Loop models of solar flares: Revisions and comparisons

Due to developments in solar flare observations which appear to show that a particular class of solar flares result from instabilities occurring in magnetic loops we re-examine the Alfvén-Carlqvist flare model to show that it is workable and we update the Spicer loop model of a flare. It is noted that the Alfvén-Carlqvist model of necessity requires an external current driver which must maintain the current driven instability at marginal stability during the duration of the flare. In addition, it is argued that if the Alfvén-Carlqvist model is to work the current density must rise in a time shorter than an MHD or resistive tearing mode time scale. Otherwise, the dominant flare mechanism must be an ideal MHD or tearing type instability. Further, the distinctions between the two models are highlighted and a new hybrid model of the Alfvén-Carlqvist and Spicer models is introduced.     

Magnetic reconnection model for X-ray flare loop interaction

The subtle interactions between the magnetohydrodynamics (MHD) and transverse plasmons are investigated. It is shown that there is a resistive instability by the plasmon's soliton in a current sheet, which eventually turns into an eruptive instability at the magnetic field reconnection. In the case of ion-acoustic turbulence, the high temperature current sheet model must adopt the aromalous conductivity instead of the Coulomb conductivity. The numerical results are consistent with the observations obtained by Hanaoka (1994). Thus the flare caused by X-ray loop coalescence can be basically interpreted by this model of magnetic field reconnection driven by ponderomotive force.     

Soliton and strong Langmuir turbulence in solar flare processes

The occurrence of modulational instability in the current sheet is investigated. Particular attention is drawn to the plasma micro-instability in this current sheet (i.e., the diffusion region) and its relation to the flare process. It is found that the solitons or strong Langmuir turbulence is likely to occur in the diffusion region under solar flare conditions in which the electric resistivity could be greatly enhanced by several orders of magnitude in this diffusion region. The result is a significant heating and stochastic acceleration of particles. Physically, the occurrence of soliton and strong Langmuir turbulence can be identified with a sudden eruption of an electric current leading to a local vacuum in which an electric potential is formed and results in the release of a huge amount of free energy. A numerical example is used to demonstrate the transition of the magnetic field, velocity, and plasma density from the outer MHD region into the diffusive (resistive) region and, then, back out again with the completion of the energy conversion process. This is all made possible by an increase of resistivity by 4–5 orders of magnitude over the classical value.     

Unsteady State of the Turbulent Current Sheet of a Flare

The stability of the turbulent current sheet of a flare is analyzed. It is argued that the equilibrium state of the current sheet is extremely unstable relative to certain processes: dissipative tearing instabilities, MHD instabilities of line pinches, overheating of the turbulent plasma, and the threshold dependence of conductivity on the current value. The final state of a flare current sheet must be an extremely inhomogeneous layer containing numerous clusters of bad, turbulent, low-conductivity domains and good, normal ones. The propagation of current in this medium is a percolation process with certain fundamental properties: a threshold regime for current dissipation, which explains the threshold character of the flare phenomenon itself, a universal power-law spectrum of the statistical dependence on flare parameters, and a universal power-law energetic spectrum for the accelerated high-energy particles.     

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.     

Current‐driven instabilities in weakly ionized disks

Cool weakly ionized gaseous rotating disk form the basis for many models in astrophysics objects. Instabilities against perturbations in such disks play an important role in the theory of the formation of stars and planets. Traditionally, axisymmetric magnetohydrodynamic (MHD) and recently Hall‐MHD instabilities have been thoroughly studied as providers of an efficient mechanism for radial transfer of angular momentum, and of density radial stratification. In the current work, the Hall instability against axisymmetric perturbations in incompressible rotating fluid in external poloidal and toroidal magnetic field is considered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A magnetic bald-patch flare in solar active region 11117

With SDO observations and a data-constrained magnetohydrodynamics(MHD)model,we identify a confined multi-ribbon flare that occurred on 2010 October 25 in solar active region 11117 as a magnetic bald patch(BP)flare with strong evidence.From the photospheric magnetic field observed by SDO/HMI,we find there are indeed magnetic BPs on the polarity inversion lines(PILs)which match parts of the flare ribbons.From the 3D coronal magnetic field derived from an MHD relaxation model constrained by the vector magnetograms,we find strikingly good agreement of the BP separatrix surface(BPSS)footpoints with the flare ribbons,and the BPSS itself with the hot flaring loop system.Moreover,the triggering of the BP flare can be attributed to a small flux emergence under the lobe of the BPSS,and the relevant change of coronal magnetic field through the flare is reproduced well by the pre-flare and post-flare MHD solutions,which match the corresponding pre-and post-flare AIA observations,respectively.Our work contributes to the study of non-typical flares that constitute the majority of solar flares but which cannot be explained by the standard flare model.     

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.     

Slow-shock heating in post-flare arches

The heating of a coronal arch, following the occurrence of a dynamic (two-ribbon) flare, is discussed. We investigate whether slow-shock heating, occurring during the reconnection process in the dynamic flare and responsible for the heating of the post-flare loops, is also a workable proposition for the heating of a coronal arch. Contrary to the flare loops, the shock structure in the arch is generally not modified greatly by thermal conduction effects. As a result slow-shock heating may be investigated in terms of the familiar MHD shock jump relations. The observed enhanced arch density with respect to the surrounding corona is explained as a direct consequence of the reconnection process. For a combination of high arch temperatures and low values of coronal magnetic field and density thermal conduction may become important and will lead to an extra density enhancement in the arch. Our interpretation of the arch of 21–22 May, 1980 suggests that the formation of the arch took approximately one hour, and that observed temperature, density and maximum energy content can be consistently explained by the slow-shock heating mechanism.Currently: Center for Astrophysics and Space Sciences, C-011, University of California at San Diego, La Jolla, CA 92093, U.S.A.     

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.     

Current sheet creation by a super-Alfvénic jet in a bipolar field

Energy accumulation in a current sheet (CS) can occur during the injection of a fast plasma jet in a perpendicular magnetic field. A similar situation can occur in the solar corona when a flux of plasma appears under a magnetic arch. The flare can be produced at the CS disruption. The CS creation during plasma jet interaction with the magnetic field is demonstrated by numerical MHD simulation. The choice of dimensionless parameters Re, Re_m,, II, which are suitable for simulation of coronal phenomena, is discussed. When jet injection ceases, the CS evolution produces an unstable state and fast magnetic energy dissipation is observed.     

On line tying

We discuss the claim frequently found in the solar physics literature that line tying in the photosphere is capable of stabilizing certain classes of both ideal and resistive MHD instabilities. Our approach is to present a picture of the physical origins of line tying and how resistive effects will affect it.     

1986年2月4日耀斑与电流环合并不稳定性

本文收集了１９８６年２月４日大耀斑的Ｈα、微波、Ｘ射线和γ射线全波段的观测资料。利用暗条电流环模型分析了该耀斑的物理过程，测量了活动暗条的上升运动，求解了动量方程和能量方程。结果表明：（１）１９８６年２月４日的３Ｂ／Ｘ３耀斑可能是由暗条电流环之间的合并不稳定性所致；（２）电阻撕裂摸不稳定性是一种有效的耀斑前预热机制；（３）耀斑的高能观测资料进一步表明了电流环合并不稳定性是引起该大耀斑期间所有高能粒     

Exact MHD solutions for rotating,magnetic stars

Simple exact solutions of the magnetohydrodynamic equations are found for rotating, magnetic stars. The velocity and magnetic field are axisymmetric and purely toroidal, and the magnetic energy density equals the kinetic energy density. For constant mass density, the solution reduces to that of Chandrasekhar (1956), which is stable even against non-axisymmetric perturbations. For an ideal gas equation of state, the condition for radiative thermal equilibrium is solved to lowest order in the non-spherical perturbation. The velocity, magnetic field and non-spherical pressure and temperature perturbations all vanish within cones centered around the rotation axis, |cos |>x _i a zero of a Legendre polynomial. Low-order, long-period stellar oscillations may be excited by MHD instabilities near the equatorial region which become damped near the axis.     

The footpoints of giant arches

We have detected chromospheric footpoints of the giant post-flare coronal arches discovered by HXIS a few years ago. H photographs obtained at Big Bear and Udaipur Solar Observatories show chromospheric signatures associated with 5 sequential giant arch events observed in the interval from 6 to 10 November, 1980. The set of footpoints at one end of the arches consists of enhancements within a plage at the northeast periphery of the active region and the set of footpoints at the other end of the arch consists of brightenings of the chromosphere south of the active region. Both sets of footpoints show very slow brightness variations correlated in time with the brightness variations of the X-ray arches. Current-free modelling of the coronal magnetic field by Kopp and Poletto (1989), based on a Kitt Peak magnetogram, confirms the identification of the two sets of footpoints by showing magnetic field lines connecting them.The brightenings appear as a succession of point-like enhancements whose individual lifetimes are of the time-scale of minutes but which continue to occur for periods of several hours. This behaviour allows us to infer a fine structure in the coronal arches, undetectable in the X-ray images. The discovery of these brightenings and their location at the periphery of the active region also alters our conception of the relationship of the giant arches to the flares that begin concurrently with them. The giant arch phenomenon appears now to be either: (1) a long-lived, semi-permanent, coronal structure which is revived and fed with plasma and energy by underlying dynamic flares, or alternatively (2) a system of high-altitude loops which open at the onset of every such flare and subsequently reconnect over intervals of many hours.     

Large-scale active coronal phenomena in Yohkoh SXT images

We discuss Yohkoh SXT observations of stationary giant post-flare arches which occurred on 3–6 May, 1992 and study in detail the last arch, associated with the flare at 19:02 UT on 5 May, which extended above the west limb. The arch was similar to the first giant arch discovered on board the SMM, on 21–22 May, 1980. We demonstrate that the long lifetimes of these structures necessarily imply additional energy input from the underlying active region: otherwise, conduction would cool these arches in less than one hour and even with the unlikely assumption of conduction inhibited, pure radiative cooling would not produce the temperature decrease observed. All arch tops, although varying in brightness, stayed for several days at a fairly constant altitude of 100 000 km, and the arch studied, on 5–6 May, was just a new brightening of the pre-existing decaying structure. The brightening was apparently due to inflow of hot plasma from the flare region. Yohkoh data confirm that these stationary arches are rare phenomena when compared with the rising arches studied in Paper I and with Uchida et al.'s expanding active regions.     

Magnetic equilibria and instabilities

Solar flares are understood as a process of explosive liberation of magnetic energy, coming after a slow phase of energy build-up. The slow evolution of magnetic equilibria may end up with (a) the termination of an equilibrium sequence, or (b) an instability. The distinction between the two can be made by drawing schematic potential curves. Case (a) has been extensively studied in two-dimensional models. The appearance of multiple solutions, or disappearance of a solution takes place as the system evolves away from the current-free configuration. Case (b) can be discussed in terms of ideal MHD or resistive MHD instabilities. A possible route to explosive energy release is suggested by combining these two cases.     

The generation of MHD shock waves during the impulsive phase of the February 27, 1992 flare

In this paper a unique 2.3–4.2 GHz radio spectrum of the flare impulsive phase, showing fast positively drifting bursts superimposed on a slowly negatively drifting burst, is presented. Analyzing this radio spectrum it was found that the flare started somewhere near the transition region, where upward propagating MHD waves were generated during the whole impulsive phase. Moreover, it was found that behind a front of these ascending MHD waves the downward propagating electron beams, which bombarded dense layers of the solar atmosphere, were accelerated. It seems that, simultaneously with the increase of beam bombardment intensity, the intensity of MHD waves was increasing and thus the MHD shock wave generation and the electron beam acceleration and bombardment formed a self-consistently amplifying flare process. At higher coronal heights this process was followed by a type II radio burst, i.e. by the MHD flare shock. To verify this concept, the numerical modeling of the shock-wave generation and propagation in space from a flare site near the transition region up to 3 solar radii was made. Comparing the thermal and magnetic field disturbances, it was found that those of magnetic origin are more relevant in this case. Combining the results of interpretation and numerical simulation, a model of the February 27, 1992 flare is suggested and new aspects of this model are discussed.     

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.     

Interaction between sheared flow and resistive tearing mode

We investigate the nonlinear evolution of resistive tearing mode in a current sheet with a sheared flow in a long, thin cylinder. The results show that a hyperbolic secant (sech) flow field will lead to instability of the resistive tearing mode, formation of magnetic islands and rapid release of magnetic energy. The coupling between sheared flow and the tearing mode and interaction between suprathermal instabilities change the degree of shear in the magnetic field (the electric current gradient) and drive the development of the instability. This process may be one of the mechanisms of solar flares.