The possibility of energy accumulation in a current sheet above the NOAA 9077 active region prior to the flare on 14 July 2000

Current sheet (CS) creation and energy accumulation above the NOAA 9077 active region have been numerically simulated. The magnetic spots are approximated by vertical dipoles placed under the photosphere, and the system of resistive 3D MHD equations is solved for compressible plasma with anisotropic thermal conduction. Two neutral magnetic lines are present in the corona above the NOAA 9077 active region, and a vertical CS emerges in the vicinity of one of them. The energy accumulated in this CS is about 5×10³² erg. The j×B/c force in it accelerates plasma upward. The other neutral line is not suitable for CS creation.     

Current sheet creation by a super-Alfvénic jet in a bipolar field

Energy accumulation in a current sheet (CS) can occur during the injection of a fast plasma jet in a perpendicular magnetic field. A similar situation can occur in the solar corona when a flux of plasma appears under a magnetic arch. The flare can be produced at the CS disruption. The CS creation during plasma jet interaction with the magnetic field is demonstrated by numerical MHD simulation. The choice of dimensionless parameters Re, Re_m,, II, which are suitable for simulation of coronal phenomena, is discussed. When jet injection ceases, the CS evolution produces an unstable state and fast magnetic energy dissipation is observed.     

Calculation of force-free magnetic field with non-constant α

A numerical method is developed for solving the force-free magnetic field equation, × B = B, with spatially-varying . The boundary conditions required are the distribution of B _n (viz. normal component of the field on the photosphere) as well as the value of in the region of positive (or negative) B _n . Examples of calculations are presented for a simple model of a solar bipolar magnetic region. It is found that the field configuration and the energy stored in the field depend crucially on the distribution of . The present method can be applied to a more complex configuration observed on the Sun by making use of actual magnetic field measurements.On leave of absence from Department of Astronomy, University of Tokyo.     

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.     

Resistive tearing in line-tied magnetic fields: Slab geometry

The resistive tearing-mode instability of a current carrying plasma sheet is investigated including the stabilising photospheric line-tying boundary conditions. This end condition prohibits a single Fourier mode and so requires a series expansion in harmonics of the fundamental sheet excitation. Equilibria in which there exist field lines that do not connect to the photosphere are unstable provided the ratio of the sheet length to characteristic transverse scale is smaller than a critical value that depends on the equilibrium profile. Line-tying has a strong stabilising effect on the fundamental periodic mode. That tearing mode harmonic which develops close to the instability threshold, leads to a configuration with one X point and one 0 point. Its linear growth rate follows the usual constant- scaling with resistivity S ^-3/5, where S is the magnetic Reynolds number.     

The behaviour of neutral lines in two-dimensional magnetohydrodynamic equilibria

Nonlinear equilibrium solutions for two-dimensional magnetic arcades (/z = 0) using a Grad-Shafranov equation in which the axial magnetic field and the pressure are specified as functions of the component of the vector potential in the z direction are re-examined.To compute nonlinear solutions one is restricted to seeking solutions on finite computational domains with specified boundary conditions. We consider two basic models which have appeared in the literature. In one model the field is laterally restricted by means of Dirichlet boundary conditions and free to extend vertically by means of a Neumann condition at the top of the domain. For such fields, bifurcating solutions only appear for a narrow range of values for the parameter (the ratio of a typical length scale of the field to the gravitational scale height). Nevertheless, we show that the presence of this parameter is essential for bifurcating solutions in such domains. For the second model with Neumann conditions on three sides of the domain representing the region above the photosphere we do not find bifurcating solutions. Instead high-energy solutions with detached field lines evolve smoothly from low-energy solutions which have all field lines attached to the photosphere. Again the presence or absence of detached flux is dependent on the magnitude of for those fields which are evolved quasi-statically via an increase in the plasma pressure.     

Magnetic reconnection in the temperature minimum region and prominence formation

Magnetic reconnection at the photospheric boundary is an essential part of some theories for prominence formation. We consider a simple model for reconnection in this region. Parameters of the reconnecting current sheet are expressed in terms of the concentration and temperature of the outside dense and cold plasma, magnetic field intensity, and velocity of convective flows at the photosphere. The reconnection process is shown to be most efficient in a layer several hundred kilometers thick coinciding with the temperature minimum region of the solar atmosphere. The calculated upward flux of matter through the current sheet ( 10¹¹–10¹² g s^–1) is amply sufficient for prominence formation in the upper chromosphere or lower corona.     

Spectropolarimetric investigation of an Ellerman bomb: 2. Photospheric models

Semiempirical models of the photosphere of an Ellerman bomb in the NOAA 11024 active region were obtained using profiles of Stokes parameters I, Q, U, and V of photospheric lines. Spectropolarimetric observations were conducted using the French–Italian THEMIS telescope (Tenerife, Spain). The SIR inversion code [28] was used in the modeling. The models have two components: a magnetic flux tube and nonmagnetic surroundings. The dependences of temperature, magnetic field strength, inclination of the magnetic field vector, and line-of-sight velocity in the tube on the optical depth were obtained. The models demonstrate that the thermodynamic parameters of the Ellerman bomb photosphere differ considerably from those of the quiet photosphere. The temperature in the tube model varied nonmonotonically with height and deviated by up to 700–900 K from its values for the quiet photosphere. Downflows were observed in the lower and the upper photospheric layers. The line-of-sight velocity in the upper layers of the photosphere was as high as 17 km/s. The magnetic field strength in the models varied from 0.1–0.13 T in the lower photospheric layers to 0.04–0.07 T in the upper ones. The physical state of the photosphere did change in the course of observations.     

Explorer 34 magnetic field measurements near the tail current sheet and auroral activity

Explorer 34 (Imp 4) 2.56 s magnetic data during 131 traversals of the tail current sheet are presented along with simultaneous 2.5 min auroral electrojet indices AE and AL. The normal magnetic field,B , satellite crossing times and positions are tabulated for these 131 crossings.B is defined in the center of the sheet: it is the vector magnetic field at the time of field minimum during the crossing (B _x component changes sign). It is remarkable that the only normal components too large in magnitude to be classified as fine structure occur near the time of onset of an AE event. Cases are discussed where the normal component, defined near the plasma sheet edges, has the opposite sign compared to the normal component defined at the sheet center. For quiet times, the current sheet may be only about 1000 km thick within a 3R _e (Earth-radii) plasma sheet, and may carry some 10–15% of the total tail current.     

Coronal magnetic field equilibrium with discrete flux sources

A model of the equilibrium structure of the coronal magnetic field is developed, taking account of the fact that field lines are rooted in the photosphere, where field is concentrated into isolated flux tubes. The field is force-free, described by ×B = B, with constant; this field has special physical significance, being the state of mininum energy after small-scale reconnections, and is also mathematically convenient in that the principle of superposition can be used to construct complex geometries. First a model of a single loop is presented, with a flux source and sink pair at the photosphere; both point flux tubes and finite radius flux tubes are considered. Then more complex topologies with multiple sources and sinks are investigated. It is shown that significant topology changes arise for different values of, indicating the possibility that there can be energy changes through magnetic reconnection if the field evolves ideally and then relaxes to a linear state.     

Coronal force-free magnetic field: Source-surface model

Models of the magnetic field in the solar chromosphere and corona are still mainly based on theoretical extrapolations of photospheric measurements. For the practical calculation of the global field, the so-called source-surface model has been introduced, in which the influence of the solar wind is described by the requirement that the field be radial at some exterior (source) surface. Then the assumption that the field is current-free in the volume between the photosphere and this surface allows for its determination from the photospheric measurement. In the present paper a generalization of the source-surface model to force-free fields is proposed. In the generalized model the parameter( = ×B·B/B ²)must be non-constant (or vanish identically) and currents are restricted to regions with closed field lines. A mathematical algorithm for computing the field from boundary data is devised.     

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.     

Flare-like energy release by flux pile-up reconnection

Flux pile-up magnetic merging solutions are discussed using the simple robust arguments of traditional steady-state reconnection theory. These arguments determine a unique scaling for the field strength and thickness of the current layer, namely B _s^–1/3, l^2/3, which are consistent with a variety of plasma inflow conditions. Next we demonstrate that flux pile-up merging can also be understood in terms of exact magnetic annihilation solutions. Although simple annihilation models cannot provide unique reconnection scalings, we show that the previous current sheet scalings derive from an optimized solution in which the peak dynamic and magnetic pressures balance in the reconnection region. The build-up of magnetic field in the current sheet implicit in flux pile-up solutions naturally leads to the idea of saturation. Hydromagnetic pressure effects limit the magnetic field in the sheet, yielding an upper limit on the reconnection rate for such solutions. This rate is still far superior to the Sweet–Parker merging rate, which can be derived by seeking solutions that avoid all forms of saturation. Finally we compare time dependent numerical simulations of the coalescence instability with the optimized flux pile-up models. This comparison suggests that merging driven by the relatively slow approach of large flux systems may be favored in practice.     

Photospheric vortex flows as a cause for two-ribbon flares: A topological model

By using a topological model for the potential magnetic field above the photosphere, the appearance and development of the separator as a result of vortex plasma flows in the locality of the photospheric neutral line is considered. The possible relation of such vortex flows with a flare activity is revealed. The arrangement and shape of the flare ribbons in the chromosphere, the formation of X-ray intersecting loops, the early appearance of bright knots on flare ribbon edges are naturally explained by the model provided a reconnecting current sheet arises along the separator in the coronal magnetic field of active regions as a result of the evolution of the magnetic field sources in the photosphere.     

On polarimetry in solar active regions

Measurements of the circular polarization V in different lines show that the deduced magnetic field strength and flux are systematically influenced by variations of the line absorption coefficient from photosphere to spot and faculae.Disbalances between preceding and following flux seem to be due mainly to such variations rather than to real physical conditions in active regions.The spatial distribution of the normal component of the magnetic field in an active region near the disc center have been observed during two days using the temperature insensitive line Fe 6302.5. The initial field structure seems to become more and more bipolar. The increase of the flux exceeds that of the area thus suggesting the appearance of new magnetic fields. Backward extrapolation in time leads to a date of first appearance of the magnetic field which agrees with the appearance of first H anomalies.     

Active-Region Magnetic Structure Observed in the Photosphere and Chromosphere

The full magnetic vector has been measured in both the photosphere and chromosphere across sunspots and plage in NOAA Active Region 8299. We investigate the vertical magnetic structure above the umbral, penumbral and plage regions using quantitative statistical comparisons of the photospheric and chromospheric magnetic data. The results include: (1) a general decrease in average magnetic flux density with height; (2) the direct detection of the superpenumbral canopy in the chromosphere; (3) values for dB/dz which are consistent with earlier investigations when derived from a straight difference between the two measurements, but which are somewhat small when derived from the B=0 condition, (4) a monolithic structure in the umbrae which extends well into the upper chromosphere, with a very complex and varied structure in penumbrae and plage, as evidenced by (5) a uniform magnetic scale height in the umbrae with an abrupt jump to widely varying scale heights in penumbral and plage regions. Further, we find (6) evidence that field extrapolations using the photospheric flux as the boundary may not agree with expectations or with observed coronal structures as well as those which use the chromospheric magnetic flux as the extrapolation starting point.     

On the reconstruction of the nonlinear force-free coronal magnetic field from boundary data

Using a simple model in which the corona is represented by the half-space domain = {z > 0} and the photosphere by the boundary plane = {z = 0}, we discuss some important aspects of the general problem of the reconstruction of the magnetic field B in a small isolated coronal region from the values of the vector B¦ measured by a magnetograph over its whole basis. Assuming B to be force-free in : (i) we derive a series of relations which must be necessarily satisfied by the boundary field B¦ , and then by the magnetograph data if the force-free assumption is actually correct; (ii) we show how to extract directly from the measured B¦ some useful informations about the energy of B in and the topological structure of its field lines; (iii) we present a critical discussion of the two methods which have been proposed so far for computing effectively B in from B¦ .     

p Modes in and Away from a Sunspot

A time series of GONG Dopplergrams for the period 10–14 May 1997 from Udaipur and Big Bear sites has been used to measure the velocity fluctuations in a sunspot (NOAA active region 8038) and quiet photosphere simultaneously. We observe that the power of pre-dominant p mode is reduced in the sunspot as compared to quiet photosphere by 39–52% depending on the location of the sunspot region on the solar disk. We also observe a relative peak frequency deviation of p modes in the sunspot, of the order of 80–310 Hz, which shows a linear dependence on the magnetic field gradient in the active region. The maximum frequency deviation of 310 Hz on 12 May appears to be an influence of a long-duration solar flare that occurred in this active region. We interpret this relative peak frequency deviation as either due to power re-distribution of p modes in the sunspot or a consequence of frequency modulation of these modes along the magnetic flux tubes due to rapidly varying magnetic field structure.     

Thermal evolution of current sheets and flash phase of solar flares

The physical conditions in a stationary flow of the Petchek type, allowing reconnection between flux emerging from below the solar photosphere and a preexisting magnetic field, are discussed. It is shown that, when rising in the solar atmosphere, the reconnection region has at first a rather low temperature as compared with its environment. Above a certain critical height, however, this low temperature thermal equilibrium often ceases to be possible, and the sheet rapidly heats, seeking a new thermal equilibrium. During this dynamical process, current-driven microinstabilities may be triggered in the current sheet, giving rise to an enhanced resistivity. High energy particles might be produced by the induced electric field developed during the rapid readjustment of MHD flows that results from this change in the transport properties of the plasma.