Footpoint Sources Research Articles

Precise timing of solar flare footpoint sources from mid-infrared observations

ABSTRACT Solar flares are powerful particle accelerators, and in the accepted standard flare model most of the flare energy is transported from a coronal energy-release region by accelerated electrons that stop collisionally in the chromosphere, heating and ionizing the plasma, producing a broad-band enhancement to the solar radiative output. We present a time-delay analysis of the infrared (IR) emission from two chromospheric sources in the flare SOL2014-09-24T17:50 taken at the McMath–Pierce telescope. By cross-correlating the intensity signals, measured with 1 s cadence, from the two spatially resolved IR sources we find a delay of $0.75\pm 0.07$ s at $8.2\,\mu$m, where the uncertainties are quantified by a Monte Carlo analysis. The sources correlate well in brightness but have a time lag larger than can be reasonably explained by the energy transport dominated by non-thermal electrons precipitating from a single acceleration site in the corona. If interpreted as a time-of-flight difference between electrons travelling to each footpoint, we estimate time delays between 0.14 and 0.42 s, for a reconnection site at the interior quasi-separatrix layer, or at the null-point of the spine-fan topology inferred for this event. We employed modelling of electron transport via time-dependent Fokker–Planck and radiative hydrodynamic simulations to evaluate other possible sources of time-delay in the generation of the IR emission, such as differing ionization time-scales under different chromospheric conditions. Our results demonstrate that they are also unable to account for this discrepancy. This flare appears to require energy transport by some means other than electron beams originating in the corona.

A Joint Microwave and Hard X-Ray Study toward Understanding the Transport of Accelerated Electrons During an Eruptive Solar Flare

The standard flare model, despite its success, is limited in comprehensively explaining the various processes involving nonthermal particles. One such missing ingredient is a detailed understanding of the various processes involved during the transport of accelerated electrons from their site of acceleration to different parts of the flare region. Here we use simultaneous radio and X-ray observations from the Expanded Owens Valley Solar Array and the Spectrometer/Telescope for Imaging X-rays on board the Solar Orbiter, respectively, from two distinct viewing perspectives, to study the electron transport processes. Through detailed spectral modeling of the coronal source using radio data and footpoint sources using X-ray spectra, we compare the nonthermal electron distribution at the coronal and footpoint sources. We find that the flux of the nonthermal electrons precipitated at the footpoint is an order of magnitude greater than that trapped in the looptop, consistent with earlier works that primarily used X-ray for their studies. In addition, we find that the electron spectral indices obtained from X-ray footpoints are significantly softer than the spectral hardness of the nonthermal electron distribution in the corona. We interpret these differences based on transport effects and the difference in sensitivity of microwave and X-ray observations to different regimes of electron energies. Such an understanding is crucial for leveraging different diagnostic methods of nonthermal electrons simultaneously to achieve a more comprehensive understanding of the electron acceleration and transport processes of solar flares.

Spectral Observations and Modeling of a Solar White-light Flare Observed by CHASE

The heating mechanisms of solar white-light flares remain unclear. We present an X1.0 white-light flare on 2022 October 2 (SOL2022-10-02T20:25) observed by the Chinese Hα Solar Explorer that provides two-dimensional spectra in the visible light for the full solar disk with a seeing-free condition. The flare shows a prominent enhancement of ∼40% in the photospheric Fe i line at 6569.2 Å, and the nearby continuum also exhibits a maximum enhancement of ∼40%. For the continuum near the Fe i line at 6173 Å from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, it is enhanced up to ∼20%. At the white-light kernels, the Fe i line at 6569.2 Å has a symmetric Gaussian profile that is still in absorption and the Hα line at 6562.8 Å displays a very broad emission profile with a central reversal plus a red or blue asymmetry. The white-light kernels are cospatial with the microwave footpoint sources observed by the Expanded Owens Valley Solar Array and the time profile of the white-light emission matches that of the hard X-ray emission above 30 keV from the Gamma-ray Burst Monitor (GBM) on Fermi. These facts indicate that the white-light emission is qualitatively related to a nonthermal electron beam. We also perform a radiative hydrodynamic simulation with the electron-beam parameters constrained by the hard X-ray observations from Fermi/GBM. The result reveals that the white-light enhancement cannot be well explained by a pure electron-beam heating together with its induced radiative backwarming but may need additional heating sources such as Alfvén waves.

Statistical Studies on Modified Neupert Effect

The qualitative description of the Neupert effect is that there is a causal relationship between the pulse component (hard X-ray, microwave burst) and the gradual component (soft X-ray emission) in a flare. The initial energy of the flare is released in the form of accelerating particles. The energetic particles produce HXR (hard X-ray) via nonthermal electron-ion bremsstrahlung as they lose their energies in the chromosphere. The SXR (soft X-ray) emission of the flare is the response of energetic particles injected into the chromosphere. According to the quantitative description of the classic Neupert effect, SXR should reach maximum instantly at the end of HXR emission (sign of nonthermal electron injection). However, previous observations have found that for quite a number of flares the SXR peak time (t2) is significantly later than the end time of HXR (t1) (τ=t2−t1,τ>0), deviating from the classic Neupert effect. In order to study the events deviating from the classic Neupert effect or not, we checked the RHESSI (Reuven Ramaty High Energy Solar Spectroscopic Imager) and GOES (Geostationary Operational Environmental Satellites) events list from 2002 to 2015, and found out flare samples that have simple lightcurves at 25–50 keV together with other criteria. A total of 276 flare samples were finally selected. We have analysed the τ distribution of these flares, as well as the relationship between the loop length (represented by the distance between two footpoint sources d) and τ. We found that: (1) 227 sample flares present τ>0, which means that about 82% of total samples deviate from the classical Neupert effect; (2) there is a roughly linear correlation between τ and d, that is, the longer the loop is, the later the maximum time of SXR with respect to the end of HXR; (3) there seems to have a critical distance, within which the classic Neupert effect works. These results confirm the necessity of modifying Neupert effect, and expound its physical significance.

Inferring the Magnetic Field Asymmetry of Solar Flares from the Degree of Polarisation at Millimetre Wavelengths

Polarisation measurements of solar flares at millimetre-waves were used to investigate the magnetic field configuration of the emitting sources. We analyse two solar flares (SOL2013-02-17 and SOL2013-11-05) observed by the POlarisation Emission of Millimetre Activity at the Sun (POEMAS) at 45 and 90 GHz, at microwaves from 1 – 15 GHz by the Radio Solar Telescope Network (RSTN), and at high frequencies (212 GHz) by the Solar Submillimetre Telescope (SST). Also, hard X-rays from these flares were simultaneously detected by the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI). The flux and polarisation radio spectra were fit using a model that simulates gyrosynchrotron emission in a spatially-varying 3D magnetic field loop structure. For the modelling, the magnetic loop geometry was fixed and the field strength was the only free parameter of the magnetic field. In addition, a uniform electron distribution was assumed by the model, with the number density of energetic electrons and the electron spectral index as free parameters. The fitted model reproduced reasonably well the observed degree of polarisation and radio flux spectra for each event yielding the physical parameters of the loop and flaring sources. Our results indicate that the high degree of polarisation during a solar flare can be explained by two sources located at the footpoints of highly asymmetric magnetic loops whereas low polarisation degrees arise from footpoint sources of symmetric magnetic loops.

Broken-up spectra of the loop-top hard X-ray source during a solar limb flare

Solar hard X-rays (HXRs) appear in the form of either footpoint sources or coronal sources. Each individual source provides its own critical information on acceleration of nonthermal electrons and plasma heating. Earlier studies found that the HXR emission in some events manifests a broken-up power-law spectrum, with the break energy around a few hundred keV based on spatially-integrated spectral analysis, and it does not distinguish the contributions from individual sources. In this paper, we report on the broken-up spectra of a coronal source studied using HXR data recorded by Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) during the SOL2017–09–10T16:06 (GOES class X8.2) flare. The flare occurred behind the western limb and its footpoint sources were mostly occulted by the disk. We could clearly identify such broken-up spectra pertaining solely to the coronal source during the flare peak time and after. Since a significant pileup effect on the RHESSI spectra is expected for this intense solar flare, we have selected the pileup correction factor, p = 2. In this case, we found the resulting RHESSI temperature (∼30 MK) to be similar to the GOES soft X-ray temperature and break energies of 45–60 keV. Above the break energy, the spectrum hardens with time from spectral index of 3.4 to 2.7, and the difference in spectral indices below and above the break energy increases from 1.5 to 5 with time. However, we note that when p = 2 is assumed, a single power-law fitting is also possible with the RHESSI temperature higher than the GOES temperature by ∼10 MK. Possible scenarios for the broken-up spectra of the loop-top HXR source are briefly discussed.

Quasi-periodic pulsations in hard X-rays of partially occulted solar flares

We investigated solar flares partially occulted by the solar disk observed by the Yohkoh satellite. We found that about 30–40% of them show quasi-periodic pulsations (QPPs) in hard X-rays (HXR). A lack of usually brighter footpoint sources allowed us to reconstruct coronal HXR sources with a higher quality. We analyzed 28 partially occulted flares showing the QPPs and for the first time present results for such events as a group. In our opinion, the majority of the observed HXR loop-top sources can be explained as successive compression and rarefaction of magnetic traps described in a model of oscillating magnetic traps (OMT). In this model a particular value of a ratio between the diameter of traps and the period of pulsations is postulated. In our modification of this model, different values of the ratio are possible, with the exception of a lower range, where low values of magnetic field strength and high values of electron density number can excess the plasma-β parameter above unity (ballooning instability).

Identification of Multiple Hard X-Ray Sources in Solar Flares: A Bayesian Analysis of the 2002 February 20 Event.

The hard X-ray emission in a solar flare is typically characterized by a number of discrete sources, each with its own spectral, temporal, and spatial variability. Establishing the relationship among these sources is critical to determining the role of each in the energy release and transport processes that occur within the flare. In this paper we present a novel method to identify and characterize each source of hard X-ray emission. The method permits a quantitative determination of the most likely number of subsources present, and of the relative probabilities that the hard X-ray emission in a given subregion of the flare is represented by a complicated multiple source structure or by a simpler single source. We apply the method to a well-studied flare on 2002 February 20 in order to assess competing claims as to the number of chromospheric footpoint sources present, and hence to the complexity of the underlying magnetic geometry/topology. Contrary to previous claims of the need for multiple sources to account for the chromospheric hard X-ray emission at different locations and times, we find that a simple two-footpoint-plus-coronal-source model is the most probable explanation for the data. We also find that one of the footpoint sources moves quite rapidly throughout the event, a factor that presumably complicated previous analyses. The inferred velocity of the footpoint corresponds to a very high induced electric field, compatible with the fields in thin reconnecting current sheets.

Electron Acceleration in Collapsing Magnetic Traps during the Solar Flare on July 19, 2012: Observations and Models

AbstractUsing the appropriate kinetic equation, we considered the problem of propagation of accelerated electrons into the solar corona and chromosphere. Its analytical solution was used for modelling the M7.7 class limb flare occurred on July 19, 2012. Coronal above-the-loop-top hard X-Ray source was interpreted in the thin-target approximation, the foot-point source - in the thick-target approximation with account of the reverse-current electric field. For the foot-point source we found a good accordance with the RHESSI observations. For the coronal source we also got very accurate estimate of the power-law spectral index, but significant differences between the modelled and observed hard X-ray intensities were noticed. The last discrepancy was solved by adding the coronal magnetic trap model to the thin target model. The former one implies that the trap collapses in two dimensions, locks and accelerates particles inside itself. In our report, we confirm an existence and high efficiency of the electron acceleration in collapsing magnetic traps during solar flares. Our new results represent (e.g. for RHESSI observations) the theoretical prediction of the double step particle acceleration in solar flares, when the first step is the acceleration in reconnection area and the second one – the acceleration in coronal trap.

Analysis and modelling of recurrent solar flares observed with Hinode/EIS on March 9, 2012

Three homologous C-class flares and one last M-class flare were observed by both the Solar Dynamics Observatory (SDO) and the Hinode EUV Imaging Spectrometer (EIS) in the AR 11429 on March 9, 2012. All the recurrent flares occurred within a short interval of time (less than 4 hours), showed very similar plasma morphology and were all confined, until the last one when a large-scale eruption occurred. The C-class flares are characterized by the appearance, at approximatively the same locations, of two bright and compact footpoint sources of $\approx$~3--10~MK evaporating plasma, and a semi-circular ribbon. During all the flares, the continuous brightening of a spine-like hot plasma ($\approx$~10~MK) structure is also observed. Spectroscopic observations with Hinode/EIS are used to measure and compare the blueshift velocities in the \fexxiii\ emission line and the electron number density at the flare footpoints for each flare. Similar velocities, of the order of 150--200~km~s$^{-1}$, are observed during the C2.0 and C4.7 confined flares, in agreement with the values reported by other authors in the study of the last M1.8 class flare. On the other hand, lower electron number densities and temperatures tend to be observed in flares with lower peak soft X-ray flux.In order to investigate the homologous nature of the flares, we performed a Non-Linear Force-Free Field (NLFFF) extrapolation of the 3D magnetic field configuration in the corona. The NLFFF extrapolation and the Quasi-Separatrix Layers (QSLs) provide the magnetic field context which explains the location of the kernels, spine-like and semi-circular brightenings observed in the (non-eruptive) flares. Given the absence of a coronal null point, we argue that the homologous flares were all generated by the continuous recurrence of bald patch reconnection.

FORMATION AND ERUPTION OF A FLUX ROPE FROM THE SIGMOID ACTIVE REGION NOAA 11719 AND ASSOCIATED M6.5 FLARE: A MULTI-WAVELENGTH STUDY

ABSTRACT We investigate the formation, activation, and eruption of a flux rope (FR) from the sigmoid active region NOAA 11719 by analyzing E(UV), X-ray, and radio measurements. During the pre-eruption period of ∼7 hr, the AIA 94 Å images reveal the emergence of a coronal sigmoid through the interaction between two J-shaped bundles of loops, which proceeds with multiple episodes of coronal loop brightenings and significant variations in the magnetic flux through the photosphere. These observations imply that repetitive magnetic reconnections likely play a key role in the formation of the sigmoidal FR in the corona and also contribute toward sustaining the temperature of the FR higher than that of the ambient coronal structures. Notably, the formation of the sigmoid is associated with the fast morphological evolution of an S-shaped filament channel in the chromosphere. The sigmoid activates toward eruption with the ascent of a large FR in the corona, which is preceded by the decrease in photospheric magnetic flux through the core flaring region, suggesting tether-cutting reconnection as a possible triggering mechanism. The FR eruption results in a two-ribbon M6.5 flare with a prolonged rise phase of ∼21 minutes. The flare exhibits significant deviation from the standard flare model in the early rise phase, during which a pair of J-shaped flare ribbons form and apparently exhibit converging motions parallel to the polarity inversion line, which is further confirmed by the motions of hard X-ray footpoint sources. In the later stages, the flare follows the standard flare model and the source region undergoes a complete sigmoid-to-arcade transformation.

PRE-FLARE CORONAL JET AND EVOLUTIONARY PHASES OF A SOLAR ERUPTIVE PROMINENCE ASSOCIATED WITH THE M1.8 FLARE: SDO AND RHESSI OBSERVATIONS

ABSTRACT We investigate the triggering, activation, and ejection of a solar eruptive prominence that occurred in a multi-polar flux system of active region NOAA 11548 on 2012 August 18 by analyzing data from the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory, the Reuven Ramaty High Energy Solar Spectroscopic Imager, and the Extreme Ultraviolet Imager/Sun Earth Connection Coronal and Heliospheric Investigation on board the Solar Terrestrial Relation Observatory. Prior to the prominence activation, we observed striking coronal activities in the form of a blowout jet, which is associated with the rapid eruption of a cool flux rope. Furthermore, the jet-associated flux rope eruption underwent splitting and rotation during its outward expansion. These coronal activities are followed by the prominence activation during which it slowly rises with a speed of ∼12 km s−1 while the region below the prominence emits gradually varying EUV and thermal X-ray emissions. From these observations, we propose that the prominence eruption is a complex, multi-step phenomenon in which a combination of internal (tether-cutting reconnection) and external (i.e., pre-eruption coronal activities) processes are involved. The prominence underwent catastrophic loss of equilibrium with the onset of the impulsive phase of an M1.8 flare, suggesting large-scale energy release by coronal magnetic reconnection. We obtained signatures of particle acceleration in the form of power-law spectra with hard electron spectral index (δ ∼ 3) and strong HXR footpoint sources. During the impulsive phase, a hot EUV plasmoid was observed below the apex of the erupting prominence that ejected in the direction of the prominence with a speed of ∼177 km s−1. The temporal, spatial, and kinematic correlations between the erupting prominence and the plasmoid imply that the magnetic reconnection supported the fast ejection of prominence in the lower corona.

HOW IMPORTANT ARE ELECTRON BEAMS IN DRIVING CHROMOSPHERIC EVAPORATION IN THE 2014 MARCH 29 FLARE?

We present high spatial resolution observations of chromospheric evaporation in the flare SOL2014-03-29T17:48. Interface Region Imaging Spectrograph (IRIS) observations of the FeXXI 1354.1 A line indicate evaporating plasma at a temperature of 10 MK along the flare ribbon during the flare peak and several minutes into the decay phase with upflow velocities between 30 km s$^{-1}$ and 200 km s$^{-1}$. Hard X-ray (HXR) footpoints were observed by RHESSI for two minutes during the peak of the flare. Their locations coincided with the locations of the upflows in parts of the southern flare ribbon but the HXR footpoint source preceded the observation of upflows in FeXXI by 30-75 seconds. However, in other parts of the southern ribbon and in the northern ribbon the observed upflows were not coincident with a HXR source in time nor space, most prominently during the decay phase. In this case evaporation is likely caused by energy input via a conductive flux that is established between the hot (25 MK) coronal source, which is present during the whole observed time-interval, and the chromosphere. The presented observations suggest that conduction may drive evaporation not only during the decay phase but also during the flare peak. Electron beam heating may only play a role in driving evaporation during the initial phases of the flare.

Particle acceleration and transport in reconnecting twisted loops in a stratified atmosphere

Twisted coronal loops should be ubiquitous in the solar corona. Twisted magnetic fields contain excess magnetic energy, which can be released during magnetic reconnection, causing solar flares. The aim of this work is to investigate magnetic reconnection, and particle acceleration and transport in kink-unstable twisted coronal loops, with a focus on the effects of resistivity, loop geometry and atmospheric stratification. Another aim is to perform forward-modelling of bremsstrahlung emission and determine the structure of hard X-ray sources. We use a combination of magnetohydrodynamic (MHD) and test-particle methods. First, the evolution of the kinking coronal loop is considered using resistive MHD model, incorporating atmospheric stratification and loop curvature. Then, the obtained electric and magnetic fields and density distributions are used to calculate electron and proton trajectories using a guiding-centre approximation, taking into account Coulomb collisions. It is shown that electric fields in twisted coronal loops can effectively accelerate protons and electrons to energies up to 10 MeV. High-energy particles have hard, nearly power-law energy spectra. The volume occupied by high-energy particles demonstrates radial expansion, which results in the expansion of the visible hard X-ray loop and a gradual increase in hard X-ray footpoint area. Synthesised hard X-ray emission reveals strong footpoint sources and the extended coronal source, whose intensity strongly depends on the coronal loop density.

CHROMOSPHERIC AND CORONAL OBSERVATIONS OF SOLAR FLARES WITH THE HELIOSEISMIC AND MAGNETIC IMAGER

We report observations of white-light ejecta in the low corona, for two X-class flares on the 2013 May 13, using data from the Helioseismic and Magnetic Imager (HMI) of the Solar Dynamics Observatory. At least two distinct kinds of sources appeared (chromospheric and coronal), in the early and later phases of flare development, in addition to the white-light footpoint sources commonly observed in the lower atmosphere. The gradual emissions have a clear identification with the classical loop-prominence system, but are brighter than expected and possibly seen here in the continuum rather than line emission. We find the HMI flux exceeds the radio/X-ray interpolation of the bremsstrahlung produced in the flare soft X-ray sources by at least one order of magnitude. This implies the participation of cooler sources that can produce free-bound continua and possibly line emission detectable by HMI. One of the early sources dynamically resembles "coronal rain", appearing at a maximum apparent height and moving toward the photosphere at an apparent constant projected speed of 134 $\pm$ 8 $\mathrm{km s^{-1}}$. Not much literature exists on the detection of optical continuum sources above the limb of the Sun by non-coronagraphic instruments, and these observations have potential implications for our basic understanding of flare development, since visible observations can in principle provide high spatial and temporal resolution.

Multiwavelength diagnostics of the precursor and main phases of an M1.8 flare on 2011 April 22

We study the temporal, spatial and spectral evolution of the M1.8 flare, which occurred in NOAA AR 11195 (S17E31) on 22 April 2011, and explore the underlying physical processes during the precursors and their relation to the main phase. The study of the source morphology using the composite images in 131 {\deg}A wavelength observed by the SDO/AIA and 6-14 keV revealed a multiloop system that destabilized systematically during the precursor and main phases. In contrast, HXR emission (20-50 keV) was absent during the precursor phase, appearing only from the onset of the impulsive phase in the form of foot-points of emitting loop/s. This study has also revealed the heated loop-top prior to the loop emission, although no accompanying foot-point sources were observed during the precursor phase. We estimate the flare plasma parameters viz. T, EM, power-law index, and photon turn-over energy by forward fitting RHESSI spectral observations. The energy released in the precursor phase was thermal and constituted ~1 per cent of the total energy released during the flare. The study of morphological evolution of the filament in conjunction with synthesized T and EM maps has been carried out which reveals (a) Partial filament eruption prior to the onset of the precursor emission, (b) Heated dense plasma over the polarity inversion line and in the vicinity of the slowly rising filament during the precursor phase. Based on the implications from multi-wavelength observations, we propose a scheme to unify the energy release during the precursor and main phase emissions in which, the precursor phase emission has been originated via conduction front formed due to the partial filament eruption. Next, the heated leftover S-shaped filament has undergone slow rise and heating due to magnetic reconnection and finally erupted to produce emission during the impulsive and gradual phases.

Transient Artifacts in a Flare Observed by the Helioseismic and Magnetic Imager on the Solar Dynamics Observatory

The Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) provides a new tool for the systematic observation of white-light flares, including Doppler and magnetic information as well as continuum. In our initial analysis of the highly impulsive \(\mathrm{\gamma}\)-ray flare SOL2010-06-12T00:57 (Martínez Oliveros et al., Solar Phys. 269, 269, 2011), we reported the signature of a strong blueshift in the two footpoint sources. Concerned that this might be an artifact due to aliasing peculiar to the HMI instrument, we undertook a comparative analysis of Global Oscillation Network Group (GONG++) observations of the same flare, using the PArametric Smearing Correction ALgorithm (PASCAL) algorithm to correct for artifacts caused by variations in atmospheric smearing. This analysis confirms the artifactual nature of the apparent blueshift in the HMI observations, finding weak redshifts at the footpoints instead. We describe the use of PASCAL with GONG++ observations as a complement to the SDO observations and discuss constraints imposed by the use of HMI far from its design conditions. With proper precautions, these data provide rich information on flares and transients.

Observational consequences of the local re-acceleration thick-target model

In our contribution we compare the efficiency of the hard X-ray production and the vertical sizes and positions of the hard X-ray sources for the classical collisional thick-target model and for its recently proposed modification, the local re-acceleration thick-target model. The latter model has been proposed in order to ease some of the severe theoretical problems of the collisional thick-target model related to interpretation of the observational properties of the foot-point HXR sources in solar flares. The results are obtained using a relativistic test-particle approach for a fully ionised atmosphere with a converging magnetic field and a single (compact) flare loop.

Implications for electron acceleration and transport from non-thermal electron rates at looptop and footpoint sources in solar flares

The interrelation of hard X-ray (HXR) emitting sources and the underlying physics of electron acceleration and transport presents one of the major questions in high-energy solar flare physics. Spatially resolved observations of solar flares often demonstrate the presence of well-separated sources of bremsstrahlung emission, so-called coronal and footpoint sources. Using spatially resolved X-ray observations by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and recently improved imaging techniques, we investigate in detail the spatially resolved electron distributions in a few well-observed solar flares. The selected flares can be interpreted as having a standard geometry with chromospheric HXR footpoint sources related to thick-target X-ray emission and the coronal sources characterised by a combination of thermal and thin-target bremsstrahlung. Using imaging spectroscopy techniques, we deduce the characteristic electron rates and spectral indices required to explain the coronal and footpoint X-ray sources. We found that, during the impulsive phase, the electron rate at the looptop is several times (a factor of 1.7-8) higher than at the footpoints. The results suggest that a sufficient number of electrons accelerated in the looptop explain the precipitation into the footpoints and imply that electrons accumulate in the looptop. We discuss these results in terms of magnetic trapping, pitch-angle scattering, and injection properties. Our conclusion is that the accelerated electrons must be subject to magnetic trapping and/or pitch-angle scattering, keeping a fraction of the population trapped inside the coronal loops. These findings put strong constraints on the particle transport in the coronal source and provide quantitative limits on deka-keV electron trapping/scattering in the coronal source.

The calculation of coronal magnetic field and density of nonthermal electrons in the 2003 October 27 microwave burst

Based on Dulk and Marsh's approximate theory about nonthermal gyrosynchrotron radiation, one simple impulsive microwave burst with a loop-like structure is selected for radio diagnostics of the coronal magnetic field and column density of nonthermal electrons, which are calculated from the brightness temperature, polarization degree, and spectral index, as well as the turnover frequency, observed by using the Nobeyama Radioheliograph and the Nobeyama Radio Polarimeters, respectively. Very strong variations (up to one or two orders of magnitude) of the calculated transverse and longitudinal magnetic fields with respect to the line-of-sight, as well as the calculated electron column density, appear in the looptop and footpoint sources during the burst. The absolute magnitude and varied range of the transverse magnetic field are evidently larger than those of the longitudinal magnetic field. The time evolution of the transverse magnetic field is always anti-correlated with that of the longitudinal magnetic field, but positively correlated with that of the electron column density. These results strongly support the idea that quantifying the energy released in a flare depends on a reconstruction of the coronal magnetic field, especially for the transverse magnetic field, and they are basically consistent with the recent theoretical and observational studies on the photospheric magnetic field in solar flares.