Numerical simulation of reconnection in an emerging magnetic flux region

The resistive MHD equations are numerically solved in two dimensions for an initial-boundary-value problem which simulates reconnection between an emerging magnetic flux region and an overlying coronal magnetic field. The emerging region is modelled by a cylindrical flux tube with a poloidal magnetic field lying in the same plane as the external, coronal field. The plasma betas of the emerging and coronal regions are 1.0 and 0.1, respectively, and the magnetic Reynolds number for the system is 2 × 10³. At the beginning of the simulation the tube starts to emerge through the base of the rectangular computational domain, and, when the tube is halfway into the computational domain, its position is held fixed so that no more flux of plasma enters through the base. Because the time-scale of the emergence is slower than the Alfvén time-scale, but faster than the reconnection time-scale, a region of closed loops forms at the base. These loops are gradually opened and reconnected with the overlying, external magnetic field as time proceeds.The evolution of the plasma can be divided into four phases as follows: First, an initial, quasi-steady phase during which most of the emergence is completed. During this phase, reconnection initially occurs at the slow rate predicted by the Sweet model of diffusive reconnection, but increases steadily until the fast rate predicted by the Petschek model of slow-shock reconnection is approached. Second, an impulsive phase with large-scale, super-magnetosonic flows. This phase appears to be triggered when the internal mechanical equilibrium inside the emerging flux tube is upset by reconnection acting on the outer layers of the flux tube. During the impulsive phase most of the flux tube pinches off from the base to form a cylindrical magnetic island, and temporarily the reconnection rate exceeds the steady-state Petschek rate. (At the time of the peak reconnection rate, the diffusion region at the X-line is not fully resolved, and so this may be a numerical artifact.) Third, a second quasi-steady phase during which the magnetic island created in the impulsive phase is slowly dissipated by continuing, but low-level, reconnection. And fourth, a static, non-evolving phase containing a potential, current-free field and virtually no flow.During the short time in the impulsive phase when the reconnection rate exceeds the steady-state Petschek rate, a pile-up of magnetic flux at the neutral line occurs. At the same time the existing Petschek-slow-mode shocks are shed and replaced by new ones; and, for a while, both new and old sets of slow shocks coexist.     

Numerical Simulations of the Flux Tube Tectonics Model for Coronal Heating

In this paper we present results from 3D MHD numerical simulations based on the flux tube tectonics method of coronal heating proposed by Priest, Heyvaerts, and Title (2002). They suggested that individual coronal loops connect to the photosphere in many different magnetic flux fragments and that separatrix surfaces exist between the fingers connecting a loop to the photosphere and between individual loops. Simple lateral motions of the flux fragments could then cause currents to concentrate along the separatrices which may then drive reconnection contributing to coronal heating. Here we have taken a simple configuration with four flux patches on the top and bottom of the numerical domain and a small background axial field. Then we move two of the flux patches on the base between the other two using periodic boundary conditions such that when they leave the box they re-enter it at the other end. This simple motion soon causes current sheets to build up along the quasi-separatrix layers and subsequently magnetic diffusion/reconnection occurs.     

The magnetic structure of arch filament systems

Photographic-type magnetograms are used in conjunction with H filtergrams to study the structure and evolution of magnetic fields associated with arch filament systems. The magnetograms show that the opposite ends of the arch filaments are indeed rooted in photospheric magnetic fields of opposite polarity. Furthermore, these magnetic field systems are in every case new magnetic flux appearing at the solar surface. Time lapse studies show the detailed process by which the flux tubes emerge through the surface. First, supergranules bring individual strands of magnetic flux to the surface and sweep the two feet of the flux tube to opposite sides of the supergranule. Then, the flux tube rises through the chromosphere, creating a visible arch filament. It is also shown that the observed rotation of the axis of an arch filament system in the plane of the solar surface is caused by the emergence of successive flux loops, each possessing different axial tilts.     

The Magnetic Topological Structure and Energy of the 2B/X2 Flare in NOAA 8100

In this paper, we reconstruct the finite energy force-free magnetic field of the active region NOAA 8100 on 4 November 1997 above the photosphere. In particular, the 3-D magnetic field structures before and after a 2B/X2 flare at 05:58 UT in this region are analyzed. The magnetic field lines were extrapolated in close coincidence with the Yohkoh soft X-ray (SXR) loops accordingly. It is found that the active region is composed of an emerging flux loop, a complex loop system with differential magnetic field shear, and large-scale, or open field lines. Similar magnetic connectivity has been obtained for both instants but apparent changes of the twisting situations of the calculated magnetic field lines can be observed that properly align with the corresponding SXR coronal loops. We conclude that this flare was triggered by the interaction of an emerging flux loop and a large loop system with differential magnetic field shear, as well as large-scale, or open field lines. The onset of the flare was at the common footpoints of several interacting magnetic loops and confined near the footpoints of the emerging flux loop. The sheared configuration remained even after the energetic flare, as demonstrated by calculated values of the twist for the loop system, which means that the active region was relaxed to a lower energy state but not completely to the minimum energy state (two days later another X-class flare occurred in this region).     

Modeling of Local Magnetic Field Enhancements within Solar Flux Ropes

To model and study local magnetic-field enhancements in a solar flux rope we consider the magnetic field in its interior as a superposition of two linear (constant α) force-free magnetic-field distributions, viz. a global one, which is locally similar to a part of the cylinder, and a local torus-shaped magnetic distribution. The newly derived solution for a toroid with an aspect ratio close to unity is applied. The symmetry axis of the toroid and that of the cylinder may or may not coincide. Both the large and small radii of the toroid are set equal to the cylinder’s radius. The total magnetic field distribution yields a flux tube which has a variable diameter with local minima and maxima. In principle, this approach can be used for the interpretation and analysis of solar-limb observations of coronal loops.     

Numerical simulations of rotating axisymmetric sunspots

A numerical model of axisymmetric convection in the presence of a vertical magnetic flux bundle and rotation about the axis is presented. The model contains a compressible plasma described by the non-linear MHD equations, with density and temperature gradients simulating the upper layer of the Sun's convection zone. The solutions exhibit a central magnetic flux tube in a cylindrical numerical domain, with convection cells forming collar flows around the tube. When the numerical domain is rotated with a constant angular velocity, the plasma forms a Rankine vortex, with the plasma rotating as a rigid body where the magnetic field is strong, as in the flux tube, while experiencing sheared azimuthal flow in the surrounding convection cells, forming a free vortex. As a result, the azimuthal velocity component has its maximum value close to the outer edge of the flux tube. The azimuthal flow inside the magnetic flux tube and the vortex flow is prograde relative to the rotating cylindrical reference frame. A retrograde flow appears at the outer wall. The most significant convection cell outside the flux tube is the location for the maximum value of the azimuthal magnetic field component. The azimuthal flow and magnetic structure are not generated spontaneously, but decay exponentially in the absence of any imposed rotation of the cylindrical domain.     

The Importance of Photospheric Intense Flux Tubes for Coronal Heating

Dissipation of magnetic energy in the corona requires the creation of very fine scale-lengths because of the high magnetic Reynolds number of the plasma. The formation of current sheets is a natural possible solution to this problem and it is now known that a magnetic field that is stressed by continous photospheric motions through a series of equilibria can easily form such sheets. Furthermore, in a large class of 3D magnetic fields without null points there are locations, called quasi-separatrix layers (QSLs), where the field-line linkage changes drastically. They are the relevant generalisation of normal separatrices to configurations without nulls: along them concentrated electric currents are formed by smooth boundary motions and 3D magnetic reconnection takes place when the layers are thin enough. With a homogenous normal magnetic field component at the boundaries, the existence of thin enough QSL to dissipate magnetic energy rapidly requires that the field is formed by flux tubes that are twisted by a few turns. However, the photospheric field is not homogeneous but is fragmented into a large number of thin flux tubes. We show that such thin tubes imply the presence of a large number of very thin QSLs in the corona. The main parameter on which their presence depends is the ratio between the magnetic flux located outside the flux tubes to the flux inside. The thickness of the QSLs is approximately given by the distance between neighbouring flux tubes multiplied by the ratio of fluxes to a power between two and three (depending on the density of flux tubes). Because most of the photospheric magnetic flux is confined in thin flux tubes, very thin QSLs are present in the corona with a thickness much smaller than the flux tube size. We suggest that a turbulent resistivity is triggered in a QSL, which then rapidly evolves into a dynamic current sheet that releases energy by fast reconnection at a rate that we estimate to be sufficient to heat the corona. We conclude that the fragmentation of the photospheric magnetic field stimulates the dissipation of magnetic energy in the corona.     

An Analysis of the Formation of Interconnecting Loops

Fifty interconnecting loops (ILs) that are induced by new-born active regions are investigated. The formation period of four ILs including two same-hemisphere interconnecting loops (HILs) and two transequatorial loops (TLs) are analyzed. The magnetic flux related with these loops is studied. Considering the active region pairs related with the IL as a magnetic system, the total magnetic flux has a tendency of increasing for this system, the signs of net magnetic flux tend to be opposite for the active region pairs. There is no difference between HILs and TLs in this aspect.     

Flares in Sigmoidal Coronal Structures – a Case Study

We analyze radio observations, magnetograms and extrapolated field line maps, Hα filtergrams, and X-ray observations of two flare events (6 February 1992 in AR 7042 and 25 October 1994 in AR 7792) and study properties, evolution and energy release signatures of sigmoidal loop systems. During both events, the loop configuration seen in soft X-ray (SXR) images changes from a preflare sigmoidal shape to a relaxed post-flare loop system. The underlying magnetic field system consists of a quadrupolar configuration formed by a sheared arcade core and a remote field concentration. We demonstrate two possibilities: a sigmoidal SXR pattern can be due to a single continuous flux tube (the 1992 event). Alternatively, it can be due to a set of independent loops appearing like a sigmoid (the 1994 event). In both cases, the preflare and post-flare loops can be well reproduced by a linear force-free field and potential field, respectively, computed using preflare magnetograms. We find that thermal and non-thermal flare energy release indicators of both events become remarkably similar after applying spatial and temporal scale transformations. Using the spatial scaling between both events we estimated that the non-thermal energy release in the second event liberated about 1.7 times more energy per unit volume. A two-and-a-half times faster evolution indicates that the rate of the energy release per unit volume is more than four times higher in this event. A coronal type II burst reveals ignition and propagation of a coronal shock wave. In contrast, the first event, which was larger and released about a 10 times more energy during the non-thermal phase, was associated with a CME, but no type II burst was recorded. During both events, in addition to the two-ribbon flare process an interaction was observed between the flaring arcade and an emerging magnetic flux region of opposite polarity next to the dominant leading sunspot. The arcade flare seems to stimulate the reconnection process in an `emerging flux-type' configuration, which significantly contributes to the energy release. This regime is characterized by the quasiperiodic injection of electron beams into the surrounding extended field line systems. The repeated beam injections excite pulsating broadband radio emission in the decimetric-metric wavelength range. Each radio pulse is due to a new electron beam injection. The pulsation period (seconds) reflects the spatial scale of the emerging flux-type field configuration. Since broadband decimetric-metric radio pulsations are a frequent radio flare phenomenon, we speculate that opposite-polarity small-scale flux intrusions located in the vicinity of strong field regions may be an essential component of the energy release process in dynamic flares.     

Dynamics of magnetic flux loops in cooling-flow clusters of galaxies

We study the dynamics of magnetic flux loops embedded in an intracluster medium. In order to perform the calculations semi-analytically we make several simplifying assumptions, which include a treatment of only the two ends of the magnetic flux loops, assuming a simple relation between the density and the magnetic field and neglecting heat conduction. Our results indicate that the existence of a large number of magnetic flux loops can naturally lead to a multiphase intracluster medium. A multiphase intracluster medium is inferred from observations of the mass deposition rate in many cooling-flow clusters. The loops will be observed as 'filaments' having different density and temperature from their surroundings, namely X-ray filaments. X-ray filaments have been discovered in a few cases, although their discovery is controversial. Our model predicts that many such X-ray filaments will be discovered with future high-spatial-resolution X-ray telescopes, such as AXAF .     

Diagnostics of magnetic flux tube oscillations on the Sun based on fine-structure characteristics of the radio spectrum

The possibility of obtaining information about oscillation processes in magnetic flux tubes on the Sun by analyzing the undulating frequency drift of the zebra pattern in the dynamic spectrum of solar radio emission is discussed. It is shown that the oscillatory variation in the frequency of zebra stripes can be associated with fast magnetoacoustic (FMA) oscillations in a flux tube, which lead to oscillations in the magnetic field strength and electron number density. The October 25, 1994 event recorded by the radio spectrograph of the Astrophysical Institute Potsdam is used as an example to demonstrate the possibility of determining the parameters of FMA oscillations and the physical conditions in coronal magnetic loops from the observed zebra-pattern characteristics.     

Heating of coronal loops by fast mode MHD waves

A possible mechanism for the formation and heating of coronal loops through the propagation and damping of fast mode waves is proposed and studied in detail. Loop-like field structures are represented by a dipole field with the point dipole at a given distance below the solar surface. The density of the medium is determined by hydrostatic equilibrium along the field lines in an isothermal atmosphere. The fast mode waves propagating outward from the coronal base are refracted into regions with a low Alfvén speed and suffer collisionless damping when the gas pressure becomes comparable to the magnetic pressure. The propagation and damping of these waves are studied for three different cases: a uniform density at the coronal base, a density depletion within a given flux tube, and a density enhancement within a given flux tube. The fast mode waves are found to be important in the formation and heating of the loops if the wave energy flux density is of the order 10⁵ ergs cm^-2 s^-1 at the coronal base.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Constructing the Coronal Magnetic Field By Correlating Parameterized Magnetic Field Lines With Observed Coronal Plasma Structures

A method is presented for constructing the coronal magnetic field from photospheric magnetograms and observed coronal loops. A set of magnetic field lines generated from magnetogram data is parameterized and then deformed by varying the parameterized values. The coronal flux tubes associated with this field are adjusted until the correlation between the field lines and the observed coronal loops is maximized. A mathematical formulation is described which ensures that (i) the normal component of the photospheric field remains unchanged, (ii) the field is given in the entire corona over an active region, (iii) the field remains divergence-free, and (iv) electric currents are introduced into the field. It is demonstrated that a parameterization of a potential field, comprising a radial stretching of the field, can provide a match for a simple bipolar active region, AR 7999, which crossed the central meridian on 1996 November 26. The result is a non-force-free magnetic field with the Lorentz force being of the order of 10^–5.5 g cm s^–2 resulting from an electric current density of 0.079 A m^–2. Calculations show that the plasma beta becomes larger than unity at a relatively low height of 0.25 r supporting the non-force-free conclusion. The presence of such strong non-radial currents requires large transverse pressure gradients to maintain a magnetostatic atmosphere, required by the relatively persistent nature of the coronal structures observed in AR 7999. This scheme is an important tool in generating a magnetic field solution consistent with the coronal flux tube observations and the observed photospheric magnetic field.     

Asymmetric flux loops in active regions,II

We propose that magnetic flux loops in the subphotospheric layers of the Sun are seriously asymmetrical as a consequence of the drag force exerted on them because of the different rotational rate of the surrounding plasma. In numerical models of stationary slender flux loops in the plane parallel approximation we show that a serious tilt is both possible and probable. Observational facts (see van Driel-Gesztelyi and Petrovay, 1989; Paper I) strongly support the case for high asymmetry. The different stability of p and f spots may also be related to such an asymmetry.The tilts are very sensitive to the rotational profile and to the magnetic field structure. Nevertheless the characteristic maximal tilts can be tentatively estimated to be 20° for thin flux tubes and 5° for thick tubes.For two of the five observational consequences of such a tilt (described in detail in Paper I) order-of-magnitude estimates of the effects are given. The estimates are in reasonable accord with observations.We also explore the possibilities of an inverse treatment of the problem whereby subphotospheric rotation and/or flux tube shapes can be inferred from observations of velocities of photospheric spot motions. In particular we demonstrate how analytic inverse solutions can be obtained in special cases.     

Twisted magnetic flux tubes: Effect of small twist

The shape of a magnetic flux tube is investigated when photospheric motion causes small twist at the magnetic footpoints. Using a Fourier-Bessel series expansion, the previous results of Zweibel and Boozer (1985) and Steinolfson and Tajima (1987), when the twist is small, are substantiated. A twisting motion that is restricted to a finite region is investigated. Inside the twisted region, the tube contracts, but in the outer region the field remains straight, except for a slight expansion at the outside of the loop near the footpoints. The amount of twist depends on the radial position and can in fact be larger in the contracted region with the twist decreasing as the tube expands. An axial boundary-layer region is present, as noted by the above authors, through which the field adjusts to the line-tied magnetic footpoint positions. An analysis of the boundary layer shows that the thickness remains constant as the loop-length is increased with the result that the main part of the loop has constant cross-sectional area and can be described by cylindrically-symmetric fields. This new 1-D model predicts the main behaviour of the loop without the need to solve the more complicated 2-D problem directly. It is speculated that the boundary layers will remain even when the twist becomes large and a simple example is presented. A detailed parametric study of different twist profiles shows how the central part of the loop responds.Using the result that the majority of the loop can be described by a constant cross-sectional area, a model for a toroidal loop is presented that models coronal loops in a more realistic manner. The main result from this section is that the coronal loops can only remain in equilibrium if they are confined by an external magnetic field (possibly potential in nature) and not by a gas pressure unless additional physical effects are included.     

Spot signatures of a solar‐type dynamo in close binary stars

Magnetic activity signatures in the atmosphere of active stars can be used to place constrains on the underlying processes of flux transport and dynamo operation in its convective envelope. The ‘solar paradigm’ for magnetic activity suggests that the magnetic field is amplified and stored at the base of the convection zone. Once a critical field strength is exceeded, perturbations initiate the onset of instabilities and the growth of magnetic flux loops, which rise through the convection zone, emerge at the stellar surface, and eventually lead to the formation of starspots and active regions. In close binaries, the proximity of the companion star breaks the rotational symmetry. Although the magnitude of tidal distortions is rather small, non‐linear MHD simulations have nevertheless shown in the case of main‐sequence binary components that they can cause non‐uniform surface distributions of flux tube eruptions. The present work extends the investigation to post‐mainsequence components to explore the specific influence of the stellar structure on the surface pattern of erupting flux tubes. In contrast to the case of main‐sequence components, where the consistency between simulation results and observations supports the presumption of a solar‐like dynamo mechanism, the numerical results here do not recover the starspot properties frequently observed on evolved binary components. This aspect points out an insufficiency of the applied flux tube model and leads to the conclusion that additional flux transport and possibly amplification mechanisms have to be taken into account. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetic field rearrangement by accelerated particles near a shock front

We solve the self-consistent problem of the generation of a static magnetic field by the electric current of accelerated particles near a strong plane MHD shock front. We take into account the back reaction of the field on the particle diffusion tensors and the background plasma parameters near the front. Various states that differ significantly in static magnetic-field strength are shown to be possible near a strong front. If the initial field has a component normal to the front, then its components parallel to the front are suppressed by accelerated particles by several orders of magnitude. Only the component perpendicular to the front remains. This field configuration for uniform particle injection at the front does not lead to the generation of an additional field, and, in this sense, it is stable. If the initial field is parallel to the front, then either its significant enhancement by two or three orders of magnitude or its suppression by several orders of magnitude is possible. The phenomenon under consideration is an example of the self-organization of plasma with a magnetic field in a strongly nonequilibrium system. It can significantly affect the efficiency of particle acceleration by the shock front and the magnetobremsstrahlung of the accelerated particles.     

Radiative transfer across a magnetic flux tube

In the coming years, some solar telescopes will be able to yield the Stokes' parameters of polarized light with a resolution better than 1 arc sec (0.3 arc sec for THEMIS). We have simulated the Stokes' parameters of a solar magnetic flux tube as seen with such a resolution. We have shown that, observing with a line-of-sight not parallel to the axis of the flux tube (assumed vertical and axisymmetric), it is possible to see differences between different configurations of the magnetic field inside the flux tube (presence, and in what direction, of an azimuthal component of the field). Furthermore, along such a line-of-sight, the polarization profiles of any atomic line are strongly absorbed at the line center. We then suggest a strategy to infer the structure of the magnetic field from observations at high spatial resolution.     

Topological Departures from Translational Invariance along a Filament Observed by THEMIS

We study the topology of the 3D magnetic field in a filament channel to address the following questions: Is a filament always formed in a single flux tube? How does the photospheric magnetic field lead to filament interruptions and to feet formation? What is the relation between feet-related field lines and the parasitic polarities? What can topological analyses teach us about EUV filament channels? To do so, we consider a filament observed on 6 October 2004 with THEMIS/MTR, in Hα with the full line profile simultaneously and cospatially with its photospheric vector magnetic field. The coronal magnetic field was calculated from a “linear magnetohydrostatic” extrapolation of a composite THEMIS-MDI magnetogram. Its free parameters were adjusted to get the best match possible between the distribution of modeled plasma-supporting dips and the Hα filament morphology. The model results in moderate plasma β≤1 at low altitudes in the filament, in conjunction with non-negligible departures from force-freeness measured by various metrics. The filament here is formed by a split flux tube. One part of the flux tube is rooted in the photosphere aside an observed interruption in the filament. This splitted topology is due to strong network polarities on the edge of the filament channel, not to flux concentrations closer to the filament. We focus our study to the northwest portion of the filament. The related flux tube is highly fragmented at low altitudes. This fragmentation is due to small flux concentrations of two types. First, some locally distort the tube, leading to noticeable thickness variations along the filament body. Second, parasitic polarities, associated with filament feet, result in secondary dips above the related local inversion line. These dips belong to long field lines that pass below the flux tube. Many of these field lines are not rooted near the related foot. Finally, the present model shows that the coronal void interpretation cannot be ruled out to interpret the wideness of EUV filament channels.