Theory Of Solar Flares Research Articles

A magnetohydrodynamic model for multiwavelength flares from Sagittarius A⋆ (I): model and the near-infrared and X-ray flares

Flares from the supermassive black hole in our Galaxy, Sagittarius A⋆ (Sgr A⋆), are routinely observed over the last decade or so. Despite numerous observational and theoretical efforts, the nature of such flares still remains poorly understood, although a few phenomenological scenarios have been proposed. In this work, we develop the Yuan et al. scenario into a magnetohydrodynamic model for Sgr A⋆ flares. This model is analogous with the theory of solar flares and coronal mass ejection in solar physics. In the model, magnetic field loops emerge from the accretion flow on to Sgr A⋆ and are twisted to form flux ropes because of shear and turbulence. The magnetic energy is also accumulated in this process until a threshold is reached. This then results in a catastrophic evolution of a flux rope with the help of magnetic reconnection in the current sheet. In this catastrophic process, the magnetic energy is partially converted into the energy of non-thermal electrons. We have quantitatively calculated the dynamical evolution of the height, size and velocity of the flux rope, as well as the magnetic field in the flare regions, and the energy distribution of relativistic electrons in this process. We further calculate the synchrotron radiation from these electrons and compare the obtained light curves with the observed ones. We find that the model can reasonably explain the main observations of near-infrared and X-ray flares including their light curves and spectra. It can also potentially explain the frequency-dependent time delay seen in radio flare light curves.

AN ALTERNATIVE VIEW OF THE “MASUDA” FLARE

The limb flare on 1992 January 13, the so-called Masuda flare, has stimulated scientists to refine theory of solar flares based on two-dimensional magnetic reconnection. This is primarily because of the hard X-ray (HXR) source seen above the clearly defined flare loop, and the outward motions in soft X-rays (SXRs) interpreted as ejections. We have revisited Yohkoh HXR and SXR data for this and other limb flares and found that the Masuda flare is still unique in terms of the location and spectral properties of the coronal HXR source. However, the outward motions in SXR outside the flare loop may not be as simply characterized as plasmoid ejections as in other flares, nor are they particularly fast. The motions appear complex partly because we also see trans-equatorial loops in motion, one of whose legs anchors close to the main flare loop. It is possible that these large-scale loops represent post-flare loops, and that the flare may also be explained in terms of three-dimensional quadrupolar reconnection, similar to those flares where a pair of two loops exchange their footpoints through magnetic reconnection. It appears that expansion and brightening of large-scale loops offset from the main flare loop are not common, possibly providing a reason for the unusual coronal HXR source in the Masuda flare.

Solar flare theory and light curves

During the last few years several models have been developed to explain the onset and energy release in large, eruptive solar flares. Although there is no consensus yet about the precise mechanism which triggers the onset of an eruption, there is a consensus that the mechanism involves the release of magnetic energy stored in the solar corona. Several of the proposed models use an ideal-MHD loss of equilibrium to trigger the eruption, but these models still require magnetic reconnection to extract the bulk of the magnetic energy. Coupling the ideal loss-of-equilibrium process with the non-ideal reconnection processes, and incorporating thermal conduction, chromospheric evaporation, and radiative cooling, shows great promise as a way to account for the light curves of both solar and stellar flares.

The magnetic nature of solar flares

The main challenge for the theory of solar eruptions has been to understand two basic aspects of large flares. These are the cause of the flare itself and the nature of the morphological features which form during its evolution. Such features include separating ribbons of H $\alpha$ emission joined by a rising arcade of soft x-ray loops, with hard x-ray emission at their summits and at their feet. Two major advances in our understanding of the theory of solar flares have recently occurred. The first is the realisation that a magnetohydrodynamic (MHD) catastrophe is probably responsible for the basic eruption and the second is that the eruption is likely to drive a reconnection process in the field lines stretched out by the eruption. The reconnection is responsible for the ribbons and the set of rising soft x-ray loops, and such a process is well supported by numerical experiments and detailed observations from the Japanese satellite Yohkoh. Magnetic energy conversion by reconnection in two dimensions is relatively well understood, but in three dimensions we are only starting to understand the complexity of the magnetic topology and the MHD dynamics which are involved. How the dynamics lead to particle acceleration is even less well understood. Particle acceleration in flares may in principle occur in a variety of ways, such as stochastic acceleration by MHD turbulence, acceleration by direct electric fields at the reconnection site, or diffusive shock acceleration at the different kinds of MHD shock waves that are produced during the flare. However, which of these processes is most important for producing the energetic particles that strike the solar surface remains a mystery.

Conventional solar flare theory re-examined

Major objections are raised to the fundamental paradigm underlying conventional solar flare theory, viz., that the required free energy can be stored in situ at the requisite density in the corona in nonpotential magnetic fields by the action of photospheric convective motion, that it can be released rapidly through magnetic reconnection by a triggering event, and that a significant fraction of this energy is converted to x rays. An alternative explanation that avoids these difficulties requires that magnetic energy in the form of strongly sheared flux tubes be stored subphotospherically prior to the flare. It is the emergence of this subphotospherically stored magnetic shear energy into the photosphere and above, and its rapid conversion through internal magnetic reconnection to other forms that constitutes an actual flare.

The theory of solar flares and the scientific inheritance of S. I. Syrovatskii

The hypothesis of energy accumulation in a current layer proposed by S. I. Syrovatskii has resulted in the development of the current flare model. The quasistationary current layer, which is formed above the active region in the corona, can become unstable. In this case plasma flows are ejected from the current layer. The current layer generates the field- aligned currents that are closed in the photosphere. The electrons accelerated in the field- aligned currents produce visible radiation, X- rays, and radio bursts.

Solar Flares: Current Dissipation or Magnetic Annihilation?

Solar flares involve the explosive release of energy, 1022_1025 J in 102-103 s, in the solar corona. A substantial fraction of this energy goes into energetic (~10 keY) electrons, and these produce most of the familiar signatures of flares, such as Ha emission, hard X-ray bursts and type III radio bursts. Solar flares occur in magnetic flux tubes in which the fields are highly stressed with associated large currents, I ~ 1012 A, flowing into the corona. Despite the enormous variety of detailed data on solar flares, there is no wide consensus on the essential theoretical ingredients in an acceptable flare model. Since the first detailed flare models were proposed in the 1940s, there have been two competing types: models based on an electric-current viewpoint and models based on a magnetic-field viewpoint. In principle these are equivalent, but in practice they have led to different and seemingly incompatible models. In this paper the theory of solar flares is reviewed, comparing and contrasting these two viewpoints. It is argued that all models, as presently formulated, contain serious deficiencies. One feature that is unsatisfactory is the treatment of energy propagation into a flare kernel. A specific model for such energy propagation is outlined.

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.

Dynamics of intense Langmuir waves in current-carrying plasmas

Basic equations including ponderomotive effects of Langmuir waves in a current-carrying plasma are presented. In such a system, dynamics of an initially monochromatic plasma wave is investigated both analytically and numerically. Various regimes of developed modified decay and modulational instabilities of the wave are modelled by using a macroparticle numerical code. In this way the cooperative nature of both ponderomotive and drift effects supporting plasma heating is demonstrated. The underlying physical processes are discussed and relation to the solar flare theory is suggested.

Solar flares and the dynamics of Langmuir waves in current-carrying plasmas

The dynamics of intense Langmuir waves in current-carrying plasmas is studied both analytically and numerically. Starting with the widely used Zakharov equations, adapted to these systems, specific features of this problem are pointed out. Further, the role of resonant particles is analyzed. By using 1-D macroparticle numerical code, nonlinear regimes of the modified-decay and modulational instabilities are then modelled. Efficient cooperation of essentially ponderomotive and electron-ion drift effects its demonstrated. It appears that the heating of a current-carrying plasma can be activated through releasing of the inductively stored energy, due to the enhanced conversion of energy associated with the electron drift motion. The underlying physics is discussed and its relationship to solar flare theory is suggested.

Magnetohydrodynamic theories of solar flares

Our current understanding of the MHD of the flare process is summarised, with some emphasis on processes which produce strong impulsive electric fields and current filamentation. As an introduction, a description of the two main types of flare (i.e., simple-loop and two-ribbon) is given, together with an account of the two branches of reconnection theory (tearing modes and the Petschek-Sonnerup mechanism). Modern numerical experiments of reconnection suggest impulsive bursty acceleration of particles in many small regions of width a hundred kilometres or less. This is followed by a discussion of the eruptive instability thought to initiate a large flare and of the reconnection process of energy release. Finally, the role of emerging flux and horizontally moving satellite sunspots is discussed briefly.

Magnetic theories of solar flares

The basic processes of evaporation and magnetic reconnection have recently been developed in much greater detail. They may be important in the two main types of flaring event, namely simple-loop flares and two-ribbon flares. The first type could be produced by kink instability, thermal nonequilibrium, or emerging flux. The second type is thought to be the result of an eruptive MHD instability that is either spontaneous or triggered from outside. After the eruption the magnetic field lines that have been blown open reconnect back down in a way that has now been simulated numerically.

Invariant structures of magnetic flux tubes

The basic properties of a screened magnetic flux tube possessing a finite radius of curvature are discussed in order to complement the findings of Parker (1974, 1976) and improve their accuracy. Conditions of equilibrium, twisting equilibrium, and twisting oscillations are discussed, showing that a twisted magnetic loop or arch is capable of executing elastic oscillations about an equilibrium state. This property can in particular be used in the theory of solar flares. Invariant structures of a force-free magnetic tube are analyzed, showing that invariant structures of the field preserve their form when the geometrical parameters of the flux tube are changed. In a quasi-equilibrium transition of the tube from one state to another the length and pitch of the tube spiral change in proportion to the radius of its cross section.

The Alfv�n-Carlquist double-layer theory of solar flares

We use the Vlasov equations for ions and electrons to develop a theory of a double layer in which there are both free and trapped electrons and ions. We find the equations which replace the Langmuir condition and the Bohm conditions and by numerically solving the resultant differential equation we find for particular choices of distribution functions the potential distribution in the layer. We discuss the applicability of this theory to solar flares, and show that conditions in solar flares may be such that double layers can exist for which the free particles have a power-law energy distribution. These particles will be accelerated in a double layer and may in this way account for the production of high-energy particles during the impulsive phase of solar flares.

Problems of solar flare theory

Problems of solar flare theory

The Alfv�n-wave theory of solar flares

Evidence is discussed showing that a representative solar flare event comprises three or more separate but related phenomena requiring separate mechanisms. In particular it is possible to separate the most energetic effect (the interplanetary blast) from the thermal flare and from the rapid acceleration of particles to high energies. The phenomena are related through the magnetic structure characteristic of a composite flare event, being a bipolar surface field with most of its field lines ‘closed’. Of primary importance are helical twists on all scales, starting with the ‘flux rope’ of the spot pair which was fully twisted before it emerged. Subsequent untwisting by the upward propagation of an Alfven twist wave provides the main flare energy.

Millimeter Radio Evidence for Containment Mechanisms in Solar Flares

Recent theories of solar flares are reviewed with emphasis on the aspects of pre-flare heating. The heating evident at 3.3-mm wavelength is analyzed in the form of daily maps of the solar disk and synoptic maps compiled from the daily maps. It is found that isotherms defining antenna temperature enhancements of 340 K correspond in shape and location to facular areas reported by Waldmeier. Maximum enhancements occur over sunspots or near neutral lines of the longitudinal magnetic fields which indicates heating associated with chromospheric currents. These enhancements are correlated with flare importance number and are observed to increase during several days preceding flaring. This evidence for a containment mechanism in the chromosphere is collated with current theories of solar flares.

Dynamo theories of the solar and galactic magnetic fields

Earlier criticisms of solar and galactic dynamo theories are extended to answer Parker's rebuttal, and the major modification made to his models to include Sweet's magnetic field annihilation mechanism as invoked in some theories of solar flares. His kinematic and weak-field analyses appear irrelevant because they ignore magnetic stresses which are of major importance and whose effects are evident in sunspots and elsewhere. It is shown that, even if Sweet's mechanism is effective under the most favourable conditions, these conditions are most unlikely in the solar convection zone or galactic disk. The problem is resolved by observational data which show that the fields are not tangled down to the scales required for dissipation byany known mechanism in the times available. Spot groups and many other patterns show that the solar fields are much too ordered to be products of a region of turbulence or to be dissipated by turbulence; the toroidal field must leave the Sun entirely to complete each 11-yr cycle. Faraday rotation, H I gas observations and extra-galactic fields provide strong evidence against a galactic dynamo and for a primordial field.

A model of solar flares and faculae

Theories of solar flares based on the storage of energy (usually as magnetic energy) in the solar atmosphere are shown to be incompatible with observational data.

The Relation Between Dashes and Flares (Physical Nature of the Dash Phenomena)

The phenomenon of dashes in the eruptive loop prominences is found to represent the part of the solar flare process which includes all the levels of the Sun's atmosphere. For 75% of observations a coincidence of dashes and flares in space and time was discovered. The rest of the dash observations may be interpreted as the excitation of dashes by the flares arising outside the limb.Following the solar flare theory of Alfvén and Carlquist, the possibility to interpret the dashes as the eruptive instability of the pinch-effect is discussed. The computation of flare-current magnetic field gives the value H ∼ 3·104 oersted, its order being in agreement with the observed value.