arXiv subjects

A. Gordon Emslie

Publications and source records attributed to A. Gordon Emslie.

At least 19 recordsLinked to original sources

arXiv2026

Energy Transport and Heating by Non-Thermal Electrons in a Turbulent Solar Flare Environment

The impulsive phase of a solar flare is known to generate strong turbulence and to transfer magnetic energy into accelerated electrons. Recognizing the importance of angular diffusion on the dynamics of the accelerated electrons, we extend previous treatments by deriving analytic solutions for the electron flux and associated energy deposition in two regimes: scattering dominated by inelastic Coulomb collisions and scattering dominated by elastic interactions with turbulent scattering centers. We show that the turbulence-dominated scattering term strongly reshapes the spatial distribution of the plasma heating: compared to the traditional collisional thick-target approach, turbulent scattering could lead to an order-of-magnitude increase in coronal heating and an even greater suppression of chromospheric heating. Scattering also acts to reduce the anisotropy of the electron distribution and so reduces the net current associated with the nonthermal electrons. The return-current Ohmic heating is accordingly reduced to a level that renders it negligible compared to direct collisional heating. The results have significant implications for models of atmospheric response to impulsive phase energy release, in particular chromospheric evaporation, flare-driven coronal heating, the formation of loop-top hard X-ray sources, and the longstanding discrepancy between modeled and observed soft X-ray line profiles.

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arXiv2025

Ion-scale Turbulence and Energy Cascade Rate in the Solar Corona and Inner Heliosphere

Plasma turbulence cascading from MHD to kinetic scales in the heliospheric plasma is believed to play a key role in coronal heating and fast solar wind acceleration, but the properties of the turbulence remain poorly constrained by observations. Here we compare the ion-scale density fluctuation levels inferred from the properties of solar radio bursts with the magnetic field fluctuation levels obtained through in-situ measurements in the inner heliosphere. We find that the observed magnetic and density fluctuation amplitudes are consistent with excitation by kinetic Alfvén waves and/or KAW structures over broad range of distances from the Sun. We then use the radio diagnostics and the KAW scenario to deduce the radial variation of magnetic fluctuation amplitudes in regions close to the Sun where in-situ measurements cannot be obtained. Further, we calculate the energy cascade rate (plasma heating rate) profile over a region that extends from the low corona ($\sim 0.1$~R$_\odot$) into the heliosphere (out to $\sim 1$~au), and compare it to the energy deposition rate required to drive the solar wind. The cascade rate agrees with the available in-situ measurements and also provides predictions closer than $\sim 10$~R$_\odot$ where in-situ approaches are not available. The results provide unique diagnostics of the ion-scale plasma turbulence amplitude and energy cascade rate spanning over three orders of magnitude in solar distance.

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arXiv2025

Tracing the Heliospheric Magnetic Field via Anisotropic Radio-Wave Scattering

Astrophysical radio sources are embedded in turbulent magnetised environments. In the 1 MHz sky, solar radio bursts are the brightest sources, produced by electrons travelling along magnetic field lines from the Sun through the heliosphere. We demonstrate that the magnetic field not only guides the emitting electrons, but also directs radio waves via anisotropic scattering from density irregularities in the magnetised plasma. Using multi-vantage-point type III solar radio burst observations and anisotropic radio wave propagation simulations, we show that the interplanetary field structure is encoded in the observed radio emission directivity, and that large-scale turbulent channelling of radio waves is present over large distances, even for relatively weak anisotropy in the embedded density fluctuations. Tracing the radio emission at many frequencies (distances), the effects of anisotropic scattering can be disentangled from the electron motion along the interplanetary magnetic field, and the emission source locations are unveiled. Our analysis suggests that magnetic field structures within turbulent media could be reconstructed using radio observations and is found consistent with the Parker field, offering a novel method for remotely diagnosing the large-scale field structure in the heliosphere and other astrophysical plasmas.

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arXiv2024

Plasma motions and compressive wave energetics in the solar corona and solar wind from radio wave scattering observations

Radio signals propagating via the solar corona and solar wind are significantly affected by compressive waves, impacting properties of solar bursts as well as sources viewed through the turbulent solar atmosphere. While static fluctuations scatter radio waves elastically, moving, turbulent or oscillating density irregularities act to broaden the frequency of the scattered waves. Using a new anisotropic density fluctuation model from the kinetic scattering theory for solar radio bursts, we deduce the plasma velocities required to explain observations of spacecraft signal frequency broadening. The inferred velocities are consistent with motions that are dominated by the solar wind at distances $\gtrsim 10$ $R_\odot$, but the levels of frequency broadening for $\lesssim 10$ $R_\odot$ require additional radial speeds $\sim (100-300)$ km s$^{-1}$ and/or transverse speeds $\sim (20-70)$ km s$^{-1}$. The inferred radial velocities also appear consistent with the sound or proton thermal speeds, while the speeds perpendicular to the radial direction are consistent with non-thermal motions measured via coronal Doppler-line broadening, interpreted as Alfvénic fluctuations. Landau damping of parallel propagating ion-sound (slow MHD) waves allow an estimate of the proton heating rate. The energy deposition rates due to ion-sound wave damping peak at a heliocentric distance of $\sim(1-3)$ $R_\odot$ are comparable to the rates available from a turbulent cascade of Alfvénic waves at large scales, suggesting a coherent picture of energy transfer, via the cascade or/and parametric decay of Alfvén waves to the small scales where heating takes place.

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arXiv2023

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, changing their observed time characteristics, sizes, and positions. The same turbulence causes angular broadening and scintillation of galactic and extra-galactic compact radio sources observed through the solar atmosphere. Using large-scale simulations of radio-wave transport, the characteristics of anisotropic density turbulence from $0.1 \, R_\odot$ to $1$ au are explored. For the first time, a profile of heliospheric density fluctuations is deduced that accounts for the properties of extra-solar 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 $(4-7) \, R_\odot$, 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 $\langleδ{n_i}^2 \rangle (r) \simeq 2 \times 10^7 \, (r/R_\odot-1)^{-3.7}$ 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 $q_\parallel/q_\perp =0.25-0.4$, 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.

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arXiv2023

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 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 $\sim$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 \emph{RHESSI} hard X-ray and and 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 $\sim 10^{-2}$ on the number density of nonthermal ($\ge 20$~keV) electrons, expressed as a fraction of the number density of ambient protons in the same volume. This upper limit is about two 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.

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arXiv2023

Robust construction of differential emission measure profiles using a regularized maximum likelihood method

Extreme-ultraviolet (EUV) observations provide considerable insight into evolving physical conditions in the active solar atmosphere. For a prescribed density and temperature structure, it is straightforward to construct the corresponding differential emission measure profile $ξ(T)$, such that $ξ(T) \, dT$ is proportional to the emissivity from plasma in the temperature range $[T, T + dT]$. Here we study the inverse problem of obtaining a valid $ξ(T)$ profile from a set of EUV spectral line intensities observed at a pixel within a solar image. Our goal is to introduce and develop a regularized maximum likelihood (RML) algorithm designed to address the mathematically ill-posed problem of constructing differential emission measure profiles from a discrete set of EUV intensities in specified wavelength bands, specifically those observed by the Atmospheric Imaging Assembly (AIA) on the NASA Solar Dynamics Observatory. The RML method combines features of maximum likelihood and regularized approaches used by other authors. It is also guaranteed to produce a positive definite differential emission measure profile. We evaluate and compare the effectiveness of the method against other published algorithms, using both simulated data generated from parametric differential emission profile forms, and AIA data from a solar eruptive event on 2010 November 3. Similarities and differences between the differential emission measure profiles and maps reconstructed by the various algorithms are discussed. The RML inversion method is mathematically rigorous, computationally efficient, and produces acceptable measures of performance in the following three key areas: fidelity to the data, accuracy in the reconstruction, and robustness in the presence of data noise. As such, it shows considerable promise for computing differential emission measure profiles from datasets of discrete spectral lines.

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arXiv2022

Temperature and Differential Emission Measure Profiles in Turbulent Solar Active Region Loops

We examine the temperature structure of static coronal active region loops in regimes where thermal conductive transport is driven by Coulomb collisions, by turbulent scattering, or by a combination of the two. (In the last case collisional scattering dominates the heat transport at lower levels in the loop where temperatures are low and densities are high, while turbulent scattering dominates the heat transport at higher temperatures/lower densities.) Temperature profiles and their corresponding differential emission measure distributions are calculated and compared to observations, and earlier scaling laws relating the loop apex temperature and volumetric heating rate to the loop length and pressure are revisited. Results reveal very substantial changes, compared to the wholly collision-dominated case, to both the loop scaling laws and the temperature/density profiles along the loop. They also show that the well-known excess of differential emission measure at relatively low temperatures in the loop may be a consequence of for by the flatter temperature gradients (and so increased amount of material within a specified temperature range) that results from the predominance of turbulent scattering in the upper regions of the loop.

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arXiv2022

Solar Flare Heating with Turbulent Suppression of Thermal Conduction

During solar flares plasma is typically heated to very high temperatures, and the resulting redistribution of energy via thermal conduction is a primary mechanism transporting energy throughout the flaring solar atmosphere. The thermal flux is usually modeled using Spitzer's theory, which is based on local Coulomb collisions between the electrons carrying the thermal flux and those in the background. However, often during flares, temperature gradients become sufficiently steep that the collisional mean free path exceeds the temperature gradient scale size, so that thermal conduction becomes inherently non-local. Further, turbulent angular scattering, which is detectable in nonthermal widths of atomic emission lines, can also act to increase the collision frequency and so suppress the heat flux. Recent work by Emslie & Bian (2018) extended Spitzer's theory of thermal conduction to account for both non-locality and turbulent suppression. We have implemented their theoretical expression for the heat flux (which is a convolution of the Spitzer flux with a kernel function) into the RADYN flare-modeling code and performed a parameter study to understand how the resulting changes in thermal conduction affect flare dynamics and hence the radiation produced. We find that models with reduced heat fluxes predict slower bulk flows, less intense line emission, and longer cooling times. By comparing features of atomic emission lines predicted by the models with Doppler velocities and nonthermal line widths deduced from a particular flare observation, we find that models with suppression factors between 0.3 to 0.5 relative to the Spitzer value best reproduce observed Doppler velocities across emission lines forming over a wide range of temperatures. Interestingly, the model that best matches observed nonthermal line widths has a kappa-type velocity distribution function.

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arXiv2020

Scaling Laws for Dynamic Solar Loops

The scaling laws which relate the peak temperature $T_M$ and volumetric heating rate $E_H$ to the pressure $P$ and length $L$ for static coronal loops were established over 40 years ago; they have proved to be of immense value in a wide range of studies. Here we extend these scaling laws to {\it dynamic} loops, where enthalpy flux becomes important to the energy balance, and study impulsive heating/filling characterized by upward enthalpy flows. We show that for collision-dominated thermal conduction, the functional dependencies of the scaling laws are the same as for the static case, when the radiative losses scale as $T^{-1/2}$, but with a different constant of proportionality that depends on the Mach number $M$ of the flow. The dependence on the Mach number is such that the scaling laws for low to moderate Mach number flows are almost indistinguishable from the static case. When thermal conduction is limited by turbulent processes, however, the much weaker dependence of the scattering mean free path (and hence thermal conduction coefficient) on temperature leads to a limiting Mach number for return enthalpy fluxes driven by thermal conduction between the corona and chromosphere.

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arXiv2020

Solar Flare Energy Partitioning and Transport -- the Impulsive Phase (a Heliophysics 2050 White Paper)

Solar flares are a fundamental component of solar eruptive events (SEEs; along with solar energetic particles, SEPs, and coronal mass ejections, CMEs). Flares are the first component of the SEE to impact our atmosphere, which can set the stage for the arrival of the associated SEPs and CME. Magnetic reconnection drives SEEs by restructuring the solar coronal magnetic field, liberating a tremendous amount of energy which is partitioned into various physical manifestations: particle acceleration, mass and magnetic-field eruption, atmospheric heating, and the subsequent emission of radiation as solar flares. To explain and ultimately predict these geoeffective events, the heliophysics community requires a comprehensive understanding of the processes that transform and distribute stored magnetic energy into other forms, including the broadband radiative enhancement that characterises flares. This white paper, submitted to the Heliophysics 2050 Workshop, discusses the flare impulsive phase part of SEEs, setting out the questions that need addressing via a combination of theoretical, modelling, and observational research. In short, by 2050 we must determine the mechanisms of particle acceleration and propagation, and must push beyond the paradigm of energy transport via nonthermal electron beams, to also account for accelerated protons & ions and downward directed Alfven waves.

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arXiv2020

Solar Flare Energy Partitioning and Transport -- the Gradual Phase (a Heliophysics 2050 White Paper)

Solar flares are a fundamental component of solar eruptive events (SEEs; along with solar energetic particles, SEPs, and coronal mass ejections, CMEs). Flares are the first component of the SEE to impact our atmosphere, which can set the stage for the arrival of the associated SEPs and CME. Magnetic reconnection drives SEEs by restructuring the solar coronal magnetic field, liberating a tremendous amount of energy which is partitioned into various physical manifestations: particle acceleration, mass and magnetic-field eruption, atmospheric heating, and the subsequent emission of radiation as solar flares. To explain and ultimately predict these geoeffective events, the heliophysics community requires a comprehensive understanding of the processes that transform and distribute stored magnetic energy into other forms, including the broadband radiative enhancement that characterises flares. This white paper, submitted to the Heliophysics 2050 Workshop, discusses the flare gradual phase part of SEEs, setting out the questions that need addressing via a combination of theoretical, modelling, and observational research. In short, the flare gradual phase persists much longer than predicted so, by 2050, we must identify the characteristics of the significant energy deposition sustaining the gradual phase, and address the fundamental processes of turbulence and non-local heat flux.

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arXiv2019

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

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 $\sim 0.3$ 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.

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arXiv2019

Coronal Loop Scaling Laws for Various Forms of Parallel Heat Conduction

The solar atmosphere is dominated by loops of magnetic flux which connect the multi-million-degree corona to the much cooler chromosphere. The temperature and density structure of quasi-static loops is determined by the continuous flow of energy from the hot corona to the lower solar atmosphere. Loop scaling laws provide relationships between global properties of the loop (such as peak temperature, pressure, and length); they follow from the physical variable dependencies of various terms in the energy equation, and hence the form of the loop scaling law provides insight into the key physics that controls the loop structure. Traditionally, scaling laws have been derived under the assumption of collision-dominated thermal conduction. Here we examine the impact of different regimes of thermal conduction -- collision-dominated, turbulence-dominated, and free-streaming -- on the form of the scaling laws relating the loop temperature and heating rate to its pressure and half-length. We show that the scaling laws for turbulence-dominated conduction are fundamentally different than those for collision-dominated and free-streaming conduction, inasmuch as the form of the scaling laws now depend primarily on conditions at the low-temperature, rather than high-temperature, part of the loop. We also establish regimes in temperature and density space in which each of the applicable scaling laws prevail.

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arXiv2019

Determination of the total accelerated electron rate and power using solar flare hard X-ray spectra

Solar flare hard X-ray 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, and 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 self-consistent warm-target approach which involves the use of both hard X-ray spectroscopy and imaging data. The 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 the {\em RHESSI} spacecraft, we demonstrate that using the standard cold-target methodology, the low-energy cutoff (and hence the energy content in electrons) is essentially undetermined. However, the warm-target methodology can determine the low-energy electron cutoff with $\sim$7\% uncertainty at the $3σ$ level and hence permits an accurate quantitative study of the importance of accelerated electrons in solar flare energetics.

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arXiv2018

Coronal hard X-ray sources revisited

This paper reports on the re-analysis of solar flares in which the hard X-rays (HXRs) come predominantly from the corona rather than from the more usual chromospheric footpoints. All of the 26 previously analyzed event time intervals, over 13 flares, are re-examined for consistency with a flare model in which electrons are accelerated near the top of a magnetic loop that has a sufficiently high density to stop most of the electrons by Coulomb collisions before they can reach the footpoints. Of particular importance in the previous analysis was the finding that the length of the coronal HXR source increased with energy in the 20 - 30 keV range. However, after allowing for the possibility that footpoint emission at the higher energies affects the inferred length of the coronal HXR source, and using analysis techniques that suppress the possible influence of such footpoint emission, we conclude that there is no longer evidence that the length of the HXR coronal sources increase with increasing energy. In fact, for the 6 flares and 12 time intervals that satisfied our selection criteria, the loop lengths decreased on average by 1.0 +/- 0.2 arcsec between 20 and 30 keV, with a standard deviation of 3.5 arcsec. We find strong evidence that the peak of the coronal HXR source increases in altitude with increasing energy. For the thermal component of the emission, this is consistent with the standard CHSKP flare model in which magnetic reconnection in a coronal current sheet results in new hot loops being formed at progressively higher altitudes. The explanation for the nonthermal emission is not so clear.

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arXiv2017

Heating and cooling of coronal loops with turbulent suppression of parallel heat conduction

Using the "enthalpy-based thermal evolution of loops" (EBTEL) model, we investigate the hydrodynamics of the plasma in a flaring coronal loop in which heat conduction is limited by turbulent scattering of the electrons that transport the thermal heat flux. The EBTEL equations are solved analytically in each of the two (conduction-dominated and radiation-dominated) cooling phases. Comparison of the results with typical observed cooling times in solar flares shows that the turbulent mean free-path $λ_T$ lies in a range corresponding to a regime in which classical (collision-dominated) conduction plays at most a limited role. We also consider the magnitude and duration of the heat input that is necessary to account for the enhanced values of temperature and density at the beginning of the cooling phase and for the observed cooling times. We find through numerical modeling that in order to produce a peak temperature $\simeq 1.5 \times 10^7$~K and a 200~s cooling time consistent with observations, the flare heating profile must extend over a significant period of time; in particular, its lingering role must be taken into consideration in any description of the cooling phase. Comparison with observationally-inferred values of post-flare loop temperatures, densities, and cooling times thus leads to useful constraints on both the magnitude and duration of the magnetic energy release in the loop, as well as on the value of the turbulent mean free-path $λ_T$.

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arXiv2016

The role of diffusion in the transport of energetic electrons during solar flares

The transport of the energy contained in suprathermal electrons in solar flares plays a key role in our understanding of many aspects of flare physics, from the spatial distributions of hard X-ray emission and energy deposition in the ambient atmosphere to global energetics. Historically the transport of these particles has been largely treated through a deterministic approach, in which first-order secular energy loss to electrons in the ambient target is treated as the dominant effect, with second-order diffusive terms (in both energy and angle) being generally either treated as a small correction or even neglected. We here critically analyze this approach, and we show that spatial diffusion through pitch-angle scattering necessarily plays a very significant role in the transport of electrons. We further show that a satisfactory treatment of the diffusion process requires consideration of non-local effects, so that the electron flux depends not just on the local gradient of the electron distribution function but on the value of this gradient within an extended region encompassing a significant fraction of a mean free path. Our analysis applies generally to pitch-angle scattering by a variety of mechanisms, from Coulomb collisions to turbulent scattering. We further show that the spatial transport of electrons along the magnetic field of a flaring loop can be modeled rather effectively as a Continuous Time Random Walk with velocity-dependent probability distribution functions of jump sizes and occurrences, both of which can be expressed in terms of the scattering mean free path.

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