Solar Flare Model Research Articles

Exploring Flaring Behaviour on Low Mass Stars, Solar-type Stars and the Sun

AbstractWe report on our project to study the activity in both the Sun and low mass stars. Utilising high cadence, Hα observations of a filament eruption made using the CRISP spectropolarimeter mounted on the Swedish Solar Telescope has allowed us to determine 3D velocity maps of the event. To gain insight into the physical mechanism which drives the event we have qualitatively compared our observation to a 3D MHD reconnection model. Solar-type and low mass stars can be highly active producing flares with energies exceeding erg. Using K2 and TESS data we find no correlation between the number of flares and the rotation phase which is surprising. Our solar flare model can be used to aid our understanding of the origin of flares in other stars. By scaling up our solar model to replicate observed stellar flare energies, we investigate the conditions needed for such high energy flares.

A Parameterized Model of X‐Ray Solar Flare Effects on the Lower Ionosphere and HF Propagation

AbstractWe present a parameterized X‐ray solar flare effects model relating the physics of radiation transport to the observable impact of solar flares on low‐altitude ionospheric absorption of High Frequency (HF) signals. Tunable parameters of time‐varying flare spectral energy density and characteristic flare temperature provide a novel capability to simulate HF experiments over a wide range of X‐ray solar flare behavior. Results from our model are consistent with HF propagation data collected over a period of heightened solar flare activity during 5–7 September 2017, including M and X class solar flares. Our predictions and measurements are compared with results from D Region Absorption Prediction (Akmaev et al., 2010, https://www.ngdc.noaa.gov/stp/drap/DRAP-V-Report1.pdf) and the Wait Very Low Frequency (VLF)‐driven model (Wait & Spies, 1964).

K2 Ultracool Dwarfs Survey. IV. Monster Flares Observed on the Young Brown Dwarf CFHT-BD-Tau 4

Abstract We present photometric measurements of two superflares observed on a very young brown dwarf, CFHT-BD-Tau 4, observed during Campaign 13 of the Kepler K 2 mission. The stronger of the two superflares brightened by a factor of ∼48 relative to the quiescent photospheric level, with an increase in Kepler magnitude . It has an equivalent duration of ∼107 hr, a flare duration of 1.7 days, and an estimated total bolometric (ultraviolet/optical/infrared) energy up to 2.1 × 1038 erg. The weaker of the two superflares is a complex (multipeaked) flare with an estimated total bolometric (UV/optical/IR) energy up to 4.7 × 1036 erg. They are the strongest flares observed on any brown dwarf so far. The flare energies are strongly dependent on the value of the visual extinction parameter A V used for extinction correction. If we apply a solar flare model to interpret the two superflares, we find that the magnetic fields are required to be stronger by as much as an order of magnitude than previous reports of field measurements in CFHT-BD-Tau 4 by Reiners et al. On the other hand, if we interpret our data in terms of accretion, we find that the requisite rate of accretion for the stronger superflare exceeds the rates that have been reported for other young brown dwarfs.

Principle of Minimum Energy in Magnetic Reconnection in a Self-organized Critical Model for Solar Flares

Abstract Solar flares are an abrupt release of magnetic energy in the Sun’s atmosphere due to reconnection of the coronal magnetic field. This occurs in response to turbulent flows at the photosphere that twist the coronal field. Similar to earthquakes, solar flares represent the behavior of a complex system, and expectedly their energy distribution follows a power law. We present a statistical model based on the principle of minimum energy in a coronal loop undergoing magnetic reconnection, which is described as an avalanche process. We show that the distribution of peaks for the flaring events in this self-organized critical system is scale-free. The obtained power-law index of 1.84 ± 0.02 for the peaks is in good agreement with satellite observations of soft X-ray flares. The principle of minimum energy can be applied for general avalanche models to describe many other phenomena.

Time-resolved spectroscopic observations of an M-dwarf flare star EV Lacertae during a flare

Abstract We have performed five night spectroscopic observations of the Hα line of EV Lac with a medium wavelength resolution (R ∼ 10000) using the 2 m Nayuta telescope at the Nishi-Harima Astronomical Observatory. EV Lac always possesses the Hα emission line; however, its intensity was stronger on 2015 August 15 than during the other four night periods. On this night, we observed a rapid rise (∼20 min) and a subsequent slow decrease (∼1.5 hr) of the emission-line intensity of Hα, which was probably caused by a flare. We also found an asymmetrical change in the Hα line on the same night. The enhancement has been observed in the blue wing of the Hα line during each phase of this flare (from the flare start to the flare end), and absorption components were present in its red wing during the early and later phases of the flare. Such blue enhancement (blue asymmetry) of the Hα line is sometimes seen during solar flares, but only during the early phases. Even for solar flares, little is known about the origin of the blue asymmetry. Compared with solar flare models, the presented results can lead to better understanding of the dynamics of stellar flares.

Reconnection in the Post-impulsive Phase of Solar Flares

Abstract Using a recently developed analytical procedure, we determine the rate of magnetic reconnection in the “standard” model of eruptive solar flares. During the late phase, the neutral line is located near the lower tip of the reconnection current sheet, and the upper region of the current sheet is bifurcated into a pair of Petschek-type shocks. Despite the presence of these shocks, the reconnection rate remains slow if the resistivity is uniform and the flow is laminar. Fast reconnection is achieved only if there is some additional mechanism that can shorten the length of the diffusion region at the neutral line. Observations of plasma flows by the X-ray telescope on Hinode imply that the diffusion region is, in fact, quite short. Two possible mechanisms for reducing the length of the diffusion region are localized resistivity and MHD turbulence.

Expanding and Contracting Coronal Loops as Evidence of Vortex Flows Induced by Solar Eruptions

Abstract Eruptive solar flares were predicted to generate large-scale vortex flows at both sides of the erupting magnetic flux rope. This process is analogous to a well-known hydrodynamic process creating vortex rings. The vortices lead to advection of closed coronal loops located at the peripheries of the flaring active region. Outward flows are expected in the upper part and returning flows in the lower part of the vortex. Here, we examine two eruptive solar flares, the X1.1-class flare SOL2012-03-05T03:20 and the C3.5-class SOL2013-06-19T07:29. In both flares, we find that the coronal loops observed by the Atmospheric Imaging Assembly in its 171 Å, 193 Å, or 211 Å passbands show coexistence of expanding and contracting motions, in accordance with the model prediction. In the X-class flare, multiple expanding and contracting loops coexist for more than 35 minutes, while in the C-class flare, an expanding loop in 193 Å appears to be close by and cotemporal with an apparently imploding loop arcade seen in 171 Å. Later, the 193 Å loop also switches to contraction. These observations are naturally explained by vortex flows present in a model of eruptive solar flares.

Spatial Offsets in Flare-CME Current Sheets

Abstract Magnetic reconnection plays an integral part in nearly all models of solar flares and coronal mass ejections (CMEs). The reconnection heats and accelerates the plasma, produces energetic electrons and ions, and changes the magnetic topology to form magnetic flux ropes and to allow CMEs to escape. Structures that appear between flare loops and CME cores in optical, UV, EUV, and X-ray observations have been identified as current sheets and have been interpreted in terms of the nature of the reconnection process and the energetics of the events. Many of these studies have used UV spectral observations of high temperature emission features in the [Fe xviii] and Si xii lines. In this paper, we discuss several surprising cases in which the [Fe xviii] and Si xii emission peaks are spatially offset from each other. We discuss interpretations based on asymmetric reconnection, on a thin reconnection region within a broader streamer-like structure, and on projection effects. Some events seem to be easily interpreted as the projection of a sheet that is extended along the line of sight that is viewed an angle, but a physical interpretation in terms of asymmetric reconnection is also plausible. Other events favor an interpretation as a thin current sheet embedded in a streamer-like structure.

The challenges of the models of solar flares

The challenges of ‘standard’ model of solar flares motivated by new observations with the spacecrafts and ground-based telescopes are presented. The most important problems are in situ heating of photospheric and chromospheric loop footpoints up to the coronal temperatures without precipitating particle beams accelerated in the corona, and the sunquakes which are unlikely to be explained by the impact of highenergy particles producing hard X-ray emission. There is also the long-standing ‘number problem’ in the physics of solar flares. It is shown that modern observations favored an important role of the electric currents in the energy release processes in the low solar atmosphere. Particle acceleration mechanism in the electric fields driven by the magnetic Rayleigh-Taylor instability in the chromosphere is proposed. The electric current value I ≥ 1010 A, needed for the excitation of super-Dreicer electric fields in the chromosphere is determined. It is shown that both Joule dissipation of the electric currents and the particles accelerated in the chromosphere can be responsible for in situ heating of the low solar atmosphere. Alternative model of the solar flare based on the analogy between the flaring loop and an equivalent electric circuit which is good tool for the electric current diagnostics is presented. Interaction of a current-carrying loop with the partially-ionized plasma of prominence in the context of particle acceleration is considered. The role of plasma radiation mechanism in the sub-THz emission from the chromosphere is discussed.

SLIPPING MAGNETIC RECONNECTION, CHROMOSPHERIC EVAPORATION, IMPLOSION, AND PRECURSORS IN THE 2014 SEPTEMBER 10 X1.6-CLASS SOLAR FLARE

ABSTRACT We investigate the occurrence of slipping magnetic reconnection, chromospheric evaporation, and coronal loop dynamics in the 2014 September 10 X-class flare. Slipping reconnection is found to be present throughout the flare from its early phase. Flare loops are seen to slip in opposite directions toward both ends of the ribbons. Velocities of 20–40 km s−1 are found within time windows where the slipping is well resolved. The warm coronal loops exhibit expanding and contracting motions that are interpreted as displacements due to the growing flux rope that subsequently erupts. This flux rope existed and erupted before the onset of apparent coronal implosion. This indicates that the energy release proceeds by slipping reconnection and not via coronal implosion. The slipping reconnection leads to changes in the geometry of the observed structures at the Interface Region Imaging Spectrograph slit position, from flare loop top to the footpoints in the ribbons. This results in variations of the observed velocities of chromospheric evaporation in the early flare phase. Finally, it is found that the precursor signatures, including localized EUV brightenings as well as nonthermal X-ray emission, are signatures of the flare itself, progressing from the early phase toward the impulsive phase, with the tether-cutting being provided by the slipping reconnection. The dynamics of both the flare and outlying coronal loops is found to be consistent with the predictions of the standard solar flare model in three dimensions.

Ensemble forecasting of major solar flares: First results

AbstractWe present the results from the first ensemble prediction model for major solar flares (M and X classes). The primary aim of this investigation is to explore the construction of an ensemble for an initial prototyping of this new concept. Using the probabilistic forecasts from three models hosted at the Community Coordinated Modeling Center (NASA‐GSFC) and the NOAA forecasts, we developed an ensemble forecast by linearly combining the flaring probabilities from all four methods. Performance‐based combination weights were calculated using a Monte Carlo‐type algorithm that applies a decision threshold Pth to the combined probabilities and maximizing the Heidke Skill Score (HSS). Using the data for 13 recent solar active regions between years 2012 and 2014, we found that linear combination methods can improve the overall probabilistic prediction and improve the categorical prediction for certain values of decision thresholds. Combination weights vary with the applied threshold and none of the tested individual forecasting models seem to provide more accurate predictions than the others for all values of Pth. According to the maximum values of HSS, a performance‐based weights calculated by averaging over the sample, performed similarly to a equally weighted model. The values Pth for which the ensemble forecast performs the best are 25% for M‐class flares and 15% for X‐class flares. When the human‐adjusted probabilities from NOAA are excluded from the ensemble, the ensemble performance in terms of the Heidke score is reduced.

Towards understanding the frequency distribution of solar flares—part 1: a Stochastic-Diffusive model of solar flares

Systematic relationships of the subclass-averaged rise, decay times and durations of flare events as a function of the logarithmic peak flux ( $\operatorname{ln}f$ ) are investigated, employing the soft X-ray flares observed by GOES during the period from September 1975 to October 2014. Different behaviors are found before and after 1997. Since 1997 they all vary linearly with $\operatorname{ln}f$ , obeying the RV model. However, prior to 1997 they vary quadratically with $\operatorname{ln}f$ , implying a different energy storage/release process of flaring. The discrepancy may be related to the variation in the turbulence in the corona caused by the weakening magnetic field strength in the recent two decades. This motivates us to propose a Stochastic-Diffusive model for explaining the above result, by assuming that the temporal rate of flare energy resulted by external forces is proportional to the total energy already stored in the flare system and inversely proportional to the size scale of diffusion.

OPTIMAL ELECTRON ENERGIES FOR DRIVING CHROMOSPHERIC EVAPORATION IN SOLAR FLARES

In the standard model of solar flares, energy deposition by a beam of electrons drives strong chromospheric evaporation leading to a significantly denser corona and much brighter emission across the spectrum. Chromospheric evaporation was examined in great detail by Fisher et al., who described a distinction between two different regimes, termed explosive and gentle evaporation. In this work, we examine the importance of electron energy and stopping depths on the two regimes and on the atmospheric response. We find that with explosive evaporation, the atmospheric response does not depend strongly on electron energy. In the case of gentle evaporation, lower energy electrons are significantly more efficient at heating the atmosphere and driving up-flows sooner than higher energy electrons. We also find that the threshold between explosive and gentle evaporation is not fixed at a given beam energy flux, but also depends strongly on the electron energy and duration of heating. Further, at low electron energies, a much weaker beam flux is required to drive explosive evaporation.

From Coronal Observations to MHD Simulations, the Building Blocks for 3D Models of Solar Flares (Invited Review)

Solar flares are energetic events taking place in the Sun's atmosphere, and their effects can greatly impact the environment of the surrounding planets. In particular, eruptive flares, as opposed to confined flares, launch coronal mass ejections into the interplanetary medium, and as such, are one of the main drivers of space weather. After briefly reviewing the main characteristics of solar flares, we summarize the processes that can account for the build up and release of energy during their evolution. In particular, we focus on the development of recent 3D numerical simulations that explain many of the observed flare features. These simulations can also provide predictions of the dynamical evolution of coronal and photospheric magnetic field. Here we present a few observational examples that, together with numerical modelling, point to the underlying physical mechanisms of the eruptions.

Reverse-current effect in present-day models of solar flares: Theory and high-accuracy observations

We propose an accurate analytical model for the source of hard X-ray emission from a flare in the form of a “thick target” with a reverse current to explain the results of present-day observations of solar flares onboard the GOES, Hinode, RHESSI, and TRACE satellites. The model, one-dimensional in coordinate space and two-dimensional in velocity space, self-consistently takes into account the fact that the beam electrons lose the kinetic energy of their motion along the magnetic field almost without any collisions under the action of the reverse-current electric field. Some of the electrons return from the emission source to the acceleration region without losing the kinetic energy of their transverse motion. Based on the observed hard X-ray bremsstrahlung spectrum, the model allows the injection spectrum of accelerated electrons to be reconstructed with a high accuracy. As an example, we consider the white-light flare of December 6, 2006, which was observed with a high spatial resolution in the optical wavelength range at the main maximum of hard X-ray emission. Within the framework of our model, we show that to explain the hard X-ray spectrum, the flux density of the energy transferred by electrons with energies above 18 keV was ∼3 × 1013 erg cm−2 s−1. This exceeds the habitual values typical of the classical model of a thick target without a reverse current by two orders of magnitude. The electron density in the beam is also very high: ∼1011 cm−3. A more careful consideration of plasma processes in such dense electron beams is needed when the physical parameters of a flare are calculated.

SLIPPING MAGNETIC RECONNECTION DURING AN X-CLASS SOLAR FLARE OBSERVED BYSDO/AIA

We present SDO/AIA observations of an eruptive X-class flare of July 12, 2012, and compare its evolution with the predictions of a 3D numerical simulation. We focus on the dynamics of flare loops that are seen to undergo slipping reconnection during the flare. In the AIA 131A observations, lower parts of 10 MK flare loops exhibit an apparent motion with velocities of several tens of km/s along the developing flare ribbons. In the early stages of the flare, flare ribbons consist of compact, localized bright transition-region emission from the footpoints of the flare loops. A DEM analysis shows that the flare loops have temperatures up to the formation of Fe XXIV. A series of very long, S-shaped loops erupt, leading to a CME observed by STEREO. The observed dynamics are compared with the evolution of magnetic structures in the "standard solar flare model in 3D". This model matches the observations well, reproducing both the apparently slipping flare loops, S-shaped erupting loops, and the evolution of flare ribbons. All of these processes are explained via 3D reconnection mechanisms resulting from the expansion of a torus-unstable flux rope. The AIA observations and the numerical model are complemented by radio observations showing a noise storm in the metric range. Dm-drifting pulsation structures occurring during the eruption indicate plasmoid ejection and enhancement of reconnection rate. The bursty nature of radio emission shows that the slipping reconnection is still intermittent, although it is observed to persist for more than an hour.

Deterministically Driven Avalanche Models of Solar Flares

We develop and discuss the properties of a new class of lattice-based avalanche models of solar flares. These models are readily amenable to a relatively unambiguous physical interpretation in terms of slow twisting of a coronal loop. They share similarities with other avalanche models, such as the classical stick–slip self-organized critical model of earthquakes, in that they are driven globally by a fully deterministic energy-loading process. The model design leads to a systematic deficit of small-scale avalanches. In some portions of model space, mid-size and large avalanching behavior is scale-free, being characterized by event size distributions that have the form of power-laws with index values, which, in some parameter regimes, compare favorably to those inferred from solar EUV and X-ray flare data. For models using conservative or near-conservative redistribution rules, a population of large, quasiperiodic avalanches can also appear. Although without direct counterparts in the observational global statistics of flare energy release, this latter behavior may be relevant to recurrent flaring in individual coronal loops. This class of models could provide a basis for the prediction of large solar flares.

SCATTERING POLARIZATION IN SOLAR FLARES

There is ongoing debate about the origin and even the very existence of a high degree of linear polarization of some chromospheric spectral lines observed in solar flares. The standard explanation of these measurements is in terms of the impact polarization caused by non-thermal proton and/or electron beams. In this work, we study the possible role of resonance line polarization due to radiation anisotropy in the inhomogeneous medium of the flare ribbons. We consider a simple two-dimensional model of the flaring chromosphere and we self-consistently solve the non-LTE problem taking into account the role of resonant scattering polarization and of the Hanle effect. Our calculations show that the horizontal plasma inhomogeneities at the boundary of the flare ribbons can lead to a significant radiation anisotropy in the line formation region and, consequently, to a fractional linear polarization of the emergent radiation of the order of several percent. Neglecting the effects of impact polarization, our model can provide a clue for resolving some of the common observational findings, namely: (1) why a high degree of polarization appears mainly at the edges of the flare ribbons; (2) why polarization can also be observed during the gradual phase of a flare; and (3) why polarization is mostly radial or tangential. We conclude that radiation transfer in realistic multi-dimensional models of solar flares needs to be considered as an essential ingredient for understanding the observed spectral line polarization.

THE ROLE OF A FLUX ROPE EJECTION IN A THREE-DIMENSIONAL MAGNETOHYDRODYNAMIC SIMULATION OF A SOLAR FLARE

We investigated the dynamic evolution of a three-dimensional (3D) flux rope eruption and magnetic reconnection process in a solar flare by simply extending the two-dimensional (2D) resistive magnetohydrodynamic simulation model of solar flares with low β plasma to a 3D model. We succeeded in reproducing a current sheet and bi-directional reconnection outflows just below the flux rope during the eruption in our 3D simulations. We calculated four cases of a strongly twisted flux rope and a weakly twisted flux rope in 2D and 3D simulations. The time evolution of a weakly twisted flux rope in the 3D simulation shows behaviors similar to those of the 2D simulation, while a strongly twisted flux rope in the 3D simulation clearly shows a different time evolution from the 2D simulation except for the initial phase evolution. The ejection speeds of both strongly and weakly twisted flux ropes in 3D simulations are larger than in the 2D simulations, and the reconnection rates in 3D cases are also larger than in the 2D cases. This indicates positive feedback between the ejection speed of a flux rope and the reconnection rate even in the 3D simulation, and we conclude that the plasmoid-induced reconnection model can be applied to 3D. We also found that small-scale plasmoids are formed inside a current sheet and make it turbulent. These small-scale plasmoid ejections have a role in locally increasing the reconnection rate intermittently as observed in solar flares, coupled with a global eruption of a flux rope.

The interaction and eruption of two adjacent filaments

We present a case study of two successive filament eruptions at the southeast limb of the Sun observed by Solar Dynamics Observatory (SDO) on 2012 April 19. At the initial stage of the first filament (F1) eruption, one leg of the F1 moved toward the second filament (F2) and swept the F2. The interaction between two filaments occurred. After the leg of the F1 swept the F2, it returned from northeast to southwest following the F1 expansion. During the F1 eruption, the middle of the F1 exhibited an obvious twisted structure. The rising speed of the F1 was 85.6 km/s. The partial material of the F1 fell back to the surface along the other leg of the F1 after the F1 eruption and the falling speed was 311.6 km/s. A CME was observed by SOHO/LASCO after the F1 eruption. One of the bright flare ribbons and the dimming regions formed after the F1 eruption were found to move toward the F2. The propagation speeds of the flare ribbons were 4.7 km/s and 4.1 km/s and the propagation speeds of the dimmings were 3 km/s and 6.3 km/s. The small active region was emerging in the northern flank of the F2. The ejection and the falling plasma in the small active region produced the disturbance to the right part of the F2. When the F1 erupted, the large-scale overlying coronal loops of the F1 were pushed out toward the southeast of the Sun by its expanding. During the F1 eruption, the large-scale overlying coronal loops of the F2 began to open toward the southeast. Following the opening of the large-scale overlying coronal loops, the F2 became instable and began to erupt. The rising speed of the F2 was 300.1 km/s. A two-ribbon flare and a weak CME were formed after the F2 eruption. These observations evidenced that the interaction of two filaments and the opening of the large-scale overlying coronal loops caused by the F1 eruption are the most important reason that led to the F2 eruption. Our observations also support the standard solar flare model.