Solar Flare Plasma Research Articles

Spectral Imager of the Solar Atmosphere: The First Extreme-Ultraviolet Solar Integral Field Spectrograph Using Slicers

Particle acceleration, and the thermalisation of energetic particles, are fundamental processes across the universe. Whilst the Sun is an excellent object to study this phenomenon, since it is the most energetic particle accelerator in the Solar System, this phenomenon arises in many other astrophysical objects, such as active galactic nuclei, black holes, neutron stars, gamma ray bursts, solar and stellar coronae, accretion disks and planetary magnetospheres. Observations in the Extreme Ultraviolet (EUV) are essential for these studies but can only be made from space. Current spectrographs operating in the EUV use an entrance slit and cover the required field of view using a scanning mechanism. This results in a relatively slow image cadence in the order of minutes to capture inherently rapid and transient processes, and/or in the spectrograph slit ‘missing the action’. The application of image slicers for EUV integral field spectrographs is therefore revolutionary. The development of this technology will enable the observations of EUV spectra from an entire 2D field of view in seconds, over two orders of magnitude faster than what is currently possible. The Spectral Imaging of the Solar Atmosphere (SISA) instrument is the first integral field spectrograph proposed for observations at ∼180 Å combining the image slicer technology and curved diffraction gratings in a highly efficient and compact layout, while providing important spectroscopic diagnostics for the characterisation of solar coronal and flare plasmas. SISA’s characteristics, main challenges, and the on-going activities to enable the image slicer technology for EUV applications are presented in this paper.

Generation of X-Ray Spikes in Solar Flare Plasma

Generation of X-Ray Spikes in Solar Flare Plasma

Soft X-Ray Spectral Diagnostics of Multithermal Plasma in Solar Flares with Chandrayaan-2 XSM

Spectroscopic observations in X-ray wavelengths provide excellent diagnostics of the temperature distribution in solar flare plasma. The Solar X-ray Monitor (XSM) on board the Chandrayaan-2 mission provides broadband disk-integrated soft X-ray solar spectral measurements in the energy range of 1–15 keV with high spectral resolution and time cadence. In this study, we analyze the X-ray spectra of three representative GOES C-class flares obtained with the XSM to investigate the evolution of various plasma parameters during the course of the flares. Using the soft X-ray spectra consisting of the continuum and well-resolved line complexes of major elements like Mg, Si, and Fe, we investigate the validity of the isothermal and multithermal assumptions on the high-temperature components of the flaring plasma. We show that the soft X-ray spectra during the impulsive phase of the high-intensity flares are inconsistent with isothermal models and are best fitted with double-peaked differential emission measure distributions where the temperature of the hotter component rises faster than that of the cooler component. The two distinct temperature components observed in differential emission measure models during the impulsive phase of the flares suggest the presence of the directly heated plasma in the corona and evaporated plasma from the chromospheric footpoints. We also find that the abundances of low first ionization potential elements Mg, Si, and Fe reduce from near coronal to near photospheric values during the rising phase of the flare and recover back to coronal values during the decay phase, which is also consistent with the chromospheric evaporation scenario.

A Magnetogram-matching Method for Energizing Magnetic Flux Ropes Toward Eruption

We propose a new “helicity-pumping” method for energizing coronal equilibria that contain a magnetic flux rope (MFR) toward an eruption. We achieve this in a sequence of magnetohydrodynamics relaxations of small line-tied pulses of magnetic helicity, each of which is simulated by a suitable rescaling of the current-carrying part of the field. The whole procedure is “magnetogram-matching” because it involves no changes to the normal component of the field at the photospheric boundary. The method is illustrated by applying it to an observed force-free configuration whose MFR is modeled with our regularized Biot–Savart law method. We find that, in spite of the bipolar character of the external field, the MFR eruption is sustained by two reconnection processes. The first, which we refer to as breakthrough reconnection, is analogous to breakout reconnection in quadrupolar configurations. It occurs at a quasi-separator inside a current layer that wraps around the erupting MFR and is caused by the photospheric line-tying effect. The second process is the classical flare reconnection, which develops at the second quasi-separator inside a vertical current layer that is formed below the erupting MFR. Both reconnection processes work in tandem with the magnetic forces of the unstable MFR to propel it through the overlying ambient field, and their interplay may also be relevant for the thermal processes occurring in the plasma of solar flares. The considered example suggests that our method will be beneficial for both the modeling of observed eruptive events and theoretical studies of eruptions in idealized magnetic configurations.

Zebra Stripes with High Gyro-Harmonic Numbers

Solar radio zebras are used in the determination of the plasma density and magnetic field in solar flare plasmas. Analyzing observed zebra stripes and assuming their generation by the double-plasma resonance (DPR) instability, high values of the gyro-harmonic number are found. In some cases they exceed one hundred, in disagreement with the DPR growth rates computed up to now, which decrease with increasing gyro-harmonic number. We address the question of how zebras with high values of the gyro-harmonic numbers s are generated. For this purpose, we compute the growth rates of the DPR instability in a very broad range of s, considering a loss-cone kappa-distribution of superthermal electrons and varying the loss-cone angle, electron energies, and background plasma temperature. We have numerically calculated the dispersion relations and the growth rates of the upper-hybrid waves and found that the growth rates increase with increasing gyro-harmonic numbers if the loss-cone angles are sim80^{circ}. The highest growth rates for these loss-cone angles are obtained for velocity v_{kappa}= 0.15,c. The growth rates as a function of the gyro-harmonic number still show well distinct peaks, which correspond to zebra-stripe frequencies. The contrast between peak growth rates and surrounding growth rate levels increases as the kappa index increases and the background temperature decreases. Zebras with high values of s can be generated in regions where loss-cone distributions of superthermal electrons with large loss-cone angles (sim80^{circ}) are present. Furthermore, owing to the high values of s, the magnetic field is relatively weak and has a small spatial gradient in such regions.

Simulations of solar radio zebras

Context.Solar radio zebras are used in diagnostics of solar flare plasmas and it is of great importance to construct accurate models to correctly characterize them.Aims.We simulated two zebras to verify their double-plasma resonance (DPR) model.Methods.In our zebra simulations, we used the DPR model in an expanding and compressing part of the loop as well as with the wave propagating along the loop.Results.Using the DPR model in such a loop, we successfully simulated zebras from the 1 August 2010 and 21 June 2011 flares. We found that increasing the density or decreasing the magnetic field in the part of the loop, where zebra-stripe sources are located, the zebra stripes are shifted to higher frequencies and vice versa. In the case of the 21 June 2011 flare, we confirm that small deviations of zebra-stripe frequencies from their mean values can be explained by waves propagating along the loop. We also confirm high values for the gyro-harmonic number of zebra stripes. We explain an inconsistency in the wave velocities derived from the plasma parameters and from the frequency drift in combination with the density model of the solar atmosphere. Finally, we discuss the high values of the gyro-harmonic number found in the studied zebras.

Stochastic Electron Acceleration by Temperature Anisotropy Instabilities under Solar Flare Plasma Conditions

Abstract Using 2D particle-in-cell plasma simulations, we study electron acceleration by temperature anisotropy instabilities, assuming conditions typical of above-the-loop-top sources in solar flares. We focus on the long-term effect of T e,⊥ > T e,∥ instabilities by driving the anisotropy growth during the entire simulation time through imposing a shearing or a compressing plasma velocity (T e,⊥ and T e,∥ are the temperatures perpendicular and parallel to the magnetic field). This magnetic growth makes T e,⊥/T e,∥ grow due to electron magnetic moment conservation, and amplifies the ratio ω ce/ω pe from ∼0.53 to ∼2 (ω ce and ω pe are the electron cyclotron and plasma frequencies, respectively). In the regime ω ce/ω pe ≲ 1.2–1.7, the instability is dominated by oblique, quasi-electrostatic modes, and the acceleration is inefficient. When ω ce/ω pe has grown to ω ce/ω pe ≳ 1.2–1.7, electrons are efficiently accelerated by the inelastic scattering provided by unstable parallel, electromagnetic z modes. After ω ce/ω pe reaches ∼2, the electron energy spectra show nonthermal tails that differ between the shearing and compressing cases. In the shearing case, the tail resembles a power law of index α s ∼ 2.9 plus a high-energy bump reaching ∼300 keV. In the compressing runs, α s ∼ 3.7 with a spectral break above ∼500 keV. This difference can be explained by the different temperature evolutions in these two types of simulations, suggesting that a critical role is played by the type of anisotropy driving, ω ce/ω pe, and the electron temperature in the efficiency of the acceleration.

Моделирование коронального источника жесткого рентгеновского излучения в турбулентной плазме солнечных вспышек

The kinetics of electron beams accelerated in the collisional plasma of solar (stellar) flares is considered, taking into account the stationary ion-acoustic mode localized at the magnetic looptop and magnetic fluctuations. The astrophysical aspect of the propagation process is related to the interpretation of hard X-rays in the plasma of flare loops. It is shown that when the plasma density in the coronal part of the solar flare loops does not exceed 1010 cm-3, taking into account the additional scattering on the ion-acoustic mode with the ratio of the turbulence energy density to the thermal energy of the plasma ~5 * 10-5-10-3 and magnetic fluctuations with a level of 5·10-2 does not lead to the appearance of a bright hard X-ray source in the coronal part of the loop in the model with the isotropic pitch-angle distribution of accelerated electrons. In the anisotropic case with a hard electron energy spectrum, the coronal hard X-ray source, in the presence of ion-acoustic turbulence, can exist for a short time after the beginning of turbulence generation. And only in the case of a soft energy spectrum of accelerated electrons (power spectrum index >5) and a relatively high plasma density at the magnetic looptop >1010 cm-3, a bright coronal hard X-ray source is generated at energies of 25-50 keV, regardless of the pitch-angular distribution of accelerated electrons at the moment of injection. A significant effect of turbulence on the distribution of the linear degree of hard X-ray polarization along the loop is shown, leading to a decrease in the extreme values in the coronal part by 5-35%. The integral values of the hard X-ray polarization do not exceed 10%.

RESIK and RHESSI observations of the 20 September 2002 flare

Context. Soft X-ray spectra (3.33 Å–6.15 Å) from the RESIK instrument on CORONAS-F constitute a unique database for the study of the physical conditions of solar flare plasmas, enabling the calculation of differential emission measures. The two RESIK channels for the shortest wavelengths overlap with the lower end of the Ramaty High Energy Solar Spectroscopic Imager (RHESSI) spectral energy range, which is located around 3 keV, making it possible to compare both data sets. Aims. We aim to compare observations from RESIK and RHESSI spectrometers and cross-correlate these instruments. Observations are compared with synthetic spectra calculated based on the results of one-dimensional hydrodynamical (1D-HD) modelling. The analysis was performed for the flare on 20 September 2002 (SOL2002-09-20T09:28). Methods. We estimated the geometry of the flaring loop, necessary for 1D-HD modelling, based on images from RHESSI and the Extreme-Ultraviolet Imaging Telescope aboard the Solar and Heliospheric Observatory. The distribution of non-thermal electrons (NTEs) was determined from RHESSI spectra. The 1D-HD model assumes that non-thermal electrons with a power-law spectrum were injected at the apex of the flaring loop. The NTEs then heat and evaporate the chromosphere, filling the loop with hot and dense plasma radiating in soft X-rays. The total energy of electrons was constrained by comparing observed and calculated fluxes from Geostationary Operational Environmental Satellite 1–8 Å data. We determined the temperature and density at every point of the flaring loop throughout the evolution of the flare, calculating the resulting X-ray spectra. Results. The synthetic spectra calculated based on the results of hydrodynamic modelling for the 20 September 2002 flare are consistent within a factor of two with the observed RESIK spectra during most of the duration of the flare. This discrepancy factor is probably related to the uncertainty on the cross-calibration between RESIK and RHESSI instruments.

A comparative study of non-thermal parameters of the X-class solar flare plasma obtained from cold and warm thick-target models; error estimation by Monte Carlo simulation method

The electron transport and relaxation in the non-thermal plasma of solar flare are often described by cold thick-target model. Recently introduced warm thick-target model however is also found to be more consistent for describing it and hence provide the accurate estimate of parameters of non-thermal solar flare plasma. In this study, we evaluate the consistency of cold and warm thick-target models by estimating non-thermal parameters viz., low-energy cutoff (${E_{c}/E_{wc}} $), kinetic power of non-thermal electrons (${P _{nth}/P_{wnth}} $) and non-thermal energy (${E_{nth}/E_{wnth}} $), along with standard error (SE) and their linear statistical analysis with respect to flare duration (${t _{f}}$). We further evaluate the accuracy of these parameters using Monte Carlo simulation data in $2 \sigma $ limits. We found that cold thick-target model gives high values of mean and SE of the estimated parameters compare to warm thick-target model those were also found consistent with the Monte Carlo data (in both cases). Here, we also found that the variation of ${E_{c}/E_{wc}} $ and ${P _{nth}/P_{wnth}} $ with respect to ${t_{f}} $ give a negative/positive and positive values of correlation coefficient ($r$) and slope ($b$) respectively which account for upper and lower limits of ${E_{c}/E_{wc}} $ and high and slow rate of thermalization of non-thermal electrons. Our results show that the warm thick-target model is more consistent model compare to cold thick-target model that could also lead a multi-temperature component in the thermalized plasma.

Zebra-stripe sources in the double-plasma resonance model of solar radio zebras

Context. Radio bursts with fine structures are used in diagnostics of solar flare plasmas, of which zebra structures are the most important. However, there is still a debate about their origin.Aims. The most probable model of zebras is that based on double-plasma resonance (DPR) instability. The paper wants to contribute to a verification of this model.Methods. We used analytical methods.Results. We studied the DPR model in two scenarios: a model with the zebra-stripe sources in a single loop and a model with the zebra-stripe sources moving through a fan of magnetic field lines. In the first case, we found several new relations among the parameters of zebra stripes and their sources, which can be used to analyze observed zebras and thus to verify if the zebra is generated according to the DPR model. These relations were derived for the zebra-stripe sources distributed along the loop and also for those having some extent in the loop radius. In the scenario with the moving zebra-stripe sources, we determined the parameters of the 14 December 2006 zebra and estimated a change of the ratio of magnetic field and density scales causing the change of zebra-stripe frequencies. In this case we found that this zebra can be also explained in the model with the zebra-stripe sources in a single loop. Both the interpretations are discussed.

Growth Rates of the Upper-Hybrid Waves for Power-Law and Kappa Distributions with a Loss-Cone Anisotropy

Fine structures of radio bursts play an important role in diagnostics of the solar flare plasma. Among them the zebras, which are prevalently assumed to be generated by the double plasma resonance instability, belong to the most important. In this paper we compute the growth rate of this instability for two types of the electron distribution: a) for the power-law distribution and b) for the kappa distribution, in the both cases with the loss-cone type anisotropy. We found that the growth rate of the upper-hybrid waves for the power-law momentum distribution strongly depends on the pitch-angle boundary. The maximum growth rate was found for the pitch-angle $\theta_\mathrm{c} \approx$ 50$^\circ$. For small angles the growth rate profile is very flat and for high pitch-angles the wave absorption occurs. Furthermore, analyzing the growth rate of the upper hybrid waves for the kappa momentum distribution we found that a decrease of the characteristic momentum $p_\kappa$ shifts the maximum of the growth rate to lower values of the ratio of the electron-plasma and electron-cyclotron frequencies, and the frequency widths of the growth rate peaks are very broad. But, if we consider the kappa distribution which is isotropic up to some large momentum $p_m$ and anisotropic with loss-cone above this momentum then distinct peaks of the growth rate appear and thus distinct zebra stripes can be generated. It means that the restriction for small momenta for the anisotropic part of distributions is of principal importance for the zebra stripes generation. Finally, for the 1 August 2010 zebra stripes, the growth rates in dependence on radio frequency were computed. It was shown that in this case the growth rate peaks are more distinct than in usually presented dependencies of growth rates on the ratio of the plasma and cyclotron frequencies.

Double plasma-resonance surfaces in flare loops and radio zebra emission

Aims. The zebra structures observed in radio waves during solar flares are some of the most important structures used as diagnostics of solar flare plasmas. We here not only analyze the so-called double plasma-resonance (DPR) surfaces, but also estimate the effects of their form on the size of the zebra sources and brightness temperature.Methods. To compute the DPR surfaces, we used numerical and analytical methods.Results. We found that except for the case of a constant magnetic field across the loop, the DPR surfaces deviate from the constant plasma density surfaces. We found that the regime with a finite height scale has three forms of resonance surfaces depending on the magnetic field variation across the loop. This magnetic field variation also determines if in the generated zebra structure, an increase in gyro-harmonic number leads to an increase or decrease of the zebra stripe frequency. In the case with an infinite height scale, the resonance surfaces are parallel to the loop axis. Furthermore, we found that for highly polarized zebra structures that are generated at DPR surfaces close to the plasma frequency, the zebra emission is limited to the narrow escaping cone and the emitting source area increases with increasing viewing angle compared to the loop axis. Moreover, with increasing deviation of the DPR surfaces from those of constant density surfaces, the frequency bandwidth of the DPR emission increases and can cause the zebra stripes to overlap, which limits the zebra generation. For the zebra structures observed on 14 February 1999, 6 June 2000, and 1 August 2010 and the observed view perpendicular to the loop axis, we estimated that the brightness temperature is 3.67 × 1014K, 6.58 × 1013K, and 7.35 × 1015K, respectively. These brightness temperatures are much lower than those derived for the view along the loop axis (up to 1017K), and thus are more realistic. The area of the emitting source for coronal loops in the view perpendicular to the loop axis can be larger by several orders of magnitude than that in the view along the loop axis.

X-ray line coincidence photopumping in a solar flare

Line coincidence photopumping is a process where the electrons of an atomic or molecular species are radiatively excited through the absorption of line emission from another species at a coincident wavelength. There are many instances of line coincidence photopumping in astrophysical sources at optical and ultraviolet wavelengths, with the most famous example being Bowen fluorescence (pumping of O III 303.80 A by He II), but none to our knowledge in X-rays. However, here we report on a scheme where a He-like line of Ne IX at 11.000 A is photopumped by He-like Na X at 11.003 A, which predicts significant intensity enhancement in the Ne IX 82.76 A transition under physical conditions found in solar flare plasmas. A comparison of our theoretical models with published X-ray observations of a solar flare obtained during a rocket flight provides evidence for line enhancement, with the measured degree of enhancement being consistent with that expected from theory, a truly surprising result. Observations of this enhancement during flares on stars other than the Sun would provide a powerful new diagnostic tool for determining the sizes of flare loops in these distant, spatially-unresolved, astronomical sources.

The two solar flares diagnostics based on the soft X-ray emission recording

The time history of the temperature and the emission measure of the solar flare plasma have been studied relying upon the experimental data on the soft X-rays recorded by the IRIS spectrometer on June 29, 2002 (F1) and March 27, 2003 (F2). F1 was a thermal flare and was not accompanied by hard X-rays. This data analysis revealed that at least two sequential energy-release processes occurred during the F1 event. The F2 event took place behind the limb, so only the top part of the flare loop being the soft X-ray source was recorded by the satellite-based spectrometer. From this data analysis it appeared that fast plasma heating occurred in the initial stage of F2 and then the flare region expanded and the emission measure of flare plasma increased.

Discontinuous plasma flows near reconnecting current layers in solar flares

A model for magnetic reconnection in high-conductivity plasma in the solar corona is analyzed in a strong-magnetic-field approximation. The model includes a Syrovatskii current layer and magnetohydrodynamic (MHD) discontinuities attached to the ends of the layer. A two-dimensional analytical solution for the magnetic field is used to compute the distributions of the plasma flow velocity and plasma density in the vicinity of the corresponding current configuration. The properties of jumps in the density and velocity along the attached discontinuities are studied. Based on the character of the variations of the magnetic field and plasma flows at the MHD discontinuities, it is shown that, with the parameter values considered, an MHDdiscontinuity can include regions of trans-Alfvenic, fast, and slowshocks. The results obtained could be useful to explain the presence of “super-hot” (with effective electron temperatures exceeding 10 keV) plasma in solar flares. Other possible applications of the theory of discontinuous flows near regions of magnetic reconnection to analogous non-stationary phenomena in astrophysical plasmas are noted.

An assessment of Fe xx–Fe xxii emission lines in SDO/EVE data as diagnostics for high-density solar flare plasmas using EUVE stellar observations

The Extreme Ultraviolet Variability Experiment (EVE) on the Solar Dynamics Observatory obtains extreme-ultraviolet (EUV) spectra of the full-disk Sun at a spectral resolution of ~1 A and cadence of 10 s. Such a spectral resolution would normally be considered to be too low for the reliable determination of electron density (N_e) sensitive emission line intensity ratios, due to blending. However, previous work has shown that a limited number of Fe XXI features in the 90-60 A wavelength region of EVE do provide useful N_e-diagnostics at relatively low flare densities (N_e ~ 10^11-10^12 cm^-3). Here we investigate if additional highly ionised Fe line ratios in the EVE 90-160 A range may be reliably employed as N_e-diagnostics. In particular, the potential for such diagnostics to provide density estimates for high N_e (~10^13 cm^-3) flare plasmas is assessed. Our study employs EVE spectra for X-class flares, combined with observations of highly active late-type stars from the Extreme Ultraviolet Explorer (EUVE) satellite plus experimental data for well-diagnosed tokamak plasmas, both of which are similar in wavelength coverage and spectral resolution to those from EVE. Several ratios are identified in EVE data which yield consistent values of electron density, including Fe XX 113.35/121.85 and Fe XXII 114.41/135.79, with confidence in their reliability as N_e-diagnostics provided by the EUVE and tokamak results. These ratios also allow the determination of density in solar flare plasmas up to values of ~10^13 cm^-3.

Analysis of Hard X-Ray, Microwave and Millimeter Emission in Solar Flare Plasma on 5 July 2012

Analysis of Hard X-Ray, Microwave and Millimeter Emission in Solar Flare Plasma on 5 July 2012

Hard X-ray generation in the turbulent plasma of solar flares

The influence of scattering of accelerated electrons in the turbulent plasma on the transformation of their distribution function is studied. The turbulence is connected with the emergence of magnetic inhomogeneities and ion-sound mode. The level of ion-sound turbulence is specified by the ratio Ws/nkBTe = 10−3, while the value of magnetic fluctuations is δB/B = 10–3. Different initial angular distributions of the function of accelerated-electron source are regarded: from isotropic to narrow directional distributions. For the chosen energy-density values of the ion-sound turbulence and the level of magnetic fluctuations, it is shown that both types of turbulence lead to a qualitative change in the hard X-ray brightness along the loop, moreover their influence was found to be different. Models with magnetic fluctuations and the ion sound can be distinguished not only by the difference in the hard X-ray distribution along the loop but also by the photon spectrum.

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

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.