The importance of photospheric magnetic field complexity for coronal energy storage

Possibilities for the storage of energy in coronal electric currents in different magnetic background field configurations are investigated in the framework of the solar flare energy build-up model of Van Tend and Kuperus (1978). The results are compared to characteristics of filaments and X-ray loops. Empirical flare predictors are interpreted theoretically.     

X-ray,Hα, and radio observations of the two-ribbon flare of 16 May, 1981

The paper is a contribution to the study of two-ribbon flares. A variety of observational material, i.e. Hα pictures, radio spectrum in the frequency band of 150–1000 MHz, radio map at 6 cm, fluxes at other frequencies, magnetograms and X-ray flux in a broad energy interval, enabled us to study the development of the 16 May, 1981 flare. The onset of the flare could be described by the model of Van Tend and Kuperus. A diminishing of the magnetic shear during the activation of the filament was observed. From radio and X-ray data it was found that pulsed acceleration took place in the region under the rising filament, the electrons propagating in a limited region both upwards to greater heights and downwards into the footpoints. Internal oscillations of the filament were observed. A manifestation of the primary process of interplanetary shock-wave generation was found. The 6 cm radio sources could be localized in the footpoints of magnetic loops.     

The eruption of active region filaments and its relation to the triggering of a solar flare

The formation and eruption of active region filaments is supposed to be caused by the increase of a concentrated current embedded in the active region background magnetic field of an active region according to the theory of Van Tend and Kuperus (1978).The onset of a filament eruption is due to either changes in the background magnetic field or the increase of the filament current intensity. Both processes can be caused by the emergence of new magnetic flux as well as by the motion of the photospheric footpoints of the magnetic field lines. It is shown that if the background field evolves from a potential field to a nearly force-free field the vertical equilibrium of the current filament is not affected, but large forces are generated along the filament axis. This is identified as the cause of filament activation and the increase in filament turbulence during the flare build-up phase. Depending on the evolution of the background field and the current filament, two different scenarios for flare build-up and filament eruption are distinguished.This work was done while one of the authors (M.K.) was participating in the CECAM workshop on Physics of Solar Flares held at Orsay, France, in June 1979.     

Spatially coherent oscillations in microwave bursts

Solar microwave burst observations (made with the WSRT) with high time and high spatial resolution show large-scale (> 8000 km) short-period (1.5 s) modulations of the source. It is argued that an interpretation in terms of Alfvén oscillations in the microwave source is ruled out by this observation. Instead it must be the source of the fast electrons, that produce the microwaves, that is oscillating. The fluctuating acceleration region is identified with a volume where a sheared field is compressed against a flux tube by an unstable current. MHD oscillations in the overlying fluxtube are caused by the pushing force. The rapidly expanding current plays a major role in the flare theory of van Tend and Kuperus (1978).     

A circuit model for filament eruptions and two-ribbon flares

We derive a circuit model for solar filament eruptions and two-ribbon flares which reproduces the slow energy build up and eruption of the filament, and the energy dissipation in a current sheet at the top of post-flare loops during the two-ribbon flare. In our model the free magnetic energy is concentrated in a current through the filament, another current through an underlying current sheet, and surface return currents. The magnetic field configuration, generated by these currents and a general photospheric background field, has a topology similar to the field topology derived from observations.We consider two circuits, that of the filament and its return current, and that of the current sheet and its return current. These circuits are inductively coupled and free energy stored in the filament in the pre-flare phase is found to be transferred to the sheet during the impulsive phase, and rapidly dissipated there. A comparable amount of magnetic energy is converted into kinetic energy of the ejected filament. The basic equations of the model are the momentum equations for the filament and the current sheet, and the induction equations for the filament and sheet circuits. The derivation of the equations is an extension of previous models by Kuperus and Raadu, Van Tend and Kuperus, Syrovatskii, and Kaastra. The set of equations is closed in the sense that only the initial conditions and a number of parameters, all related to pre-flare observables, are needed to calculate the evolution of the system. The pre-flare observations we need to determine these parameters, are: (1) a magnetogram, (2) an picture, (3) a measurement of the coronal density in the region, and (4) estimates of the photospheric velocity fields in the region.In the solutions for the evolution of the filament current sheet system we distinghuish 4 phases: (1) a slow energy build up, lasting for almost two days, during which the filament evolves quasi-statically, (2) a metastable state, lasting for about three hours, during which the filament is susceptible to flare triggers, and during which a current sheet emerges, (3) the eruptive phase, with strong acceleration of the filament, during which a large current is induced and dissipated in the current sheet, and energy is injected in the post-flare loops, and finally (4) a post-flare phase, in which the filament acceleration declines and the current sheet vanishes.From further numerical work we derive the following conclusions: (1) The magnetic flux input into the filament circuit has to surpass a certain threshold for an eruption to occur. Below that threshold we find solutions representing quiescent filaments. (2)Flare triggers are neither necessary nor sufficient for an eruption, but may set off the eruption during the metastable state. (3) The model reproduces the increase in shear in the filament prior to the eruption, through adecline of the filament current, in contrast to most models for filament eruptions. (4) The ratio of energy lost as kinetic energy of ejecta to the energy radiated away in the post-flare loops is sensitively dependent on the resistance of the current sheet. (5) Flare prediction is possible with this model, but the potential for triggering during the metastable state complicates the prediction of the exact moment of eruption.Former NAS/NRC Resident Research Associate.ST Systems Corporation.     

Coronal X-ray activity preceding solar flares

A comprehensive survey of Skylab S-054 soft X-ray images was performed to investigate the characteristics of coronal enhancements preceding solar flares. A search interval of 30 min before flare onset was used. A control sample was developed and tests of the statistical results performed. X-ray images with preflare enhancements were compared with high resolution H images and photospheric magnetograms.The results are as follows: preflare X-ray enhancements were found in a statistically significant number of the preflare intervals, and consisted of one to three loops, kernels or sinuous features per interval. Typically, the preflare feature was not at the flare site and did not reach flare brightness. There was no systematically observed time within the preflare interval for the preflare events to appear and no correlation of preflare event characteristics with the subsequent flare energy. Gas pressures of several preflare features were calculated to be on the order of several dyne cm^–2, typical of active region loops, not flares. These results suggest that observations with both high spatial resolution and low coronal temperature sensitivity are required to detect these small, low pressure enhancements that preceded the smaller flares typical of the Skylab epoch. H brightenings were associated with nearly all of the preflare X-ray enhancements. Changing H absorption features in the form of surges or filament activations were observed in about half of the cases. These results do not provide observational support for models which involve preheating of the flare loop, but they are consistent with some current sheet models which invoke the brightening of structures displaced from the flare site tens of min before onset.     

Towards the circuit theory of solar flares

It has been shown that the main problems of the circuit theory of solar flares - unlikely huge current growth time and the origin of the current interruption - have been resolved considering the case of magnetic loop emergence and the correct application of Ohm's law. The generalized Ohm's law for solar flares is obtained. The conditions for flare energy release are as follows: large current value, > 10¹¹ A, nonsteady-state character of the process, and the existence of a neutral component in a flare plasma. As an example, the coalescence of a flare loop and a filament is considered. It has been shown that the current dissipation has increased drastically as compared with that in a completely ionized plasma. The current dissipation provides effective Joule heating of the plasma and particle acceleration in a solar flare. The ion-atom collisions play the decisive role in the energy release process. As a result the flare loop resistance can grow by 8–10 orders of magnitude. For this we do not need the anomalous resistivity driven by small-scale plasma turbulence. The energy release emerging from the upper part of a flare loop stimulates powerful energy release from the chromospheric level.     

Simulation of the current sheet in a flare-active region and comparison to radio data

Numerical three-dimensional MHD simulations demonstrated that a current sheet (CS) was formed over active region AR 0365 before the flare of May 27, 2003, and the energy was accumulated in its magnetic field. Maps of the photospheric magnetic field in its preflare state were used in the simulations to define the boundary conditions instead of the usually applied approximation of the field in an active region by dipoles or magnetic charges. The CS was formed in the vicinity of a singular line as a result of focusing the magnetic field disturbances observed before the flare. The calculated CS position corresponded to the maximum brightness temperature of the flare detected by the Siberian Solar Radio Telescope SSRT (Institute of Solar-Terrestrial Physics, Russian Academy of Sciences, Siberian Branch, Irkutsk). This testifies that the flare could result from the dissipation of energy accumulated in the field of the CS, which arose over the active region.     

Pulsations of optical radiation during the flare of YZ CMi occurred on February 9, 2008

One of the most powerful and long-lived flares on the active red dwarf YZ CMi is considered. The flare was observed in the U band at the Terskol Peak Observatory on February 9, 2008. During the formation of the flare over the course of 30 seconds, the flare-induced stellar luminosity increased and became more than 180 times the preflare value. The total duration of the flare was approximately one hour. At the flare maximum, quasi-periodic pulsations having a specified period of approximately 11 s, an initial modulation depth of 5.5%, and an exponential damping time of 29 s were discovered using wavelet analysis. Assuming that the pulsations were caused by fast magnetohydrodynamic oscillations of a flare loop, the following parameters were determined in the region of energy release using coronal seismology methods: plasma concentration (2 × 10¹⁰ cm⁻³), temperature (3 × 10⁷ K), and magnetic field strength (0.015 T).     

Chromospheric downflow velocities as a diagnostic in solar flares

We explore the dynamics of chromospheric condensations driven by evaporation during the impulsive phase of solar flares. Specifically, we find that the maximum chromospheric downflow speed obeys the approximate relation υ_d= 0.4 (F/ϱ_ch)^1/3, where F is that part of the flare energy flux driving chromospheric evaporation, and ϱ_ch is the mass density in the preflare chromosphere just below the preflare transition region. This implies that chromospheric downflows as measured by Hα asymmetries may be a powerful probe of flare energetics.

     

A current ribbon model for energy storage and release with application to the flare of 7 January 1992

Observations of the flare on 7 January 1992 are interpreted using a topological model of the magnetic field. The model, developed here, applies a theory of three-dimensional reconnection to the inferred magnetic field configuration for 7 January. In the model field a new bipole ( 10²¹ Mx) emerges amidst pre-existing active region flux. This emergence gives rise to two current ribbons along the boundaries (separators) separating the distinct, new and old, flux systems. Sudden reconnection across these boundary curves transfers 3 ×10²⁰ Mx of flux from the bipole into the surrounding flux. The model also predicts the simultaneous (sympathetic) flaring of the two current ribbons. This explains the complex two-loop structure noted in previous observations of this flare. We subject the model predictions to comparisons with observations of the flare. The locations of current ribbons in the model correspond closely with those of observed soft X-ray loops. In addition the footpoints and apexes of the ribbons correspond with observed sources of microwave and hard X-ray emission. The magnitude of energy stored by the current ribbons compares favorably to the inferred energy content of accelerated electrons in the flare.     

Spatial relations between preflares and flares

We have conducted an initial search for discrete preflare brightenings as observed in soft X-radiation by Yohkoh. The Yohkoh images allow us to identify, to within a few arc seconds, the location of a preflare event relative to the succeeding flare. Our initial motivation in this study was to search for early coronal brightenings leading to flare effects, as had been suggested by earlier studies; thus we concentrated on Yohkoh limb events. We find no evidence for such early coronal brightenings. Between 15% and 41% of the 131 suitable events matched our criteria for preflare brightening: the same active region; brightening within one hour of the flare peak; preflare brightness less than 30% of the flare peak. In the great majority of the preflare cases, we found that physically separate nearby structures brightened initially. Often these structures appeared to share a common footpoint location with the flare brightening itself. In a few cases the preflare could have occurred in exactly the same structure as the flare.     

Plasma waves caused by transient heat conduction in a coronal loop and anomalous resistivity

Numerical simulation is made of the transient heat conduction during local heating in a model coronal magnetic loop with an axial electric current. It is assumed that a segment near the top of the normal coronal loop is heated to above 10⁷ K by a sufficiently small heat input as compared with the total flare energy. A hump appears in the velocity distribution of electrons moving down the temperature gradient with speeds slightly below the thermal one. Consequently, electron plasma waves are excited. The high intensity of the waves persists in the upper region of the loop for more than a second until the termination of the simulation. The energy density of the plasma waves normalized with respect to thermal density is 10^–3.5 at maximum. A theoretical estimate gives an anomalous resistivity 5 orders of magnitude greater than an initial value. Based on the above result, we propose a model for impulsive loop flares.     

The 4 February, 1986 flare and flare-filament current model

In this paper, the observational data in H, radio, soft X-ray, hard X-ray, and -ray emissions for the 3B/X3.0 solar flare on 4 February, 1986 are collected. This flare is studied in detail by using the flare-filament current model. The momentum equations and the energy equations of the filament current have been solved. The influence of the highly sheared background magnetic field on the motion of the filaments is studied through numerical calculation. The results show that the resistive tearing instability is a possible pre-heating mechanism in the preflare phase, and both the rotation of the spiral sunspots and the highly sheared background field are necessary for the energy storage of this flare. The high-energy data of the flare imply that the current-loop coalescence instability is a possible eruptive mechanism.     

Small-scale Langmuir wave instability in preflare chromosphere of solar active region

Necessary conditions have been investigated for the appearance of instability of high-frequency electron Langmuir waves in plasma of solar chromosphere near the foot-point of loop structure. We have considered the earliest stage of a flare process in solar active region. At the chromospheric part of current circuit of a flare loop such instability can appear and develop as the result of combined action of large-scale electric field, Landau damping and collisional processes in preflare plasma. We have investigated the process of instability development for two possible scenarios: (a) when preflare loop plasma has a classical Coulomb conductivity and (b) when anomalous resistance appears due to saturation of Bernstein turbulence. The growth rates of instability have been obtained and analyzed in detail. It has been assumed in the process of calculation that preflare plasma can be described by the FAL model of the solar atmosphere, which takes into account the process of helium diffusion. It has been shown that Langmuir wave instability can appear in its marginal form in the area under investigation either in the presence of Coulomb conductivity or in the presence of saturated Bernstein turbulence. Existence of instability with the growth rate, which changes its sign, proves the principal possibility of generation of nondamping Langmuir waves with small amplitudes.     

Coincidence between Hα flare kernels and peaks of observed longitudinal electric current densities

We compare large-scale filtergrams of a hitherto neglected class 1B flare with previously published vector magnetograms and maps of photospheric longitudinal electric current density (Hagyard et al., 1985). The vector magnetic fields were mapped simultaneously with the eruption of this flare. We find a coincidence, to within the ±2″ registration accuracy of the data, between the flare kernels and the locations of maximum shear and of peak values in the longitudinal electric current density. The kernels brighten in a way which implies that the preflare heating and the main release of flare energy are spatially coincident within the limits of resolution (≈2″). A pronounced magnetic shear exists in the vertical direction at the location of the strongest flare kernels. We provide evidence that the electric currents could be maintained by the energy stored in the sheared transverse magnetic field and that the amount of energy released is proportional to the amount stored. These circumstances are consistent with theories in which flares are triggered by plasma instabilities due to surplus electric currents.     

On the Origin of Pulsations of Sub-THz Emission from Solar Flares

We propose a model to explain fast pulsations in sub-THz emission from solar flares. The model is based on the approach of a flaring loop as an equivalent electric circuit and explains the pulse-repetition rate, the high-quality factor, Q≥10³, low modulation depth, pulse synchronism at different frequencies, and the dependence of the pulse-repetition rate on the emission flux, observed by Kaufmann et al. (Astrophys. J. 697, 420, 2009). We solved the nonlinear equation for electric current oscillations using a Van der Pol method and found the steady-state value for the amplitude of the current oscillations. Using the pulse rate variation during the flare on 4 November 2003, we found a decrease of the electric current from 1.7×10¹² A in the flare maximum to 4×10¹⁰ A just after the burst. Our model is consistent with the plasma mechanism of sub-THz emission suggested recently by Zaitsev, Stepanov, and Melnikov (Astron. Lett. 39, 650, 2013).     

On the Cascading Acceleration of the Quasi-Thermal Electrons by mhd Turbulence in Solar Flares

A model of the cascading acceleration of quasi-thermal electrons by MHD turbulence in solar flares is considered. Analysis shows that fast magnetoacoustic wave modes with large wavenumbers (>3×10^–8 cm^–1) strongly damp due to ion viscosity for both preflare and flare conditions. The viscous damping of fast magnetoacoustic wave modes is 10–100 times more efficient than Fermi or transit-time electron acceleration.     

Current sheet models of solar flares

Current sheets have been suggested as the site for flare energy release because they can convert magnetic energy very rapidly into both heat and directed plasma energy. Also they contain electric fields with the potential of accelerating particles to high energies.The basic properties of current sheets are first reviewed. For instance, magnetic flux may be carried into a current sheet and annihilated. An exact solution for such a process in an infinitely long sheet has been found; it describes the annihilation of fields which are inclined at any angle, not just 180°. Moreover, field lines which are expelled from the ends of a current sheet can be described as having been reconnected. The only workable model for fast reconnection in the solar atmosphere, namely Petschek's mechanism, has recently been put on a firm foundation; it gives a reconnection rate which depends on the electrical conductivity but is typically a tenth or a hundredth of the Alfvén speed. A current sheet may be formed when the sources of an initially potential field start to move; a simple analytic technique for finding the position and shape of such a sheet in two dimensions now exists. Finally, a sheet with no transverse magnetic field component is subject to the tearing-mode instability, which rapidly produces a series of loops in the field.The main ways in which current sheets have been used for solar flare models is described. Syrovatskii's mechanism relies on the increase of the electric current density during the formation of a sheet, to a value in excess of the critical value j ^* for the onset of microinstabilities. But Anzer has recently demonstrated that the critical value is most unlikely to be reached during the initial formation process. Sturrock, on the other hand, has advocated the occurrence of the tearing-mode instability in an open streamer-like configuration (which may result from the eruption of a force-free field). But recent observations do not point to that as the relevant configuration. Rather, they suggest that flares are triggered by the emergence of new magnetic flux from below the solar photosphere. This has led Heyvaerts, Priest, and Rust (1976) to propose a new emerging flux model, according to which, as more and more flux emerges, so reconnection occurs, producing some preflare heating. When the current sheet reaches such a height (around the transition region) that its current density exceeds j ^*, then the impulsive phase of the flare is triggered. The main phase is caused by an enhanced level of magnetic energy conversion in a turbulent current sheet. The type of flare depends on the magnetic environment in which the emerging flux finds itself. A surge flare results if the flux appears near a strong unipolar region such as a simple sunspot, whereas a two ribbon flare may be produced by flux emergence near an active region filament, in which case the main phase energy is released from the field that surrounds the filament.     

Chromospheric downflow velocities as a diagnostic in solar flares

We explore the dynamics of chromospheric condensations driven by evaporation during the impulsive phase of solar flares. Specifically, we find that the maximum chromospheric downflow speed obeys the approximate relation _d = 0.4 (F/ _ch )^1/3, where F is that part of the flare energy flux driving chromospheric evaporation, and _ch is the mass density in the preflare chromosphere just below the preflare transition region. This implies that chromospheric downflows as measured by H asymmetries may be a powerful probe of flare energetics.