Hard X rays of relativistic electrons accelerated in solar flares

The direction and polarization degree of hard X rays (HXRs) in solar flares are studied. The continuous injection of relativistic electrons, which is implemented in powerful flares, is considered. The stationary relativistic kinetic equation is studied by using the method of expansion in terms of the Legendre polynomial and by integrating the equations for the expansion coefficients. The HXR characteristics are calculated using the bremsstrahlung relativistic cross-section for different angular and energetic electron distributions in the acceleration region. A high linear polarization degree of HXRs (??35%) has been obtained for narrow (??cos⁶??) beams of electrons with a soft spectrum (??E ^?6); the polarization degree decreases with increasing quanta energy, whereas the directivity of a high-energy emission increases. This effect is absent for a nonrelativistic approximation. The considered model is applied to one of the most powerful flares in cycle 23, registered on October 28, 2003. The measured polarization degree values at relativistic energies (0.2?C0.4 and 0.4?C1 MeV) agree with the results achieved in the considered model when the electron energy spectrum index (?? = 2.5), angular distribution part (??cos⁶??), and the spectrum cutoff energy (E _max = 1.3 MeV) were specified.     

Time structure of the X-ray emission of thermal solar flares

Based on observations of electromagnetic radiation, a concept of thermal solar flares has been proposed. The absence of hard X-ray emission implies no accelerated electrons. This fact is the basis of the proposed concept of thermal flares. Since the acceleration rate should not exceed the electron energy loss rate, plasma density in the acceleration range must be at least 10¹¹ cm^?3. The temperature of plasma emitting in the soft X-ray range is of the order of 10⁷ K. In the simplified problem of heated plasma hydrodynamics, we calculated the temperature profiles and their changes over time and by coordinate. The emission measure values determined from observations of the soft X-ray emission of flares is of the order of 10⁴⁵ cm^?3. The geometry of the source is an axial symmetric straight cylinder with a section of 10¹⁶ cm² and an axial coordinate determined by the depth of plasma heating. Time profiles of soft X-ray emission were calculated for different sources of plasma heating, which were simulated using the Gaussian distribution law with respect to the coordinate and time. We have considered two modes of plasma heating: single (in time) and multipulse modes with different pulse intervals. The dynamics of plasma heating and cooling was shown to control the experimentally observed time profiles of soft X-ray emission. A comparison of numerical results with observational data allows us to confirm the implications of the proposed concept of thermal flares and, in addition, to perform diagnostics of plasma parameters in the emission source.     

Intensity and polarization of the hard X-ray radiation of solar flares at the top and footpoints of a magnetic loop

The spatial distributions of the intensity and polarization of hard X-rays (HXR) were modeled based on a numerical solution of the nonstationary kinetic Fokker-Plank equation. Two cases of nonstationary long injections (??10 s) of nonthermal electrons at the top of a flaring loop are considered. In the first case, the injection occurs anisotropically in a cone directed along the field to one of the loop??s footpoints. In the second case, electrons are injected isotropically. In the case of the anisotropic injection, the degree of HXR polarization in the footpoints is low and does not exceed 8%. At the same time, the polarization of the radiation from the top in a range of photon energies from 30 to 60 keV reaches 43% at the beginning of injection. Significantly different spatial distributions of HXR characteristics are obtained for the isotropic injection of electrons. In this case, the calculated degree of HXR polarization from the top exhibits a strong variability: it reaches 15?C18% at the beginning of injection at photon energies of 30?C90 keV, decreases to zero after 5 s, and then, changing its sign, increases to 8%. In the footpoint of the loop, HXR is in fact nonpolarized. The features of the spatial distributions obtained in the simulation process can be measured with X-ray telescopes-polarimeters in future experiments and used for diagnosing the pitch angle distribution of accelerated electrons.     

The challenges of the models of solar flares

The challenges of ‘standard’ model of solar flares motivated by new observations with the spacecrafts and ground-based telescopes are presented. The most important problems are in situ heating of photospheric and chromospheric loop footpoints up to the coronal temperatures without precipitating particle beams accelerated in the corona, and the sunquakes which are unlikely to be explained by the impact of highenergy particles producing hard X-ray emission. There is also the long-standing ‘number problem’ in the physics of solar flares. It is shown that modern observations favored an important role of the electric currents in the energy release processes in the low solar atmosphere. Particle acceleration mechanism in the electric fields driven by the magnetic Rayleigh-Taylor instability in the chromosphere is proposed. The electric current value I ≥ 10¹⁰ A, needed for the excitation of super-Dreicer electric fields in the chromosphere is determined. It is shown that both Joule dissipation of the electric currents and the particles accelerated in the chromosphere can be responsible for in situ heating of the low solar atmosphere. Alternative model of the solar flare based on the analogy between the flaring loop and an equivalent electric circuit which is good tool for the electric current diagnostics is presented. Interaction of a current-carrying loop with the partially-ionized plasma of prominence in the context of particle acceleration is considered. The role of plasma radiation mechanism in the sub-THz emission from the chromosphere is discussed.     

Magnetohydrodynamic simulation of a solar flare: 2. Flare model and simulation using active-region magnetic maps

The results of a three-dimensional MHD simulation and data obtained using specialized spacecraft made it possible to construct an electrodynamic model of solar flares. A flare results from explosive magnetic reconnection in a current sheet above an active region, and electrons accelerated in field-aligned currents cause hard X rays on the solar surface. In this review, we considered works where the boundary and initial conditions on the photosphere were specified directly from the magnetic maps, obtained by SOHO MDI in the preflare state, in order to simulate the formation of a current sheet. A numerical solution of the complete set of MHD equations, performed using the new-generation PERESVET program, demonstrated the formation of several current sheets before a series of flares. A comparison of the observed relativistic proton spectra and the simulated proton acceleration along a magnetic field singular line made it possible to estimate the magnetic reconnection rate during a flare (∼10⁷ cm s⁻¹). Great flares (of the X class) originate after an increase in the active region magnetic flux up to 10²² Mx.     

Time structure and energy spectrum evolution of the solar flare X-rays measured by the IRIS spectrometer onboard the CORONAS-F spacecraft

The time structure and energy spectrum evolution of the X-ray emission of solar flares, observed by the IRIS spectrometer onboard the CORONAS-F spacecraft, are investigated. It has been found out that one or two quasi-periodic components with periods of 1–20 s, which are absent in the background preflare emission, appear in the flare soft X rays. It has been indicated that the variation in the shape of the energetic spectra of the C-class flare hard X rays reflects the evolution of the accelerated electron distribution function.     

Effect of a self-induced electric field on the electron beam kinetics and resulting hard X-ray and microwave emissions in flares

The kinetics of beam electron precipitation from the top of a loop into the solar atmosphere with density gradients and an increasing magnetic field have been generally described. The Fokker-Planck equations are solved with regard to Coulomb collisions and the effect of the electric field induced by this beam. The photon spectra and polarization degree in hard X-ray (10–300 keV) and microwave (1–80 GHz) emissions are simulated under different assumptions regarding the beam electron distribution function. The simulation results are compared with the flare observations on March 10, 2001, and July 23, 2002, visible at different position angles. It has been indicated that the coincidence of the theoretical photon spectra with simultaneous observations of the hard X-ray and microwave emissions of these flares is the best for models that not only take into account collisions, but also the electric field induced by electron fluxes propagating in flare loops with very weakly or moderately converging magnetic fields.     

Studying instrumental linear polarization at the Large Solar Vacuum Telescope (LSVT)

Impact linear polarization in solar flares is studied with the Large Solar Vacuum Telescope (LSVT) using the spectral polarimetric method. This method makes it possible to minimize the effect of instrumental polarization with an error of up to 10⁻² owing to the normalization of the spectral line intensity to the continuum spectrum intensity with negligible linear polarization. As a result, the Hα line intensity in two orthogonally polarized spectral stripes coincides in the absence of solar polarization. However, in the presence of linear polarization in a flare, the spectral polarimetric method does not rule out that the error can be present in determining the Stokes parameters Q and U because of their possible relative “leakage.” Linear instrumental polarization of LSVT has been performed using polaroid rotation before the major mirror. Twelve elements of a telescope matrix, characterizing linear polarization, have been determined. The usage of a matrix makes it possible to specify the observed Q and U values accurate to 10⁻³ of their magnitude.     

Subsecond Hard X-Ray Spikes from Solar Flares: Limitations on the Electron Acceleration Mechanism

Geomagnetism and Aeronomy - The X-ray spike structure for solar flares recorded by the CGRO/BATSE spectrometer is discussed, and the kinetics of accelerated electrons propagating in the plasma of a...     

Dynamics of accelerated electron beams and X rays in solar flares with sub-THz radiation

Unique measurements by a solar submillimeter radio telescope (SST) have been carried out in the sub-THz radiation at 212 and 405 THz over the past decade. The spectrum of RF radiation in this region increased with frequency for the three flares of November 2 and 4, 2003, and December 6, 2006, and the flux value reached 5 × 10³?2 × 10⁴ sfu at 405 GHz (Kaufman et al., 2009). In this work, we consider a set of nonlinear equations for an accelerated electrons beam and the Langmuir wave energy density. The distribution functions of the accelerated electron beam and wave energy density are calculated taking into account Coulomb collisions, electron scattering by waves, and wave scattering by plasma ions. In addition, the source of accelerated particles and the heat level of the Langmuir turbulence are specified. The beam and plasma parameters are chosen based on the aims of a problem. The plasma concentration varies from n = 10¹³ to 10¹⁵ cm^?3, the electron plasma frequency f _p = (3 × 10¹⁰?3 × 10¹¹) Hz in this case. The ratio of plasma and beam concentrations, sufficient to explain the value of the radio flux at a frequency of 300 GHz, is n _b/n = 10^?3. The Langmuir turbulence is excited due to the instability of the accelerated electron beam with an initial distribution function of the ??bump-in-tail?? type. Then, the parameters of radiowaves are calculated in the sub-THz range under the assumption of coalescence of two plasma waves. The calculation results show that a sub-THz radio flux can be obtained under the condition of injection of accelerated electrons. The fine time structure of radio flux observed is easily simulated based on this statement by the pulsed time structure of electron beams and their dynamics in overdense plasma. X-ray and gamma radiation was recorded during the events under study. Hard X-ray radiation is bremsstrahlung radiation from accelerated electron beams.     

Disturbances in the topside ionosphere during solar flares

The results of studying the ionospheric response to solar flares, obtained from the data of the GPS signal observations and incoherent scatter radars and as a result of the model calculations, are presented. It is shown that, according to the GPS data, a flare can cause a decrease in the electron content at altitudes of the topside ionosphere (h > 300 km). Similar effects of formation of a negative disturbance in the ionospheric F region were also observed during the solar flares of May 21 and 23, 1967, with the Arecibo incoherent scatter radar. The mechanism by which negative disturbances appear in the topside ionosphere during solar flares has been studied in this work based on the theoretical model of the ionosphere-plasmasphere coupling. It has been indicated that the formation of the electron density negative disturbance in the topside ionosphere is caused by an intense removal of O⁺ ions into the overlying plasmasphere under the action of an abrupt increase in the ion production rate and thermal expansion of the ionospheric plasma.     

Spatial brightness distribution of hard X-Ray emission along flare loops

The work is devoted to the simulation of recently discovered hard X-ray and gamma radiation sources localized near the top of solar flare loops. The calculations were performed in the context of a model of a flare magnetic loop inhomogeneous with respect to the magnetic field. Two cases of injection were considered: isotropic and anisotropic along the loop axis. The distributions of electrons along the loop are found by solving the nonstationary relativistic kinetic equation in the Fokker-Planck form. Based on the calculated electron distribution functions, the spatial brightness distribution of hard X-ray and gamma radiation has been calculated. Radiation characteristics are compared for different sets of injection parameters.     

Variations in ionospheric parameters during solar flares

Results of studying the ionospheric response to solar flares, obtained based on the incoherent scatter radar observations of the GPS signals and as a result of the model simulations, are presented. The method, based on the effect of partial “shadowing” of the atmosphere by the globe, has been used to analyze the GPS data. This method made it possible to estimate the value of a change in the electron content in the upper ionosphere during the solar flare of July 14, 2000. It has been shown that a flare can cause a decrease in the electron content at heights of the upper ionosphere (h > 300 km) according to the GPS data. Similar effects in the formation of a negative disturbance in the ionospheric F region were also observed during the solar flares of May 21 and 23, 1967, at the Arecibo incoherent scatter radar. The mechanism by which negative disturbances are formed in the upper ionosphere during solar flares has been studied based on the theoretical model of the ionosphere-plasmasphere coupling. It has been shown that an intense ejection of O⁺ ions into the above located plasmasphere under the action of a sharp increase in the ion production rate and the thermal expansion of the ionospheric plasma cause the formation of a negative disturbance in the electron concentration in the upper ionosphere.     

Effect of active processes on alpha particle density in the solar wind

The properties of alpha particle fluxes, the density of which increase under the action of flares and development of coronal mass ejections (CMEs) and solar wind structural inhomogeneities, have been studied. The maximal alpha particle density in plasma fine structure volumes reaches 12 cm^?3. The amount of ?? particles is sometimes higher than that of protons. This is explained by the effect of the mechanism by which individual solar wind zones are nonuniformly enriched in helium nuclei when strong flares develop.     

Ultraviolet radiation diagnostics of the flare transient layer

The correlation between the pulsed and smooth components of ultraviolet radiation and hard X-rays from solar flares has been interpreted on the basis of the time behavior of the energy flux penetrating from the magnetic field reconnection region to the boundary of the heated region. It has been shown that the time behavior of the primary flare energy flux is easily reconstructed from the time profile of the intensity of hard X-rays, and the time profile of the intensity of ultraviolet radiation represents the release of the flare energy in the flare transient layer. The smooth or pulsed component of the ultraviolet radiation depends on the form of the primary energy release. Information on the dynamics of the heating process and the formation and equalization of the gas pressure in the flare transient layer has been obtained from the observed temperature dependence of the emission measure. The described scheme explains the set of flare phenomena and the correlation between hard X-rays with pulsed ultraviolet bursts.     

Allowance for motion in a steady-state thermal flux pattern

The correlation between the pulsed and smooth components of ultraviolet radiation and hard X-rays from solar flares has been interpreted on the basis of the time behavior of the energy flux penetrating from the magnetic field reconnection region to the boundary of the heated region. It has been shown that the time behavior of the primary flare energy flux is easily reconstructed from the time profile of the intensity of hard X-rays, and the time profile of the intensity of ultraviolet radiation represents the release of the flare energy in the flare transient layer. The smooth or pulsed component of the ultraviolet radiation depends on the form of the primary energy release. Information on the dynamics of the heating process and the formation and equalization of the gas pressure in the flare transient layer has been obtained from the observed temperature dependence of the emission measure. The described scheme explains the set of flare phenomena and the correlation between hard X-rays with pulsed ultraviolet bursts.     

Flare coronal loop heating and hard X-ray emission from solar flares of August 23, 2005, and November 9, 2013

The thermal balance and hard X-ray emission of coronal loops for two solar events have been considered in the scope of a “standard” flare model. An important role of the thermal energy release is justified by the event of August 23, 2005, as an example. For the flare of November 9, 2013, it has been established that electrons accelerated at a flare loop top cannot maintain the observed hard X-ray fluxes from the flare footpoints, which indicates that charged particles are additionally accelerated in the chromosphere.

     

Radio-heliographic diagnostics of the potential flare productivity of active regions

As deduced from the data with high spatial resolution obtained at the radio heliographs of the Siberian Solar Radio Telescope (SSRT, 5.7 GHz) and the Nobeyama radio heliograph (NoRH, 17 GHz), radio brightness centers in the distribution of the Stokes parameter I are shifted relative to the distribution of the parameter V 1–2 days before an intense flare. It has been shown that this phenomenon can be related to the behavior of quasi-stationary sources over the inversion line of the radial component of the magnetic field (neutral-line associated sources (NLSs)). These sources have a brightness temperature up to 106 K and a circular polarization up to 90%. The origination of NLSs is associated with the outflow of a new magnetic flux into the atmosphere of an active region that is a classical factor of the flare activity. Therefore, an NLS is a precursor of power solar flares and can be used as a forecast factor. Owing to the high resolution of the SSRT, the deviation of the observed polarization distribution of microwave radiation of the active region from the normal one within the solar disk zone containing the active region can be used as a precursor of the preflare state of the active region. As a result, the single-frequency Tanaka-Enome criterion is modified. The use of the data from two radio heliographs (SSRT and NoRH) allows us to propose a two-frequency criterion of normal longitudinal zones that is more efficient for short-term forecasting of solar flares. Preflare features associated with the displacement of brightness centers in I and V, which is manifested as the transformation of NLSs into spot sources, are fine attributes added to forecast according to the two-frequency criterion. This is illustrated by an example of active region 10930, which produced power proton flares on December 6 and 13, 2006.     

A possible mechanism of stimulation of seismic activity by ionizing radiation of solar flares

A possible mechanism of earthquake triggering by ionizing radiation of solar flares is considered. A theoretical model and results of numerical calculations of disturbance of electric field, electric current, and heat release in lithosphere associated with variation of ionosphere conductivity caused by absorption of ionizing radiation of solar flares are presented. A generation of geomagnetic field disturbances in a range of seconds/tens of seconds is possible as a result of large-scale perturbation of a conductivity of the bottom part of ionosphere in horizontal direction in the presence of external electric field. Amplitude-time characteristics of the geomagnetic disturbance depend upon a perturbation of integral conductivity of ionosphere. Depending on relation between integral Hall and Pedersen conductivities of disturbed ionosphere the oscillating and aperiodic modes of magnetic disturbances may be observed. For strong perturbations of the ionosphere conductivities amplitude of pulsations may obtain ~10² nT. In this case the amplitude of horizontal component of electric field on the Earth surface obtains 0.01 mV/m, electric current density in lithosphere –10^–6 A/m², and the power density of heat release produced by the generated current is 10^–7 W/m³. It is shown that the absorption of ionizing radiation of solar flares can result in variations of a density of telluric currents in seismogenic faults comparable with a current density generated in the Earth crust by artificial pulsed power systems (geophysical MHD generator " Pamir-2” and electric pulsed facility " ERGU-600”), which provide regional earthquake triggering and spatiotemporal variation of seismic activity. Therefore, triggering of seismic events is possible not only by man-made pulsed power sources but also by the solar flares. The obtained results may be a physical basis for a novel approach to solve the problem of short-term earthquake prediction based on electromagnetic triggering phenomena.     

Analysis of the events that occurred on July 30, 2005, according to ground-based observations in the Ca II 8498 ? line and on board spacecraft

The observations of active region (AR) NOAA 10792 in the Ca II 8498 ? line with an ATB-1 solar telescope at the Sternberg State Astronomical Institute, Moscow State University (SSAI MSU) on July 30, 2005, are illustrated, and the events are analyzed using the data obtained on spacecraft. Three flares and accompanying coronal mass ejections (CMEs) are considered. It has been indicated that the beginning of the first compact CME lagged behind the flare onset by 3 min. Plasma ascended with acceleration that reached 0.4 km/s² at the flare maximum. The matter was also apparently accelerated after the flare maximum, since an ejection could only appear at the edge of the occulting C 2 LASCO coronograph disk at 0557 UT when acceleration is about 0.5 km/s². The second CME (of the halo type) leaded the beginning of the corresponding flare.