Topology and current ribbons: A model for current,reconnection and flaring in a complex,evolving corona

Magnetic field enters the corona from the interior of the Sun through isolated magnetic features on the solar surface. These features correspond to the tops of submerged magnetic flux tubes, and coronal field lines often connect one flux tube to another, defining a pattern of inter-linkage. Using a model field, in which flux tubes are represented as point magnetic charges, it is possible to quantify this inter-linkage. If the coronal field were current-free then motions of the magnetic features would change the inter-linkage through implicit (vacuum) magnetic reconnection. Without reconnection the conductive corona develops currents to avoid changing the flux linkage. This current forms singular layers (ribbons) flowing along topologically significant field lines called separators. Current ribbons store magnetic energy as internal stress in the field: the amount of energy stored is a function of the flux tube displacement. To explore this process we develop a model called the minimum-current corona (MCC) which approximates the current arising on a separator in response to displacement of photospheric flux. This permits a model of the quasi-static evolution of the corona above a complex active region. We also introduce flaring to rapidly change the flux inter-linkage between magnetic features when the internal stress on a separator becomes too large. This eliminates the separator current and releases the energy stored by it. Implementation of the MCC in two examples reveals repeated flaring during the evolution of simple active regions, releasing anywhere from 10²⁷–10²⁹ ergs, at intervals of hours. Combining the energy and frequency gives a general expression for heat deposition due to flaring (i.e., reconnection).     

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.     

Interpretation of multiwavelength observations of November 5, 1980 solar flares by the magnetic topology of AR 2766

We present a detailed analysis of the magnetic topology of AR 2776 together with Hα UV, X-rays, and radio observations of the November 5, 1980 flares in order to understand the role of the active region large-scale topology on the flare process. As at present the coronal magnetic field is modeled by an ensemble of sub-photospheric sources whose positions and intensities are deduced from a least-square fit between the computed and observed longitudinal magnetic fields. Charges and dipole representations are shown to lead to similar modeling of the magnetic topology provided that the number of sources is great enough. However, for AR 2776, departure from a potential field has to be taken into account, therefore a linear force-free field extrapolation is used. The locations of the four bright off-band Hα kernels in quadrupolar active regions have been studied previously. In this new study the active region is bipolar and shows a two-ribbon structure. We show that these two ribbons are a consequence of the bipolar photospheric field (the four kernels of quadrupolar regions merge into two bipolar regions). The two ribbons are found to be located at the intersection of the separatrices with the chromosphere when the shear, deduced from the fibril direction, is taken into account. This study supports the hypothesis that magnetic energy is stored in field-aligned currents and released by magnetic reconnection at the location of the separator, before being transported along field lines to the chromospheric level. It is also possible that part of the magnetic energy could be stored and released on the separatrices. Our study shows that meeting just one of two conditions- the presence of intense coronal currents or of a separator in a magnetic field configuration - is not sufficient for flaring. In order to release the stored energy, the coronal currents need either to be formed along the separatrices or to be transported towards the separator or separatrices. The location of the observed photospheric current concentrations on the computed separatrices supports this view. Member of the Carrera del Investigador Científico, CONICET.     

The formation of current sheets during the emergence of new magnetic flux from below the photosphere

Solar flares are frequently observed to occur where new magnetic flux is emerging and pressing up against strong active region magnetic fields. Since the solar plasma is highly conducting, current sheets develop at the boundary between the emergent and ambient flux, provided the two magnetic fields are inclined at a non-zero angle to one another.The present paper gives a simple two-dimensional model for the development of such sheets under the assumptions that no reconnection occurs and that the surrounding field remains a potential one. By using complex variable techniques, the position, orientation and shape of a current sheet may be determined, as well as the excess magnetic energy associated with it. Two examples are considered. The first, in which the ambient field is bipolar, may model new flux emergence near the edge of an active region, while the second example assumes a constant ambient field and may approximate the so-called fibril crossings which occur prior to some flares. In each case, the current sheets are curved, and the magnetic energy which is stored in excess of potential is sufficient to supply a solar flare when the sheets are long enough.     

Magnetic nulls and topology in a class of solar flare models

We study the magnetic field-line topology in a class of solar flare models with four magnetic dipoles. By introducing a series of symmetry-breaking perturbations to a fully symmetric potential field model, we show that isolated magnetic nulls generally exist above the photosphere. These nulls are physically important because they determine the magnetic topology above the photosphere. In some special cases, there may be a single null above the photosphere with quasi two-dimensional properties. For such a model, aquasi null line connects the null to the photosphere. In the limit of small non-ideal effects, boundary layers and current sheetsmay develop along the quasi null line and the associated separatrix surfaces. Field lines can then reconect across the quasi null line, as in two-dimensional reconnection. In a more general force-free case, the field contains a pair of nulls above the photosphere, with a field line (theseparator) connecting the two nulls. In the limit of small non-ideal effects, boundary layers and current sheets develop along the separator and the associated separatrix surfaces. The system exhibits three-dimensional reconnection across the separator, over which field lines exchange identity. The separatrices are related to preferable sites of energy release during solar flares.     

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.     

A Quantitative Study on Magnetic Configuration for Active Regions

As compared with the Mount Wilson Magnetic Classification (MWMC), effective distance (d _E) is a useful parameter because it gives a quantitative measure of magnetic configuration in active regions. We have analyzed magnetograms of 24 active regions of different types with MWMC. We have studied the evolution of magnetic fields of five active regions using d _E, total flux (F _t) and tilt angle (Tilt) quantitatively. Furthermore, 43 flare-associated and 25 CME-associated active regions have been studied to investigate and quantify the statistical correlation between flares/CMEs and the three parameters. The main results are as follows: (1) There is a basic agreement between d _E and MWMC. (2) The evolution of magnetic fields can be described in three aspects quantitatively and accurately by the three parameters, in particular by d _E on the analysis of δ-type active regions. (3) The high correlation between d _E and flares/CMEs means that d _E could be a promising measure to predict the flare-CME activity of active regions.     

An interpretation of rapid changes in the magnetic field associated with solar flares

The energy source of a flare is the magnetic field in the corona. A topological model of the magnetic field is used here for interpreting the recently discovered drastic changes in magnetic field associated with solar flares. The following observational results are self‐consistently explained: (1) the transverse field strength decreases at outer part of active regions and increases significantly in their centers; (2) the center‐of‐mass positions of opposite magnetic polarities converge towards the magnetic neutral line just after flares onset; (3) the magnetic flux of active regions decreases steadily during the course of flares. For X‐class flares, almost 50% events show such changes. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Relationship between magnetic field evolution and flaring sites in AR 6659 in June 1991

During the international campaign of June 1991, the active region AR 6659 produced six very large, long-duration flares (X10/12) during its passage across the solar disk. We present the characteristics of four of them (June 4, 6, 9, 15). Precise measurements of the spot motions from Debrecen and Tokyo white-light pictures are used to understand the fragmentation of the main sunspot group with time. This fragmentation leads to a continuous restructuring of the magnetic field pattern while rapid changes are evidenced due to fast new flux emergence (magnetograms of MFSC, Huairou). The first process leads to a shearing of the field lines along which there is energy storage; the second one is the trigger which causes the release of energy by creating a complex topology. We conjecture that these two processes with different time scales are relevant to the production of flares.     

Suppression of the kink instability for magnetic flux ropes in the chromosphere

Energy storage in chromospheric flux ropes is discussed, in the context of solar flares. The structure is represented by a cylindrically symmetric magnetic field of finite length. The field is assumed to be approximately force-free. The stability of the field to a kink perturbation is investigated. Flux ropes are rooted in dense photospheric material. So the ends of the field lines are taken to be fixed on rigid boundaries for all perturbations. An energy perturbation method is used and the boundary conditions give a stabilizing effect. It is shown that for a moderate degree of twisting the fields are stable to a kink perturbation. Thus energy can be stored in cylindrical fields prior to release in a solar flare.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Structure and evolution of magnetic fields associated with solar eruptions

This paper reviews the studies of solar photospheric magnetic field evolution in active regions and its relationship to solar flares. It is divided into two topics, the magnetic structure and evolution leading to solar eruptions and rapid changes in the photospheric magnetic field associated with eruptions. For the first topic, we describe the magnetic complexity, new flux emergence, flux cancelation, shear motions, sunspot rotation and magnetic helicity injection, which may all contribute to the storage and buildup of energy that trigger solar eruptions. For the second topic, we concentrate on the observations of rapid and irreversible changes of the photospheric magnetic field associated with flares, and the implication on the restructuring of the three-dimensional magnetic field. In particular, we emphasize the recent advances in observations of the photospheric magnetic field, as state-of-the-art observing facilities(such as Hinode and Solar Dynamics Observatory) have become available. The linkages between observations, theories and future prospectives in this research area are also discussed.     

A Twisted Flux Rope Model for Coronal Mass Ejections and Two-Ribbon Flares

We present a new approach to the theory of large-scale solar eruptive phenomena such as coronal mass ejections and two-ribbon flares, in which twisted flux tubes play a crucial role. We show that it is possible to create a highly nonlinear three-dimensional force-free configuration consisting of a twisted magnetic flux rope representing the magnetic structure of a prominence (surrounded by an overlaying, almost potential, arcade) and exhibiting an S-shaped structure, as observed in soft X-ray sigmoid structures. We also show that this magnetic configuration cannot stay in equilibrium and that a considerable amount of magnetic energy is released during its disruption. Unlike most previous models, the amount of magnetic energy stored in the configuration prior to its disruption is so large that it may become comparable to the energy of the open field.     

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。     

Vertical current and a 3B/X12 flare in a highly sheared active region (NOAA 6659) on June 9, 1991

NOAA active region 6659, during its June 1991 transit across the solar disk, showed highly sheared vector magnetic field structures and produced numerous powerful flares, including five white-light flares. Photospheric vector magnetograms of this active region were obtained at the Huairou Solar Observing Station of the Beijing Astronomical Observatory. After the resolution of the 180° ambiguity of the transverse magnetic field and transformation of off-center vector magnetograms to the heliographic plane, we have determined the photospheric vertical current density and discussed the relationship with powerful flares. The following results were obtained: (a) The powerful 3B/X12 flare on June 9, 1991 was triggered by the interaction between the large-scale electric current system and magnetic flux of opposite polarity. (b) The kernels of the powerful Hβ flare (sites of the white-light flare) were close to the peaks of the vertical electric current density. (c) Some small-scale structures of the vertical current relative to the magnetic islands of opposite polarity have not been found. This probably implies that the electric current is not always parallel to the magnetic field in solar active regions.     

Development of a topological model for solar flares

The main theoretical studies of the process involved in solar flares have been made in the two-dimensional approximation. However, the preliminary studies made with three field components suggest that reconnection could take place in the separatrices, the separator (intersection of separatrices) being a privileged location for this process. As a consequence the sites of flare kernels must be located on the intersections of the separatrices with the photosphere. Therefore, in order to understand the role of interacting large-scale structures in solar flares, we have analysed the topology of three-dimensional potential and linear force-free fields. The magnetic field has been modelled by a distribution of charges or dipoles located below the photosphere. This modelling permits us to define the field connectivity by the charges or the dipoles at both ends of every field line.We found that the appearance of a separator above the photosphere is more likely when a parasitic bipole emerges outside the axis that joins the main polarities and when the field lines are characteristic of a field created by dipoles. The separatrices derived in the potential and force-free hypothesis have different shapes. However, in the strong field regions where flares usually occur, the separatrices of the potential and force-free field models become closer. This property makes possible the use of the potential field, as a first estimate, for computing the location in the photosphere of the separatrices and for comparing this location with the position of observed H kernels. Displacements of the separatrices of a force-free field result from modifications of the free energy of the field. Then force-free fields have the further capability of predicting the kernel displacement. In all cases a configuration suitable for prominence support is found above the separator.     

Chromospheric downflow velocities as a diagnostic in solar flares

We explore the dynamics of chromospheric condensations driven by evaporation during the impulsive phase of solar flares. Specifically, we find that the maximum chromospheric downflow speed obeys the approximate relation υ_d= 0.4 (F/ϱ_ch)^1/3, where F is that part of the flare energy flux driving chromospheric evaporation, and ϱ_ch is the mass density in the preflare chromosphere just below the preflare transition region. This implies that chromospheric downflows as measured by Hα asymmetries may be a powerful probe of flare energetics.

     

The Magnetic Structure and Generation of EUV Flare Ribbons

The `ribbons' of two-ribbon flares show complicated patterns reflecting the linkages of coronal magnetic field lines through the lower solar atmosphere. We describe the morphology of the EUV ribbons of the July 14, 2000 flare, as seen in SOHO, TRACE, and Yohkoh data, from this point of view. A successful co-alignment of the TRACE, SOHO/MDI and Yohkoh/HXT data has allowed us to locate the EUV ribbon positions on the underlying field to within ∼ 2′′, and thus to investigate the relationship between the ribbons and the field, and also the sites of electron precipitation. We have also made a determination of the longitudinal magnetic flux involved in the flare reconnection event, an important parameter in flare energetic considerations. There are several respects in which the observations differ from what would be expected in the commonly-adopted models for flares. Firstly, the flare ribbons differ in fine structure from the (line-of-sight) magnetic field patterns underlying them, apparently propagating through regions of very weak and probably mixed polarity. Secondly, the ribbons split or bifurcate. Thirdly, the amount of line-of-sight flux passed over by the ribbons in the negative and positive fields is not equal. Fourthly, the strongest hard X-ray sources are observed to originate in stronger field regions. Based on a comparison between HXT and EUV time-profiles we suggest that emission in the EUV ribbons is caused by electron bombardment of the lower atmosphere, supporting the hypothesis that flare ribbons map out the chromospheric footpoints of magnetic field lines newly linked by reconnection. We describe the interpretation of our observations within the standard model, and the implications for the distribution of magnetic fields in this active region.     

Spherical magnetic vortex in a uniform gravity field: A new exact solution and its applications for modeling solar flares and coronal spiders

The well-known Chandrasekhar-Prendergastmagnetostatic solution for a sphericalmagnetic vortex with axial symmetry squeezed externally by a potential magnetic field is of considerable interest both for describing the magnetic field of a star as a whole and for modeling solar active phenomena (flares, coronal spiders, etc.). This solution is generalized to the case of a uniform gravity field. In contrast to the Chandrasekhar-Prendergast model, the dependence of the plasma density in the spherical vortex on magnetic flux appears in the new solution. This expands considerably the class of magnetoplasma equilibria being analyzed and allows new scenarios for energy release in solar flares and coronal spiders to be proposed.     

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.     

Characteristics of active-region sources of solar wind near solar maximum

Previous studies of the source regions of solar wind sampled by ACE and Ulysses showed that some solar wind originates from open magnetic flux rooted in active regions. These solar wind sources were labeled active-region sources when the open flux was from a strong field region with no corresponding coronal hole in the NSO He 10830 Å synoptic coronal-hole maps. Here, we present a detailed investigation of several of these active-region sources using ACE and Ulysses solar wind data, potential field models of the corona, and solar imaging data. We find that the solar wind from these active-region sources has distinct signatures, e.g., it generally has a higher oxygen charge state than wind associated with helium-10830 Å coronal-hole sources, indicating a hotter source region, consistent with the active region source interpretation. We compare the magnetic topology of the open field lines of these active-region sources with images of the hot corona to search for corresponding features in EUV and soft X-ray images. In most, but not all, cases, a dark area is seen in the EUV and soft X-ray image as for familiar coronal-hole sources. However, in one case no dark area was evident in the soft X-ray images: the magnetic model showed a double dipole coronal structure consistent with the images, both indicating that the footpoints of the open field lines, rooted deep within the active region, lay near the separatrix between loops connecting to two different opposite polarity regions.