electrons interacting with the Whistler waves, taking into account the variation of Fokker-Planck coefficients with physical quantities of the background medium. The numerical Fokker-Planck solutions are then used to calculate microwave spectra and hard X-ray spectra for agreement with observations. Our model results are as follows: in a stronger field region, the energy loss by electron escape due to scattering by the waves is greatly enhanced resulting in steep particle distributions that reproduce the observed hard X-ray spectra. In a region with weaker fields and lower density, this loss term is reduced allowing high energy electrons to survive longer so that microwaves can be emitted there in excess of hard X-rays during the decay phase of the flare. Our results based on spectral fitting of a flare event are discussed in comparison with previous studies of microwaves and hard X-rays based on either temporal or spatial information.     

Observational Studies of the X-Ray Quasi-Periodic Oscillations of a Solar Flare

We study an M2.6 flare observed with RHESSI on 22 August 2005. The light curves of the hard X-rays (counts and photon fluxes), the derived number fluxes, as well as the energy fluxes of energetic electrons all presented a damped quasi-periodic oscillation. The modulation depth of the hard X-rays increased with the energies. For the energy fluxes of energetic electrons, the modulation depth can be as high as 90%. During the oscillations, however, the plasma temperature had no apparent change. No correspondence was found between the motions of the flare loops and the quasi-periodic oscillations. We conclude that an oscillation with a high modulation depth for a period of about four minutes cannot be easily explained with the existing mechanisms.     

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.

     

The interpretation of hard X-ray polarization measurements in solar flares

We review recent observations of polarization of moderately hard X-rays in solar flares and compare them with the predictions of recent detailed modeling of hard X-ray bremsstrahlung production by non-thermal electrons. We find that the recent advances in the complexity of the modeling lead to substantially lower predicted polarizations than in earlier models and more fully highlight how various parameters play a role in determining the polarization of the radiation field. The new predicted polarizations are comparable to those predicted by thermal modeling of solar flare hard X-ray production, and both are in agreement with the observations. In the light of these results, we propose new polarization observations with current generation instruments which could be used to discriminate between non-thermal and thermal models of hard X-ray production in solar flares.     

Nonthermal electrons in the thick-target reverse-current model for hard X-ray bremsstrahlung

The behaviour of the accelerated electrons escaping from a high-temperature source of primary energy in a solar flare is investigated. The direct current of fast electrons is supposed to be balanced by the reverse current of thermal electrons in the ambient colder plasma inside flare loops. The self-consistent kinetic problem is formulated; and the reverse-current electric field and the fast electron distribution function are found from its solution. The X-ray bremsstrahlung polarization is then calculated from the distribution function. The difference of results from those in the case of thermal runaway electrons (Diakonov and Somov, 1988) is discussed. The solutions with and without account of the affect of a reverse-current electric field are also compared.     

First phase acceleration mechanisms and implications for hard X-ray burst models in solar flares

Requirements for the number of nonthermal electrons which must be accelerated in the impulsive phase of a flare are reviewed. These are uncertain by two orders of magnitude depending on whether hard X-rays above 25 keV are produced primarily by hot thermal electrons which contain a small fraction of the flare energy or by nonthermal streaming electrons which contain > 50% of the flare energy. Possible acceleration mechanisms are considered to see to what extent either X-ray production scenario can be considered viable. Direct electric field acceleration is shown to involve significant heating. In addition, candidate primary energy release mechanisms to convert stored magnetic energy into flare energy, steady reconnection and the tearing mode instability, transfer at least half of the stored energy into heat and most of the remaining energy to ions. Acceleration by electron plasma waves requires that the waves be driven to large amplitude by electrons with large streaming velocities or by anisotropic ion-acoustic waves which also require streaming electrons for their production. These in turn can only come from direct electric field acceleration since it is shown that ion-acoustic waves excited by the primary current cannot amplify electron plasma waves. Thus, wave acceleration is subject to the same limitations as direct electric field acceleration. It is concluded that at most 0.1% of the flare energy can be deposited into nonthermal streaming electrons with the energy conversion mechanisms as they have been proposed and known acceleration mechanisms. Thus, hard X-ray production above 10 keV primarily by hot thermal electrons is the only choice compatible with models for the primary energy release as they presently exist.     

MICROWAVE EMISSION FROM CORONAL HEIGHTS: STUDY OF A NON-THERMAL RADIO FLARE

Two small radio flares following the great gamma-ray burst on 11 June 1991 are studied. We analyse the different association of emission features at microwaves, decimeter waves, and soft and hard X-rays for the events. The first flare has well-defined emission features in microwaves and soft and hard X-rays, and a faint decimetric signature well after the hard X-ray burst. It is not certain if the decimetric event is connected to the burst features. The second event is characterized by an almost simultaneous appearance of hard X-ray burst maxima and decimetric narrowband drift bursts, but soft X-ray emission is missing from the event. With the exception of the possibility that the soft X-ray emission is absorbed along the way, the following models can explain the reported differences in the second event: (1) Microwave emission in the second event is produced by 150 keV electrons spiraling in the magnetic field relatively low in the corona, while the hard X-ray emission is produced at the beginning of the burst near the loop top as thick-target emission. If the bulk of electrons entered the loop, the low-energy electrons would not be effectively mirrored and would eventually hit the footpoints and cause soft X-ray emission by evaporation, which was not observed. The collisions at the loop top would not produce observable plasma heating. The observed decimetric type III bursts could be created by plasma oscillations caused by electron beams traveling along the magnetic field lines at low coronal heights. (2) Microwave emission is caused by electrons with MeV energies trapped in the large magnetic loops, and the electrons are effectively mirrored from the loop footpoints. The hard X-ray emission can come both from the loop top and the loop footpoints as the accelerated lower energy electrons are not mirrored. The low-energy electrons are not, however, sufficient to create observable soft X-ray emission. The type III emission in this case could be formed either at low coronal heights or in local thick regions in the large loops, high in the corona.     

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.     

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.     

Comptonization and QPO origins in accreting neutron star systems

We develop a simple, time-dependent Comptonization model to probe the origins of spectral variability in accreting neutron star systems. In the model, soft 'seed photons' are injected into a corona of hot electrons, where they are Compton upscattered before escaping as hard X-rays. The model describes how the hard X-ray spectrum varies when the properties of either the soft photon source or the Comptonizing medium undergo small oscillations. Observations of the resulting spectral modulations can determine whether the variability is due to (i) oscillations in the injection of seed photons, (ii) oscillations in the coronal electron density, or (iii) oscillations in the coronal energy dissipation rate. Identifying the origin of spectral variability should help clarify how the corona operates and its relation to the accretion disc. It will also help in finding the mechanisms underlying the various quasi-periodic oscillations (QPOs) observed in the X-ray outputs of many accreting neutron star and black hole systems. As a sample application of our model, we analyse a kilohertz QPO observed in the atoll source 4U 1608–52. We find that the QPO is driven predominantly by an oscillation in the electron density of the Comptonizing gas.