Eduard Kontar | University of Glasgow (original) (raw)

Papers by Eduard Kontar

Research paper thumbnail of REGULARIZED RECONSTRUCTION OF THE DIFFERENTIAL EMISSION MEASURE FROM SOLAR FLARE HARD X-RAY SPECTRA

We address the problem of how to test whether an observed solar hard X-ray bremsstrahlung spectru... more We address the problem of how to test whether an observed solar hard X-ray bremsstrahlung spectrum (I ()) is consistent with a purely thermal (locally Maxwellian) distribution of source electrons, and, if so, how to reconstruct the corresponding differential emission measure (ξ (T)). Unlike previous analysis based on the Kramers and Bethe-Heitler approximations to the bremsstrahlung cross-section, here we use an exact (solid-angle-averaged) cross-section. We show that the problem of determining ξ (T) from measurements of I () invOlves two successive inverse problems: the first, to recover the mean source-electron flux spectrum (F(E)) from I () and the second, to recover ξ (T) fromF(E). We discuss the highly pathological numerical properties of this second problem within the framework of the regularization theory for linear inverse problems. In particular, we show that an iterative scheme with a positivity constraint is effective in recovering δ-like forms of ξ (T) while first-order Tikhonov regularization with boundary conditions works well in the case of power-lawlike forms. Therefore, we introduce a restoration approach whereby the low-energy part ofF(E), dominated by the thermal component, is inverted by using the iterative algorithm with positivity, while the high-energy part, dominated by the power-law component, is inverted by using first-order regularization. This approach is first tested by using simulatedF(E) derived from a priori known forms of ξ (T) and then applied to hard X-ray spectral data from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI).

Research paper thumbnail of Data-constrained Solar Modeling with GX Simulator

To facilitate the study of solar flares and active regions, we have created a modeling framework,... more To facilitate the study of solar flares and active regions, we have created a modeling framework, the freely distributed GX Simulator IDL package, that combines 3D magnetic and plasma structures with thermal and nonthermal models of the chromosphere, transition region, and corona. Its object-based modular architecture, which runs on Windows, Mac, and Unix/Linux platforms, offers the ability to either import 3D density and temperature distribution models, or to assign numerically defined coronal or chromospheric temperatures and densities, or their distributions, to each individual voxel. GX Simulator can apply parametric heating models involving average properties of the magnetic field lines crossing a given voxel, as well as compute and investigate the spatial and spectral properties of radio, (sub)millimeter, EUV, and X-ray emissions calculated from the model, and quantitatively compare them with observations. The package includes a fully automatic model production pipeline that, based on minimal users input, downloads the required SDO/HMI vector magnetic field data, performs potential or nonlinear force-free field extrapolations, populates the magnetic field skeleton with parameterized heated plasma coronal models that assume either steady-state or impulsive plasma heating, and generates non-LTE density and temperature distribution models of the chromosphere that are constrained by photospheric measurements. The standardized models produced by this pipeline may be further customized through specialized IDL scripts, or a set of interactive tools provided by the graphical user interface. Here, we describe the GX Simulator framework and its applications.

Research paper thumbnail of An Anisotropic Density Turbulence Model from the Sun to 1 au Derived from Radio Observations

Solar radio bursts are strongly affected by radio-wave scattering on density inhomogeneities, cha... more Solar radio bursts are strongly affected by radio-wave scattering on density inhomogeneities, changing their observed time characteristics, sizes, and positions. The same turbulence causes angular broadening and scintillation of galactic and extragalactic compact radio sources observed through the solar atmosphere. Using large-scale simulations of radio-wave transport, the characteristics of anisotropic density turbulence from 0.1 R e to 1 au are explored. For the first time, a profile of heliospheric density fluctuations is deduced that accounts for the properties of extrasolar radio sources, solar radio bursts, and in situ density fluctuation measurements in the solar wind at 1 au. The radial profile of the spectrum-weighted mean wavenumber of density fluctuations (a quantity proportional to the scattering rate of radio waves) is found to have a broad maximum at around (4-7) R e , where the slow solar wind becomes supersonic. The level of density fluctuations at the inner scale (which is consistent with the proton resonance scale) decreases with heliocentric distance as () () n r r R 2 10 1 i 2 7 3.7   d á ñ´-cm −6. Due to scattering, the apparent positions of solar burst sources observed at frequencies between 0.1 and 300 MHz are computed to be essentially cospatial and to have comparable sizes, for both fundamental and harmonic emission. Anisotropic scattering is found to account for the shortest solar radio burst decay times observed, and the required wavenumber anisotropy is q ∥ /q ⊥ = 0.25-0.4, depending on whether fundamental or harmonic emission is involved. The deduced radio-wave scattering rate paves the way to quantify intrinsic solar radio burst characteristics.

Research paper thumbnail of Source positions of an interplanetary type III radio burst and anisotropic radio-wave scattering

Interplanetary solar radio type III bursts provide the means to remotely study and track energeti... more Interplanetary solar radio type III bursts provide the means to remotely study and track energetic electrons propagating in the interplanetary medium. Due to the lack of direct radio source imaging, several methods have been developed to determine the source positions from space-based observations. Moreover, none of the methods consider the propagation effects of anisotropic radio-wave scattering, which would strongly distort the trajectory of radio waves, delay their arrival times, and affect their apparent characteristics. We investigate the source positions and directivity of an interplanetary type III burst simultaneously observed by Parker Solar Probe, Solar Orbiter, STEREO, and Wind and we compare the results of applying the intensity fit and timing methods with ray-tracing simulations of radio-wave propagation with anisotropic density fluctuations. The simulation calculates the trajectories of the rays, their time profiles at different viewing sites, and the apparent characteristics for various density fluctuation parameters. The results indicate that the observed source positions are displaced away from the locations where emission is produced, and their deduced radial distances are larger than expected from density models. This suggests that the apparent position is affected by anisotropic radio-wave scattering, which leads to an apparent position at a larger heliocentric distance from the Sun. The methods to determine the source positions may underestimate the apparent positions if they do not consider the path of radio-wave propagation and incomplete scattering at a viewing site close to the intrinsic source position.

Research paper thumbnail of The Solar Particle Acceleration Radiation and Kinetics (SPARK) Mission Concept

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Research paper thumbnail of An Anisotropic Density Turbulence Model from the Sun to 1 au Derived from Radio Observations

Astrophysical Journal, 2023

Solar radio bursts are strongly affected by radio-wave scattering on density inhomogeneities, cha... more Solar radio bursts are strongly affected by radio-wave scattering on density inhomogeneities, changing their observed time characteristics, sizes, and positions. The same turbulence causes angular broadening and scintillation of galactic and extragalactic compact radio sources observed through the solar atmosphere. Using large-scale simulations of radio-wave transport, the characteristics of anisotropic density turbulence from 0.1 R e to 1 au are explored. For the first time, a profile of heliospheric density fluctuations is deduced that accounts for the properties of extrasolar radio sources, solar radio bursts, and in situ density fluctuation measurements in the solar wind at 1 au. The radial profile of the spectrum-weighted mean wavenumber of density fluctuations (a quantity proportional to the scattering rate of radio waves) is found to have a broad maximum at around (4-7) R e , where the slow solar wind becomes supersonic. The level of density fluctuations at the inner scale (which is consistent with the proton resonance scale) decreases with heliocentric distance as () () n r r R 2 10 1 i 2 7 3.7   d á ñ´-cm −6. Due to scattering, the apparent positions of solar burst sources observed at frequencies between 0.1 and 300 MHz are computed to be essentially cospatial and to have comparable sizes, for both fundamental and harmonic emission. Anisotropic scattering is found to account for the shortest solar radio burst decay times observed, and the required wavenumber anisotropy is q ∥ /q ⊥ = 0.25-0.4, depending on whether fundamental or harmonic emission is involved. The deduced radio-wave scattering rate paves the way to quantify intrinsic solar radio burst characteristics.

Research paper thumbnail of Determination of the Total Accelerated Electron Rate and Power Using Solar Flare Hard X-Ray Spectra

Solar flare hard X-ray (HXR) spectroscopy serves as a key diagnostic of the accelerated electron ... more Solar flare hard X-ray (HXR) spectroscopy serves as a key diagnostic of the accelerated electron spectrum. However, the standard approach using the collisional cold thick-target model poorly constrains the lower-energy part of the accelerated electron spectrum, hence the overall energetics of the accelerated electrons are typically constrained only to within one or two orders of magnitude. Here, we develop and apply a physically selfconsistent, warm-target approach that involves the use of both HXR spectroscopy and imaging data. This approach allows an accurate determination of the electron distribution low-energy cutoff, and hence the electron acceleration rate and the contribution of accelerated electrons to the total energy released, by constraining the coronal plasma parameters. Using a solar flare observed in X-rays by RHESSI, we demonstrate that using the standard cold-target methodology, the low-energy cutoff (hence the energy content in electrons) is essentially undetermined. However, the warm-target methodology can determine the low-energy electron cutoff with ∼7% uncertainty at the 3σ level, hence it permits an accurate quantitative study of the importance of accelerated electrons in solar flare energetics.

Research paper thumbnail of The Efficiency of Electron Acceleration during the Impulsive Phase of a Solar Flare

Solar flares are known to be prolific electron accelerators, yet identifying the mechanism(s) for... more Solar flares are known to be prolific electron accelerators, yet identifying the mechanism(s) for such efficient electron acceleration in solar flare (and similar astrophysical settings) presents a major challenge. This is due in part to a lack of observational constraints related to conditions in the primary acceleration region itself. Accelerated electrons with energies above ∼20 keV are revealed by hard X-ray (HXR) bremsstrahlung emission, while accelerated electrons with even higher energies manifest themselves through radio gyrosynchrotron emission. Here, we show, for a well-observed flare on 2017 September 10, that a combination of RHESSI HXR and and the Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA) EUV observations provides a robust estimate of the fraction of the ambient electron population that is accelerated at a given time, with an upper limit of 10 −2 on the number density of nonthermal (20 keV) electrons, expressed as a fraction of the number density of ambient protons in the same volume. This upper limit is about 2 orders of magnitude lower than previously inferred from microwave observations of the same event. Our results strongly indicate that the fraction of accelerated electrons in the coronal region at any given time is relatively small but also that the overall duration of the HXR emission requires a steady resupply of electrons to the acceleration site. Simultaneous measurements of the instantaneous accelerated electron number density and the associated specific electron acceleration rate provide key constraints for a quantitative study of the mechanisms leading to electron acceleration in magnetic reconnection events.

Research paper thumbnail of Radio Echo in the Turbulent Corona and Simulations of Solar Drift-pair Radio Bursts

The Astrophysical Journal, Volume 898, Issue 2, id.94, 2020

Drift-pair bursts are an unusual type of solar low-frequency radio emission, which appear in the ... more Drift-pair bursts are an unusual type of solar low-frequency radio emission, which appear in the dynamic spectra as two parallel drifting bright stripes separated in time. Recent imaging spectroscopy observations allowed for the quantitative characterization of the drifting pairs in terms of source size, position, and evolution. Here, the drift-pair parameters are qualitatively analyzed and compared with the newly developed Monte Carlo ray-tracing technique simulating radio-wave propagation in the inhomogeneous anisotropic turbulent solar corona. The results suggest that drift-pair bursts can be formed due to a combination of refraction and scattering processes, with the trailing component being the result of turbulent reflection (turbulent radio echo). The formation of drift-pair bursts requires an anisotropic scattering with the level of plasma density fluctuations comparable to that in type III bursts, but with a stronger anisotropy at the inner turbulence scale. The anisotropic radio-wave scattering model can quantitatively reproduce the key properties of drift-pair bursts: the apparent source size and its increase with time at a given frequency, the parallel motion of the source centroid positions, and the delay between the burst components. The trailing component is found to be virtually cospatial and following the main component. The simulations suggest that drift-pair bursts are likely to be observed closer to the disk center and below 100 MHz due to the effects of free-free absorption and scattering. The exciter of drift pairs is consistent with propagating packets of whistlers, allowing for a fascinating way to diagnose the plasma turbulence and the radio emission mechanism.

Research paper thumbnail of Fine structure of type III solar radio bursts from Langmuir wave motion in turbulent plasma

Nature Astronomy, Volume 5, p. 796-804, 2021

The Sun frequently accelerates near-relativistic electron beams that travel out through the solar... more The Sun frequently accelerates near-relativistic electron beams that travel out through the solar corona and interplanetary space. Interacting with their plasma environment, these beams produce type III radio bursts, the brightest astrophysical radio sources seen from the Earth. The formation and motion of type III fine frequency structures is a puzzle but is commonly believed to be related to plasma turbulence in the solar corona and solar wind. Combining a theoretical framework with kinetic simulations and high-resolution radio type III observations using the Low Frequency Array, we quantitatively show that the fine structures are caused by the moving intense clumps of Langmuir waves in a turbulent medium. Our results show how type III fine structure can be used to remotely analyse the intensity and spectrum of compressive density fluctuations, and can infer ambient temperatures in astrophysical plasma, both significantly expanding the current diagnostic potential of solar radio emission.

Research paper thumbnail of First Frequency-time-resolved Imaging Spectroscopy Observations of Solar Radio Spikes

The Astrophysical Journal Letters, 2021

Solar radio spikes are short duration and narrow bandwidth fine structures in dynamic spectra obs... more Solar radio spikes are short duration and narrow bandwidth fine structures in dynamic spectra observed from the GHz to tens of MHz range. Their very short duration and narrow frequency bandwidth are indicative of subsecond small-scale energy release in the solar corona, yet their origin is not understood. Using the LOw Frequency ARray, we present spatially, frequency, and time resolved observations of individual radio spikes associated with a coronal mass ejection. Individual radio spike imaging demonstrates that the observed area is increasing in time and the centroid positions of the individual spikes move superluminally parallel to the solar limb. Comparison of spike characteristics with that of individual Type IIIb striae observed in the same event show similarities in duration, bandwidth, drift rate, polarization, and observed area, as well the spike and striae motion in the image plane suggesting fundamental plasma emission with the spike emission region on the order of ∼10 8 cm, with brightness temperature as high as 10 13 K. The observed spatial, spectral, and temporal properties of the individual spike bursts are also suggestive of the radiation responsible for spikes escaping through anisotropic density turbulence in closed loop structures with scattering preferentially along the guiding magnetic field oriented parallel to the limb in the scattering region. The dominance of scattering on the observed time profile suggests the energy release time is likely to be shorter than what is often assumed. The observations also imply that the density turbulence anisotropy along closed magnetic field lines is higher than along open field lines.

Research paper thumbnail of Fine structure of type III solar radio bursts from Langmuir wave motion in turbulent plasma

Nature Astronomy, May 31, 2021

The Sun frequently accelerates near-relativistic electron beams that travel out through the solar... more The Sun frequently accelerates near-relativistic electron beams that travel out through the solar corona and interplanetary space. Interacting with their plasma environment, these beams produce type III radio bursts, the brightest astrophysical radio sources seen from the Earth. The formation and motion of type III fine frequency structures is a puzzle but is commonly believed to be related to plasma turbulence in the solar corona and solar wind. Combining a theoretical framework with kinetic simulations and high-resolution radio type III observations using the Low Frequency Array, we quantitatively show that the fine structures are caused by the moving intense clumps of Langmuir waves in a turbulent medium. Our results show how type III fine structure can be used to remotely analyse the intensity and spectrum of compressive density fluctuations, and can infer ambient temperatures in astrophysical plasma, both significantly expanding the current diagnostic potential of solar radio emission.

Research paper thumbnail of Subsecond Time Evolution of Type III Solar Radio Burst Sources at Fundamental and Harmonic Frequencies

The Astrophysical Journal, 2020

Recent developments in astronomical radio telescopes opened new opportunities in imaging and spec... more Recent developments in astronomical radio telescopes opened new opportunities in imaging and spectroscopy of solar radio bursts at subsecond timescales. Imaging in narrow frequency bands has revealed temporal variations in the positions and source sizes that do not fit into the standard picture of type III solar radio bursts, and require a better understanding of radio-wave transport. In this paper, we utilize 3D Monte Carlo ray-tracing simulations that account for the anisotropic density turbulence in the inhomogeneous solar corona to quantitatively explain the image dynamics at the fundamental (near plasma frequency) and harmonic (double) plasma emissions observed at ∼32MHz. Comparing the simulations with observations, we find that anisotropic scattering from an instantaneous emission point source can account for the observed time profiles, centroid locations, and source sizes of the fundamental component of type III radio bursts (generated where f pe ≈32 MHz). The best agreement with observations is achieved when the ratio of the perpendicular to the parallel component of the wavevector of anisotropic density turbulence is around 0.25. Harmonic emission sources observed at the same frequency (∼32 MHz, but generated where f pe ≈16 MHz) have apparent sizes comparable to those produced by the fundamental emission, but demonstrate a much slower temporal evolution. The simulations of radio-wave propagation make it possible to quantitatively explain the variations of apparent source sizes and positions at subsecond timescales both for the fundamental and harmonic emissions, and can be used as a diagnostic tool for the plasma turbulence in the upper corona.

Research paper thumbnail of Forward Modeling of Particle Acceleration and Transport in an Individual Solar Flare

The Astrophysical Journal, 2020

The aim of this study is to generate maps of the hard X-ray emission produced by energetic electr... more The aim of this study is to generate maps of the hard X-ray emission produced by energetic electrons in a solar flare and compare them with observations. The ultimate goal is to test the viability of the combined MHD/test-particle approach for data-driven modeling of active events in the solar corona and their impact on the heliosphere. Based on an MHD model of X-class solar flare observed on 2017 September 8, we calculate trajectories of a large number of electrons and protons using the relativistic guiding-center approach. Using the obtained particle trajectories, we deduce the spatial and energy distributions of energetic electrons and protons, and calculate bremsstrahlung hard X-ray emission using the "thin-target" approximation. Our approach predicts some key characteristics of energetic particles in the considered flare, including the size and location of the acceleration region, energetic particle trajectories and energy spectra. Most importantly, the hard X-ray bremsstrahlung intensity maps predicted by the model are in good agreement with those observed by RHESSI. Furthermore, the locations of proton and electron precipitation appear to be close to the sources of helioseismic response detected in this flare. Therefore, the adopted approach can be used for observationally driven modeling of individual solar flares, including manifestations of energetic particles in the corona, as well as the inner heliosphere.

Research paper thumbnail of Radio Echo in the Turbulent Corona and Simulations of Solar Drift-pair Radio Bursts

The Astrophysical Journal, 2020

Drift-pair bursts are an unusual type of solar low-frequency radio emission, which appear in the ... more Drift-pair bursts are an unusual type of solar low-frequency radio emission, which appear in the dynamic spectra as two parallel drifting bright stripes separated in time. Recent imaging spectroscopy observations allowed for the quantitative characterization of the drifting pairs in terms of source size, position, and evolution. Here, the drift-pair parameters are qualitatively analyzed and compared with the newly developed Monte Carlo ray-tracing technique simulating radio-wave propagation in the inhomogeneous anisotropic turbulent solar corona. The results suggest that drift-pair bursts can be formed due to a combination of refraction and scattering processes, with the trailing component being the result of turbulent reflection (turbulent radio echo). The formation of drift-pair bursts requires an anisotropic scattering with the level of plasma density fluctuations comparable to that in type III bursts, but with a stronger anisotropy at the inner turbulence scale. The anisotropic radio-wave scattering model can quantitatively reproduce the key properties of drift-pair bursts: the apparent source size and its increase with time at a given frequency, the parallel motion of the source centroid positions, and the delay between the burst components. The trailing component is found to be virtually cospatial and following the main component. The simulations suggest that drift-pair bursts are likely to be observed closer to the disk center and below 100 MHz due to the effects of free-free absorption and scattering. The exciter of drift pairs is consistent with propagating packets of whistlers, allowing for a fascinating way to diagnose the plasma turbulence and the radio emission mechanism. Unified Astronomy Thesaurus concepts: Solar coronal radio emission (1993); Radio spectroscopy (1359)

Research paper thumbnail of First Observation of a Type II Solar Radio Burst Transitioning between a Stationary and Drifting State

The Astrophysical Journal, 2020

Standing shocks are believed to be responsible for stationary Type II solar radio bursts, whereas... more Standing shocks are believed to be responsible for stationary Type II solar radio bursts, whereas drifting Type II bursts are excited by moving shocks often related to coronal mass ejections (CMEs). Observations of either stationary or drifting Type II bursts are common, but a transition between the two states has not yet been reported. Here, we present a Type II burst which shows a clear, continuous transition from a stationary to a drifting state, the first observation of its kind. Moreover, band splitting is observed in the stationary parts of the burst, as well as intriguing negative and positive frequency-drift fine structures within the stationary emissions. The relation of the radio emissions to an observed jet and a narrow CME were investigated across multiple wavelengths, and the mechanisms leading to the transitioning Type II burst were determined. We find that a jet eruption generates a streamer-puff CME and that the interplay between the CME-driven shock and the streamer is likely to be responsible for the observed radio emissions.

Research paper thumbnail of Particle acceleration with anomalous pitch angle scattering in 3D separator reconnection

Astronomy and Astrophysics, 2020

Context. Understanding how the release of stored magnetic energy contributes to the generation of... more Context. Understanding how the release of stored magnetic energy contributes to the generation of non-thermal high energy particles during solar flares is an important open problem in solar physics. There is a general consensus that magnetic reconnection plays a fundamental role in the energy release and conversion processes taking place during flares. A common approach for investigating how reconnection contributes to particle acceleration is to use test particle calculations in electromagnetic fields derived from numerical magnetohydrodynamic (MHD) simulations of reconnecting magnetic fields. These MHD simulations use anomalous resistivities that are orders of magnitude larger than the Spitzer resistivity that is based on Coulomb collisions. The processes leading to such an enhanced resistivity should also affect the test particles, for example, through pitch angle scattering. This study explores the effect of such a link between the level of resistivity and its impact on particle orbits and builds on a previous study using a 2D MHD simulation of magnetic reconnection. Aims. This paper aims to extend the previous investigation to a 3D magnetic reconnection configuration and to study the effect on test particle orbits. Methods. We carried out orbit calculations using a 3D MHD simulation of reconnection in a magnetic field with a magnetic separator. The orbit calculations use the relativistic guiding centre approximation but, crucially, they also include pitch angle scattering using stochastic differential equations. The effects of varying the resistivity and the models for pitch angle scattering on particle orbit trajectories, final positions, energy spectra, final pitch angle distribution, and orbit duration are all studied in detail. Results. Pitch angle scattering widens highly collimated beams of unscattered orbit trajectories, allowing orbits to access previously unaccessible field lines; this causes final positions to spread along other topological structures which could not be accessed without scattering. Scattered orbit energy spectra are found to be predominantly affected by the level of anomalous resistivity, with the pitch angle scattering model only playing a role in specific, isolated cases. This is in contrast to the study involving a 2D MHD simulation of magnetic reconnection, where pitch angle scattering had a more noticeable effect on the energy spectra. Pitch scattering effects are found to play a crucial role in determining the pitch angle and orbit duration distributions.

Research paper thumbnail of Spatio-temporal energy partitioning in a non-thermally dominated two-loop solar flare

The Astrophysical Journal, Volume 890, Issue 1, id.75, 2020

Solar flares show remarkable variety of the energy partitioning between thermal and nonthermal co... more Solar flares show remarkable variety of the energy partitioning between thermal and nonthermal components. Those with a prominent nonthermal component but only a modest thermal one are particularly well suited to study the direct effect of the non-thermal electrons on plasma heating. Here, we analyze such a well observed, impulsive single-spike nonthermal event, a SOL2013-11-05T035054 solar flare, where the plasma heating can be entirely attributed to the energy losses of these impulsively accelerated electrons. Evolution of the energy budget of thermal and nonthermal components during the flare is analysed using X-ray, microwave, and EUV observations and three-dimensional modeling. The results suggest that (i) the flare geometry is consistent with a two-loop morphology and the magnetic energy is likely released due to interaction between these two loops; (ii) the released magnetic energy converted to the nonthermal energy of accelerated electrons only, which is subsequently converted to the thermal energy of the plasma; (iii) the energy is partitioned in these two flaring loops in comparable amounts; (iv) one of these flaring loops remained relatively tenuous but rather hot, while the other remained relatively cool but denser than the first one. Therefore, this solar flare demonstrates an extreme efficiency of conversion of the free magnetic energy to the nonthermal energy of particle acceleration and the energy flow into two loops from the non-thermal to thermal one with a negligible direct heating.

Research paper thumbnail of First imaging spectroscopy observations of solar drift pair bursts

Astronomy & Astrophysics Letters, 2019

Drift pairs are an unusual and puzzling type of fine structure sometimes observed in dynamic spec... more Drift pairs are an unusual and puzzling type of fine structure sometimes observed in dynamic spectra of solar radio emission. They appear as two identical short narrowband drifting stripes separated in time; both positive and negative frequency drifts are observed. Currently, due to the lack of imaging observations, there is no satisfactory explanation for this phenomenon. Using the Low Frequency Array (LOFAR), we report unique observations of a cluster of drift pair bursts in the frequency range of 30 − 70 MHz made on 12 July 2017. Spectral imaging capabilities of the instrument have allowed us for the first time to resolve the temporal and frequency evolution of the source locations and sizes at a fixed frequency and along the drifting pair components. Sources of two components of a drift pair have been imaged and found to propagate in the same direction along nearly the same trajectories. Motion of the second component source is seen to be delayed in time with respect to that of the first one. The source trajectories can be complicated and non-radial; positive and negative frequency drifts correspond to opposite propagation directions. The drift pair bursts with positive and negative frequency drifts, as well as the associated broadband type-III-like bursts, are produced in the same regions. The visible source velocities are variable from zero to a few 10 4 (up to ∼ 10 5) km s −1 , which often exceeds the velocities inferred from the drift rate (∼ 10 4 km s −1). The visible source sizes are of about 10 ′ − 18 ′ ; they are more compact than typical type III sources at the same frequencies. The existing models of drift pair bursts cannot adequately explain the observed features. We discuss the key issues that need to be addressed, and in particular the anisotropic scattering of the radio waves. The broadband bursts observed simultaneously with the drift pairs differ in some aspects from common type III bursts and may represent a separate type of emission.

Research paper thumbnail of Anisotropic Radio-Wave Scattering and the Interpretation of Solar Radio Emission Observations

The Astrophysical Journal, 2019

The observed properties (i.e., source size, source position, time duration, decay time) of solar ... more The observed properties (i.e., source size, source position, time duration, decay time) of solar radio emission produced through plasma processes near the local plasma frequency, and hence the interpretation of solar radio bursts, are strongly influenced by propagation effects in the inhomogeneous turbulent solar corona. In this work, a 3D stochastic description of the propagation process is presented, based on the Fokker-Planck and Langevin equations of radio-wave transport in a medium containing anisotropic electron density fluctuations. Using a numerical treatment based on this model, we investigate the characteristic source sizes and burst decay times for Type III solar radio bursts. Comparison of the simulations with the observations of solar radio bursts shows that predominantly perpendicular density fluctuations in the solar corona are required, with an anisotropy factor ∼ 0.3 for sources observed at around 30 MHz. The simulations also demonstrate that the photons are isotropized near the region of primary emission, but the waves are then focused by large-scale refraction, leading to plasma radio emission directivity that is characterized by a half-width-half-maximum of about 40 degrees near 30 MHz. The results are applicable to various solar radio bursts produced via plasma emission.

Research paper thumbnail of REGULARIZED RECONSTRUCTION OF THE DIFFERENTIAL EMISSION MEASURE FROM SOLAR FLARE HARD X-RAY SPECTRA

We address the problem of how to test whether an observed solar hard X-ray bremsstrahlung spectru... more We address the problem of how to test whether an observed solar hard X-ray bremsstrahlung spectrum (I ()) is consistent with a purely thermal (locally Maxwellian) distribution of source electrons, and, if so, how to reconstruct the corresponding differential emission measure (ξ (T)). Unlike previous analysis based on the Kramers and Bethe-Heitler approximations to the bremsstrahlung cross-section, here we use an exact (solid-angle-averaged) cross-section. We show that the problem of determining ξ (T) from measurements of I () invOlves two successive inverse problems: the first, to recover the mean source-electron flux spectrum (F(E)) from I () and the second, to recover ξ (T) fromF(E). We discuss the highly pathological numerical properties of this second problem within the framework of the regularization theory for linear inverse problems. In particular, we show that an iterative scheme with a positivity constraint is effective in recovering δ-like forms of ξ (T) while first-order Tikhonov regularization with boundary conditions works well in the case of power-lawlike forms. Therefore, we introduce a restoration approach whereby the low-energy part ofF(E), dominated by the thermal component, is inverted by using the iterative algorithm with positivity, while the high-energy part, dominated by the power-law component, is inverted by using first-order regularization. This approach is first tested by using simulatedF(E) derived from a priori known forms of ξ (T) and then applied to hard X-ray spectral data from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI).

Research paper thumbnail of Data-constrained Solar Modeling with GX Simulator

To facilitate the study of solar flares and active regions, we have created a modeling framework,... more To facilitate the study of solar flares and active regions, we have created a modeling framework, the freely distributed GX Simulator IDL package, that combines 3D magnetic and plasma structures with thermal and nonthermal models of the chromosphere, transition region, and corona. Its object-based modular architecture, which runs on Windows, Mac, and Unix/Linux platforms, offers the ability to either import 3D density and temperature distribution models, or to assign numerically defined coronal or chromospheric temperatures and densities, or their distributions, to each individual voxel. GX Simulator can apply parametric heating models involving average properties of the magnetic field lines crossing a given voxel, as well as compute and investigate the spatial and spectral properties of radio, (sub)millimeter, EUV, and X-ray emissions calculated from the model, and quantitatively compare them with observations. The package includes a fully automatic model production pipeline that, based on minimal users input, downloads the required SDO/HMI vector magnetic field data, performs potential or nonlinear force-free field extrapolations, populates the magnetic field skeleton with parameterized heated plasma coronal models that assume either steady-state or impulsive plasma heating, and generates non-LTE density and temperature distribution models of the chromosphere that are constrained by photospheric measurements. The standardized models produced by this pipeline may be further customized through specialized IDL scripts, or a set of interactive tools provided by the graphical user interface. Here, we describe the GX Simulator framework and its applications.

Research paper thumbnail of An Anisotropic Density Turbulence Model from the Sun to 1 au Derived from Radio Observations

Solar radio bursts are strongly affected by radio-wave scattering on density inhomogeneities, cha... more Solar radio bursts are strongly affected by radio-wave scattering on density inhomogeneities, changing their observed time characteristics, sizes, and positions. The same turbulence causes angular broadening and scintillation of galactic and extragalactic compact radio sources observed through the solar atmosphere. Using large-scale simulations of radio-wave transport, the characteristics of anisotropic density turbulence from 0.1 R e to 1 au are explored. For the first time, a profile of heliospheric density fluctuations is deduced that accounts for the properties of extrasolar radio sources, solar radio bursts, and in situ density fluctuation measurements in the solar wind at 1 au. The radial profile of the spectrum-weighted mean wavenumber of density fluctuations (a quantity proportional to the scattering rate of radio waves) is found to have a broad maximum at around (4-7) R e , where the slow solar wind becomes supersonic. The level of density fluctuations at the inner scale (which is consistent with the proton resonance scale) decreases with heliocentric distance as () () n r r R 2 10 1 i 2 7 3.7   d á ñ´-cm −6. Due to scattering, the apparent positions of solar burst sources observed at frequencies between 0.1 and 300 MHz are computed to be essentially cospatial and to have comparable sizes, for both fundamental and harmonic emission. Anisotropic scattering is found to account for the shortest solar radio burst decay times observed, and the required wavenumber anisotropy is q ∥ /q ⊥ = 0.25-0.4, depending on whether fundamental or harmonic emission is involved. The deduced radio-wave scattering rate paves the way to quantify intrinsic solar radio burst characteristics.

Research paper thumbnail of Source positions of an interplanetary type III radio burst and anisotropic radio-wave scattering

Interplanetary solar radio type III bursts provide the means to remotely study and track energeti... more Interplanetary solar radio type III bursts provide the means to remotely study and track energetic electrons propagating in the interplanetary medium. Due to the lack of direct radio source imaging, several methods have been developed to determine the source positions from space-based observations. Moreover, none of the methods consider the propagation effects of anisotropic radio-wave scattering, which would strongly distort the trajectory of radio waves, delay their arrival times, and affect their apparent characteristics. We investigate the source positions and directivity of an interplanetary type III burst simultaneously observed by Parker Solar Probe, Solar Orbiter, STEREO, and Wind and we compare the results of applying the intensity fit and timing methods with ray-tracing simulations of radio-wave propagation with anisotropic density fluctuations. The simulation calculates the trajectories of the rays, their time profiles at different viewing sites, and the apparent characteristics for various density fluctuation parameters. The results indicate that the observed source positions are displaced away from the locations where emission is produced, and their deduced radial distances are larger than expected from density models. This suggests that the apparent position is affected by anisotropic radio-wave scattering, which leads to an apparent position at a larger heliocentric distance from the Sun. The methods to determine the source positions may underestimate the apparent positions if they do not consider the path of radio-wave propagation and incomplete scattering at a viewing site close to the intrinsic source position.

Research paper thumbnail of The Solar Particle Acceleration Radiation and Kinetics (SPARK) Mission Concept

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Research paper thumbnail of An Anisotropic Density Turbulence Model from the Sun to 1 au Derived from Radio Observations

Astrophysical Journal, 2023

Solar radio bursts are strongly affected by radio-wave scattering on density inhomogeneities, cha... more Solar radio bursts are strongly affected by radio-wave scattering on density inhomogeneities, changing their observed time characteristics, sizes, and positions. The same turbulence causes angular broadening and scintillation of galactic and extragalactic compact radio sources observed through the solar atmosphere. Using large-scale simulations of radio-wave transport, the characteristics of anisotropic density turbulence from 0.1 R e to 1 au are explored. For the first time, a profile of heliospheric density fluctuations is deduced that accounts for the properties of extrasolar radio sources, solar radio bursts, and in situ density fluctuation measurements in the solar wind at 1 au. The radial profile of the spectrum-weighted mean wavenumber of density fluctuations (a quantity proportional to the scattering rate of radio waves) is found to have a broad maximum at around (4-7) R e , where the slow solar wind becomes supersonic. The level of density fluctuations at the inner scale (which is consistent with the proton resonance scale) decreases with heliocentric distance as () () n r r R 2 10 1 i 2 7 3.7   d á ñ´-cm −6. Due to scattering, the apparent positions of solar burst sources observed at frequencies between 0.1 and 300 MHz are computed to be essentially cospatial and to have comparable sizes, for both fundamental and harmonic emission. Anisotropic scattering is found to account for the shortest solar radio burst decay times observed, and the required wavenumber anisotropy is q ∥ /q ⊥ = 0.25-0.4, depending on whether fundamental or harmonic emission is involved. The deduced radio-wave scattering rate paves the way to quantify intrinsic solar radio burst characteristics.

Research paper thumbnail of Determination of the Total Accelerated Electron Rate and Power Using Solar Flare Hard X-Ray Spectra

Solar flare hard X-ray (HXR) spectroscopy serves as a key diagnostic of the accelerated electron ... more Solar flare hard X-ray (HXR) spectroscopy serves as a key diagnostic of the accelerated electron spectrum. However, the standard approach using the collisional cold thick-target model poorly constrains the lower-energy part of the accelerated electron spectrum, hence the overall energetics of the accelerated electrons are typically constrained only to within one or two orders of magnitude. Here, we develop and apply a physically selfconsistent, warm-target approach that involves the use of both HXR spectroscopy and imaging data. This approach allows an accurate determination of the electron distribution low-energy cutoff, and hence the electron acceleration rate and the contribution of accelerated electrons to the total energy released, by constraining the coronal plasma parameters. Using a solar flare observed in X-rays by RHESSI, we demonstrate that using the standard cold-target methodology, the low-energy cutoff (hence the energy content in electrons) is essentially undetermined. However, the warm-target methodology can determine the low-energy electron cutoff with ∼7% uncertainty at the 3σ level, hence it permits an accurate quantitative study of the importance of accelerated electrons in solar flare energetics.

Research paper thumbnail of The Efficiency of Electron Acceleration during the Impulsive Phase of a Solar Flare

Solar flares are known to be prolific electron accelerators, yet identifying the mechanism(s) for... more Solar flares are known to be prolific electron accelerators, yet identifying the mechanism(s) for such efficient electron acceleration in solar flare (and similar astrophysical settings) presents a major challenge. This is due in part to a lack of observational constraints related to conditions in the primary acceleration region itself. Accelerated electrons with energies above ∼20 keV are revealed by hard X-ray (HXR) bremsstrahlung emission, while accelerated electrons with even higher energies manifest themselves through radio gyrosynchrotron emission. Here, we show, for a well-observed flare on 2017 September 10, that a combination of RHESSI HXR and and the Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA) EUV observations provides a robust estimate of the fraction of the ambient electron population that is accelerated at a given time, with an upper limit of 10 −2 on the number density of nonthermal (20 keV) electrons, expressed as a fraction of the number density of ambient protons in the same volume. This upper limit is about 2 orders of magnitude lower than previously inferred from microwave observations of the same event. Our results strongly indicate that the fraction of accelerated electrons in the coronal region at any given time is relatively small but also that the overall duration of the HXR emission requires a steady resupply of electrons to the acceleration site. Simultaneous measurements of the instantaneous accelerated electron number density and the associated specific electron acceleration rate provide key constraints for a quantitative study of the mechanisms leading to electron acceleration in magnetic reconnection events.

Research paper thumbnail of Radio Echo in the Turbulent Corona and Simulations of Solar Drift-pair Radio Bursts

The Astrophysical Journal, Volume 898, Issue 2, id.94, 2020

Drift-pair bursts are an unusual type of solar low-frequency radio emission, which appear in the ... more Drift-pair bursts are an unusual type of solar low-frequency radio emission, which appear in the dynamic spectra as two parallel drifting bright stripes separated in time. Recent imaging spectroscopy observations allowed for the quantitative characterization of the drifting pairs in terms of source size, position, and evolution. Here, the drift-pair parameters are qualitatively analyzed and compared with the newly developed Monte Carlo ray-tracing technique simulating radio-wave propagation in the inhomogeneous anisotropic turbulent solar corona. The results suggest that drift-pair bursts can be formed due to a combination of refraction and scattering processes, with the trailing component being the result of turbulent reflection (turbulent radio echo). The formation of drift-pair bursts requires an anisotropic scattering with the level of plasma density fluctuations comparable to that in type III bursts, but with a stronger anisotropy at the inner turbulence scale. The anisotropic radio-wave scattering model can quantitatively reproduce the key properties of drift-pair bursts: the apparent source size and its increase with time at a given frequency, the parallel motion of the source centroid positions, and the delay between the burst components. The trailing component is found to be virtually cospatial and following the main component. The simulations suggest that drift-pair bursts are likely to be observed closer to the disk center and below 100 MHz due to the effects of free-free absorption and scattering. The exciter of drift pairs is consistent with propagating packets of whistlers, allowing for a fascinating way to diagnose the plasma turbulence and the radio emission mechanism.

Research paper thumbnail of Fine structure of type III solar radio bursts from Langmuir wave motion in turbulent plasma

Nature Astronomy, Volume 5, p. 796-804, 2021

The Sun frequently accelerates near-relativistic electron beams that travel out through the solar... more The Sun frequently accelerates near-relativistic electron beams that travel out through the solar corona and interplanetary space. Interacting with their plasma environment, these beams produce type III radio bursts, the brightest astrophysical radio sources seen from the Earth. The formation and motion of type III fine frequency structures is a puzzle but is commonly believed to be related to plasma turbulence in the solar corona and solar wind. Combining a theoretical framework with kinetic simulations and high-resolution radio type III observations using the Low Frequency Array, we quantitatively show that the fine structures are caused by the moving intense clumps of Langmuir waves in a turbulent medium. Our results show how type III fine structure can be used to remotely analyse the intensity and spectrum of compressive density fluctuations, and can infer ambient temperatures in astrophysical plasma, both significantly expanding the current diagnostic potential of solar radio emission.

Research paper thumbnail of First Frequency-time-resolved Imaging Spectroscopy Observations of Solar Radio Spikes

The Astrophysical Journal Letters, 2021

Solar radio spikes are short duration and narrow bandwidth fine structures in dynamic spectra obs... more Solar radio spikes are short duration and narrow bandwidth fine structures in dynamic spectra observed from the GHz to tens of MHz range. Their very short duration and narrow frequency bandwidth are indicative of subsecond small-scale energy release in the solar corona, yet their origin is not understood. Using the LOw Frequency ARray, we present spatially, frequency, and time resolved observations of individual radio spikes associated with a coronal mass ejection. Individual radio spike imaging demonstrates that the observed area is increasing in time and the centroid positions of the individual spikes move superluminally parallel to the solar limb. Comparison of spike characteristics with that of individual Type IIIb striae observed in the same event show similarities in duration, bandwidth, drift rate, polarization, and observed area, as well the spike and striae motion in the image plane suggesting fundamental plasma emission with the spike emission region on the order of ∼10 8 cm, with brightness temperature as high as 10 13 K. The observed spatial, spectral, and temporal properties of the individual spike bursts are also suggestive of the radiation responsible for spikes escaping through anisotropic density turbulence in closed loop structures with scattering preferentially along the guiding magnetic field oriented parallel to the limb in the scattering region. The dominance of scattering on the observed time profile suggests the energy release time is likely to be shorter than what is often assumed. The observations also imply that the density turbulence anisotropy along closed magnetic field lines is higher than along open field lines.

Research paper thumbnail of Fine structure of type III solar radio bursts from Langmuir wave motion in turbulent plasma

Nature Astronomy, May 31, 2021

The Sun frequently accelerates near-relativistic electron beams that travel out through the solar... more The Sun frequently accelerates near-relativistic electron beams that travel out through the solar corona and interplanetary space. Interacting with their plasma environment, these beams produce type III radio bursts, the brightest astrophysical radio sources seen from the Earth. The formation and motion of type III fine frequency structures is a puzzle but is commonly believed to be related to plasma turbulence in the solar corona and solar wind. Combining a theoretical framework with kinetic simulations and high-resolution radio type III observations using the Low Frequency Array, we quantitatively show that the fine structures are caused by the moving intense clumps of Langmuir waves in a turbulent medium. Our results show how type III fine structure can be used to remotely analyse the intensity and spectrum of compressive density fluctuations, and can infer ambient temperatures in astrophysical plasma, both significantly expanding the current diagnostic potential of solar radio emission.

Research paper thumbnail of Subsecond Time Evolution of Type III Solar Radio Burst Sources at Fundamental and Harmonic Frequencies

The Astrophysical Journal, 2020

Recent developments in astronomical radio telescopes opened new opportunities in imaging and spec... more Recent developments in astronomical radio telescopes opened new opportunities in imaging and spectroscopy of solar radio bursts at subsecond timescales. Imaging in narrow frequency bands has revealed temporal variations in the positions and source sizes that do not fit into the standard picture of type III solar radio bursts, and require a better understanding of radio-wave transport. In this paper, we utilize 3D Monte Carlo ray-tracing simulations that account for the anisotropic density turbulence in the inhomogeneous solar corona to quantitatively explain the image dynamics at the fundamental (near plasma frequency) and harmonic (double) plasma emissions observed at ∼32MHz. Comparing the simulations with observations, we find that anisotropic scattering from an instantaneous emission point source can account for the observed time profiles, centroid locations, and source sizes of the fundamental component of type III radio bursts (generated where f pe ≈32 MHz). The best agreement with observations is achieved when the ratio of the perpendicular to the parallel component of the wavevector of anisotropic density turbulence is around 0.25. Harmonic emission sources observed at the same frequency (∼32 MHz, but generated where f pe ≈16 MHz) have apparent sizes comparable to those produced by the fundamental emission, but demonstrate a much slower temporal evolution. The simulations of radio-wave propagation make it possible to quantitatively explain the variations of apparent source sizes and positions at subsecond timescales both for the fundamental and harmonic emissions, and can be used as a diagnostic tool for the plasma turbulence in the upper corona.

Research paper thumbnail of Forward Modeling of Particle Acceleration and Transport in an Individual Solar Flare

The Astrophysical Journal, 2020

The aim of this study is to generate maps of the hard X-ray emission produced by energetic electr... more The aim of this study is to generate maps of the hard X-ray emission produced by energetic electrons in a solar flare and compare them with observations. The ultimate goal is to test the viability of the combined MHD/test-particle approach for data-driven modeling of active events in the solar corona and their impact on the heliosphere. Based on an MHD model of X-class solar flare observed on 2017 September 8, we calculate trajectories of a large number of electrons and protons using the relativistic guiding-center approach. Using the obtained particle trajectories, we deduce the spatial and energy distributions of energetic electrons and protons, and calculate bremsstrahlung hard X-ray emission using the "thin-target" approximation. Our approach predicts some key characteristics of energetic particles in the considered flare, including the size and location of the acceleration region, energetic particle trajectories and energy spectra. Most importantly, the hard X-ray bremsstrahlung intensity maps predicted by the model are in good agreement with those observed by RHESSI. Furthermore, the locations of proton and electron precipitation appear to be close to the sources of helioseismic response detected in this flare. Therefore, the adopted approach can be used for observationally driven modeling of individual solar flares, including manifestations of energetic particles in the corona, as well as the inner heliosphere.

Research paper thumbnail of Radio Echo in the Turbulent Corona and Simulations of Solar Drift-pair Radio Bursts

The Astrophysical Journal, 2020

Drift-pair bursts are an unusual type of solar low-frequency radio emission, which appear in the ... more Drift-pair bursts are an unusual type of solar low-frequency radio emission, which appear in the dynamic spectra as two parallel drifting bright stripes separated in time. Recent imaging spectroscopy observations allowed for the quantitative characterization of the drifting pairs in terms of source size, position, and evolution. Here, the drift-pair parameters are qualitatively analyzed and compared with the newly developed Monte Carlo ray-tracing technique simulating radio-wave propagation in the inhomogeneous anisotropic turbulent solar corona. The results suggest that drift-pair bursts can be formed due to a combination of refraction and scattering processes, with the trailing component being the result of turbulent reflection (turbulent radio echo). The formation of drift-pair bursts requires an anisotropic scattering with the level of plasma density fluctuations comparable to that in type III bursts, but with a stronger anisotropy at the inner turbulence scale. The anisotropic radio-wave scattering model can quantitatively reproduce the key properties of drift-pair bursts: the apparent source size and its increase with time at a given frequency, the parallel motion of the source centroid positions, and the delay between the burst components. The trailing component is found to be virtually cospatial and following the main component. The simulations suggest that drift-pair bursts are likely to be observed closer to the disk center and below 100 MHz due to the effects of free-free absorption and scattering. The exciter of drift pairs is consistent with propagating packets of whistlers, allowing for a fascinating way to diagnose the plasma turbulence and the radio emission mechanism. Unified Astronomy Thesaurus concepts: Solar coronal radio emission (1993); Radio spectroscopy (1359)

Research paper thumbnail of First Observation of a Type II Solar Radio Burst Transitioning between a Stationary and Drifting State

The Astrophysical Journal, 2020

Standing shocks are believed to be responsible for stationary Type II solar radio bursts, whereas... more Standing shocks are believed to be responsible for stationary Type II solar radio bursts, whereas drifting Type II bursts are excited by moving shocks often related to coronal mass ejections (CMEs). Observations of either stationary or drifting Type II bursts are common, but a transition between the two states has not yet been reported. Here, we present a Type II burst which shows a clear, continuous transition from a stationary to a drifting state, the first observation of its kind. Moreover, band splitting is observed in the stationary parts of the burst, as well as intriguing negative and positive frequency-drift fine structures within the stationary emissions. The relation of the radio emissions to an observed jet and a narrow CME were investigated across multiple wavelengths, and the mechanisms leading to the transitioning Type II burst were determined. We find that a jet eruption generates a streamer-puff CME and that the interplay between the CME-driven shock and the streamer is likely to be responsible for the observed radio emissions.

Research paper thumbnail of Particle acceleration with anomalous pitch angle scattering in 3D separator reconnection

Astronomy and Astrophysics, 2020

Context. Understanding how the release of stored magnetic energy contributes to the generation of... more Context. Understanding how the release of stored magnetic energy contributes to the generation of non-thermal high energy particles during solar flares is an important open problem in solar physics. There is a general consensus that magnetic reconnection plays a fundamental role in the energy release and conversion processes taking place during flares. A common approach for investigating how reconnection contributes to particle acceleration is to use test particle calculations in electromagnetic fields derived from numerical magnetohydrodynamic (MHD) simulations of reconnecting magnetic fields. These MHD simulations use anomalous resistivities that are orders of magnitude larger than the Spitzer resistivity that is based on Coulomb collisions. The processes leading to such an enhanced resistivity should also affect the test particles, for example, through pitch angle scattering. This study explores the effect of such a link between the level of resistivity and its impact on particle orbits and builds on a previous study using a 2D MHD simulation of magnetic reconnection. Aims. This paper aims to extend the previous investigation to a 3D magnetic reconnection configuration and to study the effect on test particle orbits. Methods. We carried out orbit calculations using a 3D MHD simulation of reconnection in a magnetic field with a magnetic separator. The orbit calculations use the relativistic guiding centre approximation but, crucially, they also include pitch angle scattering using stochastic differential equations. The effects of varying the resistivity and the models for pitch angle scattering on particle orbit trajectories, final positions, energy spectra, final pitch angle distribution, and orbit duration are all studied in detail. Results. Pitch angle scattering widens highly collimated beams of unscattered orbit trajectories, allowing orbits to access previously unaccessible field lines; this causes final positions to spread along other topological structures which could not be accessed without scattering. Scattered orbit energy spectra are found to be predominantly affected by the level of anomalous resistivity, with the pitch angle scattering model only playing a role in specific, isolated cases. This is in contrast to the study involving a 2D MHD simulation of magnetic reconnection, where pitch angle scattering had a more noticeable effect on the energy spectra. Pitch scattering effects are found to play a crucial role in determining the pitch angle and orbit duration distributions.

Research paper thumbnail of Spatio-temporal energy partitioning in a non-thermally dominated two-loop solar flare

The Astrophysical Journal, Volume 890, Issue 1, id.75, 2020

Solar flares show remarkable variety of the energy partitioning between thermal and nonthermal co... more Solar flares show remarkable variety of the energy partitioning between thermal and nonthermal components. Those with a prominent nonthermal component but only a modest thermal one are particularly well suited to study the direct effect of the non-thermal electrons on plasma heating. Here, we analyze such a well observed, impulsive single-spike nonthermal event, a SOL2013-11-05T035054 solar flare, where the plasma heating can be entirely attributed to the energy losses of these impulsively accelerated electrons. Evolution of the energy budget of thermal and nonthermal components during the flare is analysed using X-ray, microwave, and EUV observations and three-dimensional modeling. The results suggest that (i) the flare geometry is consistent with a two-loop morphology and the magnetic energy is likely released due to interaction between these two loops; (ii) the released magnetic energy converted to the nonthermal energy of accelerated electrons only, which is subsequently converted to the thermal energy of the plasma; (iii) the energy is partitioned in these two flaring loops in comparable amounts; (iv) one of these flaring loops remained relatively tenuous but rather hot, while the other remained relatively cool but denser than the first one. Therefore, this solar flare demonstrates an extreme efficiency of conversion of the free magnetic energy to the nonthermal energy of particle acceleration and the energy flow into two loops from the non-thermal to thermal one with a negligible direct heating.

Research paper thumbnail of First imaging spectroscopy observations of solar drift pair bursts

Astronomy & Astrophysics Letters, 2019

Drift pairs are an unusual and puzzling type of fine structure sometimes observed in dynamic spec... more Drift pairs are an unusual and puzzling type of fine structure sometimes observed in dynamic spectra of solar radio emission. They appear as two identical short narrowband drifting stripes separated in time; both positive and negative frequency drifts are observed. Currently, due to the lack of imaging observations, there is no satisfactory explanation for this phenomenon. Using the Low Frequency Array (LOFAR), we report unique observations of a cluster of drift pair bursts in the frequency range of 30 − 70 MHz made on 12 July 2017. Spectral imaging capabilities of the instrument have allowed us for the first time to resolve the temporal and frequency evolution of the source locations and sizes at a fixed frequency and along the drifting pair components. Sources of two components of a drift pair have been imaged and found to propagate in the same direction along nearly the same trajectories. Motion of the second component source is seen to be delayed in time with respect to that of the first one. The source trajectories can be complicated and non-radial; positive and negative frequency drifts correspond to opposite propagation directions. The drift pair bursts with positive and negative frequency drifts, as well as the associated broadband type-III-like bursts, are produced in the same regions. The visible source velocities are variable from zero to a few 10 4 (up to ∼ 10 5) km s −1 , which often exceeds the velocities inferred from the drift rate (∼ 10 4 km s −1). The visible source sizes are of about 10 ′ − 18 ′ ; they are more compact than typical type III sources at the same frequencies. The existing models of drift pair bursts cannot adequately explain the observed features. We discuss the key issues that need to be addressed, and in particular the anisotropic scattering of the radio waves. The broadband bursts observed simultaneously with the drift pairs differ in some aspects from common type III bursts and may represent a separate type of emission.

Research paper thumbnail of Anisotropic Radio-Wave Scattering and the Interpretation of Solar Radio Emission Observations

The Astrophysical Journal, 2019

The observed properties (i.e., source size, source position, time duration, decay time) of solar ... more The observed properties (i.e., source size, source position, time duration, decay time) of solar radio emission produced through plasma processes near the local plasma frequency, and hence the interpretation of solar radio bursts, are strongly influenced by propagation effects in the inhomogeneous turbulent solar corona. In this work, a 3D stochastic description of the propagation process is presented, based on the Fokker-Planck and Langevin equations of radio-wave transport in a medium containing anisotropic electron density fluctuations. Using a numerical treatment based on this model, we investigate the characteristic source sizes and burst decay times for Type III solar radio bursts. Comparison of the simulations with the observations of solar radio bursts shows that predominantly perpendicular density fluctuations in the solar corona are required, with an anisotropy factor ∼ 0.3 for sources observed at around 30 MHz. The simulations also demonstrate that the photons are isotropized near the region of primary emission, but the waves are then focused by large-scale refraction, leading to plasma radio emission directivity that is characterized by a half-width-half-maximum of about 40 degrees near 30 MHz. The results are applicable to various solar radio bursts produced via plasma emission.

Research paper thumbnail of Beam-Plasma Structures at Propagation of Electron Beams in Plasma

In the frame of the theory of weak turbulence the propagation of electron beams is considered. U... more In the frame of the theory of weak turbulence the propagation of electron
beams is considered. Using the smallness of quasilinear time transition
from kinetic equations to gas-dynamic ones has been done. The obtained
gas-dynamic equations are solved for one, two and N monoenergetic
beams. It is shown that each beam generally propagates as a beam-plasma
structure consisting of electrons and Langmuir waves. Interaction of the
structures at their propagation leads to electron exchange and spatial shape
changing. Different situations are discussed in dependence on initial beam
velocities and densities.

Research paper thumbnail of Gasdynamic description of electron-beam flying-off in a plasma

Research paper thumbnail of Numerical and analytical study of the propagation of a monoenergetic electron beam in a plasma

Research paper thumbnail of The spread of the hot electron cloud in the solar corona

Research paper thumbnail of Propagation of a Monoenergetic Electron Beam in the Solar Corona

Research paper thumbnail of To gasdynamic description of a hot electron cloud in a cold plasma

Research paper thumbnail of Propagation of a Maxwellian Electron Cloud in a Plasma

Research paper thumbnail of Dynamics of a fast Maxwellian electron cloud in coronal plasma

Research paper thumbnail of Propagation of a fast electron cloud in a solar-like plasma of decreasing density

Research paper thumbnail of Dynamics of electron beams in the solar corona plasma with density fluctuations

Research paper thumbnail of Diffusive transport of energetic electrons in the solar corona: X-ray and radio diagnostics

Research paper thumbnail of Interplanetary Type III Bursts and Electron Density Fluctuations in the Solar Wind

Research paper thumbnail of Solar type III radio burst time characteristics at LOFAR frequencies and the implications for electron beam transport

Research paper thumbnail of Combined Radio and Space-Based Solar Observations: From Techniques to New Results - Preface

Research paper thumbnail of Shock location and CME 3D reconstruction of a solar type II radio burst with LOFAR

Research paper thumbnail of Energy Deposition by Energetic Electrons in a Diffusive Collisional Transport Model

Research paper thumbnail of Electron Distribution and Energy Release in Magnetic Reconnection Outflow Regions during the Pre-impulsive Phase of a Solar Flare

Research paper thumbnail of Preface: Solar physics advances from the interior to the heliosphere

Research paper thumbnail of A Fokker-Planck Framework for Studying the Diffusion of Radio Burst Waves in the Solar Corona

Research paper thumbnail of On the Source Position and Duration of a Solar Type III Radio Burst Observed by LOFAR

Research paper thumbnail of Implications of X-ray Observations for Electron Acceleration and Propagation in Solar Flares

High-Energy Aspects of Solar Flares, 2012

High-energy X-rays and γ-rays from solar flares were discovered just over fifty years ago. Since ... more High-energy X-rays and γ-rays from solar flares were discovered just over fifty years ago. Since that time, the standard for the interpretation of spatially integrated flare X-ray spectra at energies above several tens of keV has been the collisional thick-target model. After the launch of the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) in early 2002, X-ray spectra and images have been of sufficient quality to allow a greater focus on the energetic electrons responsible for the X-ray emission, including their origin and their interactions with the flare plasma and magnetic field. The result has been new insights into the flaring process, as well as more quantitative models for both electron acceleration and propagation, and for the flare environment with which the electrons interact. In this article we review our current understanding of electron acceleration, energy loss, and propagation in flares. Implications of these new results for the collisional thick-target model, for general flare models, and for future flare studies are discussed.

Research paper thumbnail of Deducing Electron Properties From Hard X-Ray Observations

High-Energy Aspects of Solar Flares, 2012

X-radiation from energetic electrons is the prime diagnostic of flare-accelerated electrons. The ... more 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 bremsstrahlung, photoelectric absorption and Compton back-scatter (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 using albedo, improved model-independent inference of electron energy spectra and emission measures of thermal plasma. Moreover, imaging spectroscopy has revealed hitherto unknown 2 E.P. Kontar et al. 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.

Research paper thumbnail of RHESSI Results -Time For a Rethink

Lecture Notes in Physics, 2007

Hard X-rays and γ-rays are the most direct signatures of energetic electrons and ions in the sun'... more Hard X-rays and γ-rays are the most direct signatures of energetic electrons and ions in the sun's atmosphere which is optically thin at these energies and their radiation involves no coherent processes. Being collisional they are complementary to gyro-radiation in probing atmospheric density as opposed to magnetic field and the electrons are primarily 10-100 keV in energy, complementing the (>100 keV) electrons likely responsible for microwave bursts. The pioneering results of the Ramaty High Energy Solar Spectroscopic Imager (RHESSI) are raising the first new major questions concerning solar energetic particles in many years. Some highlights of these results are discussed-primarily around RHESSI topics on which the authors have had direct research involvement-particularly when they are raising the need for rethinking of entrenched ideas. Results and issues are broadly divided into discoveries in the spatial, temporal and spectral domains, with the main emphasis on flare hard X-rays/fast electrons but touching also on γ-rays/ions, non-flare emissions, and the relationship to radio bursts.

Research paper thumbnail of Recent Advances in Understanding Particle Acceleration Processes in Solar Flares