Electrons In Flares Research Articles

SOLAR AURORAS

This paper deals with the acceleration of high-energy flare electrons by field-parallel electric fields in an approach tailored after the auroral acceleration process. Electromagnetic energy, derived from the release of magnetic shear stresses, is converted into kinetic energy of particles. The stress release is enabled by field-aligned potential drops generated by anomalous resistivity of highly filamentary currents. The high-energy flare electrons are identified with runaway particles of this process. The magnetic shear stresses originate from Alfvén waves emitted from high-beta loop-top plasma which is produced by braking of the outflow from a reconnection site higher up in the corona. Partial reflection of the waves at the interface to the chromosphere leads to evaporation of chromospheric plasma and creation of a strongly filamentary structure in the sheared coronal field. The energy conversion process propagates spontaneously, like an erosion process in three dimensions. The overall stress release site forms a thin triangular sheet growing along and perpendicular to the field. After about one second, its cross-section perpendicular to B has grown to tens of square kilometers. This spontaneous growth strongly alleviates the demands on the primary filamentary structure posed by the condition of current criticality. Energy flux and mean energy are of the magnitude typical for hard X-rays producing electrons. Their strong dependence on the ambient magnetic field in combination with the fast propagation of the energy conversion sites could lead to energy-dependent time delays of a few 100 ms, much longer than the time-of-flight effects of the electrons.

TIME DELAYS IN QUASI-PERIODIC PULSATIONS OBSERVED DURING THE X2.2 SOLAR FLARE ON 2011 FEBRUARY 15

We report observations of quasi-periodic pulsations (QPPs) during the X2.2 flare of 2011 February 15, observed simultaneously in several wavebands. We focus on fluctuations on time scale 1-30 s and find different time lags between different wavebands. During the impulsive phase, the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) channels in the range 25-100 keV lead all the other channels. They are followed by the Nobeyama RadioPolarimeters at 9 and 17 GHz and the Extreme Ultra-Violet (EUV) channels of the Euv SpectroPhotometer (ESP) onboard the Solar Dynamic Observatory (SDO). The Zirconium and Aluminum filter channels of the Large Yield Radiometer (LYRA) onboard the Project for On-Board Autonomy (PROBA2) satellite and the SXR channel of ESP follow. The largest lags occur in observations from the Geostationary Operational Environmental Satellite (GOES), where the channel at 1-8 {\AA} leads the 0.5-4 {\AA} channel by several seconds. The time lags between the first and last channels is up to 9 s. We identified at least two distinct time intervals during the flare impulsive phase, during which the QPPs were associated with two different sources in the Nobeyama RadioHeliograph at 17 GHz. The radio as well as the hard X-ray channels showed different lags during these two intervals. To our knowledge, this is the first time that time lags are reported between EUV and SXR fluctuations on these time scales. We discuss possible emission mechanisms and interpretations, including flare electron trapping.

On bremsstrahlung radiation of accelerated electrons in solar flares

We have calculated the spectrum and polarization of the bremsstrahlung hard X-ray radiation produced by nonrelativistic electrons that are accelerated during a solar flare. The distribution function of accelerated electrons is taken from the self-consistent solution of the kinetic equation allowing for Coulomb collisions and an electric field of reverse current in plasma. The computed polarization of the hard X-ray polarization is shown to be appreciably lower than the value given by simplified thick-target models without considering the reverse current.

THREE-DIMENSIONAL SIMULATIONS OF GYROSYNCHROTRON EMISSION FROM MILDLY ANISOTROPIC NONUNIFORM ELECTRON DISTRIBUTIONS IN SYMMETRIC MAGNETIC LOOPS

Microwave emission of solar flares is formed primarily by incoherent gyrosynchrotron radiation generated by accelerated electrons in coronal magnetic loops. The resulting emission depends on many factors, including pitch-angle distribution of the emitting electrons and the source geometry. In this work, we perform systematic simulations of solar microwave emission using recently developed tools (GS Simulator and fast gyrosynchrotron codes) capable of simulating maps of radio brightness and polarization as well as spatially resolved emission spectra. A 3D model of a symmetric dipole magnetic loop is used. We compare the emission from isotropic and anisotropic (of loss-cone type) electron distributions. We also investigate effects caused by inhomogeneous distribution of the emitting particles along the loop. It is found that effect of the adopted moderate electron anisotropy is the most pronounced near the footpoints and it also depends strongly on the loop orientation. Concentration of the emitting particles at the loop top results in a corresponding spatial shift of the radio brightness peak, thus reducing effects of the anisotropy. The high-frequency (around 50 GHz) emission spectral index is specified mainly by the energy spectrum of the emitting electrons; however, at intermediate frequencies (around 10-20 GHz), the spectrum shape is strongly dependent on the electron anisotropy, spatial distribution, and magnetic field nonuniformity. The implications of the obtained results for the diagnostics of the energetic electrons in solar flares are discussed.

A diffusive description of the focused transport of solar energetic particles

The transport of solar energetic charged particles along the interplanetary magnetic field in the ecliptic plane of the sun can be described roughly by a one-dimensional diffusion equation. Large-scale spatial variations of the guide magnetic field can be taken into account by adding an additional term to the diffusion equation that includes the effect of adiabatic focusing. We solve this equation analytically by assuming a point-like particle injection in time and space and a spatial power-law dependence for the focusing length and the spatial diffusion coefficient. We infer the intensity- and anisotropy-time profiles of solar energetic particles from this solution. Through these the influence of different assumptions for the diffusion parameters can be seen in a mathematically closed form. The comparison of calculated and measured intensity- and anisotropy-time profiles, which are a powerful diagnostic tool for interplanetary particle transport, gives information about the large-scale spatial dependence of the focusing length and the diffusion coefficient. For an exceptionally large solar energetic particle event, which did occur on 2001 April 15, we fit the 27−512 keV electron intensities and anisotropies observed by the Wind spacecraft using the theoretically derived profiles. We find a linear spatial dependence of the mean free path along the guiding magnetic field. We also find the mean free path to be energy independent, which supports the theory of “velocity-dependent diffusion”. This means that the intensity profiles for the discussed energies exhibit the same shape if they are plotted against the traveled distance and not against the time. In this case the profiles differ only in their maximum values and we can determine the energy spectra of the solar flare electrons out of the scaling factor we need to fit the data. The derived spectra exhibits a power-law dependence ∝E −3 kin in an energy range from ∼50 keV to ∼500 keV.

Deducing Electron Properties from Hard X-ray Observations

X-radiation from energetic electrons is the prime diagnostic of flare-accelerated electrons. The observed X-ray flux (and polarization state) is fundamentally a convolution of the cross-section for the hard X-ray emission process(es) in question with the electron distribution function, which is in turn a function of energy, direction, spatial location and time. To address the problems of particle propagation and acceleration one needs to infer as much information as possible on this electron distribution function, through a deconvolution of this fundamental relationship. This review presents recent progress toward this goal using spectroscopic, imaging and polarization measurements, primarily from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). Previous conclusions regarding the energy, angular (pitch angle) and spatial distributions of energetic electrons in solar flares are critically reviewed. We discuss the role and the observational evidence of several radiation processes: free-free electron-ion, free-free electron-electron, free-bound electron-ion, photoelectric absorption and Compton backscatter (albedo), using both spectroscopic and imaging techniques. This unprecedented quality of data allows for the first time inference of the angular distributions of the X-ray-emitting electrons and improved model-independent inference of electron energy spectra and emission measures of thermal plasma. Moreover, imaging spectroscopy has revealed hitherto unknown details of solar flare morphology and detailed spectroscopy of coronal, footpoint and extended sources in flaring regions. Additional attempts to measure hard X-ray polarization were not sufficient to put constraints on the degree of anisotropy of electrons, but point to the importance of obtaining good quality polarization data in the future.

Hinode/EIS plasma diagnostics in the flaring solar chromosphere

Context: The impulsive phase of solar flares is a time of rapid energy deposition and heating in the lower solar atmosphere, leading to changes in the temperature, density, ionisation and velocity structure of this region. Aims: We aim to study the lower atmosphere during the impulsive phase of a flare using imaging and spectroscopic data from Hinode/EIS, RHESSI and TRACE. We place these observations in context by using a wide range of temperature observations from each instrument. Methods: We analyse sparse raster data from the Hinode/EIS spectrometer to derive the density and line-of-sight velocity in flare footpoints, in a GOES C6.6 flare observed on 05-June-2007. The raster duration was 150s across the centre of a small active region, allowing multiple exposures of the flare ribbons and footpoints. Using RHESSI and Hinode/XRT we test both non-thermal and thermal models for the HXR emission. Results: During the flare impulsive phase, we find evidence from XRT for flare footpoints at temperatures exceeding 7 MK. We measure the electron number density increasing up to a few ×10¹⁰ cm⁻³ in the footpoints, at temperatures of \~1.5-2 MK, accompanied by small downflows at temperatures below Fe XIII and upflows of up to \~140 km s⁻¹ at temperatures above. This is reasonable in the context of HXR diagnostics of the flare electron beam. The electrons inferred have sufficient energy to affect the chromospheric ionisation structure. Conclusions: EIS sparse raster data coupled with RHESSI imaging and spectroscopy prove useful here in studying the lower atmosphere of solar flares, and in this event suggest heat deposition relatively high in the chromosphere drives chromospheric evaporation while increasing the observed electron densities at footpoints. However, from RHESSI spectral fitting it is not possible to say whether the data are more consistent with a model including a non-thermal beam, or purely thermal model.

Kinetic Models for Whistler Wave Scattering of Electrons in the Solar Corona and Wind

Kinetic models are necessary to describe the physical processes associated with non-Maxwellian velocity distribution functions (VDFs) of electrons or ions in the solar corona and wind. It is shown that pitch-angle scattering of electrons in the solar wind needs to be considered in kinetic solar wind models. Coulomb collisions are not efficient enough to provide this scattering, but resonant interaction with whistler waves is. A solar wind model for undisturbed fast wind is presented, and the influence of scattering on flare electron propagation is investigated. Furthermore, it is found that resonant interaction of electrons with whistler waves is capable of producing suprathermal tails of electron distributions even under quiet conditions without flare activity.

Scaling of particle acceleration in 3D reconnection at null points

Context. The strong electric fields associated with magnetic reconnection are likely to be responsible for the presence of high energy protons and electrons observed in solar flares. There is much evidence for 3D reconnection in the solar corona, and we discuss particle acceleration at 3D reconnection sites. The simplest configuration for 3D reconnection is at a 3D null point, where reconnection can take place in spine and fan modes. Aims. The aim is to understand the properties of accelerated particles generated by 3D magnetic reconnection, using a test particle approach, and thus contribute to understanding the origin of high energy protons and electrons in solar flares. We analyse the properties of electrons in the magnetic configuration we previously used to study protons. In addition, we discuss the dependence of the particle properties on the parameters of the reconnection, such as strengths of electric and magnetic fields. Methods. A theoretical framework is presented which can be used to interpret particle acceleration at 3D null points, and which shows how strong acceleration can arise. We also use a test particle approach to calculate particle trajectories in simple model 3D reconnecting nulls. A modified guiding-centre approach is used for electrons, whilst the full equation of motion is solved for protons. Results. Most particle acceleration takes place when particles closely approach the spine or fan, and we have derived scalings for the sizes of the localised regions in which strong acceleration occurs. The energy spectra of protons and electrons are compared, and it is shown that the spatial distribution of accelerated electrons differs from protons. A significant number of trapped, high-energy particles can be generated, which may be observed as coronal HXR sources. The effectiveness of acceleration increases with the electric-field magnitude, and decreases with magnetic-field magnitude. Conclusions. Both protons and electrons can be effectively accelerated at 3D reconnecting null points. The particle properties depend on the geometry and field parameters, so that, in principle, the field configuration may be inferred from observed properties of particles.

Evidence of decay of flux ratio of Fe to Fe-Ni line features with electron temperature in solar flares

We report observational evidence of the decay of the flux ratio of Fe to Fe-Ni line features as a function of plasma electron temperature in solar flares in comparison to that theoretically predicted by Phillips (2004). We present the study of spectral analysis of 14 flares observed by the Solar X-ray Spectrometer (SOXS) — Low Energy Detector (SLD) payload. The SLD payload employs the state-of-the-art solid state detectors, viz., Si PIN and Cadmium-Zinc-Telluride (CZT) devices. The sub-keV energy resolution of Si PIN detector allows us to study the Fe-line and Fe-Ni line features appearing at 6.7 and 8 keV, respectively, in greater detail. In order to best-fit the whole spectrum at one time in the desired energy range between 4 and 25 keV we considered Gaussian-line, the multi-thermal power-law and broken power-law functions. We found that the flux ratio of Fe to Fe-Ni line features decays with flare electron temperature by the asymptotic form of polynomial of inverse third order. The relative flux ratio is ∼30 at temperature 12 MK which drops to half, ∼15 at 20 MK, and at further higher temperatures it decreases smoothly reaching to ∼8 at ∼50 MK. The flux ratio, however, at a given flare plasma temperature, and its decrease with temperature is significantly lower than that predicted theoretically. We propose that the difference may be due to the consideration of higher densities of Fe and Fe-Ni lines in the theoretical model of Phillips (2004). We suggest revising the Fe and Fe-Ni line densities in the corona. The decay of flux ratio explains the variation of equivalent width and peak energy of these line features with temperature.

Inverse Compton X-rays from relativistic flare electrons and positrons

In solar flares, inverse Compton scattering (ICS) of photospheric photons might give rise to detectable hard X-ray photon fluxes from the corona where ambient densities are too low for significant bremsstrahlung or recombination. Gamma-ray lines and continuum in some large flares imply the presence of the necessary ~100 MeV electrons and positrons, the latter as by-products of GeV energy ions. Recent observations of coronal hard X-ray sources in particular prompt us to reconsider here the possible contribution of ICS. We aim to evaluate the ICS X-ray fluxes to be expected from prescribed populations of relativistic electrons and positrons in the solar corona. The ultimate aim is to determine if ICS coronal X-ray sources might offer a new diagnostic window on relativistic electrons and ions in flares. We use the complete formalism of ICS to calculate X-ray fluxes from possible populations of flare primary electrons and secondary positrons, paying attention to the incident photon angular distribution near the solar surface and thus improving on the assumption of isotropy made in previous solar discussions. Both primary electrons and secondary positrons produce very hard ICS X-ray spectra. The anisotropic primary radiation field results in pronounced centre-to-limb variation in predicted fluxes and spectra, with the most intense spectra, extending to the highest photon energies, expected from limb flares. Acceptable numbers of electrons or positrons could account for RHESSI coronal X/gamma-ray sources. Some coronal X-ray sources at least might be interpreted in terms of ICS by relativistic electrons or positrons, particularly when sources appear at such low ambient densities that bremsstrahlung appears implausible.

Local re-acceleration and a modified thick target model of solar flare electrons

The collisional thick target model (CTTM) of solar hard X-ray (HXR) bursts has become an almost 'Standard Model' of flare impulsive phase energy transport and radiation. However, it faces various problems in the light of recent data, particularly the high electron beam density and anisotropy it involves.} {We consider how photon yield per electron can be increased, and hence fast electron beam intensity requirements reduced, by local re-acceleration of fast electrons throughout the HXR source itself, after injection.} {We show parametrically that, if net re-acceleration rates due to e.g. waves or local current sheet electric (${\cal E}$) fields are a significant fraction of collisional loss rates, electron lifetimes, and hence the net radiative HXR output per electron can be substantially increased over the CTTM values. In this local re-acceleration thick target model (LRTTM) fast electron number requirements and anisotropy are thus reduced. One specific possible scenario involving such re-acceleration is discussed, viz, a current sheet cascade (CSC) in a randomly stressed magnetic loop.} {Combined MHD and test particle simulations show that local ${\cal E}$ fields in CSCs can efficiently accelerate electrons in the corona and and re-accelerate them after injection into the chromosphere. In this HXR source scenario, rapid synchronisation and variability of impulsive footpoint emissions can still occur since primary electron acceleration is in the high Alfv\'{e}n speed corona with fast re-acceleration in chromospheric CSCs. It is also consistent with the energy-dependent time-of-flight delays in HXR features.

Observations of a solar flare and filament eruption in Lyman $\mathsf{\alpha}$ and X-rays

Context. Lα is a strong chromospheric emission line, which has been relatively rarely observed in flares. The Transition Region and Coronal Explorer (TRACE) has a broad “Lyman α ” channel centered at 1216 A used primarily at the beginning of the mission. A small number of flares were observed in this channel.Aims. We aim to characterise the appearance and behaviour of a flare and filament ejection which occurred on 8th September 1999 and was observed by TRACE in Lα , as well as by the Yohkoh Soft and Hard X-ray telescopes. We explore the flare energetics and its spatial and temporal evolution. We have in mind the fact that the Lα line is a target for the Extreme Ultraviolet Imaging telescope (EUI) which has been selected for the Solar Orbiter mission, as well as the LYOT telescope on the proposed SMESE mission.Methods. We use imaging data from the TRACE 1216 A, 1600 A and 171 A channels, and the Yohkoh hard and soft X-ray telescopes. A correction is applied to the TRACE data to obtain a better estimate of the pure Lα signature. The Lα power is obtained from a knowledge of the TRACE response function, and the flare electron energy budget is estimated by interpreting Yohkoh /HXT emission in the context of the collisional thick target model. Results. We find that the Lα flare is characterised by strong, compact footpoints (smaller than the UV ribbons) which correlate well with HXR footpoints. The Lα power radiated by the flare footpoints can be estimated, and is found to be on the order of 1026 erg s-1 at the peak. This is less than 10% of the power inferred for the electrons which generate the co-spatial HXR emission, and can thus readily be provided by them. The early stages of the filament eruption that accompany the flare are also visible, and show a diffuse, roughly circular spreading sheet-like morphology, with embedded denser blobs.Conclusions. On the basis of this observation, we conclude that flare and filament observations in the Lα line with the planned EUI and LYOT telescopes will provide valuable insight into solar flare evolution and energetics, especially when accompanied by HXR imaging and spectroscopy.

ELECTRON ENERGY AND MAGNETIC FIELD DERIVED FROM SOLAR MICROWAVE BURST SPECTRA

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

A Study of the Low Energy Cutoff of Nonthermal Electrons in RHESSI Flares

The flattening at the low energy end of the hard X-ray (HXR) photon spectrum of solar flares was generally thought to be due to a cutoff of nonthermal electrons in flares. However, some authors have suggested that inverse Compton scattering (i.e., the albedo effect) or certain other reaction of flare photons with the lower atmosphere can also lead to the flattening. This paper adopts the method of deriving the cutoff proposed by Gan et al. [12–14], and makes a statistical analysis on 100 flares observed by the satellite Ramaty High Energy Solar Spectroscopy Imager (RHESSI) in 2002–2005. We found that after the albedo correction, the HXR photon spectra of 18 flares can be fitted with single powerlaw spectra, and those of 80 flares, with double power-law spectra. Besides, 21 flares can be directly interpreted with a single power-law electron spectrum plus a low energy cutoff. The range of the low energy cutoff is 20–50 keV and the mean value is approximately 30 keV. Some other possible interpretations are also investigated.

Viewing radiation signatures of solar energetic particles in interplanetary space

A current serious limitation on the studies of solar energetic particle (SEP) events is that their properties in the inner heliosphere are studied only through in situ spacecraft observations. Our understanding of spatial distributions and temporal variations of SEP events has come through statistical studies of many such events over several solar cycles. In contrast, flare SEPs in the solar corona can be imaged through their radiative and collisional interactions with solar fields and particles. We suggest that the heliospheric SEPs may also interact with heliospheric particles and fields to produce signatures which can be remotely observed and imaged. A challenge with any such candidate signature is to separate it from that of flare SEPs. The optimum case for imaging high-energy ( E > 100 MeV) heliospheric protons may be the emission of π 0-decay γ-rays following proton collisions with solar wind (SW) ions. In the case of E > 1 MeV electrons, gyrosynchrotron radio emission may be the most readily detectible remote signal. In both cases we may already have observed one or two such events. Another radiative signature from nonthermal particles may be resonant transition radiation, which has likely already been observed from solar flare electrons. We discuss energetic neutrons as another possible remote signature, but we rule out γ-ray line and 0.511 MeV positron annihilation emission as observable signatures of heliospheric energetic ions. We are already acquiring global signatures of large inner-heliospheric SW density features and of heliosheath interactions between the SW and interstellar neutral ions. By finding an appropriate observable signature of remote heliospheric SEPs, we could supplement the in situ observations with global maps of energetic SEP events to provide a comprehensive view of SEP events.

ENERGY SPECTRUM OF THE ELECTRONS ACCELERATED BY A RECONNECTION ELECTRIC FIELD: EXPONENTIAL OR POWER LAW?

The direct current (DC) electric field near the reconnection region has been proposed as an effective mechanism to accelerate protons and electrons in solar flares. A power-law energy spectrum was generally claimed in the simulations of electron acceleration by the reconnection electric field. However in most of the literature, the electric and magnetic fields were chosen independently. In this paper, we perform test-particle simulations of electron acceleration in a reconnecting magnetic field, where both the electric and magnetic fields are adopted from numerical simulations of the MHD equations. It is found that the accelerated electrons present a truncated power-law energy spectrum with an exponential tail at high energies, which is analogous to the case of diffusive shock acceleration. The influences of reconnection parameters on the spectral feature are also investigated, such as the longitudinal and transverse components of the magnetic field and the size of the current sheet. It is suggested that the DC electric field alone might not be able to reproduce the observed single or double power-law distributions.

Modelling shock drift acceleration of electrons at the reconnection outflow termination shock in solar flares

Context. The acceleration of electrons to nonthermal energies in solar flares is one of the main unsolved questions in solar physics. One possibility for producing these energetic electrons is acceleration at the reconnection outflow termination shock (TS). Aims. By comparing theoretical results with observations of nonthermal electrons, we determine whether shock drift acceleration (SDA) at the TS is a viable electron acceleration mechanism. Methods. We used radio observations to constrain the characteristics of the TS, and hard X-ray observations provided by RHESSI , INTEGRAL , and HXRS to obtain the characteristics of the injected electrons. Invoking relativistic shock-drift acceleration at the TS, we calculated electron flux spectra, which are then compared with the corresponding observational results from RHESSI . A parametric study of the model allows us to answer the question under which conditions the TS is a viable electron accelerator. Results. SDA at the TS is able to reproduce the required fluxes and kinetic power of nonthermal electrons in solar flares as long as there is significant heating of the outflow jet and a sufficiently large shock area. A prediction of the model is that the flux and power of injected electrons is higher than the values that are usually given by fitting observed spectra, since the low-energy cutoff is generally below 10 keV. The synthetic spectra are consistent with the observed spectral indices up to ≈ 100 keV. Beyond that, they soften too quickly. Possibly this is because we have not yet considered various additional effects, such as multiple reflections at the shock or some form of preacceleration. The observed relation between electron flux and spectral index is reproduced by the model, as well as the temporal evolution of the energetic electrons. We conclude that SDA at the TS is a viable electron acceleration mechanism that deserves further study.

Nonthermal Electron Measurements in Solar Flares withHinodeEIS

The spectral range of the Hinode EIS (EUV Imaging Spectrometer) instrument is 170-211 ? and 245-291 ?; lines emitted by low-energy levels in highly ionized Mn, Fe, Co, and Ni, as well as the very energetic -->1s2s3S1?1s2p3P2 transition in Fe XXV, appear in the EIS range. In this paper, we investigate the use of these lines for detecting the presence of nonthermal, high-energy electrons in flares. We first calculate line fluxes among the various lines expected in the EIS range, assuming that the electron velocity distribution is strictly Maxwellian. Then, we calculate line fluxes using a velocity distribution composed of a Maxwellian distribution plus an additional population of electrons with a temperature of 10 keV ( -->1.2 ? 108 K) providing 1%, 2%, 4%, 7%, and 10% of the total free electrons. The calculations indicate that flux ratios between the highly excited Fe XXV line and lines originating in low-lying levels of other highly ionized ions in the EIS range could shed light on the electron velocity distribution in hot flare plasmas.

RHESSIHard X‐Ray Imaging Spectroscopy of Extended Sources and the Physical Properties of Electron Acceleration Regions in Solar Flares

In this study we present the results of a new approach to studying the acceleration and propagation of bremsstrahlung-producing electrons in solar flares. The method involves an analysis of the size of extended solar flare structures as a function of photon energy. Hard X-ray images from 10 M-class limb events, observed by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) to have the general form of a single extended source, were analyzed by forward fitting to the source visibilities in each energy band. On average the source sizes σ increased slowly with photon energy as σ ~ 1/2. This behavior is consistent neither with the predictions of a single-loop thermal model nor with a model in which nonthermal electrons are injected into a constant-density structure from a compact acceleration region. While a nonuniform density distribution along the flare loop can in principle reconcile the data with a nonthermal collisional model with point-source injection, the resulting density profiles are highly questionable. On the other hand, the data are consistent with a nonthermal collisional model that incorporates an extended acceleration region, perhaps in combination with a localized thermal source. We present best-fit results on the density and length of this acceleration region. To our knowledge, this is the first quantitative empirical analysis of the physical characteristics of electron acceleration regions in solar flares.