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.     

Aspects of Three-Dimensional Magnetic Reconnection – (Invited Review)

In this review paper we discuss several aspects of magnetic reconnection theory, focusing on the field-line motions that are associated with reconnection. A new exact solution of the nonlinear MHD equations for reconnective annihilation is presented which represents a two-fold generalization of the previous solutions. Magnetic reconnection at null points by several mechanisms is summarized, including spine reconnection, fan reconnection and separator reconnection, where it is pointed out that two common features of separator reconnection are the rapid flipping of magnetic field lines and the collapse of the separator to a current sheet. In addition, a formula for the rate of reconnection between two flux tubes is derived. The magnetic field of the corona is highly complex, since the magnetic carpet consists of a multitude of sources in the photosphere. Progress in understanding this complexity may, however, be made by constructing the skeleton of the field and developing a theory for the local and global bifurcations between the different topologies. The eruption of flux from the Sun may even sometimes be due to a change of topology caused by emerging flux break-out. A CD-ROM attached to this paper presents the results of a toy model of vacuum reconnection, which suggests that rapid flipping of field lines in fan and separator reconnection is an essential ingredient also in real non-vacuum conditions. In addition, it gives an example of binary reconnection between a pair of unbalanced sources as they move around, which may contribute significantly to coronal heating. Finally, we present examples in TRACE movies of geometrical changes of the coronal magnetic field that are a likely result of large-scale magnetic reconnection. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1005248007615     

Magnetic Energy Release in Flux Pile-up Merging

The problem of pressure limitations on the rate of flux pile-up magnetic reconnection is studied. We first examine the recent suggestion of Jardine and Allen (1998) for moderating the build-up of magnetic pressure in the current sheet by considering inflows with nonzero vorticity. An analytic argument shows, however, that unbounded magnetic pressures in the limit of small resistivities can be avoided only at the cost of unphysical dynamic pressures in the plasma. Hence, the pressure limitation on the reconnection rate in a low-beta plasma cannot be avoided completely. Nevertheless, we demonstrate that reconnection can be more rapid in a new solution that balances the build-up in dynamic pressure against both the plasma and magnetic pressures. This exact MHD solution has the characteristics of merging driven by the coalescence instability. The maximum energy release rate of the model is capable of explaining a modest solar flare.     

Coronal heating by magnetic reconnection

The theory of magnetic reconnection has advanced substantially over the past few years. There now exists a new generation of fast two-dimensional models known as almost-uniform reconnection and nonuniform reconnection, depending on the boundary conditions. Also, we are beginning to explore the uncharted region of three-dimensional reconnection, where regimes of “spine reconnection” and “fan reconnection” have been discovered. Furthermore, part of the coronal heating problem appears to have been solved with recent observational support for the Converging Flux Model in which heating is produced by coronal reconnection driven by footpoint motions.     

Test particle acceleration in torsional spine magnetic reconnection

Three-dimensional (3D) magnetic reconnection is taking place commonly in astrophysical and space plasmas, especially in solar flares which are rich sources of highly energetic particles. One of the proposed mechanisms for steady-state 3D magnetic reconnection is “torsional spine reconnection”. By using the magnetic and electric fields for “torsional spine reconnection”, we numerically investigate the features of test particle acceleration with input parameters for the solar corona. We show that efficient acceleration of a relativistic proton is possible near the null point where it can gain up to 100 MeV of kinetic energy within a few milliseconds. However, varying the injection position results in different scenarios for proton acceleration. A proton is most efficiently accelerated when it is injected at the point where the magnetic field lines change their curvature in the fan plane. Moreover, a proton injected far away from the null point cannot be accelerated and, even in some cases, it is trapped in the magnetic field. In addition, adopting either spatially uniform or non-uniform localized plasma resistivity does not much influence the features of trajectory.     

The rate of flux pile-up magnetic reconnection in reduced MHD

The rate of two-dimensional flux pile-up magnetic reconnection is known to be severely limited by gas pressure in a low-beta plasma of the solar corona. As earlier perturbational calculations indicated, however, the pressure limitation should be less restrictive for three-dimensional flux pile-up. In this paper the maximum rate of reconnection is calculated in the approximation of reduced magnetohydrodynamics (RMHD), which is valid in the solar coronal loops. The rate is calculated for finite-magnitude reconnecting fields in the case of a strong axial field in the loop. Gas pressure effects are ignored in RMHD but a similar limitation on the rate of magnetic merging exists. Nevertheless, the magnetic energy dissipation rate and the reconnection electric field can increase by several orders of magnitude as compared with strictly two-dimensional pile-up. Though this is still not enough to explain the most powerful solar flares, slow coronal transients with energy release rates of order 10²⁵– 10²⁶ erg s^–1and heating of quiet coronal loops are within the compass of the model.     

Interchange Slip-Running Reconnection and Sweeping SEP Beams

We present a new model to explain how particles (solar energetic particles; SEPs), accelerated at a reconnection site that is not magnetically connected to the Earth, could eventually propagate along the well-connected open flux tube. Our model is based on the results of a low-β resistive magnetohydrodynamics simulation of a three-dimensional line-tied and initially current-free bipole, which is embedded in a non-uniform open potential field. The topology of this configuration is that of an asymmetric coronal null point, with a closed fan surface and an open outer spine. When driven by slow photospheric shearing motions, field lines, initially fully anchored below the fan dome, reconnect at the null point, and jump to the open magnetic domain. This is the standard interchange mode as sketched and calculated in 2D. The key result in 3D is that reconnected open field lines located in the vicinity of the outer spine keep reconnecting continuously, across an open quasi-separatrix layer, as previously identified for non-open-null-point reconnection. The apparent slipping motion of these field lines leads to formation of an extended narrow magnetic flux tube at high altitude. Because of the slip-running reconnection, we conjecture that if energetic particles would be traveling through, or be accelerated inside, the diffusion region, they would be successively injected along continuously reconnecting field lines that are connected farther and farther from the spine. At the scale of the full Sun, owing to the super-radial expansion of field lines below 3?R _⊙, such energetic particles could easily be injected in field lines slipping over significant distances, and could eventually reach the distant flux tube that is well-connected to the Earth.     

2 1/2-Dimensional Reconnection Model and Energy Release in Solar Flares

We employ a 2 1/2-dimensional reconnection model to analyse different aspects of the energy release in two-ribbon flares. In particular, we investigate in which way the systematic change of inflow region variables, associated with the vertical elongation of current sheet, affects the flare evolution. It is assumed that as the transversal magnetic field decreases, the ambient plasma-to-magnetic pressure ratio increases, and the reconnection rate diminishes. As the transversal field decreases due to the arcade stretching, the energy release enhances and the temperature rises. Furthermore, the magnetosonic Mach number of the reconnection outflow increases, providing the formation of fast mode standing shocks above the flare loops and below the erupting flux rope. Eventually, in the limit of a very small transversal field the reconnection becomes turbulent due to a highly non-linear response of the system to small fluctuations of the transversal field. The turbulence results in the energy release fragmentation which increases the release efficiency, and is likely to be responsible for the impulsive phase of the flare. On the other hand, as the current sheet stretches to larger heights, the ambient plasma-to-magnetic pressure ratio increases which causes a gradual decrease of the reconnection rate, energy release rate, and temperature in the late phase of flare. The described magnetohydrodynamical changes affect also the electron distribution function in space and time. At large reconnection rates (impulsive phase of the flare) the ratio of the inflow-to-outflow magnetic field strength is much smaller than at lower reconnection rates (late phase of the flare), i.e., the corresponding loss-cone angle becomes narrower. Consequently, in the impulsive phase a larger fraction of energized electrons can escape from the current sheet downwards to the chromosphere and upwards into the corona – the dominant flare features are the foot-point hard X-ray sources and type III radio bursts. On the other hand, at low reconnection rates, more particles stay trapped in the outflow region, and the thermal conduction flux becomes strongly reduced. As a result, a superhot loop-top, and above-the-loop plasma appears, as sometimes observed, to be a dominant feature of the gradual phase.     

Chaos-induced resistivity of collisionless magnetic reconnection in the presence of a guide field

One of the most puzzling problems in astrophysics is to understand the anomalous resistivity in collisionless magnetic reconnection that is believed extensively to be responsible for the energy release in various eruptive phenomena. The magnetic null point in the reconnecting current sheet, acting as a scattering center, can lead to chaotic motions of particles in the current sheet, which is one of the possible mechanisms for anomalous resistivity and is called chaos-induced resistivity. In many interesting cases, however, instead of the magnetic null point, there is a nonzero magnetic field perpendicular to the merging field lines, usually called the guide field, whose effect on chaos-induced resistivity has been an open problem. By use of the test particle simulation method and statistical analysis, we investigate chaos-induced resistivity in the presence of a constant guide field. The characteristics of particle motion in the reconnecting region, in particular, the chaotic behavior of particle orbits and evolving statistical features, are analyzed. The results show that as the guide field increases, the radius of the chaos region increases and the Lyapunov index decreases. However, the effective collision frequency, and hence the chaos-induced resistivity, reach their peak values when the guide field approaches half of the characteristic strength of the reconnection magnetic field. The presence of a guide field can significantly influence the chaos of the particle orbits and hence the chaos-induced resistivity in the reconnection sheet, which decides the collisionless reconnection rate. The present result is helpful for us to understand the microphysics of anomalous resistivity in collisionless reconnection with a guide field.     

The Pressure Limitations on Flux Pile-up Reconnection

The problem of the plasma pressure limitations on the rapidity of flux pile-up magnetic reconnection is re-examined, following the claim made by Jardine and Allen (1998) that the limitations can be removed by relaxing the assumption of zero-vorticity two-dimensional plasma flows. It is shown that for a two-dimensional stagnation point flow with nonzero vorticity the magnetic merging rate cannot exceed the Sweet–Parker scaling in a low-beta plasma. The pressure limitation appears to be much less restrictive for weak three-dimensional flux pile-up, provided the perturbation length scale in the third dimension is much less than the global length scale. The actual reconnection rate in the latter case, however, is much lower than this upper estimate unless the current sheet width is also much less than the global scale.     

Visco–Resistive Dissipation in Transient Reconnection Driven by the Orszag–Tang Vortex

Viscous effects are expected to significantly contribute to reconnective energy release mechanisms in solar flares. While simple scaling arguments based on head-on reconnection suggest that viscous dissipation may dominate resistive dissipation, it is not clear whether these findings can be applied in more general merging situations. Here we perform side-by-side planar reconnection simulations driven by the Orszag–Tang vortex, for both classical and Braginskii forms of the viscosity. This formulation has the advantage of providing an autonomous MHD system that develops strong current layers, sustained by large-scale vortical shearing flows. The dissipation rates are shown to follow analytically based scaling laws, which suggest that viscous losses generated from large-scale non-uniform velocity fields are likely to dominate resistive losses in current-sheet reconnection solutions.     

Soft X-ray emission from a hot turbulent current sheet and the precursor phase of solar flares

The properties and development of a high-temperature current sheet characterized by increasing merging velocity are studied and related to the early phases of solar flares. It is shown that the system can be described by the Petschek-type geometry for a wide range of merging velocities. In the diffusion region and the standing MHD shocks a certain low-frequency plasma microturbulence is generated from the very beginning of the reconnection process. We present qualitative solutions for the case of ion-acoustic turbulence in marginally stable state, which provide a comparison with observations. The increasing merging velocity leads to the appearance of the soft X-ray precursor. The precursor temperature maximum should appear during the current sheet formation, before the Petschek regime is established. In the Petschek regime the temperature of the hot plasma decreases due to the decrease of the magnetic field strength at the diffusion region boundary, while the soft X-ray radiation still increases, reaching precursor maximum for merging velocities about 1% of the external Alfvén velocity. The precursor phase ends when the value of the merging velocity surpasses the upper limit for the Petschek regime and the system enters into the pile-up regime, causing a new increase of plasma temperature and soft X-ray radiation.It is shown that Alfvén velocities in the range 800–1200 km s ^–1 are sufficient to explain typical soft X-ray precursors. Cases of low merging velocities and low Alfvén velocities are discussed and can be applied to describe the properties of spotless flares.     

Analytic Magnetic Reconnection Solutions in Cylindrical Geometry

In this paper we present a new class of exact reconnection solutions in cylindrical geometry. We point out that in the case of planar reconnection there is a natural cylindrical analog to the Cartesian Dawson function model for the magnetic field. Although the resistive energy release scalings of these solutions mimic the Cartesian models an important new feature is the presence of curvature in the current sheet. We go on to show that these solutions can be generalized to three dimensions.     

Interaction and Dynamics of the Photospheric Network Magnetic Elements

Small-scale magnetic elements in the quiet photospheric network are believed to play a key role in the energy flow from the solar surface to upper layers of atmosphere. Their intense hydro-magnetic activity includes merging and fragmentation of same polarity fluxes, `total' or partial cancellation of neighboring flux elements of opposite polarity, dynamic appearance and disappearance of compact bipoles, etc. We study the general features of these processes, and show that non-collinearity of flux tubes, sharp stratification of low atmosphere and finite plasma beta lead to several specific effects in the interacting flux tubes that may explain the morphological properties of network magnetic field and also provide a mechanism for the energy build up and release in the nearby chromosphere and transition region. We show that during the collision of flux tubes in the photosphere reconnection occurs regardless of whether the flux tubes are of opposite or of the same polarity. But the dynamics of reconnection products are significantly different and lead to different macroscopic effects that can be observed.     

Robust Scalings in Compressible Flux Pile-Up Reconnection

Flux pile-up magnetic reconnection is traditionally considered only for incompressible plasmas. The question addressed in this paper is whether the pile-up scalings with resistivity are robust when plasma compressibility is taken into account. A simple analytical argument makes it possible to understand why the transition from a highly compressible limit to the incompressible one is difficult to discern in typical simulations spanning a few decades in resistivity. From a practical standpoint, however, flux pile-up reconnection in a compressible plasma can lead to anomalous electric resistivity in the current sheet and flare-like energy release of magnetic energy in the solar corona.     

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.     

日冕三重无力场电流片的磁场重联

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

Three-dimensional Separator Reconnection – How Does It Occur?

In two dimensions magnetic energy release takes place at locations where the magnetic field strength becomes zero and has an x-point topology. The x-point topology can collapse into two y-points connected by a current sheet when the advection of magnetic flux into the x-point is larger than the dissipation of magnetic flux at the x-point. In three dimensions magnetic fields may also contain singularities in the form of three-dimensional null points. Three-dimensional nulls are created in pairs and are therefore, at least in the initial stages, always connected by at least one field line – the separator. The separator line is defined by the intersection of the fan planes of the two nulls. In the plane perpendicular to a single separator the field line topology locally has a two dimensional x-point structure. Using a numerical approach we find that the collapse of the separator can be initiated at the two nulls by a velocity shear across the fan plane. It is found that for a current concentration to connect the two nulls along the separator, the current sheet can only obtain two different orientations relative to the field line structure of the nulls. The sheet has to have an orientation midway between the fan plane and the spine axis of each null. As part of this process the spine axes are found to lose their identity by transforming into an integrated part of the separator surfaces that divide space into four magnetically independent regions around the current sheet.     

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

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