Natasha L. S. Jeffrey

The Sub-arcsecond Hard X-ray Structure of Loop Footpoints in a Solar Flare

The newly developed X-ray visibility forward fitting technique is applied to the RHESSI data of a limb flare to investigate the energy and height dependence on sizes, shapes, and position of hard X-ray (HXR) chromospheric footpoint sources. This provides information about the electron transport and chromospheric density structure. The spatial distribution of two footpoint X-ray sources is analyzed using PIXON, Maximum Entropy Method, CLEAN, and visibility forward fit algorithms at nonthermal energies from ~20 to ~200 keV. We report, for the first time, the vertical extents and widths of HXR chromospheric sources measured as a function of energy for a limb event. Our observations suggest that both the vertical and horizontal sizes of footpoints are decreasing with energy. Higher energy emission originates progressively deeper in the chromosphere, consistent with downward flare accelerated streaming electrons. The ellipticity of the footpoints grows with energy from ~0.5 at ~20 keV to ~0.9 at ~150 keV. The positions of X-ray emission are in agreement with an exponential density profile of scale height ~150 km. The characteristic size of the HXR footpoint source along the limb decreases with energy, suggesting a converging magnetic field in the footpoint. The vertical sizes of X-ray sources are inconsistent with simple collisional transport in a single density scale height but can be explained using a multi-threaded density structure in the chromosphere.

Positions and sizes of X-ray solar flare sources

Aims: The positions and source sizes of X-ray sources taking into account Compton backscattering (albedo) are investigated. Methods: Using a Monte Carlo simulation of X-ray photon transport including photo-electric absorption and Compton scattering, we calculate the apparent source sizes and positions of X-ray sources at the solar disk for various source sizes, spectral indices and directivities of the primary source. Results: We show that the albedo effect can alter the true source positions and substantially increase the measured source sizes. The source positions are shifted by up to ~0.5” radially towards the disk centre and 5 arcsec source sizes can be two times larger even for an isotropic source (minimum albedo effect) at 1 Mm above the photosphere. The X-ray sources therefore should have minimum observed sizes, and thus their FWHM source size (2.35 times second-moment) will be as large as ~7” in the 20-50 keV range for a disk-centered point source at a height of 1 Mm (~1.4”) above the photosphere. The source size and position change is greater for flatter primary X-ray spectra, a stronger downward anisotropy, for sources closer to the solar disk centre, and between the energies of 30 and 50 keV. Conclusions: Albedo should be taken into account when X-ray footpoint positions, footpoint motions or source sizes from e.g. RHESSI or Yohkoh data are interpreted, and we suggest that footpoint sources should be larger in X-rays than in either optical or EUV ranges.

ON THE VARIATION OF SOLAR FLARE CORONAL X-RAY SOURCE SIZES WITH ENERGY

Observations with {\em RHESSI} have enabled the detailed study of the structure of dense hard X-ray coronal sources in solar flares. The variation of source extent with electron energy has been discussed in the context of streaming of non-thermal particles in a one-dimensional cold-target model, and the results used to constrain both the physical extent of, and density within, the electron acceleration region. Here we extend this investigation to a more physically realistic model of electron transport that takes into account the finite temperature of the ambient plasma, the initial pitch-angle distribution of the accelerated electrons, and the effects of collisional pitch-angle scattering. The finite temperature results in the thermal diffusion of electrons, that leads to the observationally-inferred value of the acceleration region volume being an overestimate of its true value. The different directions of the electron trajectories, a consequence of both the non-zero injection pitch-angle and scattering within the target, cause the projected propagation distance parallel to the guiding magnetic field to be reduced, so that a one-dimensional interpretation can overestimate the actual density by a factor of up to

TEMPORAL VARIATIONS OF X-RAY SOLAR FLARE LOOPS: LENGTH, CORPULENCE, POSITION, TEMPERATURE, PLASMA PRESSURE, AND SPECTRA

\sim 6

Spatially resolved hard X-ray polarization in solar flares: effects of Compton scattering and bremsstrahlung

. The implications of these results for the determination of acceleration region properties (specific acceleration rate, filling factor, etc.) are discussed.

Collisional relaxation of electrons in a warm plasma and accelerated nonthermal electron spectra in solar flares

The spatial and spectral properties of three solar flare coronal X-ray loops are studied before, during and after the peak X-ray emission. Using observations from the Ramaty High Energy Solar Spectroscopic Imager (RHESSI), we deduce the temporal changes in emitting X-ray length, corpulence, volume, position, number density and thermal pressure. We observe a decrease in the loop length, width and volume before the X-ray peak, and an increasing number density and thermal pressure. After the X-ray peak, volume increases and loop corpulence grows due to an increasing width. The volume variations are more pronounced than the position variations, often known as magnetic line contraction. We believe this is the first dedicated study of the temporal evolution of X-ray loop lengths and widths. Collectively, the observations also show for the first time three temporal phases given by peaks in temperature, X-ray emission and thermal pressure, with minimum volume coinciding with the X-ray peak. Although the volume of the flaring plasma decreases before the peak in X-ray emission, the relationship between temperature and volume does not support simple compressive heating in a collapsing magnetic trap model. Within a low beta plasma, shrinking loop widths perpendicular to the guiding field can be explained by squeezing the magnetic field threading the region. Plasma heating leads to chromospheric evaporation and growing number density, producing increasing thermal pressure and decreasing loop lengths as electrons interact at shorter distances and we believe after the X-ray peak, the increasing loop corpulence.

First evidence of non-Gaussian solar flare EUV spectral line profiles and accelerated non-thermal ion motion

Aims. We study the polarization of hard X-ray (HXR) sources in the solar atmosphere, including Compton backscattering of photons in the photosphere (the albedo effect) and the spatial distribution of polarization across the source. Methods. HXR photon polarization and spectra produced via electron-ion bremsstrahlung emission are calculated from various electron distributions typical for solar flares. Compton scattering and photoelectric absorption are then modelled using Monte Carlo simulations of photon transport in the photosphere to study the observed (primary and albedo) sources. Polarization maps across HXR sources (primary and albedo components) for each of the modelled electron distributions are calculated at various source locations from the solar centre to the limb. Results. We show that Compton scattering produces a distinct polarization variation across the albedo patch at peak albedo energies of 20‐50 keV for all anisotropies modelled. The results show that there are distinct spatial polarization changes in both the radial and perpendicular to radial directions across the extent of the HXR source at a given disk location. In the radial direction, the polarization magnitude and direction at specific positions along the HXR source will either increase or decrease with increased photon distribution directivity towards the photosphere. We also show how high electron cutoff energies influence the direction of polarization at above ∼100 keV. Conclusions. Spatially resolved HXR polarization measurements can provide important information about the directivity and energetics of the electron distribution. Our results indicate the preferred angular resolution of polarization measurements required to distinguish between the scattered and primary components. We also show how spatially resolved polarization measurements could be used to probe the emission pattern of an HXR source, using both the magnitude and the direction of the polarization.

Imaging spectroscopy of solar radio burst fine structures

Extending previous studies of nonthermal electron transport in solar flares, which include the effects of collisional energy diffusion and thermalization of fast electrons, we present an analytic method to infer more accurate estimates of the accelerated electron spectrum in solar flares from observations of the hard X-ray spectrum. Unlike for the standard cold-target model, the spatial characteristics of the flaring region, especially the necessity to consider a finite volume of hot plasma in the source, need to be taken into account in order to correctly obtain the injected electron spectrum from the source-integrated electron flux spectrum (a quantity straightforwardly obtained from hard X-ray observations). We show that the effect of electron thermalization can be significant enough to nullify the need to introduce an ad hoc low-energy cutoff to the injected electron spectrum in order to keep the injected power in non-thermal electrons at a reasonable value. Rather, the suppression of the inferred low-energy end of the injected spectrum compared to that deduced from a cold-target analysis allows the inference from hard X-ray observations of a more realistic energy in injected non-thermal electrons in solar flares.

Turbulent kinetic energy in the energy balance of a solar flare

The properties of solar flare plasma can be determined from the observation of optically thin lines. The emitting ion distribution determines the shape of the line, with an isothermal Maxwellian ion distribution producing a Gaussian profile. Non-Gaussian lines may indicate more complex ion distributions. We investigate the possibility of determining flare-accelerated non-thermal ion or plasma velocity distributions. We study EUV spectral lines during a flare SOL2013-05-15T01:45 using the Hinode EUV Imaging Spectrometer (EIS). The flare is located close to the eastern solar limb with an extended loop structure, allowing the different flare features: ribbons, hard X-ray (HXR) footpoints and the loop-top source to be clearly observed in UV, EUV and X-rays. EUV line spectroscopy is performed in seven different regions. We study the line profiles of isolated and unblended Fe XVI lines (262.976 A) formed at temperatures of 2-4 MK. Fe XVI line profiles at one time close to the peak soft X-ray emission and free of directed mass motions are examined using: 1. a higher moments analysis, 2. Gaussian fitting, and 3. by fitting a kappa distribution profile convolved with a Gaussian to account for the EIS instrumental profile. Fe XVI line profiles in the loop-top, HXR footpoint and ribbon regions can be confidently fitted with a kappa line profile, giving low, non-thermal kappa values between 2-3.3. A higher moments analysis also finds that many of the line kurtosis values are higher than the Gaussian value of 3, even with the presence of a broad Gaussian instrumental profile. A flare-accelerated non-thermal ion population could account for both the observed non-Gaussian line profiles, and for the Fe XVI excess broadening found from Gaussian fitting, if the emitting ions are interacting with a thermalised 4 MK electron population, and the instrumental profile is well-approximated by a Gaussian.

Non-Gaussian Velocity Distributions in Solar Flares from Extreme Ultraviolet Lines: A Possible Diagnostic of Ion Acceleration

Solar radio observations provide a unique diagnostic of the outer solar atmosphere. However, the inhomogeneous turbulent corona strongly affects the propagation of the emitted radio waves, so decoupling the intrinsic properties of the emitting source from the effects of radio wave propagation has long been a major challenge in solar physics. Here we report quantitative spatial and frequency characterization of solar radio burst fine structures observed with the Low Frequency Array, an instrument with high-time resolution that also permits imaging at scales much shorter than those corresponding to radio wave propagation in the corona. The observations demonstrate that radio wave propagation effects, and not the properties of the intrinsic emission source, dominate the observed spatial characteristics of radio burst images. These results permit more accurate estimates of source brightness temperatures, and open opportunities for quantitative study of the mechanisms that create the turbulent coronal medium through which the emitted radiation propagates.Radio observations of the solar atmosphere provide a unique view on the non-thermal processes in the outer atmosphere. Here the authors use LOFAR observations to demonstrate that the observed radio burst characteristics are dominated by propagation effects rather than underlying emission variations.