Multi-Wavelength Analysis of High-Energy Electrons in Solar Flares: A Case Study of the August 20, 2002 Flare

A multi-wavelength spatial and temporal analysis of solar high-energy electrons is conducted using the August 20, 2002 flare of an unusually flat (γ₁ = 1.8) hard X-ray spectrum. The flare is studied using RHESSI, Hα, radio, TRACE, and MDI observations with advanced methods and techniques never previously applied in the solar flare context. A new method to account for X-ray Compton backscattering in the photosphere (photospheric albedo) has been used to deduce the primary X-ray flare spectra. The mean electron flux distribution has been analysed using both forward fitting and model-independent inversion methods of spectral analysis. We show that the contribution of the photospheric albedo to the photon spectrum modifies the calculated mean electron flux distribution, mainly at energies below ∼100 keV. The positions of the Hα emission and hard X-ray sources with respect to the current-free extrapolation of the MDI photospheric magnetic field and the characteristics of the radio emission provide evidence of the closed geometry of the magnetic field structure and the flare process in low altitude magnetic loops. In agreement with the predictions of some solar flare models, the hard X-ray sources are located on the external edges of the Hα emission and show chromospheric plasma heated by the non-thermal electrons. The fast changes of Hα intensities are located not only inside the hard X-ray sources, as expected if they are the signatures of the chromospheric response to the electron bombardment, but also away from them.     

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.     

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.     

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.     

Reconnection of a Kinking Flux Rope Triggering the Ejection of a Microwave and Hard X-ray Source I. Observations and Interpretation

Imaging microwave observations of an eruptive, partially occulted solar flare on 18 April 2001 suggest that the global structure of the event can be described by the helical kink instability of a twisted magnetic flux rope. This model is suggested by the inverse gamma shape of the source exhibiting crossing legs of a rising flux loop and by evidence that the legs interact at or near the crossing point. The interaction is reflected by the location of peak brightness near the crossing point and by the formation of superimposed compact nonthermal sources most likely at or near the crossing point. These sources propagate upward along both legs, merge into a single, bright source at the top of the structure, and continue to rise at a velocity >1000 km s⁻¹. The compact sources trap accelerated electrons which radiate in the radio and hard X-ray ranges. This suggests that they are plasmoids, although their internal structure is not revealed by the data. They exhibit variations of the radio brightness temperature at a characteristic time scale of ∼ 40 s, anti-correlated to their area, which also support their interpretation as plasmoids. Their propagation path differs from the standard scenario of plasmoid formation and propagation in the flare current sheet, suggesting the helical current sheet formed by the instability instead.     

The dependence of solar hard X-ray burst intensity on magnetic field strength

The measurements of peak intensities of hard X-ray bursts from hot flare plasma electrons as a function of peak frequency of associated microwave radio bursts are discussed. The latter is proportional to the magnetic field strength. The results suggest that the flare hard X-rays are emitted when the electron plasma frequency is comparable to the electron gyrofrequency. Thus, the hard X-ray peak intensity varies as B ^4.2, where B is the magnetic field strength.On leave from the Geophysical Institute, Slovak Academy of Sciences, 947 01 Hurbanovo, Czechoslovakia.Deceased 22 July, 1986.     

A study of RATAN-600 observations of solar S-component sources

A sample of 36 S-component sources observed by the radio telescope RATAN-600 was compared with calculations of gyromagnetic emission and bremsstrahlung based on recent sunspot models. The diagnostic possibilities of the spectral distributions in the radio flux, the degree of polarization, and the source sizes for the estimation of magnetic scale heights and other source parameters were checked by different methods.Depending on the magnetic field structure, the observations show different types of polarization spectra. Most regular spectra and highest values of the degree of polarization were observed from sources above the leading part of the associated spot group. Magnetic scale heights were found to be intrinsically associated with the source size of the gyromagnetic emission.The flare production rate of active regions appears to be related to their S-component flux and magnetic scale heights.     

Broadband Radio Bursts and Fine Structures during the Great Solar Event on 14 July 2000

25 MHz–7.6 GHz global and detailed (fine structure – FS) radio spectra are presented, which were observed in the NOAA 9077 active region for the Bastille Day (14 July 2000) flare at 10:10–11:00 UT. Besides broadband radio bursts, high-resolution dynamic spectra reveal metric type II burst, decimetric type IV burst and various decimetric and microwave FSs, such as type III bursts, type U bursts, reverse-slope (RS)-drifting burst, fiber bursts, patch and drifting pulsation structure (DPS). The peak-flux-density spectrum of the radio bursts over the range 1.0–7.6 GHz globally appears as a U-shaped signature. Analyzing the features of backbone and herringbones of the type II burst, the speeds of shock and relevant energetic electron beams were estimated to be 1100 km s⁻¹ and 58 500 km s⁻¹, respectively. Also the time sequence of the radio emission is analyzed by comparing with the hard X-rays (HXRs) and the soft X-rays (SXRs) in this flare. After the maxima of the X-rays, the radio emission in the range 1.0–7.6 GHz reached maxima first at the higher frequency, then drifted to the lower frequency. This comparison suggested that the flare included three successive processes: firstly the X-rays rose and reached maxima at 10:10–10:23 UT, accompanied by fine structures only in the range 2.6–7.6 GHz; secondly the microwave radio emission reached maxima accompanied by many fine structures over the range 1.0–7.6 GHz at 10:23–10:34 UT; then a decimetric type IV burst and its associated FSs (fibers) in the range 1.0–2.0 GHz appeared after 10:40 UT.     

Multiple-loop structure of a solar flare from Microwave,EUV and X-ray Imaging Data

We present the results of an analysis of a flare event of importance M2.8 that occurred at 00:56 UT 28 August 1999. The analysis is based upon observations made with the Nobeyama radioheliograph (NoRH) and polarimeters (NoRP), TRACE, SOHO/MDI, EIT, and Yohkoh/SXT. The images show a very complex flaring region. Pre-flare TRACE and EIT images at 00:24 UT show a small brightening in the region before the flare occurred. The active region in which the flare occurred had evolving magnetic fields, and new magnetic flux seems to have emerged. The X-ray and radio time profiles for this event show a double-peaked structure. The polarimeter data showed that the maximum radio emission (1200 s.f.u.) occurred at 9.4 GHz. At 17 GHz the NoRH images appear to show four different radio sources including the main spot and the main flare loop. Most of the microwave emission seems to originate from the main flare loop. Comparison of BATSE and microwave time profiles at 17 and 34 GHz from the main sunspot source shows that these profiles have similar structures and they coincide with the hard X-ray peaks. The maximum of the flare loop emission was delayed by 10 s relative to the second maximum of the sunspot associated flare emission. Analysis of SXT images during the post-flare phase shows a complex morphology – several intersecting loops and changes in the shape of the main flare loop.     

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.     

Microwave Neutral Line Associated Source and a Current Sheet

Neutral Line associated Sources (NLSs) are quasi-stationary microwave sources projected onto vicinities of the neutral line of the photospheric magnetic field. NLSs are often precursors of powerful flares, but their nature is unclear. We endeavor to reveal the structure of an NLS and to analyze a physical connection between such a source with a site of energy release in the corona above NOAA 10488 (October/November 2003). Evolution of this AR includes emergence and collision of two bipolar magnetic structures, rise of the main magnetic separator, and the appearance of an NLS underneath. The NLS appears at a contact site of colliding sunspots, whose relative motion goes on, resulting in a large shear along a tangent. Then the nascent NLS becomes the main source of microwave fluctuations in the AR. The NLS emission at 17 GHz is dominated by either footpoints or the top of a loop-like structure, an NLS loop, which connects two colliding sunspots. During a considerable amount of time, the emission dominates over that footpoint of the NLS loop, where the magnetic field is stronger. At that time, the NLS resembles a usual sunspot–associated radio source, whose brightness center is displaced towards the periphery of a sunspot. Microwave emission of an X2.7 flare is mainly concentrated in an ascending flare loop, initially coinciding with the NLS loop. The top of this loop is located at the base of a non-uniform bar-like structure visible in soft X-rays and at 34 GHz at the flare onset. We reveal i) upward lengthening of this bar before the flare onset, ii) the motion of the top of an apparently ascending flare loop along the axis of this bar, and iii) a non-thermal microwave source, whose descent along the bar was associated with the launching of a coronal ejection. We connect the bar with a probable position of a nearly vertical diffusion region, a site of maximal energy release inside an extended pre-flare current sheet. The top of the NLS loop is located at the bottom of this region. A combination of the NLS loop and diffusion region constitutes the skeleton of a quasi-stationary microwave NLS.     

Repeated Flaring from Loop–Loop Interaction

A series of solar flares was observed near the same location in NOAA active region 8996 on 18–20 May 2000. A detailed analysis of one of these flares is presented where the emitting structures in soft and hard X-rays, EUV, H, and radio at centimeter wavelengths are compared. Hard X-rays and radio emission were observed at two separate loop footpoints, while soft X-rays and EUV emission were observed mainly above the nearby positive polarity region. The flare was confined although the observed type III bursts at the time of the flare maximum indicate that some field lines were open to the corona. No flux emergence was evident but moving magnetic features were observed around the sunspot region and within the positive polarity (plage) region. We suggest that the flaring was due to loop–loop interactions over the positive polarity region, where accelerated electrons gained access to the two separate loop systems. The repeated radio flaring at the footpoint of one loop was visible because of the strong magnetic fields near the large sunspot region while at the footpoint of the other loop the electrons could precipitate and emit in hard X-rays. The simultaneous emission and fluctuations in radio and X-rays – in two different loop ends – further support the idea of a single acceleration site at the loop intersection.     

Timing analysis of hard X-ray emission and 22 GHz flux and polarization in a solar burst

A solar flare occurring on 26 February, 1981 at 19:32 UT was observed simultaneously in hard X-rays and microwaves with a time resolution of a fraction of a second. The X-ray observations were made with the Hard X-ray Monitor on Hinotori, and the microwave observations were made at 22 GHz with the 13.7 m Itapetinga mm-wave antenna. Timing accuracy was restricted to 62.5 ms, the best time resolution obtained in hard X-rays for this burst. We find that: (a) all 22 GHz flux structures were delayed by 0.2–0.9 s relative to similar structures in hard X-rays throughout the burst duration; (b) different burst structures showed different delays, suggesting that they are independent of each other; (c) the time structures of the degree of polarization at 22 GHz precede the total microwave flux time structures by 0.1–0.5 s; (d) The time evolutions of time delays of microwaves with respect to hard X-rays and also the degree of microwave polarization show fluctuations with are not clearly related to any other time structures. If we take mean values for the 32 s burst duration, we find that hard X-ray emission precedes the degree of microwave polarization by 450 ms, which in turn precedes the total microwave flux by 110 ms.     

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.     

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.     

Radio, Hard X-Ray, EUV and Optical Study of September 9, 2002 Solar Flare

The multi-wavelength analysis is performed on a flare on September 9, 2002 with data of Owens Valley Solar Arrays (OVSA), Big Bear Solar Observatory (BBSO), Ramaty High Energy Solar Spectroscopic Imager (RHESSI), and Extreme UV Imager Telescope (EIT), and The Michelson Doppler Imager (MDI) on board of the Solar and Heliospheric Observatory (SOHO). The radio sources at 4.8 and 6.2 GHz located in the intersection of two flaring loops at 195 of SOHO/EIT respectively with two dipole magnetic fields of SOHO/MDI, in which one EIT loop was coincident with an X-ray loop of RHESSI at 12–25 keV, and two H_αbright kernels a1 and a2 of BBSO, respectively at the two footpoints of this loop; the second EIT loop connected another two H_αkernels b1 and b2 and radio sources at 7.8 and 8.2 GHz of OVSA. The maximum phase of microwave bursts was evidently later than that of hard X-ray bursts and H_αkernels a1 and a2, but consistent with that of H_αkernels b1 and b2. Moreover, the flare may be triggered by the interaction of the two flaring loops, which is suggested by the cross-correlation of radio, optical, and X-ray light curves of a common quasi-periodic oscillation in the rising phase, as well as two peaks at about 7 and 9 GHz of the microwave spectra at the peak times of the oscillation, while the bi-directional time delays at two reversal frequencies respectively at 7.8 and 9.4 GHz (similar to the peak frequencies of the microwave spectra) may indicate two reconnection sites at different coronal levels. The microwave and hard X-ray footpoint sources located in different EUV and optical loops may be explained by different magnetic field strength and the pitch angle distribution of nonthermal electrons in these two loops.     

Flare SOL2012-07-06: On the Origin of the Circular Polarization Reversal Between 17 GHz and 34 GHz

The new generation of multiwavelength radioheliographs with high spatial resolution will employ microwave imaging spectropolarimetry to recover flare topology and plasma parameters in the flare sources and along the wave propagation paths. The recorded polarization depends on the emission mechanism and emission regime (optically thick or thin), the emitting particle properties, and propagation effects. Here, we report an unusual flare, SOL2012-07-06T01:37, whose optically thin gyrosynchrotron emission of the main source displays an apparently ordinary mode sense of polarization in contrast to the classical theory that favors the extraordinary mode. This flare produced copious nonthermal emission in hard X-rays and in high-frequency microwaves up to 80 GHz. It is found that the main flare source corresponds to an interaction site of two loops with greatly different sizes. The flare occurred in the central part of the solar disk, which allows reconstructing the magnetic field in the flare region using vector magnetogram data. We have investigated the three possible known reasons of the circular polarization sense reversal – mode coupling, positron contribution, and the effect of beamed angular distribution. We excluded polarization reversal due to contribution of positrons because there was no relevant response in the X-ray emission. We find that a beam-like electron distribution can produce the observed polarization behavior, but the source thermal density must be much higher than the estimate from to the X-ray data. We conclude that the apparent ordinary wave emission in the optically thin mode is due to radio wave propagation across the quasi-transverse (QT) layer. The abnormally high transition frequency (above 35 GHz) can be achieved reasonably low in the corona where the magnetic field value is high and transverse to the line of sight. This places the microwave source below this QT layer, i.e. very low in the corona.     

A classification of the X-ray and radio states of Cyg X-3 and their long-term correlations

We present a detailed classification of the X-ray states of Cyg X-3 based on the spectral shape and a new classification of the radio states based on the long-term correlated behaviour of the radio and soft X-ray light curves. We find a sequence of correlations, starting with a positive correlation between the radio and soft X-ray fluxes in the hard spectral state, changing to a negative one at the transition to soft spectral states. The temporal evolution can be in either direction on that sequence, unless the source goes into a very weak radio state, from which it can return only following a major radio flare. The flare decline is via relatively bright radio states, which results in a hysteresis loop on the flux–flux diagram. We also study the hard X-ray light curve, and find its overall anticorrelation with the soft X-rays. During major radio flares, the radio flux responds exponentially to the level of a hard X-ray high-energy tail. We also specify the detailed correspondence between the radio states and the X-ray spectral states. We compare our results to those of black hole and neutron star binaries. Except for the effect of strong absorption and the energy of the high-energy break in the hard state, the X-ray spectral states of Cyg X-3 closely correspond to the canonical X-ray states of black hole binaries. Also, the radio/X-ray correlation closely corresponds to that found in black hole binaries, but it significantly differs from that in neutron star binaries. Overall, our results strongly support the presence of a black hole in Cyg X-3.     

Hydrodynamic response of the solar chromosphere to an elementary flare burst

Impulsive heating of the upper chromosphere by a very powerful thermal flux is studied as the cause of hard X-rays during a solar flare. The electron temperature at the boundary between the corona and chromosphere is assumed to change in accordance with the hard X-ray intensity in an elementary flare burst (EFB). A maximum value of about 10⁸ K is reached after 5 s, after which the boundary temperature decreases. These high-temperature changes lead to fast propagation of heat into the chromosphere. Numerical solution of the hydrodynamic equations, which take into account all essential dissipative processes, shows that classical heat conduction is not valid due to heat flux saturation in the case of impulsive heating from a high-temperature source. The saturation effect and hydrodynamic flow along a magnetic field lead to electron temperature and density distributions such that the thermal X-ray spectrum of a high-temperature plasma can be well enough approximated by an exponential law or by two power-law spectra. According to this dissipative thermal model for the source of hard X-rays, the emission measure of the high-temperature plasma increases monotonously during the whole EFB even after the temperature maximum. Some results for the low-temperature region are discussed in connection with short-lived chromospheric bright points.