Solar Flare Loops Research Articles

Modeling Time-variable Elemental Abundances in Coronal Loop Simulations

Numerous recent X-ray observations of coronal loops in both active regions and solar flares have shown clearly that elemental abundances vary with time. Over the course of a flare, they have been found to move from coronal values toward photospheric values near the flare peak, before slowly returning to coronal values during the gradual phase. Coronal loop models typically assume that the elemental abundances are fixed, however. In this work, we introduce a time-variable abundance factor into the 0D ebtel++ code that models the changes due to chromospheric evaporation in order to understand how this affects coronal loop cooling. We find that for strong heating events (≳1 erg s−1 cm−3), the abundances quickly tend towards photospheric values. For smaller heating rates, the abundances fall somewhere between coronal and photospheric values, causing the loop to cool more quickly than the time-fixed photospheric cases (typical flare simulations) and more slowly than time-fixed coronal cases (typical AR simulations). This suggests heating rates in quiescent AR loops no larger than ≈0.1 erg s−1 cm−3 to be consistent with recent measurements of abundance factors f ≳ 2.

Variation of the electron flux spectrum along a solar flare loop as inferred from STIX hard X-ray observations

Context. Regularized imaging spectroscopy was introduced for the construction of electron flux images at different energies from count visibilities recorded by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). In this work we seek to extend this approach to data from the Spectrometer/Telescope for Imaging X-rays (STIX) on board the Solar Orbiter mission. Aims. Our aims are to demonstrate the feasibility of regularized imaging spectroscopy as a method for analysis of STIX data, and also to show how such an analysis can lead to insights into the physical processes affecting the nonthermal electrons responsible for the hard X-ray emission observed by STIX. Methods. STIX records imaging data in an intrinsically different manner from RHESSI. Rather than sweeping the angular frequency plane in a set of concentric circles (one circle per detector), STIX uses 30 collimators, each corresponding to a specific angular frequency. For this work, we derived an appropriate modification to the previous computational approach for the analysis of the visibilities observed by STIX. This approach also allows for the observed count data to be placed into nonuniformly spaced energy bins. Results. We show that the regularized imaging spectroscopy approach is not only feasible for an analysis of the visibilities observed by STIX, but also more reliable. The application of the regularized imaging spectroscopy technique to several well-observed flares reveals details of the variation of the electron flux spectrum throughout the flare sources. Conclusions. We conclude that the visibility-based regularized imaging spectroscopy approach is well suited for the analysis of STIX data. We also used STIX electron flux spectral images to track, for the first time, the behavior of the accelerated electrons during their path from the acceleration site in the solar corona toward the chromosphere.

Radiation-driven diffusive transport of fast electrons in solar flares

Fast electron scattering on plasma ions due to stimulated Bremsstrahlung is investigated and modeled. Comparison with Coulomb scattering suggests that stimulated Bremsstrahlung scattering can be dominant in low-density, radiation-driven plasmas, provided that the radiation spectrum has a sufficiently high brightness temperature in the neighborhood of the plasma frequency. While stimulated Bremsstrahlung scattering cannot be easily observed in laboratory plasmas due to their small size, it should operate in large-scale astrophysical plasmas, such as those met in the flaring solar corona. The effect of the solar microwave radiation on fast-electron scattering is evaluated through a parameterized flaring corona model. We find that stimulated Bremsstrahlung greatly enhances the fast-electron scattering frequency in the flare magnetic loop, leading the transport of deka-keV electrons to occur in the diffusion regime, characterized by significant precipitation rates. This prediction is consistent with the interpretation of the above-loop-top hard x-ray and microwave emissions from the X3.1 flare of August 24, 2002. Our analysis indicates that stimulated Bremsstrahlung may play an essential role in the dynamics of fast electrons trapped in solar flare loops.

Observation of rapid flux coalescence in merging field-reversed configurations

Rapid magnetic reconnection was experimentally observed to occur within a microsecond timescale, leading to the field-reversed configuration (FRC) comprising a single closed magnetic field structure. The compressibility of the plasma within the FRC played a crucial role in accelerating the coalescence process, making it considerably faster than the resistive process. A strong similarity between the observed experimental results and those of the coalescence of solar flare loops indicates that astrophysical phenomena and laboratory plasmas are governed by a common physics.

A Possible Mechanism for the “Late Phase” in Stellar White-light Flares

M dwarf flares observed by the Transiting Exoplanet Survey Satellite (TESS) sometimes exhibit a peak-bump light-curve morphology, characterized by a secondary, gradual peak well after the main, impulsive peak. A similar late phase is frequently detected in solar flares observed in the extreme ultraviolet from longer hot coronal loops distinct from the impulsive flare structures. White-light emission has also been observed in off-limb solar flare loops. Here, we perform a suite of one-dimensional hydrodynamic loop simulations for M dwarf flares inspired by these solar examples. Our results suggest that coronal plasma condensation following impulsive flare heating can yield high electron number density in the loop, allowing it to contribute significantly to the optical light curves via free-bound and free–free emission mechanisms. Our simulation results qualitatively agree with TESS observations: the longer evolutionary timescale of coronal loops produces a distinct, secondary emission peak; its intensity increases with the injected flare energy. We argue that coronal plasma condensation is a possible mechanism for the TESS late-phase flares.

Modeling Solar Energetic Neutral Atoms from Solar Flares and CME-driven Shocks

We examine the production of energetic neutral atoms (ENAs) in solar flares and coronal mass ejection (CME)-driven shocks and their subsequent propagation to 1 au. Time profiles and fluence spectra of solar ENAs at 1 au are computed for two scenarios: (1) ENAs are produced downstream at CME-driven shocks, and (2) ENAs are produced at large-scale post-flare loops in solar flares. Both the time profiles and fluence spectra for these two scenarios are vastly different. Our calculations indicate that we can use solar ENAs as a new probe to examine the underlying acceleration process of solar energetic particles (SEPs) and to differentiate the two acceleration sites: large loops in solar flares and downstream of CME-driven shocks, in large SEP events.

The Transition Region of Solar Flare Loops

The transition region between the Sun’s corona and chromosphere is important to the mass and energy transfer from the lower atmosphere to the corona; consequently, this region has been studied intensely with ultraviolet and extreme ultraviolet (EUV) observations. A major result of these studies is that the amount of plasma at low temperatures, <105 K, is far too large to be compatible with the standard theory of thermal conductivity. However, it is not clear whether the disagreement lies with a problem in the observations or a problem in the theory. We address this issue by analyzing high–spatial and temporal resolution EUV observations from an X1.6-class flare, taken with the Interface Region Imaging Spectrograph and the Solar Dynamic Observatory/Atmospheric Imaging Assembly (AIA). These data allow us to isolate the emission of flare loops from that of surrounding structures. We compare the emission measures (EMs) derived from the C ii 1334.525 Å and Si iv 1402.770 Å transition region spectral lines, the Fe xxi 1354.066 Å flare line, and the AIA 171 Å coronal images. We find that the EM ratios are incompatible with a standard conduction-dominated transition region model. Furthermore, the large increases in the EM magnitudes due to flare heating make it highly unlikely that the disagreement between data and theory is due to observational uncertainties in the source of the emission. We conclude that the standard Spitzer–Härm thermal conductivity must be invalid for, at least, flare loops. We discuss the possibility that turbulent suppression of thermal conduction can account for our results.

Interrogating solar flare loop models with IRIS observations 2: Plasma properties, energy transport, and future directions

During solar flares a tremendous amount of magnetic energy is released and transported through the Sun’s atmosphere and out into the heliosphere. Despite over a century of study, many unresolved questions surrounding solar flares are still present. Among those are how does the solar plasma respond to flare energy deposition, and what are the important physical processes that transport that energy from the release site in the corona through the transition region and chromosphere? Attacking these questions requires the concert of advanced numerical simulations and high spatial-, temporal-, and spectral-resolution observations. While flares are 3D phenomenon, simulating the NLTE flaring chromosphere in 3D and performing parameter studies of 3D models is largely outwith our current computational capabilities. We instead rely on state-of-the-art 1D field-aligned simulations to study the physical processes that govern flares. Over the last decade, data from the Interface Region Imaging Spectrograph (IRIS) have provided the crucial observations with which we can critically interrogate the predictions of those flare loop models. Here in Paper 2 of a two-part review of IRIS and flare loop models, I discuss how forward modelling flares can help us understand the observations from IRIS, and how IRIS can reveal where our models do well and where we are likely missing important processes, focussing in particular on the plasma properties, energy transport mechanisms, and future directions of flare modelling.

Interrogating solar flare loop models with IRIS observations 1: Overview of the models, and mass flows

Solar flares are transient yet dramatic events in the atmosphere of the Sun, during which a vast amount of magnetic energy is liberated. This energy is subsequently transported through the solar atmosphere or into the heliosphere, and together with coronal mass ejections flares comprise a fundamental component of space weather. Thus, understanding the physical processes at play in flares is vital. That understanding often requires the use of forward modelling in order to predict the hydrodynamic and radiative response of the solar atmosphere. Those predictions must then be critiqued by observations to show us where our models are missing ingredients. While flares are of course 3D phenomenon, simulating the flaring atmosphere including an accurate chromosphere with the required spatial scales in 3D is largely beyond current computational capabilities, and certainly performing parameter studies of energy transport mechanisms is not yet tractable in 3D. Therefore, field-aligned 1D loop models that can resolve the relevant scales have a crucial role to play in advancing our knowledge of flares. In recent years, driven in part by the spectacular observations from the Interface Region Imaging Spectrograph (IRIS), flare loop models have revealed many interesting features of flares. For this review I highlight some important results that illustrate the utility of attacking the problem of solar flares with a combination of high quality observations, and state-of-the-art flare loop models, demonstrating: 1) how models help to interpret flare observations from IRIS, 2) how those observations show us where we are missing physics from our models, and 3) how the ever increasing quality of solar observations drives model improvements. Here in Paper one of this two part review I provide an overview of modern flare loop models, and of electron-beam driven mass flows during solar flares.

Current-sheet Oscillations Caused by the Kelvin–Helmholtz Instability at the Loop Top of Solar Flares

Current sheets (CSs), long stretching structures of magnetic reconnection above solar flare loops, are usually observed to oscillate; their origins, however, are still puzzled at present. Based on a high-resolution 2.5D MHD simulation of magnetic reconnection, we explore the formation mechanism of CS oscillations. We find that large-amplitude transverse waves are excited by the Kelvin–Helmholtz instability at the highly turbulent cusp-shaped region. The perturbations propagate upward along the CS with a phase speed close to local Alfvén speed thus resulting in the CS oscillations we observe. Though the perturbations damp after propagating for a long distance, the CS oscillations are still detectable. In terms of detected CS oscillations, with a combination of differential emission measure techniques, we propose a new method for measuring the magnetic field strength of the CS and its distribution in height.

Annihilation of Magnetic Islands at the Top of Solar Flare Loops

Abstract The dynamics of magnetic reconnection in the solar current sheet (CS) is studied by high-resolution 2.5-dimensional MHD simulation. With the commencing of magnetic reconnection, a number of magnetic islands are formed intermittently and move quickly upward and downward along the CS. Upon collision with the semi-closed flux of the flare loops, the downflow islands cause a second reconnection with a rate comparable with that in the main CS. Though the time-integrated magnetic energy release is still dominated by the reconnection in the main CS, the second reconnection can release substantial magnetic energy, annihilating the main islands and generating secondary islands with various scales at the flare loop top. The distribution function of the flux of the secondary islands is found to follow a power law varying from f ψ ∼ ψ − 1 (small scale) to ψ −2 (large scale), which seems to be independent to background plasma β and thermal conduction (TC). However, the spatial scale and the strength of the termination shocks driven by the main reconnection outflows or islands decrease if β increases or if TC is included. We suggest that the annihilation of magnetic islands at the flare loop top, which is not included in the standard flare model, plays a nonnegligible role in releasing magnetic energy to heat flare plasma and accelerate particles.

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 &gt;5) and a relatively high plasma density at the magnetic looptop &gt;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%.

The Electron Acoustic Wave and Its Role in Solar Flaring Loops Heating

Abstract From soft X-ray emission, the solar flare temperatures are from several MK to dozens of times MK, which are higher than the preflare coronal temperatures. A combination of several heating mechanisms may contribute to the heating problem in solar flare loops. In this paper, we propose an important mechanism of solar flaring loops heating, in which the excited electron acoustic wave (EAW) by flare-accelerated fast electron beams can lead to electron heating via collisionless Landau damping effect produced by wave–particle resonant interaction. Taking account of the return-current effect of fast electron beams, by use of numerical and analytic solutions, the plasma wave instability driven by fast electron beams is investigated in typical solar flare loop plasma parameters. The results show that the EAW is the strongest unstable wave mode rather than other wave modes. The dissipation of EAW via collisionless Landau damping and its application to solar flaring loops heating are discussed in detail.

Slow and sausage loop mode excitation due to local and global spontaneous perturbations

Aims. We analyse the capability of different types of perturbations associated with usual environment energy fluctuations of the solar corona to excite slow and sausage modes in solar flaring loops. Methods. We performed numerical simulations of magnetohydrodynamic ideal equations with a consideration of straight plasma magnetic tubes subject to local and global energy depositions. Results. We find that local loop energy depositions of typical microflares [∼(1027 − 1030) erg] are prone to driving slow shock waves that induce slow-mode patterns. The slow-mode features are obtained for every tested local energy deposition inside the loop. Meanwhile, in order to obtain an observable sausage mode pattern, a global perturbation that is capable of instantaneously modifying the internal loop temperature is required; specifically, the characteristic conductive heating time must be much smaller than the radiative cooling one. Experiments carried out by varying the parameter β demonstrate that the excitation of sausage modes does not significantly depend on the value of this parameter but, rather, depends on the global or local character of the energy source.

Conditions for Whistler Generation by Nonthermal Electrons in Flare Loops

Constraints are imposed on whistler generation in solar-flare loops. It is shown that the effective generation of whistlers is possible only under specific conditions: when the anisotropy of nonthermal electrons is sufficiently strong, the magnetic field is relatively weak (less than 200 G), or the plasma density is relatively high (more than 1010 cm–3). Otherwise, whistlers in flare loops will be strongly absorbed by the nonthermal electrons accelerated in the flare.

Electromagnetic Emission Driven by Electron Beam Instability in the Jovian Polar Regions

Abstract Upward energetic electron beams are often observed simultaneously with the plasma-wave emission in the Jovian polar regions, where the electron cyclotron frequency Ωce is much larger than the plasma frequency ω pe. This study gives a comprehensive wave and instability analysis in the extreme plasma environment with Ωce ≫ ω pe. We find that energetic electron beams can effectively drive the electron acoustic/magnetoacoustic instability. The excited electron acoustic/magnetoacoustic waves distribute from the parallel direction to the highly oblique direction, and their wave frequencies are always below the plasma frequency. These waves are electrostatic at parallel propagation, and exhibit electromagnetic polarization at oblique propagation. These theoretical predictions are qualitatively consistent with the main observed features of electromagnetic fluctuations in the Jovian polar regions. Therefore, we propose that upward electron beam-driven electron acoustic/magnetoacoustic waves can contribute to the plasma-wave emission in Jupiter’s polar environments. Furthermore, energetic electron beam-driven electron acoustic/magnetoacoustic waves may exist in Saturn’s polar regions and solar flare loops, where the extreme plasma condition Ωce ≫ ω pe is satisfied in these plasma environments.

Microwave diagnostics of magnetic field strengths in solar flaring loops

We have performed microwave diagnostics of the magnetic field strengths in solar flaring loops based on the theory of gyrosynchrotron emission. From Nobeyama Radioheliograph observations of three flare events at 17 and 34 GHz, we obtained the degree of circular polarization and the spectral index of microwave flux density, which were then used to map the magnetic field strengths in post-flare loops. Our results show that the magnetic field strength typically decreases from ∼800 G near the loop footpoints to ∼100 G at a height of 10–25 Mm. Comparison of our results with magnetic field modeling using a flux rope insertion method is also discussed. Our study demonstrates the potential of microwave imaging observations, even at only two frequencies, in diagnosing the coronal magnetic field of flaring regions.

Solar flares and Kelvin-Helmholtz instabilities: A parameter survey

Context. Hard X-ray (HXR) sources are frequently observed near the top of solar flare loops, which are also bright in soft X-ray (SXR) and extreme ultraviolet (EUV) wavebands. We revisit a recent scenario proposed by Fang et al. (2016) to trigger loop-top turbulence in flaring loops, which can help explain variations seen in SXR and EUV brightenings and potentially impact and induce HXR emission. It is conjectured that evaporation flows from flare-impacted chromospheric footpoints interact with each other near the loop top and produce turbulence via the Kelvin–Helmholtz instability (KHI). Aims. By performing a rigorous parameter survey, in which we vary the duration, total amount, and asymmetry of the energy deposition at both footpoints, we assess the relevance of the KHI in triggering and sustaining loop-top turbulence. We synthesize SXR and EUV emission and discuss the possibility of HXR emission through bremsstrahlung or inverse Compton processes, which scatter SXR photons to HXR photons via the inverse Compton mechanism. Methods. We performed 2.5D numerical simulations in which the magnetohydrodynamic model incorporates a realistic photosphere to coronal stratification, parametrized heating, radiative losses, and field-aligned anisotropic thermal conduction. We focus on the trigger of the KHI and the resulting turbulence, as well as identify various oscillatory patterns that appear in the evolutions. Results. We find that a M2.2-class related amount of energy should be deposited in less than four minutes to trigger a KHI interaction. Slower deposition, or lesser energy (&lt; 0.33 × 1029 ergs) rather leads to mere loop-top compression sites bounded by shocks, without KHI development. Asymmetry in the footpoint deposition determines whether the KHI turbulent zone gets produced away from the apex, and asymmetric cases can show a slow-mode mediated, periodic displacement of the turbulent zone. Our reference simulation further demonstrates a clear 25 s periodicity in the declining phase of the SXR light curve, wherein compressional effects dominate. Conclusions. When turbulence is produced in the loop apex, an index of −5/3 can be found in the spectra of velocity and magnetic field fluctuations. Typical values for M-class flares routinely show KHI development. The synthesized SXR light curve shows a clear periodic signal related to the sloshing motion of the vortex pattern created by the KHI.

Can Flare Loops Contribute to the White-light Emission of Stellar Superflares?

Abstract Since the discovery of stellar superflares by the Kepler satellite, these extremely energetic events have been studied in analogy to solar flares. Their white-light (WL) continuum emission has been interpreted as being produced by heated ribbons. In this paper, we compute the WL emission from overlying flare loops depending on their density and temperature and show that, under conditions expected during superflares, the continuum brightening due to extended loop arcades can significantly contribute to stellar flux detected by Kepler. This requires electron densities in the loops of 1012−1013 cm−3 or higher. We show that such densities, exceeding those typically present in solar-flare loops, can be reached on M-dwarf and solar-type superflare stars with large starspots and much stronger magnetic fields. Quite importantly, the WL radiation of loops is not very sensitive to their temperature and thus both cool as well as hot loops may contribute. We show that the WL intensity emergent from optically thin loops is lower than the blackbody radiation from flare ribbons, but the contribution of loops to total stellar flux can be quite important due to their significant emitting areas. This new scenario for interpreting superflare emission suggests that the observed WL flux is due to a mixture of the ribbon and loop radiation and can be even loop-dominated during the gradual phase of superflares.

Center-to-Limb Variability of Hot Coronal EUV Emissions During Solar Flares

It is generally accepted that densities of quiet sun and active region plasma are sufficiently low to justify the optically thin approximation, and it is commonly used in the analysis of line emissions from plasma in the solar corona. However, densities of solar flare loops are substantially higher, compromising the optically thin approximation. This study begins with a radiative transfer model that uses typical solar flare densities and geometries to show that hot coronal emission lines are not generally optically thin. Further, the model demonstrates that the observed line intensity should exhibit center-to-limb variability (CTLV), with flares observed near the limb being dimmer than those occurring near disk-center. The model predictions are validated with an analysis of over 200 flares observed by EVE on SDO that uses 6 lines, with peak formation temperatures between 8.9 and 15.8 MK, to show limb flares are systematically dimmer than disk-center flares. The data are then used to show that the electron column density along the line-of-sight typically increases by 1.76 x 1019 cm-2 for limb flares over the disk-center flare value. It is shown that CTLV of hot coronal emissions reduces the amount of ionizing radiation propagating into the solar system, and changes the relative intensities of lines and bands commonly used for spectral analysis.