Role of non-thermal electrons on the generation of X-ray and EUV lines in solar flares

The energy and angular distributions of electrons have been studied by combining small angle scatterings using analytical treatment with large angle collisions using Monte Caroo calculations as a function of column density for initially power-law electron distributions and incidence angles of 0, 30, and 60°. Using these distributions the X-ray and EUV line flux as a function of column density has been computed. The flux increases with increase in column density. At the initial column densities the contribution of non-thermal electrons for the production of line flux is negligible. However, it becomes significant at intermediate column densities at which the electron energy and angular distributions have non-Maxwellian nature. X-ray and EUV flux have also been calculated as a function of electron spectral index at a fixed column density. It falls steeply with increase in spectral index. The calculated flux is compared with the observations.     

Hard X-rays from solar flares — time characteristics in correlation with energy and angular distributions of electrons

Fine time variation of hard X-rays has been explained in terms of a spread in the angle of incidence of the source electrons in non-thermal thick-target model for bremsstrahlung generation. The electron energy and angular distributions have been calculated by combining small angle scatterings using analytical treatment with a large angle collision using Monte Carlo calculations as a function of column density. The incidence angles of electrons are taken as 0, 30, and 60°. Using the Bethe-Heitler cross section and the above calculated electron distributions, the bremsstrahlung flux for different photon energies as a function of column density has been studied. The computed X-ray pulse as a function of column density has been converted into time profile. It corresponds well with the observed fine time structure. The calculated spectra of X-rays at the peak and valley are also consistent with the observations. The variation of photon flux with time has also been computed for photon energies 20, 50, and 100 keV for 90 and 180° observation angles together with the changes in spectral shapes of photon energy spectrum at different times for 90 and 180° observation angles.     

on the role of nonthermal electrons in EUV and X-ray line emissions from solar flares

The energy and angular distribution of electrons as a function of column densities initially for monoenergetic and monodirectional electron beams and incidence angles of 0‡, 30‡ and 60‡ have been studied by combining small angle scattering using analytical treatment with large angle collisions using Monte Carlo calculations. Using these distributions, X-ray and EUV-line flux have been studied as a function of column density. It is observed that the line flux increases with the increase in column density, becoming significant at intermediate column densities where the electron energies and angular distributions have a non-Maxwellian nature.     

Study of hard X-ray characteristics of solar flares - support for non-thermal processes

The spatial and angular distributions and also the energy spectrum of hard X-rays from solar flares have been studied in terms of the energy and angular distributions of the accelerated electron beam. The incident electron distributions as functions of column density have been computed by combining the analytical treatment of small-angle scattering with the Monte-Carlo calculations for large angle scattering. To start with monoenergetic electrons at 0°, 30°, and 60° incidence angles have been taken. Using the Bethe-Heitler total cross section and the Sauter differential cross section along with the calculated electron distributions, the bremsstrahlung flux and its angular distribution for different photon energies > 10 keV have been studied as function of column density. The shape of the calculated curves agrees with the observations of PVO/ISEE-3 lending support to the beamed thick-target model for X-ray generation with continuous injection.Physics Department, Vishwa Bharti Institution, Rainawari, Srinagar, India.     

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.     

Study of electron energy and angular distributions and calculations of X-ray,EUV line flux and rise times

Evolution of energy and angular distributions of electrons has been studied by combining small-angle analytical treatment with large-angle Monte Carlo calculations as a function of column density for initially monoenergetic and monodirectional electrons. The incident electron energies considered are 20, 30 and 60 keV at 0°, 30° and 60° angles of incidence. Using these distributions, time evolution of extreme ultraviolet (EUV) spectrum has been studied. The slopes of the curves calculated compare well with the experimentally observed curve.     

Calculation of anisotropy ratio of hard X-rays from solar flares — evidence for continuous electron injections/accelerations

Variation of electron energy and angular distributions has been studied as a function of column density by combining small-angle analytical treatment with large-angle Monte Carlo calculations. The distributions have been calculated for initial electron energy 300 keV and various incidence directions. Using these distributions and Sauter bremsstrahlung cross-section differential in photon energy and emission angle, we have calculated the X-ray energy and angular distributions for photon energies 10, 20, 50, 100, 150 and 200 keV. By taking the ratio of X-ray flux at 90 and 180°, we have computed the anisotropy ratio A as function of column density. Calculated anisotropy ratio compares well with ISEE-3 and PVO observations.     

Rocket observations of the interaction of auroral electrons with the atmosphere

Electron spectra obtained during the flight of Black Brant VB-31 on August 17, 1970 through a stable aurora to a height of 268 km have been analyzed in detail to obtain the pitch angle distributions from 25 to 155° and the electron energy distributions over an energy range of 18 keV to 20 eV through the region of atmospheric interaction down to 97 km. Backscatter ratios for 140° pitch angle range from 0.065 for 18 keV electrons to 0.22 for 1 keV electrons. Backscatter of lower energy electrons decreases with atmospheric depth below 200 km. The effect of the interactions between auroral electrons and the atmosphere is such as to give a peak in electron flux which moves progressively to higher energies with penetration depth. The secondary electron flux increases monotonically with height up to 200 km. The secondary electron spectrum can be approximated by an energy power over small energy ranges but its form is somewhat dependent on height and on the primary electron spectrum.     

Role of nonthermal electrons in the heating of solar atmosphere during flares

Evolution of electron energy distributions have been studied by combining small-angle scattering with analytical treatment of large-angle collision using the Monte-Carlo technique. By use of these, the distributions and energy loss have been calculated as functions of column density, the heating functions have been calculated at different depths of the solar atmosphere. From the heating functions, an increase in temperature produced by the electrons at different column densities has been computed. It is found that rise in temperature increases with an increase in incident electron energy.     

A Study of the Peak Frequency of the Geosynchronous Spectrum in a Nonuniform Source

This paper investigates in detail the peak frequency of gyrosynchrotron radiation spectrum with self and gyroresonance absorption for a model of nonuniform magnetic field. It is found that the peak frequency shifts from lower frequency to higher frequency with increases in the low-energy cutoff, number density, input depth of energetic electrons, magnetic field strength and viewing angle. When the number density and temperature of thermal electrons increase, the peak frequency also shifts to a slightly higher frequency. However, the peak frequency is independent of the energy spectral index, high-energy cutoff of energetic electrons and the height of the radio source’s upper boundary. It is also found for the first time that there is a good linear correlation between the logarithms of the peak frequency and the low-energy cutoff, number density, input depth of energetic electrons, magnetic field strength, and viewing angle, respectively. Their correlation coefficients are higher than 0.95 and the standard errors are less than 0.06.     

Maximum flux density of the gyrosynchrotron spectrum in a nonuniform source

The maximum flux density of a gyrosynchrotron radiation spectrum in a mag- netic dip|oe model with self absorption and gyroresonance is calculated. Our calculations show that the maximum flux density of the gyrosynchrotron spectrum increases with in- creasing low-energy cutoff, number density, input depth of energetic electrons, magnetic field strength and viewing angle, and with decreasing energy spectral index of energetic electrons, number density and temperature of thermal electrons. It is found that there are linear correlations between the logarithms of the maximum flux density and the above eight parameters with correlation coefficients higher than 0.91 and fit accuracies better than 10%. The maximum flux density could be a good indicator of the changes of these source parameters. In addition, we find that there are very good positive linear correla- tions between the logarithms of the maximum flux density and peak frequency when the above former five parameters vary respectively. Their linear correlation coefficients are higher than 0.90 and the fit accuracies are better than 0.5%.     

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.     

Thick-target processes and white-light flares

Observations indicate that fast electrons in solar flares, which cause the hard X-ray burst and the impulsive microwave burst, lose energy predominantly by collisional processes. This requires a thick-target theory of the emission, for which the electron spectrum inferred from the X-ray spectrum becomes 1.5 powers steeper than in the usual thin-target theory.The low-energy end of this spectrum contains enough energy above about 5 keV to supply the white-light continuum emission occasionally observed in major flares. The penetration of the nonthermal electrons creates long-lived excess ionization which enhances the free-free and free-bound continuum in the heated medium. The emission will occur high above the photosphere at small optical depth in the visible continuum. Thus its spectrum will extend into the infrared and ultraviolet.     

Synchrotron X-ray emission from supernova remnants. Exponential cut-off in the electron spectrum

We present a model which describes the evolution of the energy spectrum of relativistic electrons in supernova remnants, with radiation losses of electrons taken into account. The model can be used to calculate the synchrotron X-ray emission from supernova remnants in the uniform interstellar medium and in the uniform interstellar magnetic field. The importance of various factors in the variations of spatial distributions of nonthermal electrons and their synchrotron emissive capacity is demonstrated. We analyze the errors which arise in the magnetic field strength when it is estimated with the use of the models which ignore the detailed pattern of the evolution of the magnetic field and the electron spectrum behind the shock front in the remnant. The evolution of synchrotron emission spectrum and the ratio between the synchrotron radio and X-ray fluxes from supernova remnants are calculated.     

Analytic approach to auroral electron transport and energy degradation

The interaction of a beam of auroral electrons with the atmosphere is described by the linear transport equation, encompassing discrete energy loss, multiple scattering and secondary electrons. A solution to the transport equation provides the electron intensity as a function of altitude, pitch angle (with respect to the geomagnetic field) and energy. A multi-stream (discrete ordinate) approximation to the transport equation is developed. An analytic solution is obtained in this approximation. The computational scheme obtained by combining the present transport code with the energy degradation method of Swartz (1979) conserves energy identically. The theory provides a framework within which angular distributions can be easily calculated and interpreted. Thus, a detailed study of the angular distributions of “non-absorbed” electrons (i.e., electrons that have lost just a small fraction of their incident energy) reveals a systematic variation with incident angle and energy, and with penetration depth. The present approach also gives simple yet accurate solutions in low order multi-stream approximations. The accuracy of the four-stream approximation is generally within a few per cent, whereas two-stream results for backscattered mean intensities and fluxes are accurate to within 10–15%.     

Acceleration of Electrons and Protons in Reconnecting Current Sheets Including Single or Multiple X-points

Kinematic characteristics of electrons and protons in the magnetic reconnecting current sheet in the presence of a guide field are investigated. Particle trajectories are calculated for different values of the guide field by a test-particle calculation. The relationship between the final energy and the initial position has also been studied. We found that the addition of a guide field not only allows particles to get more energy and not only results in the separation of electrons and protons, but also causes the reconnecting electric field to selectively accelerate electrons and protons for different initial positions. The energy spectrum eventually obtained is the common power-law spectrum, and as the guide field increases, the index for the spectrum of electrons decreases rapidly. However, for a weak background magnetic field, proton spectra are not very sensitive to the guide field; but for a strong background field, the dependence of the spectrum index is similar to the electron spectrum. Meanwhile, kinematic characteristics of the accelerated particles in the current sheet including multiple X-points and O-points were also investigated. The result indicates that the existence of the multiple X- and O-points helps particles trapped in the accelerating region to gain more energy, and yields the double or multiple power-law feature.     

Formation of power-law electron spectra in collapsing magnetic traps

The energy distribution of the fast electrons captured into a collapsing magnetic trap in the solar corona is calculated as a function of the trap length and diameter. It is shown that if the electrons injected into the trap have a power-law spectrum, then their spectrum remains a power-law one with the same slope throughout the acceleration process for both the Fermi and betatron acceleration mechanisms. For electrons with a thermal injection spectrum, the model predicts two types of hard X-ray sources, thermal and nonthermal. Thermal sources are formed in traps dominated by the betatron mechanism. Nonthermal sources with a power-law spectrum are formed when electrons are accelerated by the Fermi mechanism.     

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.     

Multiple compton scattering of electrons in a photon field

Consideration is given to the motion of electrons in a photon field of the monoenergetic or power-law spectrum under the conditions when the main mechanism of energy loss is the inverse Compton scattering by field photons. This process changes the primary spectrum of electrons and converts low-energy field photons to high-energy gamma-quanta for which the electron confinement region is assumed to be optically thin. The electron and gamma-ray spectra have been obtained in a wide energy interval including the Klein-Nishina and Thomson regions. A simple qualitative dependence of the solutions found on the field parameters and the primary spectrum of electrons has been established.The electron and gamma-ray spectra have been obtained by numerically solving the kinetic equation dependent on two variables: the energy of electrons and their path (or the time of motion) in a photon field. The results dramatically differ from the solution of the steady-state kinetic equation which depends only on the electron energy and is frequently used in the given problem.     

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.