Microwave diagnostics of energetic electrons in flares

Electrons accelerated during solar flares are revealed by their electromagnetic radiation in different spectral ranges, emitted at different heights in the solar atmosphere. The observational analysis points to a common and continuous injection of particles. Based on this result, a quantitative investigation of the hard X-ray and microwave emissions observed during the 29 June, 1980 flare at 11: 40 UT has been performed. This is the first modelisation that takes into account both the inhomogeneity of the microwave source region and the dynamical evolution of the electron population. First results of our model computations demonstrate that during the most energetic phase of the event both hard X-rays and microwaves are described by electron populations resulting from the same injection function, and that the total numbers of electrons required for both emissions are compatible. Account for the inhomogeneity of the microwave source is shown to be a necessary condition for the interpretation of observed spectra.Proceedings of the Workshop on Radio Continua during Solar Flares, held at Duino (Trieste), Italy, 27–31 May, 1985.     

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.

     

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.     

Can observed hard X-ray and microwave flux from solar flares be explained by a single electron population?

In attempting to explain observed hard X-ray and microwave flux from solar flares by a single population of energetic electrons, one has met a serious discrepancy of the order of 10³–10⁵ between the calculated and observed microwave flux. In this paper it is shown that this discrepancy can be removed for impulsive flares by the assumption of a precipitation model for both X-ray and microwave sources and that the magnetic field of 500–1000 G is required in the microwave emitting region. The precipitation model is consistent with the rapid time variation exhibited in both hard X-rays and microwaves.Proceedings of the Workshop on Radio Continua during Solar Flares, held at Duino (Trieste), Italy, 27–31 May, 1985.     

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.     

The deduction of energy spectra of non-thermal electrons in flares from the observed dynamic spectra of hard X-ray bursts

The derivation of dynamic spectra of high energy electrons in flares from high resolution hard X-ray observations is considered. It is shown that the Bethe-Heitler formula for the electronproton bremsstrahlung cross-section over the 20–100 keV range of energies admits of a general analytic solution for the electron spectrum in terms of the X-ray spectrum, in a form convenient for computation. The bearing of this analysis on different models of flare conditions is considered. In examining the hypothesis that the X-rays are produced in regions of high ambient density, the duration of the burst being governed by modulation of the electron source rather than by the decay of trapped electrons injected impulsively, it is emphasised that the energy spectrum of the electrons at their source is different from their effective spectrum in the X-ray emitting region. This spectrum, at the source, is found to be much steeper than that in the X-ray region which means that the entire energy of the flare could reside in the injected electrons.     

High-Energy Emission from a Solar Flare in Hard X-rays and Microwaves

We investigate accelerated electron energy spectra for different sources in a large flare using simultaneous observations obtained with two instruments, the Nobeyama Radio Heliograph (NoRH) at 17 and 34 GHz, and the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) at hard X-rays. This flare is one of the few in which emission up to energies exceeding 200 keV can be imaged in hard X-rays. Furthermore, we can investigate the spectra of individual sources up to this energy. We discuss and compare the HXR and microwave spectra and morphology. Although the event overall appears to correspond to the standard scenario with magnetic reconnection under an eruptive filament, several of its features do not seem to be consistent with popular flare models. In particular we find that (1) microwave emissions might be optically thick at high frequencies despite a low peak frequency in the total flux radio spectrum, presumably due to the inhomogeneity of the emitting source; (2) magnetic fields in high-frequency radio sources might be stronger than sometimes assumed; (3) sources spread over a very large volume can show matching evolution in their hard X-ray spectra that may provide a challenge to acceleration models. Our results emphasize the importance of studies of sunspot-associated flares and total flux measurements of radio bursts in the millimeter range.     

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.     

Expansion of chromospheric matter in the gradual phase of solar flares

Interferometric radio observations together with soft X-ray observations are presented here to show that during the growth phase of soft X-ray flares, a large mass increase occurs simultaneously with the creation of an X-ray hot region in the corona. The lack of an increase of radio flux from pre-flare active regions absolutely excludes the possibility of the coronal accumulation of low-temperature matter just prior to flare onset. Therefore we suggest a hypothesis that a large amount of hot matter, which contains almost the entire energy in the flare, is supplied from the chromosphere into the corona during each flare. Since even small flares produce coronal hot regions radiating thermal soft X-rays and microwaves, the formation of the hot region may be a basic process in most flares. Energy, created by some instability in the corona, travels by thermal conduction to the chromosphere where the dense matter is heated and subsequently expands into the corona, producing the observed hot region. Impulsive heating of the chromosphere by nonthermal electrons which simultaneously emit hard X-rays is not sufficient to be the energy source in our model. Slower heating, which supplies the flare more energy than that supplied in the impulsive phase, is required. If the temperature of the energy source in the corona exceeds 2 × 10⁷ K, the conductive energy flux becomes sufficient to exceed the radiation loss from the chromosphere-corona transition region. This excess energy may cause the chromospheric gas expansion.     

The relation of energetic solar X-rays (hν>60 keV) and high frequency microwaves deduced from the periodic bursts of August 8, 1968 flare

Correlated sixteen-second periodic bursts were observed during the flash phase of a class 2b solar flare in energetic X-rays, microwaves, and EUV ionizing radiation. The observations of the periodic structures in the various X-ray energy channels indicate that the structures are predominantly a phenomenon of high energy electrons, E>80 keV. In view of the fact that the periodic X-ray structures were correlated extensively in microwave and EUV frequencies, a plausible conclusion is that these three types of radiation have a common energy source. The acceleration of the energetic electrons must occur deep in the chromosphere where there are sufficient solar constituents that can be ionized to produce the correlated periodic EUV radiation.     

Relative timing of hard X-rays and radio emissions during the different phases of solar flares: Consequences for the electron acceleration

Observations relevant to the relative timing of hard X-ray, microwave and lower frequency radio bursts in different phases of flare are reviewed. It is shown that such timing comparisons give important information concerning the electron acceleration/injection process, the magnetic field topology at the acceleration site and the flare development itself. In particular it is shown that acceleration begins before the flash phase of flares and that it keeps going on continuously during the entire duration of a flare. Moreover, despite their wide separation in altitude, hard X-ray, microwave and lower frequency sources appear to arise from a common injection of electrons going on continuously through the different phases of flare. In situ acceleration by shock waves giving rise to type II radio emission is briefly discussed. As an alternative interactions between small and large scale magnetic structures is proposed.Proceedings of the Workshop on Radio Continua during Solar Flares, held at Duino (Trieste), Italy, 27–31 May, 1985.     

Evidence that Synchrotron Emission from Nonthermal Electrons Produces the Increasing Submillimeter Spectral Component in Solar Flares

We investigate the origin of the increasing spectra observed at submillimeter wavelengths detected in the flare on 2 November 2003 starting at 17:17 UT. This flare, classified as an X8.3 and 2B event, was simultaneously detected by RHESSI and the Solar Submillimeter Telescope (SST) at 212 and 405 GHz. Comparison of the time profiles at various wavelengths shows that the submillimeter emission resembles that of the high-energy X rays observed by RHESSI whereas the microwaves observed by the Owens Valley Solar Array (OVSA) resemble that of ∼50 keV X rays. Moreover, the centroid position of the submillimeter radiation is seen to originate within the same flaring loops of the ultraviolet and X-ray sources. Nevertheless, the submillimeter spectra are distinct from the usual microwave spectra, appearing to be a distinct spectral component with peak frequency in the THz range. Three possibilities to explain this increasing radio spectra are discussed: (1) gyrosynchrotron radiation from accelerated electrons, (2) bremsstrahlung from thermal electrons, and (3) gyrosynchrotron emission from the positrons produced by pion or radioactive decay after nuclear interactions. The latter possibility is ruled out on the grounds that to explain the submillimeter observations requires 3000 to 2×10⁵ more positrons than what is inferred from X-ray and γ-ray observations. It is possible to model the emission as thermal; however, such sources would produce too much flux in the ultraviolet and soft X-ray wavelengths. Nevertheless we are able to explain both spectral components at microwave and submillimeter wavelengths by gyrosynchrotron emission from the same population of accelerated electrons that emit hard X rays and γ rays. We find that the same 5×10³⁵ electrons inferred from RHESSI observations are responsible for the compact submillimeter source (0.5 arcsec in radius) in a region of 4500 G low in the atmosphere, and for the traditional microwave spectral component by a more extended source (50 arcsec) in a 480 G magnetic field located higher up in the loops. The extreme values in magnetic field and source size required to account for the submillimeter emission can be relaxed if anisotropy and transport of the electrons are taken into account.     

Images of Gradual Millimeter Emission and Multi-Wavelength Observations of the 17 august 1994 Solar Flare

We present a comprehensive analysis of the 17 August 1994 flare, the first flare imaged at millimeter (86 GHz) wavelengths. The temporal evolution of this flare displays a prominent impulsive peak shortly after 01:02 UT, observed in hard X-rays and at microwave frequencies, followed by a gradual decay phase. The gradual phase was also detected at 86 GHz. Soft X-ray images show a compact emitting region (20), which is resolved into two sources: a footpoint and a loop top source. Nonthermal emissions at microwave and hard X-ray wavelengths are analyzed and the accelerated electron spectrum is calculated. This energy spectrum derived from the microwave and hard X-ray observations suggests that these emissions were created by the same electron population. The millimeter emission during the gradual phase is thermal bremsstrahlung originating mostly from the top of the flaring loop. The soft X-rays and the millimeter flux density from the footpoint source are only consistent with the presence of a multi-temperature plasma at the footpoint.     

On the origin of subsecond pulses at 17 GHz

We have analyzed three flare events with subsecond structures in hard X-rays (CGRO/ BATSE) and 17 GHz data (Nobeyama radioheliograph). It was shown that microwave subsecond brightenings (SSB) were generated by directly precipitating electrons with energy of 100–200 keV from tiny regions close to footpoints. In two events, when high correlation between microwaves and X-rays was observed, the SSB can be interpreted in terms of gyrosynchrotron emission. Plasma emission seems to be a more credible explanation of the spontaneous pulses in the event when poor correlation with X-rays was observed.     

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.     

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.     

Observation of the impulsive phase of a simple flare

We present a broad range of complementary observations of the onset and impulsive phase of a fairly large (1B, M1.2) but simple two-ribbon flare. The observations consist of hard X-ray flux measured by the SMM HXRBS, high-sensitivity measurements of microwave flux at 22 GHz from Itapetinga Radio Observatory, sequences of spectroheliograms in UV emission lines from Ov (T ≈ 2 × 10⁵ K) and Fexxi (T ≈ 1 × 10⁷ K) from the SMM UVSP, Hα and Hei D₃ cine-filtergrams from Big Bear Solar Observatory, and a magnetogram of the flare region from the MSFC Solar Observatory. From these data we conclude:

1. The overall magnetic field configuration in which the flare occurred was a fairly simple, closed arch containing nonpotential substructure.
2. The flare occurred spontaneously within the arch; it was not triggered by emerging magnetic flux.
3. The impulsive energy release occurred in two major spikes. The second spike took place within the flare arch heated in the first spike, but was concentrated on a different subset of field lines. The ratio of Ov emission to hard X-ray emission decreased by at least a factor of 2 from the first spike to the second, probably because the plasma density in the flare arch had increased by chromospheric evaporation.
4. The impulsive energy release most likely occurred in the upper part of the arch; it had three immediate products:

1. An increase in the plasma pressure throughout the flare arch of at least a factor of 10. This is required because the Fexxi emission was confined to the feet of the flare arch for at least the first minute of the impulsive phase.
2. Nonthermal energetic (～ 25 keV) electrons which impacted the feet of the arch to produce the hard X-ray burst and impulsive brightening in Ov and D₃. The evidence for this is the simultaneity, within ± 2 s, of the peak Ov and hard X-ray emissions.
3. Another population of high-energy (～100keV) electrons (decoupled from the population that produced the hard X-rays) that produced the impulsive microwave emission at 22 GHz. This conclusion is drawn because the microwave peak was 6 ± 3 s later than the hard X-ray peak.

     

Initial phase of chromospheric evaporation in a solar flare

In this paper we discuss the initial phase of chromospheric evaporation during a solar flare observed with instruments on the Solar Maximum Mission on May 21, 1980 at 20:53 UT. Images of the flaring region taken with the Hard X-Ray Imaging Spectrometer in the energy bands from 3.5 to 8 keV and from 16 to 30 keV show that early in the event both the soft and hard X-ray emissions are localized near the footpoints, while they are weaker from the rest of the flaring loop system. This implies that there is no evidence for heating taking place at the top of the loops, but energy is deposited mainly at their base. The spectral analysis of the soft X-ray emission detected with the Bent Crystal Spectrometer evidences an initial phase of the flare, before the impulsive increase in hard X-ray emission, during which most of the thermal plasma at 10⁷ K was moving toward the observer with a mean velocity of about 80 km s^-1. At this time the plasma was highly turbulent. In a second phase, in coincidence with the impulsive rise in hard X-ray emission during the major burst, high-velocity (370 km s^-1) upward motions were observed. At this time, soft X-rays were still predominantly emitted near the loop footpoints. The energy deposition in the chromosphere by electrons accelerated in the flare region to energies above 25 keV, at the onset of the high-velocity upflows, was of the order of 4 × 10¹⁰ erg s^-1 cm^-2. These observations provide further support for interpreting the plasma upflows as the mechanism responsible for the formation of the soft X-ray flare, identified with chromospheric evaporation. Early in the flare soft X-rays are mainly from evaporating material close to the footpoints, while the magnetically confined coronal region is at lower density. The site where upflows originate is identified with the base of the loop system. Moreover, we can conclude that evaporation occurred in two regimes: an initial slow evaporation, observed as a motion of most of the thermal plasma, followed by a high-speed evaporation lasting as long as the soft X-ray emission of the flare was increasing, that is as long as plasma accumulation was observed in corona.     

Solar Impulsive Hard X-Ray Emission and Two-Stage Electron Acceleration

Heating and acceleration of electrons in solar impulsive hard X-ray (HXR) flares are studied according to the two-stage acceleration model developed by Zhang for solar 3He-rich events. It is shown that electrostatic H-cyclotron waves can be excited at a parallel phase velocity less than about the electron thermal velocity and thus can significantly heat the electrons (up to 40 MK) through Landau resonance. The preheated electrons with velocities above a threshold are further accelerated to high energies in the flare-acceleration process. The flare-produced electron spectrum is obtained and shown to be thermal at low energies and power law at high energies. In the non-thermal energy range, the spectrum can be double power law if the spectral power index is energy dependent or related. The electron energy spectrum obtained by this study agrees quantitatively with the result derived from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) HXR observations in the flare of 2002 July 23. The total flux and energy flux of electrons accelerated in the solar flare also agree with the measurements.     

A Burst with Double Radio Spectrum Observed up to 212 GHz

We study a solar flare that occurred on 10 September 2002, in active region NOAA 10105, starting around 14:52 UT and lasting approximately 5 minutes in the radio range. The event was classified as M2.9 in X-rays and 1N in Hα. Solar Submillimeter Telescope observations, in addition to microwave data, give a good spectral coverage between 1.415 and 212 GHz. We combine these data with ultraviolet images, hard and soft X-ray observations, and full-disk magnetograms. Images obtained from Ramaty High Energy Solar Spectroscopic Imager data are used to identify the locations of X-ray sources at different energies, and to determine the X-ray spectrum, while ultraviolet images allow us to characterize the coronal flaring region. The magnetic field evolution of the active region is analyzed using Michelson Doppler Imager magnetograms. The burst is detected at all available radio frequencies. X-ray images (between 12 keV and 300 keV) reveal two compact sources. In the 212 GHz data, which are used to estimate the radio-source position, a single compact source is seen, displaced by 25″ from one of the hard X-ray footpoints. We model the radio spectra using two homogeneous sources, and we combine this analysis with that of hard X-rays to understand the dynamics of the accelerated particles. Relativistic particles, observed at radio wavelengths above 50 GHz, have an electron index evolving with the typical soft–hard–soft behavior.