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.     

2 1/2-Dimensional Reconnection Model and Energy Release in Solar Flares

We employ a 2 1/2-dimensional reconnection model to analyse different aspects of the energy release in two-ribbon flares. In particular, we investigate in which way the systematic change of inflow region variables, associated with the vertical elongation of current sheet, affects the flare evolution. It is assumed that as the transversal magnetic field decreases, the ambient plasma-to-magnetic pressure ratio increases, and the reconnection rate diminishes. As the transversal field decreases due to the arcade stretching, the energy release enhances and the temperature rises. Furthermore, the magnetosonic Mach number of the reconnection outflow increases, providing the formation of fast mode standing shocks above the flare loops and below the erupting flux rope. Eventually, in the limit of a very small transversal field the reconnection becomes turbulent due to a highly non-linear response of the system to small fluctuations of the transversal field. The turbulence results in the energy release fragmentation which increases the release efficiency, and is likely to be responsible for the impulsive phase of the flare. On the other hand, as the current sheet stretches to larger heights, the ambient plasma-to-magnetic pressure ratio increases which causes a gradual decrease of the reconnection rate, energy release rate, and temperature in the late phase of flare. The described magnetohydrodynamical changes affect also the electron distribution function in space and time. At large reconnection rates (impulsive phase of the flare) the ratio of the inflow-to-outflow magnetic field strength is much smaller than at lower reconnection rates (late phase of the flare), i.e., the corresponding loss-cone angle becomes narrower. Consequently, in the impulsive phase a larger fraction of energized electrons can escape from the current sheet downwards to the chromosphere and upwards into the corona – the dominant flare features are the foot-point hard X-ray sources and type III radio bursts. On the other hand, at low reconnection rates, more particles stay trapped in the outflow region, and the thermal conduction flux becomes strongly reduced. As a result, a superhot loop-top, and above-the-loop plasma appears, as sometimes observed, to be a dominant feature of the gradual phase.     

Models for the motions of flare loops and ribbons

We have found a conformal mapping which is valid for any magnetic boundary condition at the photosphere and which can be used to determine the evolution of an open, two-dimensional magnetic field configuration as it relaxes to a closed one. Solutions obtained with this mapping are in quasi-static equilibrium, and they contain a vertical current sheet and have line-tied boundary conditions. As a specific example, we determine the solution for a boundary condition corresponding to a submerged, two-dimensional dipole below the photosphere. We assume that the outer edges of the hottest X-ray loops correspond to field lines mapping from the outer edges of the H ribbon to the lower tip of the current sheet where field lines reconnect at aY-type neutral line which rises with time. The cooler H loops are assumed to lie along the field lines mapping to the inner edges of the flare ribbons. With this correspondence between the plasma structures and the magnetic field we determine the shrinkage that field lines are observed to undergo as they are disconnected from the neutral line. During the early phase of the flare, we predict that shrinkage inferred from the height of the H and X-ray loops is close to 100% of the loop height. However, the shrinkage should rapidly decrease with time to values on the order of 20% by the late phase. We also predict that the shrinkage in very large loops obeys a universal scaling law which is independent of the boundary condition, provided that the field becomes self-similar (i.e., all field lines have the same shape) at large distances. Specifically, for any self-similar field containing aY-type neutral line, the observed shrinkage at large distances should decrease as (X/X _R)^–2/3, where X is the ribbon width andX _Ris the ribbon separation. Finally, we discuss the relation between the electric field at the neutral line and the motions of the flare loops and ribbons.     

Neutral line motion due to reconnection in two-ribbon solar flares and magnetospheric substorms

Two kinematic models of line-tied reconnection are considered which describe the motion of a magnetic neutral line (NL) during the main phase of a two-ribbon solar flare and during the recovery phase of a magnetospheric substorm in the geomagnetic tail. The models are kinematic in that they use only the magnetic induction equation, which suffices to determine the position and velocity of the NL as functions of time if the rate of reconnection is prescribed. The solar flare model shows that the observed large decrease in the rate at which “post”-flare loops rise upward from the photosphere during the main phase does not require a corresponding decrease in the rate of reconnection. Instead it is found that a constant rate of reconnection can account for the motion of the loops for almost the entire period during which they are observed. By contrast, application of the same procedures to the recovery phase of the magnetospheric substorm in the tail predicts a slightly increasing speed of NL motion if the rate of reconnection is constant. Furthermore, it is found that the motion of the NL relative to the ambient medium may account for much of the observed asymmetry in the magnetic field in the plasma sheet during recovery. Due to this motion, the plasma sheet thickness may be up to 4 times smaller and the normal magnetic field component up to 2 times weaker in the region tailward of the NL than in the corresponding region earthward of the NL.     

Evaluating Mean Magnetic Field in Flare Loops

We analyze multiple-wavelength observations of a two-ribbon flare exhibiting apparent expansion motion of the flare ribbons in the lower atmosphere and rising motion of X-ray emission at the top of newly-formed flare loops. We evaluate magnetic reconnection rate in terms of V _r B _r by measuring the ribbon-expansion velocity (V _r) and the chromospheric magnetic field (B _r) swept by the ribbons. We also measure the velocity (V _t) of the apparent rising motion of the loop-top X-ray source, and estimate the mean magnetic field (B _t) at the top of newly-formed flare loops using the relation 〈V _t B _t〉≈〈V _r B _r〉, namely, conservation of reconnection flux along flare loops. For this flare, B _t is found to be 120 and 60 G, respectively, during two emission peaks five minutes apart in the impulsive phase. An estimate of the magnetic field in flare loops is also achieved by analyzing the microwave and hard X-ray spectral observations, yielding B=250 and 120 G at the two emission peaks, respectively. The measured B from the microwave spectrum is an appropriately-weighted value of magnetic field from the loop top to the loop leg. Therefore, the two methods to evaluate coronal magnetic field in flaring loops produce fully-consistent results in this event.     

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.     

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.     

Coronal Mass Ejection of 15 May 2001: II. Coupling of the Cme Acceleration and the Flare Energy Release

We analyze the relationship between the dynamics of the coronal mass ejection (CME) of 15 May 2001 and the energy release in the associated flare. The flare took place behind the east limb and was disclosed by a growing system of hot soft X-ray (SXR) loops that appeared from behind the limb around the onset of the rapid acceleration of the CME. The highly correlated behavior of the SXR light-curve derivative and the time profile of the CME acceleration reveals an intrinsic relationship between the CME dynamics and the flare energy release. Furthermore, we found that the CME acceleration peak occurs simultaneously with the fastest growth (100 km s^-1) of X-ray loops, indicating that the reconnection plays an essential role in the eruption. Inspecting the CME/flare morphology we recognized in the Yohkoh-SXT images an oval feature that formed within the rising structure at the onset of the rapid acceleration phase, simultaneously with the appearance of the X-ray loops. The eruptive prominence was imbedded within the lower half of the oval, suggestive of a flux-rope/prominence magnetic configuration. We interpret the observed morphological evolution in terms of a reconnection process in the current sheet that presumably formed below the erupting flux-rope at the onset of the CME acceleration. Measurements of the tip-height of the cusped X-ray loop system and the height of the lower edge of the oval, enable us to trace the stretching of the current sheet. The initial distance between the oval and the loops amounted to 35 – 40 Mm. In about 1 h the inferred length of the current sheet increased to 150 – 200 Mm, which corresponds to a mean elongation speed of 35 – 45 km s^-1. The results are discussed in the framework of CME models that include the magnetic reconnection below the erupting flux-rope.     

Evidence of two-stage magnetic reconnection in the 2005 January 15 X2.6 flare

We analyze in detail the X2.6 flare that occurred on 2005 January 15 in the NOAA AR 10720 using multiwavelength observations. There are several interesting properties of the flare that reveal possible two-stage magnetic reconnection similar to that in the physical picture of tether-cutting, where the magnetic fields of two separate loop systems reconnect at the flare core region, and subsequently a large flux rope forms, erupts, and breaks open the overlying arcade fields. The observed manifestations include: (1) remote Hα brightenings appear minutes before the main phase of the flare; (2) separation of the flare ribbons has a slow and a fast phase, and the flare hard X-ray emission appears in the later fast phase; (3) rapid transverse field enhancement near the magnetic polarity inversion line (PIL) is found to be associated with the flare. We conclude that the flare occurrence fits the tether-cutting reconnection picture in a special way, in which there are three flare ribbons outlining the sigmoid configuration. We also discuss this event in the context of what was predicted by Hudson et al. (2008), where the Lorentz force near the flaring PIL drops after the flare and consequently the magnetic field lines there turn to be more horizontal as we observed.     

Solar flares： radio and X-ray signatures of magnetic reconnection processes

This review summarizes new trends in studies of magnetic reconnection in solar flares. It is shown that plasmoids play a very important role in this primary flare process. Using the results of magnetohydrodynamic and particle-in-cell simulations, we describe how the plasmoids are formed, how they move and interact, and how a flare current sheet is fragmented into a cascade of plasmoids. Furthermore, it is shown that during the interactions of these plasmoids electrons are not only very efficiently accelerated and heated, but electromagnetic（radio） emission is also produced.We also describe possible mechanisms for the triggering of magnetic reconnection.The relevant X-ray and radio signatures of these processes（such as radio drifting pulsation structures, narrowband dm-spikes, and the loop-top and above-the-loop-top X-ray sources） are then described. It is shown that plasmoids can also be formed in kinked magnetic ropes. A mapping of X-points of the magnetic reconnection on the chromosphere（as e.g. a splitting of flare ribbons） is mentioned. Supporting EUV and white-light observations of plasmoids are added. The significance of all these processes for the fast magnetic reconnection and electron acceleration is outlined. Their role in fusion experiments is briefly mentioned.     

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.     

The formation of flare loops by magnetic reconnection and chromospheric ablation

Slow-mode shocks produced by reconnection in the corona can provide the thermal energy necessary to sustain flare loops for many hours. These slow shocks have a complex structure because strong thermal conduction along field lines dissociates the shocks into conduction fronts and isothermal subshocks. Heat conducted along field lines mapping from the subshocks to the chromosphere ablates chromospheric plasma and thereby creates the hot flare loops and associated flare ribbons. Here we combine a non-coplanar compressible reconnection theory with simple scaling arguments for ablation and radiative cooling, and predict average properties of hot and cool flare loops as a function of the coronal vector magnetic field. For a coronal field strength of 100 G the temperature of the hot flare loops decreases from 1.2 × 10⁷ K to 4.0 × 10⁶ K as the component of the coronal magnetic field perpendicular to the plane of the loops increases from 0% to 86% of the total field. When the perpendicular component exceeds 86% of the total field or when the altitude of the reconnection site exceeds 10⁶km, flare loops no longer occur. Shock enhanced radiative cooling triggers the formation of cool H flare loops with predicted densities of 10¹³ cm^–3, and a small gap of 10³ km is predicted to exist between the footpoints of the cool flare loops and the inner edges of the flare ribbons.     

Erratum to: The Maunder Minimum and the Sun as the Possible Source of Particles Creating Increased Abundance of the <Superscript>14</Superscript>C Carbon Isotope

Solar flares take place in regions of strong magnetic fields and are generally accepted to be the result of a resistive instability leading to magnetic reconnection. When new flux emerges into a pre-existing active region it can act as a flare and coronal mass ejection trigger. In this study we observed active region 10955 after the emergence of small-scale additional flux at the magnetic inversion line. We found that flaring began when additional positive flux levels exceeded 1.38×10²⁰ Mx (maxwell), approximately 7 h after the initial flux emergence. We focussed on the pre-flare activity of one B-class flare that occurred on the following day. The earliest indication of activity was a rise in the non-thermal velocity one hour before the flare. 40 min before flaring began, brightenings and pre-flare flows were observed along two loop systems in the corona, involving the new flux and the pre-existing active region loops. We discuss the possibility that reconnection between the new flux and pre-existing loops before the flare drives the flows by either generating slow mode magnetoacoustic waves or a pressure gradient between the newly reconnected loops. The subsequent B-class flare originated from fast reconnection of the same loop systems as the pre-flare flows.     

Magnetic reconnection and coronal transients

Every two-ribbon flare observed during the Skylab period produced an observable coronal transient, provided the flare occurred close enough to the limb. The model presented here treats these two events as a combined process. Transients that occur without flares are believed to involve magnetic fields that are too weak to produce significant chromospheric emission. Adopting the hypothesis that the rising flare loop systems observed during two-ribbon flares are exhibiting magnetic reconnection, a model of a coronal transient is proposed which incorporates this reconnection process as the driving force. When two oppositely directed field lines reconnect a lower loop is created rooted to the solar surface (the flare loop) and an upper disconnected loop is produced which is free to rise. The magnetic flux of these upper loops is proposed as the driver for the transient. The force is produced by the increase in magnetic pressure under the filament and transient.A quantitative model is developed which treats the transient configuration in terms of four distinct parts- the transient itself with its magnetic field and material, the region just below the transient but above the filament, the filament with its magnetic field, and the reconnected flux beneath the filament. Two cases are considered - one in which all the prominence material rises with the transient and one in which the material is allowed to fall out of the transient. The rate of rise of the neutral line during the reconnection process is taken from the observations of the rising X-ray flare loop system during the 29 July, 1973 flare. The MHD equations for the system are reduced to four non-linear ordinary coupled differential equations which are solved using parameters believed to be realistic for solar conditions. The calculated velocity profiles, widths, etc., agree quite well with the observed properties of coronal transients as seen in white light. Since major flares are usually associated with a filament eruption about 10–15 min before the flare and since this model associates the transient with the filament eruption, we suspect that the transient is actually initiated some time before the actual flare itself.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Model for flare loops,fast motions,and opening of magnetic field in the corona

A model is presented for the penetration into the corona of a new magnetic field of a developing bipolar region and for its interaction with an old large-scale coronal field. An important feature of the model is a reconnection of the old and new fields inside the current sheet arising along the zero line of the total magnetic field calculated in the potential approximation. The magnetic reconnection and accumulation of plasma inside the current sheet can explain the appearance of dense coronal loops and the energy source at their tops. The plasma together with the magnetic lines is flowed into the sheet from both its sides. This fact explains the appearance of coronal cavities above the loops. If the large-scale field gradually decreases with the height, the loop motion is slowed down. The account of the dipolar structure of the magnetic field at large heights explains the possibility of a rapid break of the new field through the corona and the appearance of transients and open field regions - the coronal holes. In this case a fast rising current sheet can be a source of accelerated particles and of type II radio burst, instead of the shock wave considered usually.     

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。     

Electric Currents at imf Sector Boundaries

Numerical simulation of magnetic field reconnection at IMF sector boundaries shows that the reconnection line may be carried by the solar wind out of the region of the anomalous resistivity. This makes it possible to observe magnetic loops at the Earth's orbit open to the Sun as well as from it. Besides, it is shown that the current sheet in the vicinity of the reconnection line has to split into two currents.Experimental data on the structure of the sector boundaries are analyzed, and it is shown that the currents at sector boundaries are indeed often splitted.The thickness of the splitted boundaries may amount to 18×106 km; taking into account this value, the heliocentric distance of the region of anomalous resistivity in the interplanetary current sheet is estimated as 0.4–0.5 AU.The probability of observing magnetic loops open towards the Sun seems to be greater than that of loops open from the Sun, which suggests an essential asymmetry of the field reversal regions.     

A Quantitative Model of Energy Release and Heating by Time-dependent,Localized Reconnection in a Flare with Thermal Loop-top X-ray Source

We present a quantitative model of the magnetic energy stored and then released through magnetic reconnection for a flare on 26 February 2004. This flare, well observed by RHESSI and TRACE, shows evidence of non-thermal electrons for only a brief, early phase. Throughout the main period of energy release there is a super-hot (T?30 MK) plasma emitting thermal bremsstrahlung atop the flare loops. Our model describes the heating and compression of such a source by localized, transient magnetic reconnection. It is a three-dimensional generalization of the Petschek model, whereby Alfvén-speed retraction following reconnection drives supersonic inflows parallel to the field lines, which form shocks: heating, compressing, and confining a loop-top plasma plug. The confining inflows provide longer life than a freely expanding or conductively cooling plasma of similar size and temperature. Superposition of successive transient episodes of localized reconnection across a current sheet produces an apparently persistent, localized source of high-temperature emission. The temperature of the source decreases smoothly on a time scale consistent with observations, far longer than the cooling time of a single plug. Built from a disordered collection of small plugs, the source need not have the coherent jet-like structure predicted by steady-state reconnection models. This new model predicts temperatures and emission measure consistent with the observations of 26 February 2004. Furthermore, the total energy released by the flare is found to be roughly consistent with that predicted by the model. Only a small fraction of the energy released appears in the super-hot source at any one time, but roughly a quarter of the flare energy is thermalized by the reconnection shocks over the course of the flare. All energy is presumed to ultimately appear in the lower-temperature (T?20 MK) post-flare loops. The number, size, and early appearance of these loops in TRACE’s 171 Å band are consistent with the type of transient reconnection assumed in the model.     

Energetics of two-ribbon solar flares

A theory of two-ribbon solar flares is presented which identifies the primary energy release site with the tops of the flare loops. The flare loops are formed by magnetic reconnection of a locally opened field configuration produced by the eruption of a pre-flare filament. Such eruptions are commonly observed about 15 min prior to the flare itself. It is proposed that the flare loops represent the primary energy release site even during the earliest phase of the flare, i.e., the flare loops are in fact the flare itself.Based upon the supposition that the energy release at the loop tops is in the form of Joulean dissipation of magnetic energy at the rising reconnection site, a quantitative model of the energy release process is developed based upon an analytic reconnecting magnetic field geometry believed to represent the basic process. Predicted curves of energy density vs time are compared with X-ray observations taken aboard Skylab for the events of 29 July, 13 August, and 21 August in 1973. Considering the crudity of the model, the comparisons appear reasonable. The predicted field strengths necessary to produce the observed energy density curves are also reasonable, being in the range 100–1000 G.The National Center for Atmospheric Research is sponsored by the National Science Foundation.