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.     

Polarity neutral lines on the solar surface and magnetic structures in the corona

This paper elucidates the topological relationship between the distribution of polarity neutral lines on the solar surface and the interspersion of closed field lines among open field lines in the corona. The solar surface contains polarity neutral lines, that are spatially nested in a series-and-parallel hierarchy. The corona is partitioned by separatrix surfaces into a corresponding hierarchy of nested magnetic cells. The complexity of the magnetic structure of the corona consists in the embedding of magnetic cells of closed field lines amid open field lines.Polarity neutral lines lie necessarily on the foot surfaces of magnetic cells that are filled with closed field lines. There are two topologically distinct types of magnetic cells of closed field lines: closed and open. Only the open cells are overlain by current sheets. Each of the heliospheric current sheets separates the open field lines encircled by an open cells from the open field lines encircling the cell. Since closed cells have no images in the outer corona, the cell structure of the latter reflects those polarity neutral lines associated with the open cells in the lower corona. Accordingly, there are fewer heliospheric current sheets, as revealed by magnetic neutral lines on the source surface, in interplanetary space than polarity neutral lines on the solar surface.     

Effects of Complexity on the Flux-Tube Tectonics Model

The quiet-Sun magnetic field emerges through the solar photosphere in a multitude of mixed-polarity magnetic concentrations and is subsequently tangled up into intricate regions of interconnecting flux. Moreover, since these discrete concentrations are likely to be extremely small in size, with fluxes of around only 10¹⁷ Mx, the number of such flux sources in, say, a supergranule, will be extremely large. The flux-tube tectonics model of Priest, Heyvaerts, and Title (2002) demonstrated how the formation and dissipation of current sheets along the separatrices that separate the regions of different connectivity are likely to make an important contribution to coronal heating. Since the full complexity of the magnetic field is below present observable scales, this study examines the effect of having the magnetic flux emerge through configurations structured on smaller and smaller scales. It is found that, by fixing the amount of flux emerging into a given 2D region, the main factors influencing the current build-up along the separatrices are the number of sources through which the flux emerges and the spatial distribution of the sources on the photosphere. The free energy (i.e., that above potential) is stored lower and lower in the atmosphere as the complexity of the system increases. A simple comparison is then made between coronal heating by separator currents and by separatrix currents. It is found that both result in comparable amounts of energy release, with separatrix heating being the more dominant.     

Observation of a Complex Solar Wind Reconnection Exhaust from Spacecraft Separated by over 1800 R E

We analyze Wind, ACE, and STEREO (ST-A and ST-B) plasma and magnetic field data in the vicinity of the heliospheric current sheet (HCS) crossed by all spacecraft between 22:15 UT on 31 March and 01:25 UT on 1 April 2007 corresponding to its observation at ST-A and ST-B, which were separated by over 1800 R _E (or over 1200 R _E across the Sun?–?Earth line). Although only Wind and ACE provided good ion flow data in accord with a solar wind magnetic reconnection exhaust at the HCS, the magnetic field bifurcation typical of such exhausts was clearly observed at all spacecraft. They also all observed unambiguous strahl mixing within the exhaust, consistent with the sunward flow deflection observed at Wind and ACE and thus with the formation of closed magnetic field lines within the exhaust with both ends attached to the Sun. The strong dawnward flow deflection in the exhaust is consistent with the exhaust and X-line orientations obtained from minimum variance analysis at each spacecraft so that the X-line is almost along the GSE Z-axis and duskward of all the spacecraft. The observation of strahl mixing in extended and intermittent layers outside the exhaust by ST-A and ST-B is consistent with the formation of electron separatrix layers surrounding the exhaust. This event also provides further evidence that balanced parallel and antiparallel suprathermal electron fluxes are not a necessary condition for identification of closed field lines in the solar wind. In the present case the origin of the imbalance simply is the mixing of strahls of substantially different strengths from a different solar source each side of the HCS. The inferred exhaust orientations and distances of each spacecraft relative to the X-line show that the exhaust was likely nonplanar, following the Parker spiral orientation. Finally, the separatrix layers and exhausts properties at each spacecraft suggest that the magnetic reconnection X-line location and/or reconnection rate were variable in both space and time at such large scales.

     

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.     

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.     

On the self-consistent model of an axisymmetric radio pulsar magnetosphere

We consider a model of axisymmetric neutron star magnetospheres. In our approach, the current density in the region of open field lines is constant and the returning current flows in a narrow layer along the separatrix. In this case, the stream equation describing the magnetic field structure is linear both in the open and closed regions; the main problem is matching the solutions along the separatrix. We demonstrate that it is the stability condition on the separatrix that allows us to obtain a unique solution of the problem. In particular, the zero point of magnetic field is shown to be located near the light cylinder. Moreover, the hypothesis of the existence of the non-linear Ohm's Law, connecting the potential drop in the pair creation region and the longitudinal electric current flowing in the magnetosphere, is confirmed.     

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.     

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.     

大型太阳活动区磁场的一个模型

用时间缓变的非线性无力场模拟超级活动区（弧岛式大型δ黑子）的磁场位形。这个复杂磁场包含了向量磁场的主要观测特征：正负磁流极端不平衡性（正负磁流之比为１：６）,Ｕ形磁反变线,局域磁场的二极子、四极子差异性。模拟结果厅用来解释一些观测结果：（１）大耀斑主要产生在Ｕ形中性线的磁性混杂区或四极子区（２）Ｕ形反变线的准双极性区几乎没有大耀斑很小。（３）活动区内部的大型旋转运动和磁沲运动会导致四极子场磁拓扑分     

On neutral sheets in the solar wind

The structure and dynamics of neutral sheets in the solar wind is examined. The internal magnetic topology of the sheet is argued to be that of thin magnetic tongues greatly distended outward by the expansion inside the sheet. Due to finite conductivity effects, outward flow takes place across field lines but is retarded relative to the ambient solar wind by the reverse J×B force. The sheet thickness as well as the internal transverse magnetic field are found to be proportional to the electrical conductivity to the inverse one third power. Estimating a conductivity appropriate for a current carried largely by the ions perpendicular to the magnetic field, we find sheet dimensions of the order of 500km representative for the inner solar corona. For a radial field of strength 1/2G at 2R , the transverse field there is about 2 × 10^–3G and decreases outward rapidly.The energy release in the form of Joulean dissipation inside the sheet is estimated. It is concluded that ohmic heating in current sheets is not a significant source of energy for the overall solar wind expansion, mainly because these structures occupy only a small percentage of the total coronal volume. However, the local energy release through this mechanism is found to be large - in fact, over 7 times that expected to be supplied by thermal conduction. Therefore, ohmic heating is probably a dominant energy source for the dynamical conditions within the sheet itself.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Theoretical study of onset conditions for solar eruptive processes

We apply the model of quasistatic equilibrium sequences to describe the time development of magnetic field structures in the plasma of the solar corona, and to determine onset points of a dynamical evolution. The representation of the magnetic field by Euler potentials provides a realistic modeling of the photospheric boundary conditions. We present a numerical method suited for the computation of magnetohydrodynamic equilibrium states and for analysing their stability against perturbations within ideal MHD. Pressure and magnetic footpoint displacement can be prescribed separately as boundary conditions. We consider magnetic arcade structures typical for large two-ribbon flares. Our results indicate that a finite pressure gradient seems to be essential for the existence of onset points. Furthermore, it is shown that magnetic shear destabilizes for intermediate values, but can have a stabilizing effect for a large amount of shear.     

A coronal magnetic field model with horizontal volume and sheet currents

When globally mapping the observed photospheric magnetic field into the corona, the interaction of the solar wind and magnetic field has been treated either by imposing source surface boundary conditions that tacitly require volume currents outside the source surface (Schatten, Wilcox, and Ness, 1969) or by limiting the interaction to thin current sheets between oppositely directed field regions (Wolfson, 1985). Yet observations and numerical MHD calculations suggest the presence of non-force-free volume currents throughout the corona as well as thin current sheets in the neighborhoods of the interfaces between closed and open field lines or between oppositely directed open field lines surrounding coronal helmet-streamer structures. This work presents a model including both horizontal volume currents and streamer sheet currents. The present model builds on the magnetostatic equilibria developed by Bogdan and Low (1986) and the current-sheet modeling technique developed by Schatten (1971). The calculation uses synoptic charts of the line-of-sight component of the photospheric magnetic field measured at the Wilcox Solar Observatory. Comparison of an MHD model with the calculated model results for the case of a dipole field and comparison of eclipse observations with calculations for CR 1647 (near solar minimum) show that this horizontal current-current-sheet model reproduces polar plumes and axes of corona streamers better than the source-surface model and reproduces coronal helmet structures better than the current-sheet model.     

Turbulence in fast-mode shocks as a triggering mechanism in a solar flare

If a solar flare originates from the dissipation of magnetic energy, available in abundance in a larger region, this dissipation must take place very rapidly. A local topological change in the magnetic field structure may be sufficient to start the dissipation process. Such a change in topology might be obtained by fast reconnection in a smaller region, such as e.g. in the Sweet-Parker model, as a result of current-driven microinstabilities.Among the candidates satisfying the requirements to obtain large enough currents, such as magnetically neutral or current sheets and MHD shocks, the latter are shown to be most probable. In a fast MHD shock the (thermal) results of turbulence do in fact destroy the conditions for turbulence. However, in this work we show numerically that the nonlinear steepening mechanism of such a shock is able to restore the driving current for a large range of parameters and over a long time. This is still true if the most difficult threshold for turbulence, being that for Langmuir turbulence, is to be achieved. The critical parameter, not only for the occurrence of turbulence but also for the restoration of the driving current, is the shock thickness.     

Magnetic flux of colinear bipolar spot pairs

It has been widely conjectured that solar flares are energized by the magnetic energy stored in complex active regions. Paradoxically, however, in attempting to show that magnetic changes cause or characterize flares, solar magnetic observations have produced equivocal results.In previous attempts at resolving the paradox, it has been contended that magnetic measurements are simply imprecise or that magnetic theories of flares are incorrect. We present an alternative explanation: the present use of magnetograms to examine active region structure through numerical integration of miscellaneous field lines (under various force-free assumptions) provides qualitative information only and does not utilize the quantitative information available. Therefore, we propose a new approach to the analysis of magnetograms which is illustrated with a highly symmetrized example that permits integration in closed form. The proposed approach exploits the cellular structure of the flux of field lines present in a complex active region. The various topological connectivities distinguish parent and daughter flux cells. A function F is developed expressing the flux partitioned into the daughter cell of interconnected field lines in a potential field. This F is a function of the location, strength, and relative motions of the photospheric sources. Then dF/dt is used as an EMF in the direct calculation of the stored magnetic energy available for flare production. In carrying out this program the flux partitioning surface (separatrix) is calculated along with its line of self-intersection (separator). The separator is the location of the principal energy release site.     

Flux linkages of bipolar sunspot groups: A computer study

Past studies of the structure of solar magnetic fields have used magnetograph data to compute selected field lines for comparison with the morphology of structures seen in various spectral wavelengths. While those analyses examine one of the integral properties of magnetic fields (field lines), they are not complete since they fail to determine the other important integral property: the boundaries of the flux of field lines of given connectivity. In the present analysis we determine such a system of boundaries, called separatrices, for the current free field of two p-f spot pairs so as to exhibit the line of self-intersection, called the separator. The analysis is compared with previous analytical work. These computer results, confirming earlier studies carried out using iron fillings, show that the separatrix has the form of two intersecting ovoids, defining four flux cells. New features which have emerged from this study include the observation that the projections of the separatrix in a plane perpendicular to the separator at its highest point do not intersect at 90° as has been widely believed, but rather closer to 60° in the case studied. The separator is very nearly circular over most of its length. The two neutral points (B = 0) which appear at the photospheric ends of the separator have the mixed radial-hyperbolic form as expected, a feature requiring every field line lying on the separatrix to connect with at least one of the two neutral points. The rotation of line direction with height (shear) is graphically illustrated in the potential field case studied here. We also exhibit a magnetic arcade.     

Interaction of Weak Shock Waves with Current Sheets in an Active Region to Produce Nanoflares and Chains of Type I Radio Bursts

Interaction of weak shock waves with a current sheet is investigated by a two-dimensional numerical magnetohydrodynamic model. In accordance with solar coronal conditions, a ratio of thermal to magnetic pressures of 0.1 and a shock Alfvén Mach number slightly above 1 are considered. It is found that even weak shock waves trigger magnetic field reconnection in current sheets. Based on this result, it is suggested that drifting chains of type I radio bursts are radio manifestations of the interactions of weakly super-Alfvénic shock waves with pre-existing current sheets distributed in an active region. This model of type I noise storms is then discussed in connection with the concept of nanoflares (localized reconnections) and the heating of the solar corona.     

Sharp Changes of Solar Wind Ion Flux and Density Within and Outside Current Sheets

Analysis of the Interball-1 spacecraft data (1995 – 2000) has shown that the solar wind ion flux sometimes increases or decreases abruptly by more than 20% over a time period of several seconds or minutes. Typically, the amplitude of such sharp changes in the solar wind ion flux (SCIFs) is larger than 0.5×10⁸ cm⁻² s⁻¹. These sudden changes of the ion flux were also observed by the Solar Wind Experiment (SWE), on board the Wind spacecraft, as the solar wind density increases and decreases with negligible changes in the solar wind velocity. SCIFs occur irregularly at 1 AU, when plasma flows with specific properties come to the Earth’s orbit. SCIFs are usually observed in slow, turbulent solar wind with increased density and interplanetary magnetic field strength. The number of times SCIFs occur during a day is simulated using the solar wind density, magnetic field, and their standard deviations as input parameters for a period of five years. A correlation coefficient of ∼0.7 is obtained between the modelled and the experimental data. It is found that SCIFs are not associated with coronal mass ejections (CMEs), corotating interaction regions (CIRs), or interplanetary shocks; however, 85% of the sector boundaries are surrounded by SCIFs. The properties of the solar wind plasma for days with five or more SCIF observations are the same as those of the solar wind plasma at the sector boundaries. One possible explanation for the occurrence of SCIFs (near sector boundaries) is magnetic reconnection at the heliospheric current sheet or local current sheets. Other probable causes of SCIFs (inside sectors) are turbulent processes in the slow solar wind and at the crossings of flux tubes.     

Analytical theory of tachocline transport at mid latitudes

We provide a theory of magnetic diffusion, momentum transport, and mixing in the solar tachocline by considering magnetohydrodynamics (MHD) turbulence on a β plane subject to a large scale shear (provided by the latitudinal differential rotation). In the strong magnetic field regime, we find that the turbulent viscosity and diffusivity are reduced by magnetic fields only, similarly to the two-dimensional MHD case (without Rossby waves). In the weak magnetic field regime, we find a crossover scale (L_R) from a Alfvén dominated regime (on small scales) to a Rossby dominated regime (on large scales). For parameter values typical of the tachocline, L_R is larger than the solar radius so that Rossby waves are unlikely to play an important role in the transport of magnetic field and angular momentum. This is mainly due to the enhancement of magnetic back-reaction by shearing which efficiently generates small scales, thus strong currents. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)