Energy Of Non-thermal Electrons Research Articles

Power conversion factor in solar flares

With RHESSI data from five solar flares taken from beginning to end, we investigate the power conversion factor µ defined as the ratio of the time derivative of total thermal energy (ERHESSI + Erad + Econd) and the kinetic power (PRHESSI) of nonthermal electrons. Here, ERHESSI is the computed energy contained in thermal plasmas traced by RHESSI SXRs. Other two contributions (Erad and Econd) to the total energy are the energies lost through radiation and conduction, both of which can be derived from the observational data. If both are not considered, µ is only positive before the SXR maximum. However, we find that for each flare studied µ is positive over the whole duration of the soalr flare after taking into account both radiation and conduction. Mean values for µ range from 11.7% to 34.6% for these five events, indicating roughly that about this fraction of the known energy in nonthermal electrons is efficiently transformed into thermal energy from start to end. This fraction is traced by RHESSI SXR observations; the rest is lost. The bulk of the nonthermal energy could heat the plasma low in the atmosphere to drive mass flows (i.e. chromospheric evaporation).

Wave-particle interactions in non-uniform plasma and the interpretation of hard X-ray spectra in solar flares

Context. High energy electrons accelerated during solar flare are abundant in the solar corona and in the interplanetary space. Commonly, the number and the energy of non-thermal electrons at the Sun is estimated using hard X-ray (HXR) spectral observations (e.g. RHESSI) and a single-particle collisional approximation. Aims. To investigate the role of the spectrally evolving Langmuir turbulence on the population of energetic electrons in the solar corona. Methods. We numerically simulate the relaxation of a power-law non-thermal electron population in a collisional inhomogeneous plasma including wave-particle, and wave-wave interactions. Results. The numerical simulations show that the long-time evolution of electron population above 20 keV deviates substantially from the collisional approximation when wave-particle interactions in non-uniform plasma are taken into account. The evolution of Langmuir wave spectrum towards smaller wavenumbers, due to large-scale density fluctuations and wave-wave interactions, leads to an effective acceleration of electrons. Furthermore, the time-integrated spectrum of non-thermal electrons, which is normally observed with HXR above 20 keV, is noticeably increased due to acceleration of non-thermal electrons by Langmuir waves. Conclusions. The results show that the observed HXR spectrum, when interpreted in terms of collisional relaxation, can lead to an overestimated number and energy of energetic electrons accelerated in the corona.

Amplification of ion-acoustic turbulence upon electron-cyclotron heating of plasma

In this paper, we present the results of the study of ion-acoustic turbulence upon electron-cyclotron heating of low-temperature plasma in a TAU-1 model setup. Two MI-167 magnetrons were used as microwave sources. The peak power of each magnetron was 1 kW, the pulse duration was 7.5 µs. An increase in the temperature of most electrons and an increase in the energy of nonthermal electrons were observed in experiments. Microwave field turning-on caused an increase by an order of magnitude in the spectral density of ion-acoustic noise in the entire frequency range from 0.3 to 3 MHz under study.

Diagnostics of the Low-Cutoff Energy of Nonthermal Electrons in Solar Microwave and Hard X-Ray Bursts

Diagnostics of the Low-Cutoff Energy of Nonthermal Electrons in Solar Microwave and Hard X-Ray Bursts

Relationship between non-thermal electron energy spectra and GOES classes

We investigate the influence of the variations of energy spectrum of non-thermal electrons on the resulting GOES classes of solar flares. Twelve observed flares with various soft to hard X-ray emission ratios were modelled using different non-thermal electron energy distributions. Initial values of the flare physical parameters including geometrical properties were estimated using observations. We found that, for a fixed total energy of non-thermal electrons in a flare, the resulting GOES class of the flare can be changed significantly by varying the spectral index and low energy cut-off of the non-thermal electron distribution. Thus, the GOES class of a flare depends not only on the total non-thermal electrons energy but also on the electron beam parameters. For example, we were able to convert a M2.7 class solar flare into a merely C1.4 class one and a B8.1 class event into a C2.6 class flare. The results of our work also suggest that the level of correlation between the cumulative time integral of HXR and SXR fluxes can depend on the considered HXR energy range.

ELECTRON ENERGY AND MAGNETIC FIELD DERIVED FROM SOLAR MICROWAVE BURST SPECTRA

Microwave bursts during solar flares are known to be sensitive to high-energy electrons and magnetic field, both of which are important ingredients of solar flare physics. This paper presents such information derived from the microwave bursts of the 412 flares that were measured with the Owens Valley Solar Array. We assumed that these bursts are predominantly due to gyrosynchrotron radiation by nonthermal electrons in a single power-law energy distribution to use the simplified formulae for gyrosynchrotron radiation in the data analysis. A second major assumption was that statistical properties of flare electrons derived from this microwave database should agree with an earlier result based on the hard X-ray burst spectrometer on Solar Maximum Mission. Magnetic field information was obtained in the form of a scaling law between the average magnetic field and the total source area, which turns out to be a narrow distribution around ~400 G. The derived nonthermal electron energy is related to the peak flux, peak frequency, and spectral index, through a multistep regression fit, which can be used for a quick estimate for the nonthermal electron energy from spatially integrated microwave spectral observations.

Nonthermal Hard X‐Ray Emission and Iron Kα Emission from a Superflare on II Pegasi

We report on an X-ray flare detected on the active binary system II Pegasi with the Swift telescope. The event triggered the Burst Alert Telescope (BAT) in the hard X-ray band on 2005 December 16 at 11:21:52 UT with a 10-200 keV luminosity of 2.2 × 1032 ergs s-1—a superflare, by comparison with energies of typical stellar flares on active binary systems. The trigger spectrum indicates a hot thermal plasma with T ~ 180 × 106 K. X-ray spectral analysis from 0.8 to 200 keV with the X-Ray Telescope and BAT in the next two orbits reveals evidence for a thermal component (T > 80 × 106 K) and Fe K 6.4 keV emission. A tail of emission out to 200 keV can be fit with either an extremely high temperature thermal plasma (T ~ 3 × 108 K) or power-law emission. Based on analogies with solar flares, we attribute the excess continuum emission to nonthermal thick-target bremsstrahlung emission from a population of accelerated electrons. We estimate the radiated energy from 0.01 to 200 keV to be ~6 × 1036 ergs, the total radiated energy over all wavelengths ~10 38 ergs, the energy in nonthermal electrons above 20 keV ~3 × 1040 ergs, and conducted energy <5 × 1043 ergs. The nonthermal interpretation gives a reasonable value for the total energy in electrons >20 keV when compared to the upper and lower bounds on the thermal energy content of the flare. This marks the first occasion in which evidence exists for nonthermal hard X-ray emission from a stellar flare. We investigate the emission mechanism responsible for producing the 6.4 keV feature, and find that collisional ionization from nonthermal electrons appears to be more plausible than the photoionization mechanism usually invoked on the Sun and pre-main-sequence stars.

The Evaporation Regime in a Confined Flare

We studied the evolution of a small eruptive flare (GOES class C1) from its onset phase using multi-wavelength observations that sample the flare atmosphere from the chromosphere to the corona. The main instruments involved were the Coronal Diagnostic Spectrometer (CDS) aboard SOHO and facilities at the Dunn Solar Tower of the National Solar Observatory/Sacramento Peak. Transition Region and Coronal Explorer (TRACE) together with Ramaty High-Energy Spectroscopic Imager (RHESSI) also provided images and spectra for this flare. Hα and TRACE images display two loop systems that outline the pre-reconnection and post-reconnection magnetic field lines and their topological changes revealing that we are dealing with an eruptive confined flare. RHESSI data do not record any detectable emission at energies ≥25 keV, and the observed count spectrum can be well fitted with a thermal plus a non-thermal model of the photon spectrum. A non-thermal electron flux F ≈ 5 × 1010 erg cm−2 s−1 is determined. The reconstructed images show a very compact source whose peak emission moves along the photospheric magnetic inversion line during the flare. This is probably related to the motion of the reconnection site, hinting at an arcade of small loops that brightens successively. The analysis of the chromospheric spectra (Ca II K, He I D3 and Hγ, acquired with a four-second temporal cadence) shows the presence of a downward velocity (between 10 and 20 km s−1) in a small region intersected by the spectrograph slit. The region is included in an area that, at the time of the maximum X-ray emission, shows upward motions at transition region (TR) and coronal levels. For the He I 58.4 and O v 62.97 lines, we determine a velocity of ≈−40 km s−1 while for the Fe XIX 59.22 line a velocity of ≈−80 km s−1 is determined with a two-component fitting. The observations are discussed in the framework of available hydrodynamic simulations and they are consistent with the scenario outlined by Fisher (1989). No explosive evaporation is expected for a non-thermal electron beam of the observed characteristics, and no gentle evaporation is allowed without upward chromospheric motion. It is suggested that the energy of non-thermal electrons can be dissipated to heat the high-density plasma, where possibly the reconnection occurs. The consequent conductive flux drives the evaporation process in a regime that we can call sub-explosive.

Radio, X-ray, and γ-ray emission models of the colliding-wind binary WR 140

We use hydrodynamical models of the wind-collision region in the archetype colliding-wind system WR 140 to determine the spatial and spectral distributions of the radio, X-ray, and γ-ray emission from shock-accelerated electrons. Our calculations are for orbital phase 0.837 when the observed radio emission is close to maximum. Using the observed thermal X-ray emission at this phase in conjunction with the radio emission to constrain the mass-loss rates, we find that the O star mass-loss rate is consistent with the reduced estimates for O4-5 supergiants by Fullerton, Massa & Prinja, and the wind-momentum ratio, η= 0.02. This is independent of the opening angle deduced from radio very long baseline interferometry observations of the WCR that we demonstrate fail to constrain the opening angle. We show that the turnover at ∼3 GHz in the radio emission is due to free–free absorption, since models based on the Razin effect have an unacceptably large fraction of energy in non-thermal electrons. We find that the spectral index of the non-thermal electron energy distribution is flatter than the canonical value for diffusive shock acceleration, namely p 2 does not exclude the possibility of shock modification, but stronger evidence than that which currently exists is necessary for its support. Tighter constraints on p and the nature of the shocks in WR 140 will be obtained from future observations at MeV and GeV energies, for which we generally predict lower fluxes than those in previous works. Since the high stellar photon fluxes prevent the acceleration of electrons beyond γ≳ 105–106, TeV emission from colliding-wind binary systems will provide unambiguous evidence of pion-decay emission from accelerated ions. We finish by commenting on the emission and physics of the multiple wind collisions in dense stellar clusters, paying particular attention to the Galactic Centre.

Motion of 3-6 keV Nonthermal Sources along the Legs of a Flare Loop

Observations of nonthermal X-ray sources me critical to studying electron acceleration and transport in solar flares. Strong thermal emission radiated from the preheated plasma before the flare impulsive phase often makes it difficult to detect low-energy X-ray sources that are produced by relatively low-energy nonthermal electrons. Knowledge of the distribution of these low-energy nonthermal electrons is particularly important in determining the total nonthermal electron energy in solar flares. We report on an 'early impulsive flare' in which impulsive hard X-ray emission was seen early in the flare before the soft X-ray emission had risen significantly, indicating limited plasma pre-heating. Early in the flare, RHESSI < 25 keV images show coronal sources that moved first downward and then upwards along the legs of a flare loop. In particular, the 3-6 keV source appeared as a single coronal source at the start of the flare, and then it involved into two coronal sources moving down along the two legs of the loop. After nearly reaching the two footpoints at the hard X-ray peak, the two sources moved back up to the looptop again. RHESSI images and light curves all indicate that nonthermal emission dominated at energies as low as 3-6 keV. We suggest that the evolution of both the spectral index and the low-energy cutoff of the injected electron distribution could result in the accelerated electrons reaching a lower altitude along the legs of the dense flare loop and hence result in the observed downward and upward motions of the nonthermal sources.

First detection of a VHE gamma-ray spectral maximum from a cosmic source: HESS discovery of the Vela X nebula

The Vela supernova remnant (SNR) is a complex region containing a number of sources of non-thermal radiation. The inner section of this SNR, within 2 degrees of the pulsar PSR B0833-45, has been observed by the H.E.S.S. gamma-ray atmospheric Cherenkov detector in 2004 and 2005. A strong signal is seen from an extended region to the south of the pulsar, within an integration region of radius 0.8 deg. around the position (RA = 08h 35m 00s, dec = -45 deg. 36' J2000.0). The excess coincides with a region of hard X-ray emission seen by the ROSAT and ASCA satellites. The observed energy spectrum of the source between 550 GeV and 65 TeV is well fit by a power law function with photon index = 1.45 +/- 0.09(stat) +/- 0.2(sys) and an exponential cutoff at an energy of 13.8 +/- 2.3(stat) +/- 4.1(sys) TeV. The integral flux above 1 TeV is (1.28 +/- 0.17 (stat) +/- 0.38(sys)) x 10^{-11} cm^{-2} s^{-1}. This result is the first clear measurement of a peak in the spectral energy distribution from a VHE gamma-ray source, likely related to inverse Compton emission. A fit of an Inverse Compton model to the H.E.S.S. spectral energy distribution gives a total energy in non-thermal electrons of ~2 x 10^{45} erg between 5 TeV and 100 TeV, assuming a distance of 290 parsec to the pulsar. The best fit electron power law index is 2.0, with a spectral break at 67 TeV.

Determination of Low‐Energy Cutoffs and Total Energy of Nonthermal Electrons in a Solar Flare on 2002 April 15

The determination of the low-energy cutoff to the spectrum of accelerated electrons is decisive for the estimation of the total nonthermal energy in solar flares. Because thermal bremsstrahlung dominates the low-energy part of flare X-ray spectra, this cutoff energy is difficult to determine with spectral fitting alone. We have used anew method that combines spatial, spectral, and temporal analysis to determine the cutoff energy for the M1.2 flare observed with RHESSI on 2002 April 15. A low-energy cutoff of 24 +/- 2 keV is required to ensure that the assumed thermal emissions always dominate over nonthermal emissions at low energies (<20 keV) and that the spectral fitting results are consistent with the RHESSI light curves and images. With this cutoff energy, we obtain a total nonthermal energy in electrons of (1.6 +/- 1) x 10(exp 30) ergs that is comparable to the peak energy in the thermal plasma, estimated from RHESSI observations to be (6 +/- 0.6) x 10(exp 29) ergs assuming a filling factor of 1.

Location and parameters of a microwave millisecond spike event

A typical microwave millisecond spike event on November 2, 1997 was observed by the radio spectrograph of National Astronomical Observatories (NAOs) at 2.6–3.8 GHz with high time and frequency resolution. This event was also recorded by Nobeyama Radio Polarimeters (NoRP) at 1–35 GHz and Radio Heliograph (NoRH) at 17 GHz. The source at 17 GHz is located in one foot-point of a small bright coronal loop of YOHKOH SXT and SOHO EIT images with strong photospheric magnetic field in SOHO MDI magnetograph. It is assumed that the electron cyclotron maser instability and gyro-resonance absorption dominate, respectively, the rising and decay phase of the spike event. For different harmonic number of gyro-frequency or magnetic field strength, a fitting program with free plasma parameters is used to minimize the difference between the observational and theoretical values of the exponential growth and decay rates for a given spike. The plasma parameters at third harmonic number are more comparable to their typical values in solar corona. Hence, it is able to provide a diagnosis for the source parameters (magnetic field, density, and temperature), the properties of radiations (wave vector and propagation angle), and the properties of non-thermal electrons (density, pitch angle, and energy). The results are also comparable with the diagnosis of the gyro-synchrotron radiation model, the frequency drift rates and a dipole magnetic field model, as well as the YOHKOH SXT and SOHO MDI data.

Calculations of the low-cutoff energy of non-thermal electrons in solar microwave and hard X-ray bursts

Two independent methods are proposed to estimate the low-cutoff energy of non-thermal electrons in solar microwave and hard X-ray bursts. At first, the observed ratio of radio flux at two frequencies (or hard X-ray count at two energies) are compared with the models based on the non-thermal gyro-synchrotron (or bremsstrahlung) radiations, excited by non-thermal electrons with a single power-law distribution, in which the low-cutoff energy is considered as the only free parameter. Some other parameters are cancelled by the ratio (such as the coefficient of the power-law distribution of non-thermal electrons), or fixed due to the insensitivity (such as the high-cutoff energy, the ambient density and temperature), or calculated from the other observations (such as the magnetic field). Secondly, the cross-point of the power-law distributions at different time of microwave or hard X-ray bursts is suggested to estimate the low or high-cutoff energies of non-thermal electrons. Two impulsive microwave bursts by Owens-Valley Solar Arrays (OVSA) associated with hard X-ray bursts by YOHKOH/HXT are selected to eliminate the contribution of thermal component around the peak time with plasma temperature of 10 6–10 7 K. The energy at the cross-points in two hard X-ray bursts is comparable with the low-cutoffs to fit the microwave and hard X-ray data at different times of the impulsive phase, i.e., 10–50 keV. These two methods can be applied only when a single power-law distribution is acceptable between the two frequency (or energy) channels in microwave (or hard X-ray) bursts.

Constraints on the energetics and plasma composition of relativistic jets in FR II sources

We explore the energetics and plasma composition in FR II sources using a new simple method of combining shock dynamics and radiation spectrum. The hot spots are identified with the reverse shocked region of jets. With the one-dimensional shock jump conditions taking account of the finite pressure of hot ICM, we estimate the rest mass and energy densities of the sum of thermal and non-thermal particles in hot spots. Independently, based on the Synchrotron Self-Compton (SSC) model, we estimate the number and energy densities of {\it non-thermal} electrons using the multi-frequency radiation spectrum of hot spots. We impose the condition that the obtained rest mass, internal energy, and number densities of non-thermal electrons should be lower than those of the total particles determined by shock dynamics. We apply this method to Cygnus A. We examine three extreme cases of pure electron-positron pair plasma (Case I), pure electron-proton plasma with separate thermalization (Case II), and pure electron-proton plasma in thermal-equilibrium (Case III). By detailed SSC analysis for Cygnus A and 3C123, we find that the energy density of non-thermal electrons is about 10 times larger than that of magnetic field. We find that the Case III is not acceptable because predicted photon spectra do not give a good fit to the observed one. We find that Case II can also be ruled out since the number density of non-thermal electrons exceeds that of the total number density. Hence, we find that only pure $e^{\pm}$ plasma (Case I) is acceptable among the three cases. Total kinetic power of jet and electron acceleration efficiency are also constrained by internal energy densities of non-thermal and total particles.

On the non-thermal high energy radiation of galaxy clusters

Institute de Physique Theorique, Universite de Lausanne, BSP 1015 Lausanne, SwitzerlandReceived / AcceptedAbstract. The origin of the nonthermal EUV and hard X-ray emission “excess” reported from some galaxyclusters has been intensively debated over last several years. The most favored models which refer this excessto relativistic electrons upscattering the 2.7 K CMBR generally requires very low magnetic field, significantlybelow the estimates derived from the Faraday Rotation Measurements, unless one invokes rather nonstandardassumptions concerning the energy and pitch angle distributions of nonthermal electrons. In this paper we suggesta new model assuming that the “nonthermal” excess is due to synchrotron radiation of ultrarelativistic (multi-TeV) electrons of “photonic” origin. These electrons are continuously introduced throughout the entire intraclustermedium by very high energy (hypothetical) γ-rays through interactions with the diffuse extragalactic radiationfields. We present numerical calculations for the Coma cluster, and briefly discuss implications of the model forother galaxy clusters both in the X- and γ-ray energy domains.Key words. X-rays: galaxies: clusters – Galaxies: clusters: individual: Coma – Gamma rays: theory

The Neupert effect and new RHESSI measures of thetotal energy in electrons accelerated in solar flares

Abstract It is believed that a large fraction of the total energy released in a solar flare goes initially into acceleratedelectrons. These electrons generate the observed hard X-ray bremsstrahlung as they lose most of their energy by coulomb collisions in the lower corona and chromosphere. Results from the Solar Maximum Mission showed that there may be even more energy in accelerated electrons with energies above 25 keV than in the soft X-ray emitting thermal plasma. If this is the case, it is difficult to understand why the Neupert Effect — the empirical result that for many flares the time integral of the hard X-ray emission closely matches the temporal variation of the soft X-ray emission — is not more clearly observed in many flares. From recent studies, it appears that the fraction of the released energy going into accelerated electrons is lower, on average, for smaller flares than for larger flares. Also, from relative timing differences, about 25% of all flares are inconsistent with the Neupert Effect. The Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) is uniquely capable of investigating the Neupert Effec since it covers soft X-rays down to 3 keV (when both attenuators are out of the field of view) and hard X-rays with keV energy resolution, arcsecond-class angular resolution, and sub-second time resolution. When combined with the anticipated observations from the Soft X-ray Imager on the next GOES satellite, these observations will provide us with the ability to track the Neupert Effect in space and time and learn more about the relation between plasma heating and particle acceleration. The early results from RHESSI show that the electron spectrum extends down to as low as 10 keV in many flares, thus increasing the total energy estimates of the accelerated electrons by an order of magnitude or more compared with the SMM values. This combined with the possible effects of filling factors smaller than unity for the soft X-ray plasma suggest that there is significantly more energy in nonthermal electrons than in the soft X-ray emitting plasma in many flares.

Hard X-ray Microflares down to 3 keV

The excellent sensitivity, spectral and spatial resolution, and energy coverage down to 3 keV provided by the Reuven Ramaty High-Energy Solar Spectroscopic Imager mission (RHESSI) allows for the first time the detailed study of the locations and the spectra of solar microflares down to 3 keV. During a one-hour quiet interval (GOES soft X-ray level around B6) on 2 May, 1:40–2:40 UT, at least 7 microflares occurred with the largest peaking at A6 GOES level. The microflares are found to come from 4 different active regions including one behind the west limb. At 7′′ resolution, some events show elongated sources, while others are unresolved point sources. In the impulsive phase of the microflares, the spectra can generally be fitted better with a thermal model plus power law above ∼ 6–7 keV than with a thermal only. The decay phase sometimes can be fitted with a thermal only, but in some events, power-law emission is detected late in the event indicating particle acceleration after the thermal peak of the event. The behind-the-limb microflare shows thermal emissions only, suggesting that the non-thermal power law emission originates lower, in footpoints that are occulted. The power-law fits extend to below 7 keV with exponents between −5 and −8, and imply a total non-thermal electron energy content between 1026–1027 erg. Except for the fact that the power-law indices are steeper than what is generally found in regular flares, the investigated microflares show characteristics similar to large flares. Since the total energy in non-thermal electrons is very sensitive to the value of the power law and the energy cutoff, these observations will give us better estimates of the total energy input into the corona. (Note that color versions of figures are on the accompanying CD-ROM.)

Sunlit Io atmospheric [O I] 6300 Å emission and the plasma torus

A large database of sunlit Io [O I] 6300 Å emission, acquired over the period 1990–1999, with extensive coverage of Io orbital phase angle ϕ and System III longitude λIII, exhibits significant long‐term and short‐term variations in [O I] 6300 Å emission intensities. The long‐term average intensity shows a clear dependence on λIII, which establishes conclusively that the emission is produced by the interaction between Io's atmosphere and the plasma torus. Two prominent average intensity maxima, 70° to 90° wide, are centered at λIII ≈ 130° and λIII ≈ 295°. A comparison of data from October 1998 with a three‐dimensional plasma torus model, based upon electron impact excitation of atomic oxygen, suggests a basis for study of the torus interaction with Io's atmosphere. The observed short‐term, erratic [O I] 6300 Å intensity variations fluctuate ∼20–50% on a timescale of tens of minutes with less frequent fluctuations of a factor of ∼2. The most likely candidate to produce these fluctuations is a time‐variable energy flux of field‐aligned nonthermal electrons identified recently in Galileo plasma science data. If true, the short‐term [O I] intensity fluctuations may be related to variable field‐aligned currents driven by inward and outward torus plasma transport and/or transient high‐latitude, field‐aligned potential drops. A correlation between the intensity and emission line width indicates molecular dissociation may contribute significantly to the [O I] 6300 Å emission. The nonthermal electron energy flux may produce O(1D) by electron impact dissociation of SO2 and SO, with the excess energy going into excitation of O and its kinetic energy. The [O I] 6300 Å emission database establishes Io as a valuable probe of the torus, responding to local conditions at Io's position.

The relation between Type-IV solar radio bursts and associated phenomena and white light flares : XIE Rui-xiang & WANG Min Yunnan Observatory, CAS, Kunming 650011

Based on a qualitative analysis of the data of the type IV radio burst and accompanying phenomena (post flare loops, radio pulsation in the decaying phase, multi-band emissions and mass ejection etc.) associated with the white light flare (WLF) of 1991 June 6, it is proposed that the WLF and radio burst come from the same electron accelerating area in the low corona. The energy transfer of the WLF may be a two-step process, the energy of nonthermal electrons from the corona is precipitated in the chromosphere, producing compression waves or a downward radiative field, and then the temperature of the upper photosphere is increased and the WLF is initiated. Moreover, the post-flare loops and radio fine structures may be the counterparts of the WLF.