Superfine time structure and polarization of hard X-ray emission during solar flares: Simulation of isolated pulses

A superfine time structure has been detected recently via hard X-ray satellite observations during solar flares. Some pulses are hundreds of milliseconds in length. Time series are sharply nonstationary sequences of overlapping pulses. We interpreted a similar time structure in a model of the nonstationary kinetics of accelerated electron beams. In this work, we present calculation results of the degree of polarization of the hard X rays of solar flares with millisecond pulses. The dependence of the polarization degree on the plasma concentration, radiation energy, and the observation angle has been derived from calculations with the thick-target nonstationary kinetics model for rectangular and triangular individual pulses of accelerated electrons in the region of injection with the angular dependence cos²ⁿ θ. It is shown that the degree of polarization does not exceed 78% and decreases down to 50–65% 20 s after the beginning of the injection.     

太阳宇宙线高能电子能谱的形成

提出了一个太阳脉冲和经变耀斑中高能太阳宇宙线电子能谱的形成模型，探讨了高能电子通过日冕捕获区的库仑损失、轫致辐射和同步辐射等物理过程，首次研究了日冕等离子体尾场对太阳宇宙线电子的加速及其能谱的形成．所得结果和观测谱能很好地符合，从而较合理地阐明了脉冲耀斑和经变耀斑两类太阳宇宙线高能电子谱的结构．     

Modeling of Physical Processes by Analysis of Hard X-Ray and Microwave Radiations in the Solar Flare of November 10, 2002

For electron acceleration during solar flares, it is very important to determine the pitch-angle and energy dependences of the electron distribution function. At present, this cannot be done directly from observations. Therefore, it is necessary to perform a numerical simulation of the propagation of accelerated electrons in the magnetic field of the flare loop (loops) and calculate the X-ray and radio emissions. For the solar flare of November 10, 2002, we have obtained qualitative and quantitative agreements of modeled X-ray and radio maps with the RHESSI satellite and Nobeyama Radioheliograph data. We have determined the flare model parameters that agree with observations. The pitch-angle anisotropy of electrons determined by highly directional functions of the S(α) = cos⁸(α) type, the energy spectrum consist of two electron populations, the low-energy part of the spectrum up to an energy of break of 350 keV is characterized by a power law with the exponent δ₁ = 2.7–2.9, and the energy spectrum is more rigid above 420 keV (δ₂ = 2–2.3).     

Diagnostic Analysis of the Solar Proton Flares of September 2017 by Their Radio Bursts

The powerful solar flares that occurred on September 4–10, 2017 are analyzed based on a quantitative diagnostics method for proton flares developed at the Institute of Terrestrial Magnetism, the Ionosphere and Radio-Wave Propagation (IZMIRAN) in the 1970–1980s. We show that the fluxes and energy spectra of the protons reached the Earth with the energies of tens of MeV qualitatively and quantitatively correspond to the intensity and frequency spectra of the microwave radio bursts in the range of 2.7–15.4 GHz. Specifically, the flare of September 4 with a peak radio flux S ~ 2000 sfu at the frequency f ~ 3 GHz (i.e., with the soft radio spectrum) was accompanied by a significant proton flux J (>10 MeV) ~100 pfu and a soft energy spectrum with the index γ ~3.0, while the strong flare on September 10 with S ~ 21000 sfu at f ~ 15 GHz (i.e., with the hard radio spectrum) led to a very intense proton event with J (>10 MeV) ~1000 pfu with a hard spectrum (γ ~ 1.4), including the ground level enhancement (GLE72). This is further evidence that microwave radio data can be successfully used in diagnostics of proton flares independently of a specific source of particle acceleration at the Sun, in particular, with the IZMIRAN method.     

Peculiarities of the outer radiation belt dynamics during the strong magnetic storm of May 15, 2005

The dynamics of energetic electrons (E _e =0.17–8 MeV) and protons (E _p =1 MeV) of the outer radiation belt during the magnetic storm of May 15, 2005, at high (GOES-10 and LANL-84 geosynchronous satellites) and low (Meteor-3M polar satellite) altitudes is analyzed. The data have been compared to the density, plasma velocity, solar wind, and magnetic field measurements on the ACE satellite and geomagnetic disturbances. During the magnetic storm main phase, the nighttime boundary of the region of trapped radiation and the center of westward electrojet shifted to L ～ 3. Enhancements of only low-energy electrons were observed on May 15, 2005. The belt of relativistic electrons with a maximum at L ～ 4 was formed during the substorm, the amplitude of which reached its maximum at ～0630 UT on May 16. The results are in good agreement with the regularity relating the position of a maximum of the new relativistic electron belt, boundaries of the trapped radiation region, and extreme low-latitude position of westward electrojet center to the Dst variation amplitude.     

Prediction of maximal daily average values of relativistic electron fluxes in geostationary orbit during the magnetic storm recovery phase

The relation of the maximal daily average values of the relativistic electron fluxes with an energy higher than 2 MeV, obtained from the measurements on GOES geostationary satellites, during the recovery phase of magnetic storms to the solar wind parameters and magnetospheric activity indices has been considered. The parameters of Pc5 and Pi1 geomagnetic pulsations and the relativistic electron fluxes during the prestorm period and the main phase of magnetic storms have been used together with the traditional indices of geomagnetic activity (A _E, K _p, D _st). A simple model for predicting relativistic electron fluxes has been proposed for the first three days of the magnetic storm recovery phase. The predicted fluxes of the outer radiation belt relativistic electrons well correlate with the observed values (R ∼ 0.8–0.9).     

磁场重联中电子加速问题的物理分析和数值研究

观测表明耀斑中电子加速发生在软X射线耀斑环上方的磁重联区域.在重联电流片中被super Dreicer电场直接加速似乎是产生能量在10keV～10MeV之间高能电子的最直接的方式.本文的结果证明纵向电磁场可以有效地将电子“锁”在重联电流片上,使得横向电场得以直接加速电子.对于解释产生相对论性粒子的脉冲式耀斑,这可能是一个有效的机制.     

Outer radiation belt of relativistic electrons during the minimum of the 23rd solar cycle

The data on fluxes of electrons with energy Ee > 1 MeV and on radiation doses under the Al shielding of about 2 g/cm² measured on the GLONASS satellite (circular orbit with altitude 20000 km and inclination 65°) for the period from December 2006 through May 2010 are analyzed. The minimum of the 23rd solar cycle turned out to be the longest for all over the space exploration age. Consequently, average semiannual electron fluxes and daily radiation doses are showing the decrease by more than an order of magnitude in comparison with the levels observed in 2007. We present an example of a diffusion wave of relativistic electrons; the wave develops in a period between magnetic storms. This process may result in a significant increase of the radiation dose measured in the orbit, even under the conditions of weak geomagnetic disturbances. The dynamics of variations in relativistic electron fluxes during the magnetic storm of April 5?C6, 2010, is discussed so far as this is the first strong flux enhancement in the 24th solar cycle.     

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.     

Response of the radiation belt electron flux to the solar wind velocity: Parameterization by radial distance and energy

The solar wind velocity is the primary driver of the electron flux variability in Earth's radiation belts. The response of the logarithmic flux (“log-flux”) to this driver has been determined at the geosynchronous orbit and at a fixed energy [Baker, D.N., McPherron, R.L., Cayton, T.E., Klebesadel, R.W., 1990. Linear prediction filter analysis of relativistic electron properties at 6.6 RE. Journal of Geophysical Research 95(A9), 15,133–15,140) and as a function of L shell and fixed energy [Vassiliadis, D., Klimas, A.J., Kanekal, S.G., Baker, D.N., Weigel, R.S., 2002. Long-term average, solar-cycle, and seasonal response of magnetospheric energetic electrons to the solar wind speed. Journal of Geophysical Research 107, doi:10.1029/2001JA000506). In this paper we generalize the response model as a function of particle energy (0.8–6.4 MeV) using POLAR HIST measurements. All three response peaks identified earlier figure prominently in the high-altitude POLAR measurements. The positive response around the geosynchronous orbit is peak P₁ (τ=2±1 d; L=5.8±0.5; E=0.8–6.4 MeV), associated with high-speed, low-density streams and the ULF wave activity they produce. Deeper in the magnetosphere, the response is dominated by a positive peak P₀ (0±1 d; 2.9±0.5R_E; 0.8–1.1 MeV), of a shorter duration and producing lower-energy electrons. The P₀ response occurs during the passage of geoeffective structures containing high IMF and high-density parts, such as ICMEs and other mass ejecta. Finally, the negative peak V₁ (0±0.5 d; 5.7±0.5R_E; 0.8–6.4 MeV) is associated with the “D_st effect” or the quasiadiabatic transport produced by ring-current intensifications. As energies increase, the P₁ and V₁ peaks appear at lower L, while the D_st effect becomes more pronounced in the region L<3. The P₀ effectively disappears for E>1.6 MeV because of low statistics, although it is evident in individual events. The continuity of the response across radial and energy scales supports the earlier hypothesis that each of the three modes corresponds to a qualitatively different type of large-scale electron acceleration and transport.     

Dynamics of radiation belt relativistic electrons in November 2004–January 2005

The radiation belt dynamics during the extreme solar events in November 2004 and January 2005 is studied based on the measurements of relativistic electrons (with energies of 0.8–8 MeV) on the Express-A2 geostationary satellite and Meteor-3M polar satellite. New radiation belts of relativistic electrons in the space (L ～ 3) between the stationary outer and inner belts were formed as a result of either superstorm (|Dst|_max = 373 and 289 nT). The position of the maximums of these belts (L _max = 2.9 and 3.1) coincides with the known dependence of L _max on the magnetic storm Dst variation amplitude: |Dst|_max = 2.75 × 10⁴/L _max ⁴ . In November–December the new belt very slowly (ΔL ～ 0.1 per month) shifted toward the Earth. During the series of moderate (～100 nT) magnetic storms that developed as a result of the extreme solar events in January 2005, the belt in the space shifted toward deeper L shells (L ～ 2.5). The moderate January storms produced new belts with L _max ≥ 4.     

Effective energy loss per electron-ion pair in proton aurora

Effective energy loss per electron-ion pair produced, <xi>(E ₀), as a function of a particle’s initial energy has been obtained for proton transport in the atmosphere. The influence of some transport parameters on the shape of <xi>(E ₀) has been studied. Comparisons with the case of electron transport and with other results were made. It has been shown that: 1. for E ₀>1 keV, <xi>(E ₀) varies within the range 30–36 eV; 2. as E ₀ increases the value of <xi>(E ₀) tries to attain an asymptotic value that is the same as for electrons (\approx35 eV); 3. <xi>(E ₀) strongly depends on the average energy of secondary electrons, but the energy distribution of secondary electrons is not as important. The range of possible changes in <xi>(E ₀) associated with discrepancies in cross sections has been obtained.     

Experimental evidence for direct penetration of ULF waves from the solar wind and their possible effect on acceleration of radiation belt electrons

The event of March 12–19, 2009, when a moderately high-speed solar wind stream flew around the Earth’s magnetosphere and carried millihertz ultralow-frequency (ULF) waves, has been analyzed. The stream caused a weak magnetic storm (D _{st min} = −28 nT). Since March 13, fluxes of energetic (up to relativistic) electrons started increasing in the magnetosphere. Comparison of the spectra of ULF oscillations observed in the solar wind and magnetosphere and on the Earth’s surface indicated that a stable common spectral peak was present at frequencies of 3–4 mHz. This fact is interpreted as evidence that waves penetrated directly from the solar wind into the magnetosphere. Possible scenarios describing the participation of oscillations in the acceleration of medium-energy (E > 0.6 MeV) and high-energy (E > 2.0 MeV) electrons in the radiation belt are discussed. Based on comparing the event with the moderate magnetic storm of January 21–22, 2005, we concluded that favorable conditions for analyzing the interaction between the solar wind and the magnetosphere are formed during a deep minimum of solar activity.     

Solar proton increases and dynamics of the electron outer radiation belt during solar events in December 2006

Increases in solar protons and variations in the electron and proton fluxes from the outer radiation belt are studied based on the GLONASS satellite measurements (the circular orbit at an altitude of ～20000 km with an inclination of ～65°) performed in December 2006. Indications in the channels, registered protons with energies of Ep = 3–70 MeV and electrons with energies of Ee > 0.04 and >0.8 MeV, are analyzed. The data on electrons with Ee = 0.8–1.2 MeV, measured on the Express-A3 geostationary satellite, are also presented. Before the strong magnetic storm of December 14 (|Dst|_max = 146 nT), the maximum of the outer belt electrons with the energy >0.7 MeV was observed at L ～ 4.5. After the storm, the fluxes of these electrons increased by more than an order of magnitude as compared to the prestorm level, and the maximum of a “new” belt shifted to L < 4 (minimal L reached by the GLONASS orbit). Under quiet geomagnetic conditions, solar protons with the energies >3 MeV fill only high-latitude legs of the GLONASS orbit. During the strong magnetic storm of December 15, the boundary of proton penetration into the magnetosphere almost merged with the orbital maximum of the proton radiation belt.     

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.     

磁层相对论电子通量变化与磁暴/亚暴的关系

本文分析了1 AU处的行星际磁场、太阳风速度、Kp指数、Dst和AE的变化关系,以及它们和地球同步轨道附近相对论电子通量的变化关系.分析说明,当行星际磁场Bz分量出现南向扰动和太阳风速度增大超过500 km/s时,地球磁层中常常发生磁暴/亚暴活动.在磁暴主相期间,相对论电子(能量E≥1 MeV)通量下降;而在磁暴恢复相期间,相对论电子通量恢复上升.但是,只有在伴随有高强度（AE≥500 nT）的持续性亚暴活动的磁暴恢复相期间,相对论电子的通量才能增长到超过暴前通量值,且能量低于300 keV的亚暴电子的通量越高,相对论电子的通量越高,反之则越低.亚暴注入电子数的多少很大程度上决定了磁暴恢复相期间相对论电子数的多少,这说明亚暴活动注入能量低于300 keV的亚暴电子是磁层相对论电子的一个重要来源.     

Horizontal electrojet associated with the sun-aligned arcs

Analysis of two strong sun-aligned arcs over the Canadian Eureka Observatory (89° CGM) near the north magnetic pole and accompanying related ground magnetometer measurements has identified an electrojet current of ∼1×10⁴ A flowing within the arcs in a sunward direction. The electrojet current was carried by low energy electrons created by impacting precipitation drifting at E×B/B² velocity within the arcs, where E is the dawn-to-dusk electric field. One of the arcs moved rapidly in a dawn to dusk direction. The measured arc velocity was 365 m/s. This agrees well with the velocity of 380 m/s inferred from the magnetic field signature of the electrojet current. This study suggests that such an electrojet is present whenever a polar arc is set up. However, a few conditions are required to observe clear ground magnetic signatures of the electrojet: (1) quiet local magnetic conditions; (2) a single sun aligned arc near or moving across zenith; and (3) arc excitation by ≥1 keV electrons.     

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.     

Intersector disbalance of the large-scale open solar magnetic field fluxes,active and passive boundaries,and solar-terrestrial extrastorms

The dynamics (from rotation to rotation) of the absolute values of the large-scale open solar magnetic field fluxes in the four-sector field structure has been considered for the first time, using CRs 2032–2035 in July–October 2005 as examples. An important role of the ratio of the fluxes at the eastern and western sector boundaries (Φ _E /Φ _W ) is confirmed. As in the cases of the two-sector structure, Φ _E /Φ _W > 1 is typical of active rigidly corotating boundaries with intense sunspot formation, flares, and interplanetary and geomagnetic disturbances. A remarkable property of the considered structure was the presence of a rapidly increasing flux in an initially narrow sector and the flux interaction with a stable rigidly corotating sector in the zone of the main active longitudes, which caused an unexpectedly strong geoeffective long-range action of flares near the corresponding active boundary.     

Powerful nonstationary processes on the sun: Spatio-temporal structure and efficient particle acceleration

Data on high-energy processes on the Sun are summarized. We refine the classification of flares and substantiate the view that a coronal mass ejection and a flare proper are manifestations of the same common process, at least for the most powerful events. Next, we analyze data on the acceleration of electrons (RHESSI, Mars Odyssey) and protons. The existence of two peaks of hard X-ray emission spaced 10–20 min apart and the evolution of its spectra are shown to be indicative of two acceleration episodes. We have analyzed the spectra of 172 proton increases identified with the ratio of the proton fluxes at energies above 10 and 100 MeV near the Earth. These spectra turn out to be virtually the same for most of the large flares under favorable conditions for the escape of particles from the corona and their propagation in the interplanetary space. This is an argument for the invariance of the main features of efficient particle acceleration in powerful events. This process takes place at the explosive phase of a flare and its source is located low, immediately above the chromosphere, in the region adjacent to sunspots. There is a reason to believe that, in this case, a rapid simultaneous acceleration of electrons and protons takes place with the capture of some fraction of the particles into magnetic traps. However, there exist a few events in which an additional number of protons with energies as high as 10–30 MeV escape from the corona at the post-eruptive phase of flare development. Analysis of these cases with softer particle spectra more likely suggests an additional particle acceleration at coronal heights (about 30 000 km) than the facilitation of particle escape from magnetic traps. We estimate the contribution from the proton flux at an energy above 10 MeV arising at the post-eruptive phase of a flare to the total particle flux at the maximum of a proton increase and discuss possible particle acceleration mechanisms at significant coronal heights.