Electrons In Flares Research Articles

A Modeling Investigation for Solar Flare X-Ray Stereoscopy with Solar Orbiter/STIX and Earth-orbiting Missions

The Spectrometer/Telescope for Imaging X-rays (STIX) on board Solar Orbiter (SolO) provides a unique opportunity to systematically perform stereoscopic X-ray observations of solar flares with current and upcoming X-ray missions at Earth. These observations will produce the first reliable measurements of hard X-ray (HXR) directivity in decades, providing a new diagnostic of the flare-accelerated electron angular distribution and helping to constrain the processes that accelerate electrons in flares. However, such observations must be compared to modeling, taking into account electron and X-ray transport effects and realistic plasma conditions, all of which can change the properties of the measured HXR directivity. Here, we show how HXR directivity, defined as the ratio of X-ray spectra at different spacecraft viewing angles, varies with different electron and flare properties (e.g., electron angular distribution, highest-energy electrons, and magnetic configuration), and how modeling can be used to extract these typically unknown properties from the data. Finally, we present a preliminary HXR directivity analysis of two flares, observed by the Fermi Gamma-ray Burst Monitor and SolO/STIX, demonstrating the feasibility and challenges associated with such observations, and how HXR directivity can be extracted by comparison with the modeling presented here.

Radiation-driven diffusive transport of fast electrons in solar flares

Fast electron scattering on plasma ions due to stimulated Bremsstrahlung is investigated and modeled. Comparison with Coulomb scattering suggests that stimulated Bremsstrahlung scattering can be dominant in low-density, radiation-driven plasmas, provided that the radiation spectrum has a sufficiently high brightness temperature in the neighborhood of the plasma frequency. While stimulated Bremsstrahlung scattering cannot be easily observed in laboratory plasmas due to their small size, it should operate in large-scale astrophysical plasmas, such as those met in the flaring solar corona. The effect of the solar microwave radiation on fast-electron scattering is evaluated through a parameterized flaring corona model. We find that stimulated Bremsstrahlung greatly enhances the fast-electron scattering frequency in the flare magnetic loop, leading the transport of deka-keV electrons to occur in the diffusion regime, characterized by significant precipitation rates. This prediction is consistent with the interpretation of the above-loop-top hard x-ray and microwave emissions from the X3.1 flare of August 24, 2002. Our analysis indicates that stimulated Bremsstrahlung may play an essential role in the dynamics of fast electrons trapped in solar flare loops.

Dreicer Electric Field Definition and Runaway Electrons in Solar Flares

We analyze electron acceleration by a large-scale electric field E in a collisional hydrogen plasma under the solar flare coronal conditions based on approaches proposed by Dreicer and Spitzer for the dynamic friction force of electrons. The Dreicer electric field E Dr is determined as a critical electric field at which the entire electron population runs away. Two regimes of strong (E ≲ E Dr) and weak (E ≪ E Dr) electric field are discussed. It is shown that the commonly used formal definition of the Dreicer field leads to an overestimation of its value by about five times. The critical velocity at which the electrons of the “tail” of the Maxwell distribution become runaway under the action of the sub-Dreiser electric fields turns out to be underestimated by 3 times in some works because the Coulomb collisions between runaway and thermal electrons are not taken into account. The electron acceleration by sub-Dreicer electric fields generated in the solar corona faces difficulties.

Exploring the Origin of Solar Energetic Electrons. I. Constraining the Properties of the Acceleration Region Plasma Environment

Solar flare electron acceleration is an efficient process, but its properties (mechanism, location) are not well constrained. Via hard X-ray (HXR) emission, we routinely observe energetic electrons at the Sun, and sometimes we detect energetic electrons in interplanetary space. We examine if the plasma properties of an acceleration region (size, temperature, density) can be constrained from in situ observations, helping to locate the acceleration region in the corona, and infer the relationship between electrons observed in situ and at the Sun. We model the transport of energetic electrons, accounting for collisional and non-collisional effects, from the corona into the heliosphere (to 1.0 au). In the corona, electrons are transported through a hot, over-dense region. We test if the properties of this region can be extracted from electron spectra (fluence and peak flux) at different heliospheric locations. We find that cold, dense coronal regions significantly reduce the energy at which we see the peak flux and fluence for distributions measured out to 1.0 au, the degree of which correlates with the temperature and density of plasma in the region. Where instrument energy resolution is insufficient to differentiate the corresponding peak values, the spectral ratio of [7–10) to [4–7) keV can be more readily identified and demonstrates the same relationship. If flare electrons detected in situ are produced in, and/or transported through, hot, over-dense regions close to HXR-emitting electrons, then this plasma signature should be present in their lower-energy spectra (1–20 keV), observable at varying heliospheric distances with missions such as Solar Orbiter.

Collisional Plasma Temperature and Betatron Acceleration of Quasi-thermal Electrons in Solar Flares

Collisional Plasma Temperature and Betatron Acceleration of Quasi-thermal Electrons in Solar Flares

Statistical Study of Release Time and Its Energy Dependence of In Situ Energetic Electrons in Impulsive Solar Flares

AbstractUsing the fraction velocity dispersion analysis method, it has been shown recently that in two impulsive solar energetic electron (SEE) events, the release times of near‐relativistic electrons at the Sun for outward‐propagating electrons are energy dependent and are delayed compared to those of the downward‐propagating electrons. In this work, we perform a statistical study of the release time and its energy dependence of near‐relativistic electrons in impulsive SEE events. We use in situ observations from the WIND spacecraft and remote hard X‐ray observations from the RHESSI and/or Fermi spacecraft. The difference in the release times between outward electrons and downward electrons for 29 events is obtained. In all events, the release of the outward‐propagating electrons is delayed from those precipitating downward. In 26 of the 29 events, the release times of outward‐propagating electrons also show clear energy dependence. In 15 of these 26 events, in situ electron data from more than five energy channels were available. The delay time as a function of energy for nine of these can be fitted by a form proposed by G. Li et al. (2021, https://doi.org/10.1029/2021GL095138). The implication of this energy‐dependent release on the Magnetohydrodynamics turbulence property at the electron acceleration site is discussed.

Spectral and Imaging Diagnostics of Spatially Extended Turbulent Electron Acceleration and Transport in Solar Flares

Solar flares are efficient particle accelerators with a large fraction of released magnetic energy (10%–50%) converted into energetic particles such as hard X-ray producing electrons. This energy transfer process is not well constrained, with competing theories regarding the acceleration mechanism(s), including MHD turbulence. We perform a detailed parameter study examining how various properties of the acceleration region, including its spatial extent and the spatial distribution of turbulence, affect the observed electron properties, such as those routinely determined from X-ray imaging and spectroscopy. Here, a time-independent Fokker–Planck equation is used to describe the acceleration and transport of flare electrons through a coronal plasma of finite temperature. Motivated by recent nonthermal line broadening observations that suggested extended regions of turbulence in coronal loops, an extended turbulent acceleration region is incorporated into the model. We produce outputs for the density-weighted electron flux, a quantity directly related to observed X-rays, modeled in energy and space from the corona to chromosphere. We find that by combining several spectral and imaging diagnostics (such as spectral index differences or ratios, energy or spatial-dependent flux ratios, and electron depths into the chromosphere) the acceleration properties, including the timescale and velocity dependence, can be constrained alongside the spatial properties. Our diagnostics provide a foundation for constraining the properties of acceleration in an individual flare from X-ray imaging spectroscopy alone, and can be applied to past, current, and future observations including those from RHESSI and Solar Orbiter.

Bridging High-density Electron Beam Coronal Transport and Deep Chromospheric Heating in Stellar Flares

The optical and near-ultraviolet (NUV) continuum radiation in M-dwarf flares is thought to be the impulsive response of the lower stellar atmosphere to magnetic energy release and electron acceleration at coronal altitudes. This radiation is sometimes interpreted as evidence of a thermal photospheric spectrum with T ≈ 104 K. However, calculations show that standard solar flare coronal electron beams lose their energy in a thick target of gas in the upper and middle chromosphere (log10 column mass/[g cm−2] ≲ −3). At larger beam injection fluxes, electric fields and instabilities are expected to further inhibit propagation to low altitudes. We show that recent numerical solutions of the time-dependent equations governing the power-law electrons and background coronal plasma (Langmuir and ion-acoustic) waves from Kontar et al. produce order-of-magnitude larger heating rates than those that occur in the deep chromosphere through standard solar flare electron beam power-law distributions. We demonstrate that the redistribution of beam energy above E ≳ 100 keV in this theory results in a local heating maximum that is similar to a radiative-hydrodynamic model with a large, low-energy cutoff and a hard power-law index. We use this semiempirical forward-modeling approach to produce opaque NUV and optical continua at gas temperatures T ≳ 12,000 K over the deep chromosphere with log10 column mass/[g cm−2] of −1.2 to −2.3. These models explain the color temperatures and Balmer jump strengths in high-cadence M-dwarf flare observations, and they clarify the relation among atmospheric, radiation, and optical color temperatures in stellar flares.

Dataset for "Statistical study of release time and its energy dependence of in-situ energetic electrons in impulsive solar flares"

Dataset for "Statistical study of release time and its energy dependence of in-situ energetic electrons in impulsive solar flares"

Dataset for "Statistical study of release time and its energy dependence of in-situ energetic electrons in impulsive solar flares"

Dataset for "Statistical study of release time and its energy dependence of in-situ energetic electrons in impulsive solar flares"

Dataset for "Statistical study of release time and its energy dependence of in-situ energetic electrons in impulsive solar flares"

Dataset for "Statistical study of release time and its energy dependence of in-situ energetic electrons in impulsive solar flares"

Slow Shock Formation Upstream of Reconnecting Current Sheets

Abstract The formation, development, and impact of slow shocks in the upstream regions of reconnecting current layers are explored. Slow shocks have been documented in the upstream regions of magnetohydrodynamic (MHD) simulations of magnetic reconnection as well as in similar simulations with the kglobal kinetic macroscale simulation model. They are therefore a candidate mechanism for preheating the plasma that is injected into the current layers that facilitate magnetic energy release in solar flares. Of particular interest is their potential role in producing the hot thermal component of electrons in flares. During multi-island reconnection, the formation and merging of flux ropes in the reconnecting current layer drives plasma flows and pressure disturbances in the upstream region. These pressure disturbances steepen into slow shocks that propagate along the reconnecting component of the magnetic field and satisfy the expected Rankine–Hugoniot jump conditions. Plasma heating arises from both compression across the shock and the parallel electric field that develops to maintain charge neutrality in a kinetic system. Shocks are weaker at lower plasma β, where shock steepening is slow. While these upstream slow shocks are intrinsic to the dynamics of multi-island reconnection, their contribution to electron heating remains relatively minor compared with that from Fermi reflection and the parallel electric fields that bound the reconnection outflow.

Characterizing Magnetic Connectivity of Solar Flare Electron Sources to STEREO Spacecraft Using ADAPT-WSA Modeling

Abstract Onsets and intensity profiles of six energetic (E > 30 keV) electron events common to STEREO A and B (STA and STB) spacecraft were analyzed by Klassen et al. with the STEREO Solar Electron and Proton Telescopes when the spacecraft were separated by <70° in solar longitude. All six events were characterized by earlier onsets and higher peak intensities for the spacecraft with magnetic footpoints at the solar longitudes of larger source separations. The 2.5 Rs footpoint locations, based on Parker spiral (PS) calculations with spacecraft solar wind (SW) speeds V sw, are compared with 5 Rs footpoint locations calculated by selected realizations of ADAPT-WSA (Air Force Data Assimilative Photospheric flux Transport—Wang–Sheeley–Arge) solar wind (SW) forecast model runs for each spacecraft. ADAPT-WSA footpoint locations support the Klassen et al. results of azimuthally nonuniform injections from two shock-associated events and confirm locations for the flare source event on 2014 July 17. Substantial footpoint differences of the two methods diminish the disparity of the flare event of 2014 May 2 but exacerbate the case of two flare electron events on 2014 August 1. As limited test cases for a comparison of ADAPT-WSA and PS methods at slightly different source surfaces, the Carrington longitude differences range from several to ∼30°. We review the importance and limitations of methods for determining the solar magnetic footpoints for solar energetic particle studies.

Design and verification of the HXI collimator on the ASO-S mission

A space-borne hard X-ray collimator, comprising 91 pairs of grids, has been developed for the Hard X-ray Imager (HXI). The HXI is one of the three scientific instruments onboard the first Chinese solar mission: the Advanced Space-based Solar Observatory (ASO-S). The HXI collimator (HXI-C) is a spatial modulation X-ray telescope designed to observe hard X-rays emitted by energetic electrons in solar flares. This paper presents the detailed design of the HXI-C for the qualification model that will be inherited by the flight model. Series tests on the HXI-C qualification model are reported to verify the ability of the HXI-C to survive the launch and to operate normally in on-orbit environments. Furthermore, results of the X-ray beam test for the HXI-C are presented to indirectly identify the working performance of the HXI-C.

Dynamical Modulation of Solar Flare Electron Acceleration due to Plasmoid-shock Interactions in the Looptop Region

Abstract A fast-mode shock can form in the front of reconnection outflows and has been suggested as a promising site for particle acceleration in solar flares. Recent developments in the study of magnetic reconnection have shown that numerous plasmoids can be produced in a large-scale current layer. Here we investigate the dynamical modulation of electron acceleration in the looptop region when plasmoids intermittently arrive at the shock by combining magnetohydrodynamics simulations with a particle kinetic model. As plasmoids interact with the shock, the looptop region exhibits various compressible structures that modulate the production of energetic electrons. The energetic electron population varies rapidly in both time and space. The number of 5–10 keV electrons correlates well with the compression area, while that of >50 keV electrons shows good correlation with the strong compression area but only moderate correlation with shock parameters. We further examine the impacts of the first plasmoid, which marks the transition from a quasi-steady shock front to a distorted and dynamical shock. The number of energetic electrons is reduced by ∼20% at 15–25 keV and nearly 40% for 25–50 keV, while the number of 5–10 keV electrons increases. In addition, the electron energy spectrum above 10 keV evolves softer with time. We also find that double or even multiple distinct sources can develop in the looptop region when the plasmoids move across the shock. Our simulations have strong implications to the interpretation of nonthermal looptop sources, as well as the commonly observed fast temporal variations in flare emissions, including the quasi-periodic pulsations.

Probing solar flare accelerated electron distributions with prospective X-ray polarimetry missions

Solar flare electron acceleration is an extremely efficient process, but the method of acceleration is not well constrained. Two of the essential diagnostics, electron anisotropy (velocity angle to the guiding magnetic field) and the high energy cutoff (highest energy electrons produced by the acceleration conditions: mechanism, spatial extent, and time), are important quantities that can help to constrain electron acceleration at the Sun but both are poorly determined. Here, by using electron and X-ray transport simulations that account for both collisional and non-collisional transport processes, such as turbulent scattering and X-ray albedo, we show that X-ray polarization can be used to constrain the anisotropy of the accelerated electron distribution and the most energetic accelerated electrons together. Moreover, we show that prospective missions, for example CubeSat missions without imaging information, can be used alongside such simulations to determine these parameters. We conclude that a fuller understanding of flare acceleration processes will come from missions capable of both X-ray flux and polarization spectral measurements together. Although imaging polarimetry is highly desired, we demonstrate that spectro-polarimeters without imaging can also provide strong constraints on electron anisotropy and the high energy cutoff.

Scattering of Energetic Electrons by Heat-flux-driven Whistlers in Flares

Abstract The scattering of electrons by heat-flux-driven whistler waves is explored with a particle-in-cell simulation relevant to the transport of energetic electrons in flares. This simulation is initiated with a large heat flux produced by using a kappa distribution of electrons with positive velocity and a cold return current beam. This system represents energetic electrons escaping from a reconnection-driven energy-release site. This heat-flux system drives large-amplitude oblique whistler waves propagating both along and against the heat flux, as well as electron acoustic waves. While the waves are dominantly driven by the low-energy electrons, including the cold return current beam, the energetic electrons resonate with and are scattered by the whistlers on timescales of the order of a hundred electron cyclotron times. Peak whistler amplitudes of and angles of ∼60° with respect to the background magnetic field are observed. Electron perpendicular energy is increased, while the field-aligned electron heat flux is suppressed. The resulting scattering mean-free-paths of energetic electrons are small compared with the typical scale size of energy-release sites in flares, which might lead to the effective confinement of energetic electrons required for the production of very energetic particles.

On Thermal Runaway Electrons and the Polarization of X-ray Emission in Solar Flares

A model for the thermal runaway of electrons in solar flares based on an approximate analytical solution of the kinetic equation with a linearized Landau collision integral is considered. Coulomb collisions are shown to make the flux of runaway electrons with a very high temperature nearly isotropic. The derived electron distribution function is used to estimate the polarization of the hard X-ray bremsstrahlung of solar flares. Since the anisotropy of the flux of electrons is low, the polarization of their bremsstrahlung does not exceed 3–4% at an energy of about 15 keV, which creates great difficulties for future extra-atmospheric polarization observations. Furthermore, the Compton scattering of hard X-ray emission by the photosphere and magnetic field inhomogeneity can severely distort the expected results and can make their interpretation difficult. The prospects for space experiments to measure the polarization of the hard X-ray emission from solar flares are discussed.

A Maximum Entropy Argument for the Slopes of Power-law Particle Spectra in Solar Flares

Abstract The maximum entropy formalism is used to infer the spectral index of power-law particle spectra in the heliosphere. The entropy-maximization argument by Brown et al. is revisited and generalized by relaxing the assumption of a particle spectrum extending to an infinite energy. The results for particle spectra with a finite upper cutoff energy are shown to be qualitatively different from those for spectra extending to infinity. The dependence of the predicted spectral index on the upper cutoff energy is determined. The relevance of the predicted values of the spectral index to the observed spectra of accelerated electrons in solar flares and ion tails in the solar wind is discussed.

Non-thermal electrons from solar nanoflares

Context. We introduce a model for including accelerated particles in pure magnetohydrodynamics (MHD) simulations of the solar atmosphere. Aims. We show that the method is viable and produces results that enhance the realism of MHD simulations of the solar atmosphere. Methods. The acceleration of high-energy electrons in solar flares is an accepted fact, but is not included in the most advanced 3D simulations of the solar atmosphere. The effect of the acceleration is not known, and here we introduce a simple method to account for the ability of the accelerated electrons to move energy from the reconnection sites and into the dense transition zone and chromosphere. Results. The method was only run for a short time and with low reconnection energies, but this showed that the reconnection process itself changes, and that there is a clear effect on the observables at the impact sites of the accelerated electrons. Further work will investigate the effect on the reconnection sites and the impact sites in detail.