RHESSI and SDO/AIA observations of the chromospheric and coronal plasma parameters during a solar flare

X-ray and EUV observations are an important diagnostic of various plasma parameters of the solar atmosphere during solar flares. Soft X-ray and EUV observations often show coronal sources near the top of flaring loops, while hard X-ray emission is mostly observed from chromospheric footpoints. Combining RHESSI with simultaneous SDO/AIA observations, it is possible for the first time to determine the density, temperature, and emission profile of the solar atmosphere over a wide range of heights during a flare, using two independent methods. Here we analyze a near limb event during the first of three hard X-ray peaks. The emission measure, temperature, and density of the coronal source is found using soft X-ray RHESSI images while the chromospheric density is determined using RHESSI visibility analysis of the hard X-ray footpoints. A regularized inversion technique is applied to AIA images of the flare to find the differential emission measure (DEM). Using DEM maps we determine the emission and temperature structure of the loop, as well as the density, and compare it with RHESSI results. The soft X-ray and hard X-ray sources are spatially coincident with the top and bottom of the EUV loop, but the bulk of the EUV emission originates from a region without co-spatial RHESSI emission. The temperature analysis along the loop indicates that the hottest plasma is found near the coronal loop top source. The EUV observations suggest that the density in the loop legs increases with increasing height while the temperature remains constant within uncertainties.Comment: 23 pages, 6 figures, accepted for publication in Ap

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

Context. Solar type III radio bursts contain a wealth of information about the dynamics of electron beams in the solar corona and the inner heliosphere; this information is currently unobtainable through other means. However, the motion of different regions of an electron beam (front, middle, and back) have never been systematically analysed before. Aims. We characterise the type III burst frequency-time evolution using the enhanced resolution of LOFAR (Low Frequency Array) in the frequency range 30–70 MHz and use this to probe electron beam dynamics. Methods. The rise, peak, and decay times with a ∼ 0.2 MHz spectral resolution were defined for a collection of 31 type III bursts. The frequency evolution was used to ascertain the apparent velocities of the front, middle, and back of the type III sources, and the trends were interpreted using theoretical and numerical treatments. Results. The type III time profile was better approximated by an asymmetric Gaussian profile and not an exponential, as was used previously. Rise and decay times increased with decreasing frequency and showed a strong correlation. Durations were shorter than previously observed. Drift rates from the rise times were faster than from the decay times, corresponding to inferred mean electron beam speeds for the front, middle, and back of 0.2, 0.17, 0.15 c, respectively. Faster beam speeds correlate with shorter type III durations. We also find that the type III frequency bandwidth decreases as frequency decreases. Conclusions. The different speeds naturally explain the elongation of an electron beam in space as it propagates through the heliosphere. The expansion rate is proportional to the mean speed of the exciter; faster beams expand faster. Beam speeds are attributed to varying ensembles of electron energies at the front, middle, and back of the beam

Langmuir Wave Electric Fields Induced by Electron Beams in the Heliosphere

Solar electron beams responsible for type III radio emission generate Langmuir waves as they propagate out from the Sun. The Langmuir waves are observed via in-situ electric field measurements. These Langmuir waves are not smoothly distributed but occur in discrete clumps, commonly attributed to the turbulent nature of the solar wind electron density. Exactly how the density turbulence modulates the Langmuir wave electric fields is understood only qualitatively. Using weak turbulence simulations, we investigate how solar wind density turbulence changes the probability distribution functions, mean value and variance of the beam-driven electric field distributions. Simulations show rather complicated forms of the distribution that are dependent upon how the electric fields are sampled. Generally the higher magnitude of density fluctuations reduce the mean and increase the variance of the distribution in a consistent manor to the predictions from resonance broadening by density fluctuations. We also demonstrate how the properties of the electric field distribution should vary radially from the Sun to the Earth and provide a numerical prediction for the in-situ measurements of the upcoming Solar Orbiter and Solar Probe Plus spacecraft.Comment: 14 pages, 11 figures, published in Astronomy and Astrophysic

Electron distribution and energy release in magnetic reconnection outflow regions during the pre-impulsive phase of a solar flare

We present observations of electron energization in magnetic reconnection outflows during the pre-impulsive phase of solar flare SOL2012-07-19T05:58. During a time-interval of about 20 minutes, starting 40 minutes before the onset of the impulsive phase, two X-ray sources were observed in the corona, one above the presumed reconnection region and one below. For both of these sources, the mean electron distribution function as a function of time is determined over an energy range from 0.1~keV up to several tens of keV, for the first time. This is done by simultaneous forward fitting of X-ray and EUV data. Imaging spectroscopy with RHESSI provides information on the high-energy tail of the electron distribution in these sources while EUV images from SDO/AIA are used to constrain the low specific electron energies. The measured electron distribution spectrum in the magnetic reconnection outflows is consistent with a time-evolving kappa-distribution with $\kappa =3.5-5.5$. The spectral evolution suggests that electrons are accelerated to progressively higher energies in the source above the reconnection region, while in the source below, the spectral shape does not change but an overall increase of the emission measure is observed, suggesting density increase due to evaporation. The main mechanisms by which energy is transported away from the source regions are conduction and free-streaming electrons. The latter dominates by more than one order of magnitude and is comparable to typical non-thermal energies during the hard X-ray peak of solar flares, suggesting efficient acceleration even during this early phase of the event.Comment: 9 pages, 5 figures, accepted for publication in Ap

Spatial expansion and speeds of type III electron beam sources in the solar corona

A component of space weather, electron beams are routinely accelerated in the solar atmosphere and propagate through interplanetary space. Electron beams interact with Langmuir waves resulting in type III radio bursts. Electron beams expand along the trajectory, and using kinetic simulations, we explore the expansion as the electrons propagate away from the Sun. Specifically, we investigate the front, peak and back of the electron beam in space from derived radio brightness temperatures of fundamental type III emission. The front of the electron beams travelled at speeds from 0.2c--0.7c, significantly faster than the back of the beam that travelled between 0.12c--0.35c. The difference in speed between the front and the back elongates the electron beams in time. The rate of beam elongation has a 0.98 correlation coefficient with the peak velocity; in-line with predictions from type III observations. The inferred speeds of electron beams initially increase close to the acceleration region and then decrease through the solar corona. Larger starting densities and harder initial spectral indices result in longer and faster type III sources. Faster electron beams have higher beam energy densities, produce type IIIs with higher peak brightness temperatures and shorter FWHM durations. Higher background plasma temperatures also increase speeds, particularly at the back of the beam. We show how our predictions of electron beam evolution influences type III bandwidth and drift-rates. Our radial predictions of electron beam speed and expansion can be tested by the upcoming in situ electron beam measurements made by Solar Orbiter and Parker Solar Probe.Comment: 19 pages, 20 figures, submitted to Ap

Small electron acceleration episodes in the solar corona

We study the energetics of nonthermal electrons produced in small acceleration episodes in the solar corona. We carried out an extensive survey spanning 2004--2015 and shortlisted 6 impulsive electron events detected at 1 AU that was not associated with large solar flares(GOES soft X-ray class $>$ C1) or with coronal mass ejections. Each of these events had weak, but detectable hard Xray (HXR) emission near the west limb, and were associated with interplanetary type III bursts. In some respects, these events seem like weak counterparts of "cold/tenuous" flares. The energy carried by the HXR producing electron population was $\approx 10^{23}$ -- $10^{25}$ erg, while that in the corresponding population detected at 1 AU was $\approx 10^{24}$--$10^{25}$ erg. The number of electrons that escape the coronal acceleration site and reach 1 AU constitute 6 % to 148 % of those that precipitate downwards to produce thick target HXR emission

Imaging Spectroscopy of Type U and J Solar Radio Bursts with LOFAR

Radio U-bursts and J-bursts are signatures of electron beams propagating along magnetic loops confined to the corona. The more commonly observed type III radio bursts are signatures of electron beams propagating along magnetic loops that extend into interplanetary space. Given the prevalence of solar magnetic flux to be closed in the corona, it is an outstanding question why type III bursts are more frequently observed than U-bursts or J-bursts. We use LOFAR imaging spectroscopy between 30-80 MHz of low-frequency U-bursts and J-bursts, for the first time, to understand why electron beams travelling along coronal loops produce radio emission less often. The different radio source positions were used to model the spatial structure of the guiding magnetic flux tube and then deduce the energy range of the exciting electron beams without the assumption of a standard density model. The radio sources infer a magnetic loop 1 solar radius in altitude, with the highest frequency sources starting around 0.6 solar radii. Electron velocities were found between 0.13 c and 0.24 c, with the front of the electron beam travelling faster than the back of the electron beam. The velocities correspond to energy ranges within the beam from 0.7-11 keV to 0.7-43 keV. The density along the loop is higher than typical coronal density models and the density gradient is smaller. We found that a more restrictive range of accelerated beam and background plasma parameters can result in U-bursts or J-bursts, causing type III bursts to be more frequently observed. The large instability distances required before Langmuir waves are produced by some electron beams, and the small magnitude of the background density gradients make closed loops less facilitating for radio emission than loops that extend into interplanetary space.Comment: 9 pages, 7 figure

Stopping Frequency of Type III Solar Radio Bursts in Expanding Magnetic Flux Tubes

Understanding the properties of type III radio bursts in the solar corona and interplanetary space is one of the best ways to remotely deduce the characteristics of solar accelerated electron beams and the solar wind plasma. One feature of all type III bursts is the lowest frequency they reach (or stopping frequency). This feature reflects the distance from the Sun that an electron beam can drive the observable plasma emission mechanism. The stopping frequency has never been systematically studied before from a theoretical perspective. Using numerical kinetic simulations, we explore the different parameters that dictate how far an electron beam can travel before it stops inducing a significant level of Langmuir waves, responsible for plasma radio emission. We use the quasilinear approach to model self-consistently the resonant interaction between electrons and Langmuir waves in inhomogeneous plasma, and take into consideration the expansion of the guiding magnetic flux tube and the turbulent density of the interplanetary medium. We find that the rate of radial expansion has a significant effect on the distance an electron beam travels before enhanced leves of Langmuir waves, and hence radio waves, cease. Radial expansion of the guiding magnetic flux tube rarefies the electron stream to the extent that the density of non-thermal electrons is too low to drive Langmuir wave production. The initial conditions of the electron beam have a significant effect, where decreasing the beam density or increasing the spectral index of injected electrons would cause higher type III stopping frequencies. We also demonstrate how the intensity of large-scale density fluctuations increases the highest frequency that Langmuir waves can be driven by the beam and how the magnetic field geometry can be the cause of type III bursts only observed at high coronal frequencies.Comment: 11 pages, 8 figures, accepted in Astronomy and Astrophysic