Predictions of Energy and Helicity in Four Major Eruptive Solar Flares

In order to better understand the solar genesis of interplanetary magnetic clouds (MCs), we model the magnetic and topological properties of four large eruptive solar flares and relate them to observations. We use the three-dimensional Minimum Current Corona model (Longcope, 1996, Solar Phys. 169, 91) and observations of pre-flare photospheric magnetic field and flare ribbons to derive values of reconnected magnetic flux, flare energy, flux rope helicity, and orientation of the flux-rope poloidal field. We compare model predictions of those quantities to flare and MC observations, and within the estimated uncertainties of the methods used find the following: The predicted model reconnection fluxes are equal to or lower than the reconnection fluxes inferred from the observed ribbon motions. Both observed and model reconnection fluxes match the MC poloidal fluxes. The predicted flux-rope helicities match the MC helicities. The predicted free energies lie between the observed energies and the estimated total flare luminosities. The direction of the leading edge of the MC’s poloidal field is aligned with the poloidal field of the flux rope in the AR rather than the global dipole field. These findings compel us to believe that magnetic clouds associated with these four solar flares are formed by low-corona magnetic reconnection during the eruption, rather than eruption of pre-existing structures in the corona or formation in the upper corona with participation of the global magnetic field. We also note that since all four flares occurred in active regions without significant pre-flare flux emergence and cancelation, the energy and helicity that we find are stored by shearing and rotating motions, which are sufficient to account for the observed radiative flare energy and MC helicity.     

EVOLUTION OF MAGNETIC HELICITY IN MAGNETIC RECONNECTION

This paper presents a definition of magnetic helicity specifically for two-dimensional magnetic fields and derives the associated helicity equation. The newly defined helicity is closely related to its three-dimensional counterpart and serves as a measure of the shear of magnetic field. Based on this, a numerical simulation is carried out on magnetic reconnection occurring in the lower solar atmosphere. It is found that the helicity dissipation due to magnetic reconnection is very small. A large amount of helicity is transferred upward and escapes from the domain of the solution, and the total helicity is approximately conserved during the magnetic reconnection and helicity transfer. This is in support of the applicability of a postulate, which was proposed by Taylor (1974, 1986) concerning the approximate conservation of magnetic helicity in the presence of resistive dissipation and magnetic reconnection in a highly conductive laboratory plasma, to the solar atmosphere.     

What helicity can tell us about solar magnetic fields

Concept of magnetic/current helicity was introduced to solar physics about 15 years ago. Earlier studies led to discovery of such fundamental properties as hemispheric helicity rule, and role of helicity in magnetic reconnection and solar eruptions. Later, the concept was successfully applied in studies of different solar processes from solar dynamo to flare and CME phenomena. Although no silver bullet, helicity has proven to be a very useful “tool” in answering many still-puzzling questions about origin and evolution of solar magnetic fields. I present an overview of some helicity studies and briefly analyze their findings.     

灾变理论在太阳物理和天体物理其他研究领域中的应用

叙述和介绍了太阳爆发的磁通量绳灾变理论和模型的发展过程,强调了建立这样的模型所需要的观测基础。讨论了由模型所预言的爆发磁结构的几个重要特征以及观测结果对这种预言的证实。在此模型的基础上,讨论了一个典型的爆发过程中所出现的不同现象及它们之间的相互关系。最后,介绍了作者的一项最新尝试:将太阳爆发的灾变理论和模型应用到对黑洞吸积盘间歇性喷流的理论研究当中,以及研究所取得的初步结果。     

CME-Flare Association Deduced from Catastrophic Model of CMEs

Based on our previous works regarding solar eruptions, we focus on the relationships among different eruptive phenomena, such as solar flares, eruptive prominences and coronal mass ejections (CMEs). The three processes show clear correlations under certain circumstances. The correlation between a CME and solar flare depends the energy that stored in the relevant magnetic structure, which is available to drive the eruption: the more energy that is stored, the better the correlation is; otherwise, the correlation is poor. The correlation between a CME and eruptive prominence, on the other hand, depends on the plasma mass concentration in the configuration prior to the eruption: if the mass concentration is significant, a CME starts with an eruptive prominence, otherwise, a CME develops an without an apparent associated eruptive prominence. These results confirm that solar flares, eruptive prominences and CMEs are different significances of a single physical process that is related to the energy release in a disrupted coronal magnetic field. The impact of gravity on CME propagation and the above correlations is also investigated. Our calculations indicate that the effect of gravity is not significant unless the strength of the background field in the disrupted magnetic configuration becomes weak, say weaker than 30 G.     

Relationship between CME dynamics and solar flare plasma

The relationship between the velocity of CMEs and the plasma temperature of the associated X-ray solar flares is investigated.The velocity of CMEs increases with plasma temperature(R=0.82)and photon index below the break energy(R=0.60)of X-ray flares.The heating of the coronal plasma appears to be significant with respect to the kinetics of a CME from the reconnection region where the flare also occurs.We propose that the initiation and velocity of CMEs perhaps depend upon the dominant process of conversion of the magnetic field energy of the active region to heating/accelerating the coronal plasma in the reconnected loops.Results show that a flare and the associated CME are two components of one energy release system,perhaps,magnetic field free energy.     

Electrostatically unstable heat flow during solar flares and its consequences

We examine some of the consequences of an electrostatically unstable return current associated with heat conduction during a solar flare. We note that an electrostatically unstable return current will lead to strong hydrodynamic effects and more rapid magnetic field thermalization, if reconnection is the source of primary energy release during a solar flare.     

3D Solar Null Point Reconnection MHD Simulations

Numerical MHD simulations of 3D reconnection events in the solar corona have improved enormously over the last few years, not only in resolution, but also in their complexity, enabling more and more realistic modeling. Various ways to obtain the initial magnetic field, different forms of solar atmospheric models as well as diverse driving speeds and patterns have been employed. This study considers differences between simulations with stratified and non-stratified solar atmospheres, addresses the influence of the driving speed on the plasma flow and energetics, and provides quantitative formulas for mapping electric fields and dissipation levels obtained in numerical simulations to the corresponding solar quantities. The simulations start out from a potential magnetic field containing a null-point, obtained from a Solar and Heliospheric Observatory (SOHO) Michelson Doppler Imager (MDI) magnetogram magnetogram extrapolation approximately 8?hours before a C-class flare was observed. The magnetic field is stressed with a boundary motion pattern similar to?–?although simpler than?–?horizontal motions observed by SOHO during the period preceding the flare. The general behavior is nearly independent of the driving speed, and is also very similar in stratified and non-stratified models, provided only that the boundary motions are slow enough. The boundary motions cause a build-up of current sheets, mainly in the fan-plane of the magnetic null-point, but do not result in a flare-like energy release. The additional free energy required for the flare could have been partly present in non-potential form at the initial state, with subsequent additions from magnetic flux emergence or from components of the boundary motion that were not represented by the idealized driving pattern.     

Interpretation of the observed motions of hard X-ray sources in solar flares

In connection with the RHESSI satellite observations of solar flares, which have revealed new properties of hard X-ray sources during flares, we offer an interpretation of these properties. The observed motions of coronal and chromospheric sources are shown to be the consequences of three-dimensional magnetic reconnection at the separator in the corona. During the first (initial) flare phase, the reconnection process releases an excess of magnetic energy related predominantly to themagnetic tensions produced before the flare by shear plasma flows in the photosphere. The relaxation of a magnetic shear in the corona also explains the downward motion of the coronal source and the decrease in the separation between chromospheric sources. During the second (main) flare phase, ordinary reconnection dominates; it describes the energy release in the terms of the “standard model” of large eruptive flares accompanied by the rise of the coronal source and an increase in the separation between chromospheric sources.     

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.     

On the magnetic reconnection of electric currents in solar flares

The role of the electric currents distributed over the volume of an active region on the Sun is considered from the standpoint of solar flare physics. We suggest including the electric currents in a topological model of the magnetic field in an active region. Typical values of the mutual inductance and the interaction energy of the coronal electric currents flowing along magnetic loops have been estimated for the M7/1N flare on April 27, 2006. We show that if these currents actually make a significant contribution to the flare energetics, then they must manifest themselves in the photosphericmagnetic fields. Depending on their orientation, the distributed currents can both help and hinder reconnection in the current layer at the separator during the flare. Asymmetric reconnection of the currents is accompanied by their interruption and an inductive change in energy. The reconnection of currents in flares differs significantly from the ordinary coalescence instability of magnetic islands in current layers. Highly accurate measurements of the magnetic fields in active regions are needed for a quantitative analysis of the role of distributed currents in solar flares.     

Magnetic reconnection in the corona and the loop prominence phenomenon

Many classes of transient solar phenomena, such as flares, flare sprays, and eruptive prominences, cause major disruptions in the magnetic geometry of the overlying corona. Typically, the results from Skylab indicate that pre-existing closed magnetic loops in the corona are torn open by the force of the disruption. We examine here some of the theoretical consequences to be expected during the extended relaxation phase which must follow such events. This phase is characterized by a gradual reconnection of the outward-distended field lines. In particular, the enhanced coronal expansion which occurs on open field lines just before they reconnect appears adequate to supply the large downward mass fluxes observed in Ha loop prominence systems that form during the post-transient relaxation. In addition, this enhanced flow may produce nonrecurrent high speed streams in the solar wind after such events. Calculations of the relaxation phase for representative field geometries and the resulting flow configurations are described.New address: Los Alamos Scientific Laboratory, Los Alamos, N.M. 87545, U.S.A.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Observational Features of Large-Scale Structures as Revealed by the Catastrophe Model of Solar Eruptions

Large-scale magnetic structures are the main carrier of major eruptions in the solar atmosphere. These structures are rooted in the photosphere and are driven by the unceas-ing motion of the photospheric material through a series of equilibrium configurations. The motion brings energy into the coronal magnetic field until the system ceases to be in equilib-rium. The catastrophe theory for solar eruptions indicates that loss of mechanical equilibrium constitutes the main trigger mechanism of major eruptions, usually shown up as solar flares, eruptive prominences, and coronal mass ejections (CMEs). Magnetic reconnection which takes place at the very beginning of the eruption as a result of plasma instabilities/turbulence inside the current sheet, converts magnetic energy into heating and kinetic energy that are responsible for solar flares, and for accelerating both plasma ejecta (flows and CMEs) and energetic particles. Various manifestations are thus related to one another, and the physics behind these relationships is catastrophe and magnetic reconnection. This work reports on re- cent progress in both theoretical research and observations on eruptive phenomena showing the above manifestations. We start by displaying the properties of large-scale structures in the corona and the related magnetic fields prior to an eruption, and show various morphological features of the disrupting magnetic fields. Then, in the framework of the catastrophe theory, we look into the physics behind those features investigated in a succession of previous works, and discuss the approaches they used.     

日冕三重无力场电流片的磁场重联

采用二维三分量磁流体力学模型,对日冕三重无力场电流片的磁场重联进行了数值研究,揭示了重联过程的基本物理特征．这类重联过程将加热和加速日冕等离子体,并导致多个高温、高密度、高磁螺度的磁岛的形成和向上喷发．这表明,多重无力场电流片的重联可能在日冕磁能释放、上行等离子体团的形成和太阳磁场螺度向行星际空间的逃逸方面起重要的作用．     

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.     

计算的磁拓扑界线与耀斑相关性

本文利用赣榆站所取得的色球精细结构资料，并采用了前苏联强磁场资料，逐日计算了１９９０年１０月１３日至１６日复合活动区ＮＯＡＡ６３０９在色球层的磁拓扑界线，并与色球精细结构资料作了比照，发现：亮谱斑或亮耀斑核均是位于界线上，或紧邻它．这个结果支持“重联是耀斑在释放能量时的主要过程，而重联发生在磁场的拓扑界面上”的观点．     

Effect of obstacles on the rate of reconnection of magnetic field lines

Further results of a laboratory magnetic field line reconnection experiment are presented. In particular, it is found that the reconnection rate can be slowed by placing solid obstacles to impede the outflow of plasma from an x-type magnetic neutral point. Without the obstacles the reconnection rate is faster and more impulsive. The fastest reconnection event has strong similarities to solar flares and geomagnetic substorms. It is suggested that more stationary features of solar activity such as prominences may be the result of reconnection slowed by obstacles such as the photosphere.     

The Evolution of Quasi-Separatrix Layer in Two Solar Eruptive Events

Quasi-separatrix layer, also called as QSL, is a region where magnetic connectivity changes drastically, and mostly well coincides with the location of flare ribbons in observations. The research on the relations of this topological structure with the 3-dimensional magnetic reconnection, and solar flares has attracted more and more attention. In this paper, using the theory of QSL we investigate a C5.7 classical two-ribbon solar flare (event 1) which occurred at AR11384 on 2011 December 26, and an M6.5 solar flare (event 2) which occurred at AR12371 on 2015 June 22, respectively. Combining the multi-wavelength data of AIA (Atmospheric Imaging Assembly) and vector magnetogrames of HMI (Helioseismic and Magnetic Imager) onboard SDO (Solar Dynamics Observatory), we extrapolate the coronal magnetic field using the PF (Potential Field) and NLFFF (Nonlinear Force Free Field) models, and calculate the evolution of the AR (Active Region) magnetic free energy. Then, we calculate the logarithmic distribution of Q-factors (magnetic squashing factor) at different heights above the solar photosphere with the results of the PF and NLFFF extrapolations, in order to determine the location of QSL. Afterward, we investigate the evolutionary relation between the QSLs at different heights above the solar photosphere and the flare ribbons observed at the corresponding heights. Finally, we study the multi-wavelength evolution features of the 2 flare events, and obtain by calculation the mean slip velocities of magnetic lines in the event 2 at 304 Å and 335 Å to be 4.6 km s^-1 and 6.3 km s^-1, respectively. We find that the calculated location of QSL in the chromosphere and corona is in good agreement with the location of flare ribbons at the same height, and the QSLs at different heights have almost the same evolutionary behavior in time as the flare ribbons of the corresponding heights, which highlights the role of QSL in the research of 3D magnetic reconnection and solar flare, and we suggest that the energy release in the flare of event 2 may be triggered by the magnetic reconnection at the place of QSL. We also suggest that the QSL is very important for us to study the essential relation between the 3D and 2D magnetic reconnections.     

An electric-current description of solar flares

The presently prevailing theories of solar flares rely on the hypothetical presence of magnetic flux tubes beneath the photosphere and the two subsequent hypotheses, their emergence above the photosphere and explosive magnetic reconnection, converting magnetic energy carried by the flux tubes to solar flare energy. In this paper, we discuss solar flares from an entirely different point of view, namely in terms of power supply by a dynamo process in the photosphere. By this process, electric currents flowing along the magnetic field lines are generated and the familiar ‘force-free’ fields or the ‘sheared’ magnetic fields are produced. Upward field-aligned currents thus generated are carried by downward streaming electrons; these electrons can excite hydrogen atoms in the chromosphere, causing the optical Hα flares or ‘low temperature flares’. It is thus argued that as the ‘force-free’ fields are being built up for the magnetic energy storage, a flare must already be in progress.     

The X10 Flare on 29 October 2003: Was It Triggered by Magnetic Reconnection between Counter-Helical Fluxes?

Vector magnetograms taken at Huairou Solar Observing Station (HSOS) and Mees Solar Observatory (MSO) reveal that the super active region (AR) NOAA 10486 was a complex region containing current helicity flux of opposite signs. The main positive sunspots were dominated by negative helicity fields, while positive helicity patches persisted both inside and around the main positive sunspots. Based on a comparison of two days of deduced current helicity density, pronounced changes associated with the occurrence of an X10 flare that peaked at 20:49 UT on 29 October 2003 were noticed. The average current helicity density (negative) of the main sunspots decreased significantly by about 50%. Accordingly, the helicity densities of counter-helical patches (positive) were also found to decay by the same proportion or more. In addition, two hard X-ray (HXR) “footpoints” were observed by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) during the flare in the 50 – 100 keV energy range. The cores of these two HXR footpoints were adjacent to the positions of two patches with positive current helicity that disappeared after the flare. This strongly suggested that the X10 flare on 29 October 2003 resulted from reconnection between magnetic flux tubes having opposite current helicity. Finally, the global decrease of current helicity in AR 10486 by ∼50% can be understood as the helicity launched away by the halo coronal mass ejection (CME) associated with the X10 flare. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.