Solar Flare Phenomena as Phase Transition Caused by Frustration of Current Percolation

We present analysis of flare process as "phase transition" phenomena caused by frustration of current percolation in turbulent current sheet. We show that numerous plasma instabilities in the sheet will form random resistors network with "bad resistors"-turbulent domains and "good resistors"-normal plasma domains. We show that current percolation in random inhomogeneous turbulent current sheet like to another percolated systems is able to produce phase transition with drastic change of global properties of system as whole (conductivity, heat-conductivity, elasticity,) on the threshold value of critical density of "bad" elements (p= p _c ). Another property of solar flares, what may be understood on the base of percolation approach is observed universal power dependence of frequency of flares and microflares (elementary events-spikes) on their amplitude: N _W ∝ W ^−k . It may be explained as natural sequence of universal power dependence of clusters' masses in percolated systems on their sizes. The slope of resulted spectra is determined by the fractal dimension of clusters and depends on feedback between current propagation and turbulence generation. We show that percolation approach allow to explain phenomena of preflare bursts-precursors observed in radio and hard X-ray. It may be understood as results of pre-catastrophic lose of elasticity of system to small disturbance on the percolation threshold, with formation of short life nuclear of "new phase". This revised version was published online in July 2006 with corrections to the Cover Date.     

Energies of Electrons Accelerated in Turbulent Reconnecting Current Sheets in Solar Flares

Yohkoh observations strongly suggest that electron acceleration in solar flares occurs in magnetic reconnection regions in the corona above the soft X-ray flare loops. Unfortunately, models for particle acceleration in reconnecting current sheets predict electron energy gains in terms of the reconnection electric field and the thickness of the sheet, both of which are extremely difficult to measure. It can be shown, however, that application of Ohm's law in a turbulent current sheet, combined with energy and Maxwell's equations, leads to a formula for the electron energy gain in terms of the flare power output, the magnetic field strength, the plasma density and temperature in the sheet, and its area. Typical flare parameters correspond to electron energies between a few tens of keV and a few MeV. The calculation supports the viewpoint that electrons that generate the continuum gamma-ray and hard X-ray emissions in impulsive solar flares are accelerated in a large-scale turbulent current sheet above the soft X-ray flare loops.     

太阳爆发过程中的大尺度磁重联电流片:理论和观测

从理论和观测两个方面来介绍和讨论出现在太阳爆发过程中的磁重联电流片及其物理本质和动力学特征。首先介绍在理论研究和理论模型中,磁重联电流片是如何在爆发磁结构当中形成并发展的,对观测研究有什么指导意义。然后介绍观测工作是从哪几个方面对理论模型预测的电流片进行证认和研究的。第三,将介绍观测研究给出了哪些过去所没有能够预期的结果,这些结果对深入研究耀斑一CME电流片以及其中的磁重联过程的理论工作有什么重要的、挑战性的意义。第四,讨论最新的与此有关的理论研究和数值实验。最后,对未来的研究方向和重要课题进行综述和展望。     

Magnetic reconnection in a high-temperature plasma of solar flares

A simple self-consistent model of a high-temperature turbulent current sheet (HTCS) is considered. The anomalous character of plasma conductivity in a sheet is assumed to be due to gradient instabilities. The possibility of a low threshold of their excitation is demonstrated by an example of temperature-drift instability.Application of the HTCS model to the hot or main phase of a solar flare is discussed. The model consistently explains many observed properties of this phase.     

A device for precise orientation of solar images

The reconnecting current sheet model for energy accumulation and release during solar flares results in the flare frequency distribution that is a power-law function of total flare energy, with the index 7/4 for sufficiently large energies. The distribution is predicted to be much steeper in the low-energy region, implying the significance of microand nanoflares for coronal heating.     

Acceleration of Electrons and Protons in Reconnecting Current Sheets Including Single or Multiple X-points

Kinematic characteristics of electrons and protons in the magnetic reconnecting current sheet in the presence of a guide field are investigated. Particle trajectories are calculated for different values of the guide field by a test-particle calculation. The relationship between the final energy and the initial position has also been studied. We found that the addition of a guide field not only allows particles to get more energy and not only results in the separation of electrons and protons, but also causes the reconnecting electric field to selectively accelerate electrons and protons for different initial positions. The energy spectrum eventually obtained is the common power-law spectrum, and as the guide field increases, the index for the spectrum of electrons decreases rapidly. However, for a weak background magnetic field, proton spectra are not very sensitive to the guide field; but for a strong background field, the dependence of the spectrum index is similar to the electron spectrum. Meanwhile, kinematic characteristics of the accelerated particles in the current sheet including multiple X-points and O-points were also investigated. The result indicates that the existence of the multiple X- and O-points helps particles trapped in the accelerating region to gain more energy, and yields the double or multiple power-law feature.     

Spontaneous magnetic reconnection

The present review concerns the relevance of collisionless reconnection in the astrophysical context. Emphasis is put on recent developments in theory obtained from collisionless numerical simulations in two and three dimensions. It is stressed that magnetic reconnection is a universal process of particular importance under collisionless conditions, when both collisional and anomalous dissipation are irrelevant. While collisional (resistive) reconnection is a slow, diffusive process, collisionless reconnection is spontaneous. On any astrophysical time scale, it is explosive. It sets on when electric current widths become comparable to the leptonic inertial length in the so-called lepton (electron/positron) “diffusion region”, where leptons de-magnetise. Here, the magnetic field contacts its oppositely directed partner and annihilates. Spontaneous reconnection breaks the original magnetic symmetry, violently releases the stored free energy of the electric current, and causes plasma heating and particle acceleration. Ultimately, the released energy is provided by mechanical motion of either the two colliding magnetised plasmas that generate the current sheet or the internal turbulence cascading down to lepton-scale current filaments. Spontaneous reconnection in such extended current sheets that separate two colliding plasmas results in the generation of many reconnection sites (tearing modes) distributed over the current surface, each consisting of lepton exhausts and jets which are separated by plasmoids. Volume-filling factors of reconnection sites are estimated to be as large as \({<}10^{-5}\) per current sheet. Lepton currents inside exhausts may be strong enough to excite Buneman and, for large thermal pressure anisotropy, also Weibel instabilities. They bifurcate and break off into many small-scale current filaments and magnetic flux ropes exhibiting turbulent magnetic power spectra of very flat power-law shape \(W_b\propto k^{-\alpha }\) in wavenumber k with power becoming as low as \(\alpha \approx 2\). Spontaneous reconnection generates small-scale turbulence. Imposed external turbulence tends to temporarily increase the reconnection rate. Reconnecting ultra-relativistic current sheets decay into large numbers of magnetic flux ropes composed of chains of plasmoids and lepton exhausts. They form highly structured current surfaces, “current carpets”. By including synchrotron radiation losses, one favours tearing-mode reconnection over the drift-kink deformation of the current sheet. Lepton acceleration occurs in the reconnection-electric field in multiple encounters with the exhausts and plasmoids. This is a Fermi-like process. It results in power-law tails on the lepton energy distribution. This effect becomes pronounced in ultra-relativistic reconnection where it yields extremely hard lepton power-law energy spectra approaching \(F(\gamma )\propto \gamma ^{-1}\), with \(\gamma \) the lepton energy. The synchrotron radiation limit becomes substantially exceeded. Relativistic reconnection is a probable generator of current and magnetic turbulence, and a mechanism that produces high-energy radiation. It is also identified as the ultimate dissipation mechanism of the mechanical energy in collisionless magnetohydrodynamic turbulent cascades via lepton-inertial-scale turbulent current filaments. In this case, the volume-filling factor is large. Magnetic turbulence causes strong plasma heating of the entire turbulent volume and violent acceleration via spontaneous lepton-scale reconnection. This may lead to high-energy particle populations filling the whole volume. In this case, it causes non-thermal radiation spectra that span the entire interval from radio waves to gamma rays.     

The Flare-Energy Distributions Generated by Kink-Unstable Ensembles of Zero-Net-Current Coronal Loops

It has been proposed that the million-degree temperature of the corona is due to the combined effect of barely detectable energy releases, called nanoflares, that occur throughout the solar atmosphere. Unfortunately, the nanoflare density and brightness implied by this hypothesis means that conclusive verification is beyond present observational abilities. Nevertheless, we investigate the plausibility of the nanoflare hypothesis by constructing a magnetohydrodynamic (MHD) model that can derive the energy of a nanoflare from the nature of an ideal kink instability. The set of energy-releasing instabilities is captured by an instability threshold for linear kink modes. Each point on the threshold is associated with a unique energy release; thus we can predict a distribution of nanoflare energies. When the linear instability threshold is crossed, the instability enters a nonlinear phase as it is driven by current sheet reconnection. As the ensuing flare erupts and declines, the field transitions to a lower energy state, which is modelled by relaxation theory; i.e., helicity is conserved and the ratio of current to field becomes invariant within the loop. We apply the model so that all the loops within an ensemble achieve instability followed by energy-releasing relaxation. The result is a nanoflare energy distribution. Furthermore, we produce different distributions by varying the loop aspect ratio, the nature of the path to instability taken by each loop and also the level of radial expansion that may accompany loop relaxation. The heating rate obtained is just sufficient for coronal heating. In addition, we also show that kink instability cannot be associated with a critical magnetic twist value for every point along the instability threshold.     

The temperature structure of chromospheric flares heated by non-thermal electrons

Heating of the deep chromosphere by a vertically descending beam of non-thermal electrons with power-law energy spectrum, in flares, is analysed. In lower regions of the flare, radiative losses can balance the energy input and the flare structure is described in terms of instantaneous quasi-steady temperature/depth profiles. Motion of the optical flare material is at constant pressure and is constrained to be purely vertical by a vertical magnetic field. The ionisation of hydrogen is determined by the same non-LTE processes as in the quiet chromosphere. Temperature profiles are obtained for a wide range of electron beam intensities and spectral indices and are discussed in terms of optical flare observations. Due to the steepness of the electron spectra, typical densities in the optical flare vary only over a narrow range, despite the diversity of beam intensities, in agreement with observation.Above a certain region, the flare material cannot attain a radiatively steady state against the electron input but evaluation of the level at which this occurs leads to an estimate of the mass of material involved in the high temperature flare plasma in this model. Results, which are again insensitive to the electron beam parameters, are found to be in satisfactory agreement with observations of the mass of flare ejecta and of soft X-ray flare emission measures.     

Possible spectral diagnostics for turbulent electric fields in solar flares

A high level of electrostatic turbulence can be generated by plasma instabilities in solar flares. The turbulence, in general, has both quasistatic (ionic) and dynamic (electronic) components. Hydrogenic line profiles develop distinct features under the simultaneous effect of the quasistatic and dynamic turbulent electric fields: these features are discussed and the possible inferences that can be drawn as to the nature of the turbulent electric fields through their observation are pointed out. Solar flare spectral diagnostics along these lines can provide an observational test of the existence of turbulent electric fields in the flare region. When a detailed determination of the characteristics of these fields is feasible, it would, in turn, help in identifying the underlying plasma instability mechanisms that give rise to these fields during the flare build-up and associated processes.     

The State of Self-organized Criticality of the Sun during the Last Three Solar Cycles. II. Theoretical Model

The observed power-law distributions of solar-flare parameters can be interpreted in terms of a nonlinear dissipative system in a state of self-organized criticality (SOC). We present a universal analytical model of an SOC process that is governed by three conditions: i) a multiplicative or exponential growth phase, ii) a randomly interrupted termination of the growth phase, and iii) a linear decay phase. This basic concept approximately reproduces the observed frequency distributions. We generalize it to a randomized exponential growth model, which also includes a (log-normal) distribution of threshold energies before the instability starts, as well as randomized decay times, which can reproduce both the observed occurrence-frequency distributions and the scatter of correlated parameters more realistically. With this analytical model we can efficiently perform Monte-Carlo simulations of frequency distributions and parameter correlations of SOC processes, which are simpler and faster than the iterative simulations of cellular automaton models. Solar-cycle modulations of the power-law slopes of flare-frequency distributions can be used to diagnose the thresholds and growth rates of magnetic instabilities responsible for solar flares.     

Catastrophic Behavior of Multiple Coronal Flux Rope System

A major solar active event called Bastille Day Event occurred in AR 9077 on July 14, 2000. Simultaneous occurrence of a filament eruption, a flare and a coronal mass ejection was observed in this event. Previous analyses of this event show that before the event, there existed an activation and eruption of a huge trans-equatorial filament, which might play a crucial role in triggering the Bastille Day event. This implies that independent flux systems are closely related to and affect each other, which has encouraged us to investigate the catastrophic behavior of a multiple coronal flux rope system with the use of a 2.5-D time-dependent MHD model. A force-free field that contains three separate coronal flux ropes is taken to be the initial state. Starting from this state, we increase either the annular or the axial flux of a certain flux rope to examine the catastrophic behavior of the system in two regimes, the ideal MHD regime and the resistive MHD regime. It is found that a catastrophe occurs if the flux exceeds a certain critical value, or the magnetic energy of the system exceeds a certain threshold: the rope of interest breaks away from the base and escapes to infinity, leaving a current sheet below. Moreover, the destiny of the remainder flux ropes relies on whether reconnection takes place across the current sheet. In the ideal MHD regime, i.e., in the absence of reconnection, these ropes remain to be attached to the base in equilibrium, whereas in the resistive MHD regime they abruptly erupt upward during reconnection and escape to infinity. Reconnection causes the field lines to close back to the base and thus changes the background field outside the attached flux ropes in such a way that the constraint on these ropes is substantially relaxed and the corresponding catastrophic energy threshold is reduced accordingly, leading to a catastrophic eruption of these ropes. Since magnetic reconnection is generally inevitable when a current sheet forms and develops through an eruption of one flux rope, the eruption of this flux rope must lead to an eruption of the others. This provides an example to demonstrate the interaction between several independent magnetic flux systems in different regions, as implied by the Bastille Day event, and may serve as a possible mechanism for sympathetic events occurring on the Sun.     

Frequency dependence of solar flare occurrence rates—inferred from power-law distribution

Based on the frequency dependence of the power-law distribution of the peak fluxes in 486 radio bursts in 1–35 GHz observed by Nobeyama Radio Polarimeters (see Song et al. in Astrophys. J. 750:160, 2012), we have first suggested in this paper that the events with power-law behaviors may be emitted from the optically-thin regions, which can be considered as a good measure for the flare energy release. This result is supported by that both the power-law and optical-thin events gradually increase with radio frequencies, which are well fitted by a power-law function with similar indices of 0.48 and 0.80, respectively. Moreover, a flare occurrence rate is newly defined by the power-law event number in per unit frequency. Its values in lower frequencies are evidently larger than those in higher frequencies, which just imply that most flares are trigged in higher corona. Hence, the frequency variation of power-law event number may indicate different energy dissipation rates on different coronal heights.     

A solar flare model including the formation and destruction of the current sheet in the corona

A numerical simulation method is used to show the possibility of forming a current sheet in the solar corona in an active region with four magnetic poles. The evolution of the quasi-stationary current sheet can lead to its transfer to an unsteady state. The MHD instability of this sheet causes its decay, accompanied by a set of events which characterizes the solar flare. The electrodynamical model of a solar flare includes a system of field-aligned currents typical of a magnetospheric substorm. Several events in substorms and solar flares are explained by the generation of field-aligned currents.     

Turbulence In The Solar Atmosphere: Manifestations And Diagnostics Via Solar Image Processing

Intermittent magnetohydrodynamical turbulence is most likely at work in the magnetized solar atmosphere. As a result, an array of scaling and multi-scaling image-processing techniques can be used to measure the expected self-organization of solar magnetic fields. While these techniques advance our understanding of the physical system at work, it is unclear whether they can be used to predict solar eruptions, thus obtaining a practical significance for space weather. We address part of this problem by focusing on solar active regions and by investigating the usefulness of scaling and multi-scaling image-processing techniques in solar flare prediction. Since solar flares exhibit spatial and temporal intermittency, we suggest that they are the products of instabilities subject to a critical threshold in a turbulent magnetic configuration. The identification of this threshold in scaling and multi-scaling spectra would then contribute meaningfully to the prediction of solar flares. We find that the fractal dimension of solar magnetic fields and their multi-fractal spectrum of generalized correlation dimensions do not have significant predictive ability. The respective multi-fractal structure functions and their inertial-range scaling exponents, however, probably provide some statistical distinguishing features between flaring and non-flaring active regions. More importantly, the temporal evolution of the above scaling exponents in flaring active regions probably shows a distinct behavior starting a few hours prior to a flare and therefore this temporal behavior may be practically useful in flare prediction. The results of this study need to be validated by more comprehensive works over a large number of solar active regions. Sufficient statistics may also establish critical thresholds in the values of the multi-fractal structure functions and/or their scaling exponents above which a flare may be predicted with a high level of confidence. Based on the author's contributed talk “Manifestations and Diagnostics of Turbulence in the Solar Atmosphere”, presented at the Solar Image Processing Workshop II, Annapolis, Maryland, USA, 3–5 November 2004.     

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.     

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.     

RHESSI耀斑中非热电子低能截止的研究

太阳耀斑中硬X射线(HXR)光子谱的低能变平过去一般认为是由于耀斑中非热电子的低能截止造成的,但现在也有作者认为耀斑光子与下层大气的逆康普顿散射(albedo效应)或者其他作用也能够使得HXR光子谱出现低能变平的情形.采用Gan etal.(2001,2002)中提出的求非热电子低能截止的方法,统计分析了Ramaty High EnergySolar Spectroscopy Imager(RHESSI)卫星在2002--2005年间观测的100个耀斑,发现经albedo校正,有18个耀斑的HXR光子谱可以利用单幂律谱来拟合,在80个可以用双幂律谱来拟合HXR光子谱的耀斑中,有21个耀斑可以直接用单幂律电子谱加一个低能截止来解释.低能截止范围为20-50keV,平均值约为30keV.同时也分析了耀斑光子谱特征的其他可能解释.     

On the possibility of the development of longitudinal wave instabilities on the background of the small-scale Bernstein turbulence in preflare chromosphere of a solar active region

The process of origination and development of instabilities of the longitudinal waves of two types, namely, low-frequency ion-acoustic and high-frequency (“electronic”) Langmuir waves, in the preflare atmosphere of an active solar region are studied. The area under study is located at the chromospheric part of the flare loop near its footpoint. A weak large-scale electric field of flaring loop is the main source of these instabilities. The velocity of an electronic flow in the preflare plasma is supposed to be much lower than thermal electron velocity. Instability development is considered against the background of small-scale Bernstein wave turbulence, which exists in the preflare plasma and has an extremely low threshold of excitation. The necessary conditions for the instability origination and development, as well as the boundary values of the main plasma and wave perturbation parameters, are calculated.     

An unstable arch model of a solar flare

The theoretical consequences of assuming that a current flows along flaring arches consistent with a twist in the field lines of these arches are examined. It is found that a sequence of magneto-hydrodynamic (MHD) and resistive MHD instabilities driven by the assumed current (which we refer to as the toroidal current) can naturally explain most manifestations of a solar flare.The principal flare instability in the proposed model is the resistive kink (or tearing mode in arch geometry) which plays the role of thermalizing some of the field energy in the arch and generating X-configured neutral points needed for particle acceleration. The difference between thermal and nonthermal flares is elucidated and explained, in part, by amplitude-dependent instabilities, generally referred to as overlapping resonances. We show that the criteria for the generation of flare shocks strongly depend on the magnitude and gradient steepness of the toroidal current, which also are found to determine the volume and rate of energy release. The resulting model is in excellent agreement with present observations and has successfully predicted several flare phenomena.