Implications of solar flare dynamics for reconnection in magnetospheric substorms

From observations of two-ribbon solar flares, we present a new line of evidence that magnetic reconnection is of key importance in magnetospheric substorms. We infer that in substorms reconnection of closed field lines in the near-Earth thinned plasma sheet both initiates and is driven by the overall MHD instability that drives the tailward expulsion of the reconnected closed field (0 loops). The general basis for this inference is the longstanding notion that two-ribbon flares and substorms are essentially similar phenomena, driven by similar processes. We give an array of observed similarities that substantiate this view. More specifically, our inference for substorms is drawn from observations of filament eruptions in two-ribbon flares, from which we conclude that the heart of the overall instability consists of reconnection and eruption of the closed magnetic field in and around the filament. We propose that essentially the same overall instability operates in substorms. Our point is not that the magnetic field configuration or the microphysics in substorms is identical to that in two-ribbon flares, but that the overall instability results from essentially the same combination of reconnection and eruption of closed magnetic field.     

Breakout and Tether-Cutting Eruption Models Are Both Catastrophic (Sometimes)

We present a simplified analytic model of a quadrupolar magnetic field and flux rope to model coronal mass ejections. The model magnetic field is two-dimensional, force-free and has current only on the axis of the flux rope and within two current sheets. It is a generalization of previous models containing a single current sheet anchored to a bipolar flux distribution. Our new model can undergo quasi-static evolution either due to changes at the boundary or due to magnetic reconnection at either current sheet. We find that all three kinds of evolution can lead to a catastrophe, known as loss of equilibrium. Some equilibria can be driven to catastrophic instability either through reconnection at the lower current sheet, known as tether cutting, or through reconnection at the upper current sheet, known as breakout. Other equilibria can be destabilized through only one and not the other. Still others undergo no instability, but they evolve increasingly rapidly in response to slow steady driving (ideal or reconnective). One key feature of every case is a response to reconnection different from that found in simpler systems. In our two-current-sheet model a reconnection electric field in one current sheet causes the current in that sheet to increase rather than decrease. This suggests the possibility for the microscopic reconnection mechanism to run away.     

Interchange Reconnection Alfvén Wave Generation

Given recent observational results of interchange reconnection processes in the solar corona and the theoretical development of the S-Web model for the slow solar wind, we extend the analysis of the 3D MHD simulation of interchange reconnection by Edmondson et al. (Astrophys. J. 707, 1427, 2009). Specifically, we analyze the consequences of the dynamic streamer-belt jump that corresponds to flux opening by interchange reconnection. Information about the magnetic field restructuring by interchange reconnection is carried throughout the system by Alfvén waves propagating away from the reconnection region, distributing the shear and twist imparted by the driving flows, including shedding the injected stress-energy and accumulated magnetic helicity along newly open fieldlines. We quantify the properties of the reconnection-generated wave activity in the simulation. There is a localized high-frequency component associated with the current sheet/reconnection site and an extended low-frequency component associated with the large-scale torsional Alfvén wave generated from the interchange reconnection field restructuring. The characteristic wavelengths of the torsional Alfvén wave reflect the spatial size of the energized bipolar flux region. Lastly, we discuss avenues of future research by modeling these interchange reconnection-driven waves and investigating their observational signatures.     

Forced reconnection by nonlinear magnetohydrodynamic waves

Forced magnetic reconnection induced by magnetohydrodynamic (MHD) waves may account for the triggering of explosive solar activities such as flares. Reconnection in a neutral sheet plasma can be driven by the ponderomotive force associated with nonlinear MHD waves accompanying plasma vortex motion. The nonlinear stage of forced reconnection by MHD waves is simulated with a MHD particle-code: Some conditions for fast reconnection are discussed with applications to solar flares.     

Magnetic reconnection model for X-ray flare loop interaction

The subtle interactions between the magnetohydrodynamics (MHD) and transverse plasmons are investigated. It is shown that there is a resistive instability by the plasmon's soliton in a current sheet, which eventually turns into an eruptive instability at the magnetic field reconnection. In the case of ion-acoustic turbulence, the high temperature current sheet model must adopt the aromalous conductivity instead of the Coulomb conductivity. The numerical results are consistent with the observations obtained by Hanaoka (1994). Thus the flare caused by X-ray loop coalescence can be basically interpreted by this model of magnetic field reconnection driven by ponderomotive force.     

Magnetic field evolution during prominence eruptions and two-ribbon flares

Simple models for the MHD eruption of a solar prominence are presented, in which the prominence is treated as a twisted magnetic flux tube that is being repelled from the solar surface by magnetic pressure forces. The effects of different physical assumptions to deal with this magneto-hydrodynamically complex phenomenon are evaluated, such as holding constant the prominence current, radius, flux or twist or modelling the prominence as a current sheet. Including a background magnetic field allows the prominence to be in equilibrium initially with an Inverse Polarity and then to erupt due to magnetic non-equilibrium when the background magnetic field is too small or the prominence twist is too great. The electric field at the neutral point below the prominence rapidly increases to a maximum value and then declines. Including the effect of gravity also allows an equilibrium with Normal Polarity to exist. Finally, an ideal MHD solution is found which incorporates self-consistently a current sheet below the prominence and which implies that a prominence will still erupt and form a current sheet even if no reconnection occurs. When reconnection is allowed it is, therefore, driven by the eruption.     

Generation of rotational discontinuities by magnetic reconnection associated with microflares

Magnetic reconnection can take place between two plasma regions with antiparallel magnetic field components. In a time-dependent reconnection event, the plasma outflow region consists of a leading bulge region and a trailing reconnection layer. Magnetohydrodynamic (MHD) discontinuities, including rotational discontinuities, can be formed in both the bulge region and the trailing layer. In this paper, we suggest that the rotational discontinuities observed in the solar wind may be generated by magnetic reconnection associated with microflares in coronal holes. The structure of the reconnection layer is studied by solving the one-dimensional Riemann problem for the evolution of an initial current sheet after the onset of magnetic reconnection as well as carrying out two-dimensional MHD simulations. As the emerging magnetic flux reconnects with ambient open magnetic fields in the coronal hole, rotational discontinuities are generated in the region with open field lines. It is also found that in the solar corona with a low plasma beta ( 0.01), the magnetic energy is converted through magnetic reconnection mostly into the plasma bulk-flow energy. Since more microflares will generate more rotational discontinuities and also supply more energy to the solar wind, it is expected that the number of rotational discontinuities observed in the solar wind would be an increasing function of solar wind speed. The observation rate of rotational discontinuities generated by microflares is estimated to be dN _RD/dt - f/63 000 s (f > 1) at 1 AU. The present mechanism favors the generation of rotational discontinuities with a large shock normal angle.     

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.     

The Flare-Energy Distributions Generated by Kink-Unstable Ensembles of Zero-Net-Current Coronal Loops

It has been proposed that the million-degree temperature of the corona is due to the combined effect of barely detectable energy releases, called nanoflares, that occur throughout the solar atmosphere. Unfortunately, the nanoflare density and brightness implied by this hypothesis means that conclusive verification is beyond present observational abilities. Nevertheless, we investigate the plausibility of the nanoflare hypothesis by constructing a magnetohydrodynamic (MHD) model that can derive the energy of a nanoflare from the nature of an ideal kink instability. The set of energy-releasing instabilities is captured by an instability threshold for linear kink modes. Each point on the threshold is associated with a unique energy release; thus we can predict a distribution of nanoflare energies. When the linear instability threshold is crossed, the instability enters a nonlinear phase as it is driven by current sheet reconnection. As the ensuing flare erupts and declines, the field transitions to a lower energy state, which is modelled by relaxation theory; i.e., helicity is conserved and the ratio of current to field becomes invariant within the loop. We apply the model so that all the loops within an ensemble achieve instability followed by energy-releasing relaxation. The result is a nanoflare energy distribution. Furthermore, we produce different distributions by varying the loop aspect ratio, the nature of the path to instability taken by each loop and also the level of radial expansion that may accompany loop relaxation. The heating rate obtained is just sufficient for coronal heating. In addition, we also show that kink instability cannot be associated with a critical magnetic twist value for every point along the instability threshold.     

Three-dimensional computer modeling of dynamic reconnection in the magnetotail

Magnetospheric substorm in the magnetotail region is studied numerically by means of a three-dimensional MHD code. The analytic solution for the quiet magnetotail is emloyed as an initial configuration. The localized solar wind is modeled to enter the simulation domain through the boundaries located in the magnetotail lobe region. As a result of the interaction between the solar wind and the magnetosphere, the magnetic field lines are stretched, and the plasma sheet becomes thinner and thinner. When the current-driven resistivity is generated, magnetic reconnection is triggered by this resistivity. The resulting plasma jetting is found to be super-magnetosonic. Although the plasmoid formation and its tailward motion is not quite clear as in the two-dimensional simulation, which is mainly because of the numerical model chosen for the present simulation, the rarification of the plasmas near thex-point is observed. Field-aligned currents are observed in the late expansive stage of the magnetospheric substorm. These field-aligned currents flow from the tail toward the ionosphere on the dawn side and from the ionosphere toward the tail on the dusk side, namely in the same sence of the region 1 current. As the field-aligned currents develop, it is found that the cross-tail current in the Earthside midnight section of the magneticx-point is reduced.     

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.     

Slip-Running Reconnection in Quasi-Separatrix Layers

Using time dependent MHD simulations, we study the nature of three-dimensional magnetic reconnection in thin quasi-separatrix layers (QSLs), in the absence of null points. This process is believed to take place in the solar atmosphere, in many solar flares and possibly in coronal heating. We consider magnetic field configurations which have previously been weakly stressed by asymmetric line-tied twisting motions and whose potential fields already possessed thin QSLs. When the line-tied driving is suppressed, magnetic reconnection is solely due to the self-pinching and dissipation of narrow current layers previously formed along the QSLs. A generic property of this reconnection process is the continuous slippage of magnetic field lines along each other, while they pass through the current layers. This is contrary to standard null point reconnection, in which field lines clearly reconnect by pair and abruptly exchange their connectivities. For sufficiently thin QSLs and high resistivities, the field line footpoints slip-run at super-Alfvénic speeds along the intersection of the QSLs with the line-tied boundary, even though the plasma velocity and resistivity are there fixed to zero. The slip-running velocities of a given footpoint have a well-defined maximum when the field line crosses the thinnest regions of the QSLs. QSLs can then physically behave as true separatrices on MHD time scales, since magnetic field lines can change their connections on time scales far shorter than the travel-time of Alfvén waves along them. Since particles accelerated in the diffusive regions travel along the field much faster than the Alfvén speed, slip-running reconnection may also naturally account for the fast motion of hard X-ray sources along chromospheric ribbons, as observed during solar flares. Electronic Supplementary Material Supplementary material is available for this article at     

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.     

Catastrophic Behavior of Multiple Coronal Flux Rope System

A major solar active event called Bastille Day Event occurred in AR 9077 on July 14, 2000. Simultaneous occurrence of a filament eruption, a flare and a coronal mass ejection was observed in this event. Previous analyses of this event show that before the event, there existed an activation and eruption of a huge trans-equatorial filament, which might play a crucial role in triggering the Bastille Day event. This implies that independent flux systems are closely related to and affect each other, which has encouraged us to investigate the catastrophic behavior of a multiple coronal flux rope system with the use of a 2.5-D time-dependent MHD model. A force-free field that contains three separate coronal flux ropes is taken to be the initial state. Starting from this state, we increase either the annular or the axial flux of a certain flux rope to examine the catastrophic behavior of the system in two regimes, the ideal MHD regime and the resistive MHD regime. It is found that a catastrophe occurs if the flux exceeds a certain critical value, or the magnetic energy of the system exceeds a certain threshold: the rope of interest breaks away from the base and escapes to infinity, leaving a current sheet below. Moreover, the destiny of the remainder flux ropes relies on whether reconnection takes place across the current sheet. In the ideal MHD regime, i.e., in the absence of reconnection, these ropes remain to be attached to the base in equilibrium, whereas in the resistive MHD regime they abruptly erupt upward during reconnection and escape to infinity. Reconnection causes the field lines to close back to the base and thus changes the background field outside the attached flux ropes in such a way that the constraint on these ropes is substantially relaxed and the corresponding catastrophic energy threshold is reduced accordingly, leading to a catastrophic eruption of these ropes. Since magnetic reconnection is generally inevitable when a current sheet forms and develops through an eruption of one flux rope, the eruption of this flux rope must lead to an eruption of the others. This provides an example to demonstrate the interaction between several independent magnetic flux systems in different regions, as implied by the Bastille Day event, and may serve as a possible mechanism for sympathetic events occurring on the Sun.     

Initiation of cmes by magnetic flux emergence

The initiation of solar Coronal Mass Ejections (CMEs) is studied in the framework of numerical magnetohydrodynamics (MHD). The initial CME model includes a magnetic flux rope in spherical, axi-symmetric geometry. The initial configuration consists of a magnetic flux rope embedded in a gravitationally stratified solar atmosphere with a background dipole magnetic field. The flux rope is in equilibrium due to an image current below the photosphere. An emerging flux triggering mechanism is used to make this equilibrium system unstable. When the magnetic flux emerges within the filament below the flux rope, this results in a catastrophic behavior similar to previous models. As a result, the flux rope rises and a current sheet forms below it. It is shown that the magnetic reconnection in the current sheet below the flux rope in combination with the outward curvature forces results in a fast ejection of the flux rope as observed for solar CMEs. We have done a parametric study of the emerging flux rate.     

Electric Currents at imf Sector Boundaries

Numerical simulation of magnetic field reconnection at IMF sector boundaries shows that the reconnection line may be carried by the solar wind out of the region of the anomalous resistivity. This makes it possible to observe magnetic loops at the Earth's orbit open to the Sun as well as from it. Besides, it is shown that the current sheet in the vicinity of the reconnection line has to split into two currents.Experimental data on the structure of the sector boundaries are analyzed, and it is shown that the currents at sector boundaries are indeed often splitted.The thickness of the splitted boundaries may amount to 18×106 km; taking into account this value, the heliocentric distance of the region of anomalous resistivity in the interplanetary current sheet is estimated as 0.4–0.5 AU.The probability of observing magnetic loops open towards the Sun seems to be greater than that of loops open from the Sun, which suggests an essential asymmetry of the field reversal regions.     

Magnetic Reconnection, Turbulence, and Collisionless Shock

A short summary of recent progress in measuring and understanding turbulence during magnetic reconnection in laboratory plasmas is given. Magnetic reconnection is considered as a primary process to dissipate magnetic energy in laboratory and astrophysical plasmas. A central question concerns why the observed reconnection rates are much faster than predictions made by classical theories, such as the Sweet–Parker model based on MHD with classical Spitzer resistivity. Often, the local resistivity is conjectured to be enhanced by turbulence to accelerate reconnection rates either in the context of the Sweet–Parker model or by facilitating setup of the Pestchek model. Measurements at a dedicated laboratory experiment, called MRX or Magnetic Reconnection Experiment, have indicated existence of strong electromagnetic turbulence in current sheets undergoing fast reconnection. The origin of the turbulence has been identified as right-hand polarized whistler waves, propagating obliquely to the reconnecting field, with a phase velocity comparable to the relative drift velocity. These waves are consistent with an obliquely propagating electromagnetic lower-hybrid drift instability driven by drift speeds large compared to the Alfven speed in high-beta plasmas. Interestingly, this instability may explain electromagnetic turbulence also observed in collisionless shocks, which are common in energetic astrophysical phenomena.     

Non-linear damping of visco-resistive Alfvén waves in solar spicules

Interaction of Alfvén waves with plasma inhomogeneities generates phase mixing which can lead to dissipate Alfvén waves and to heat the solar plasma. Here we study the dissipation of Alfvén waves by phase mixing due to viscosity and resistivity variations with height. We also consider nonlinear magnetohydrodynamic (MHD) equations in our theoretical model. Non-linear terms of MHD equations include perturbed velocity, magnetic field, and density. To investigate the damping of Alfvén waves in a stratified atmosphere of solar spicules, we solve the non-linear MHD equations in the x–z plane. Our simulations show that the damping is enhanced due to viscosity and resistivity gradients. Moreover, energy variations is influenced due to nonlinear terms in MHD equations.     

Nonplanar magnetic reconnection associated with conical slow shocks

We study a nonplanar model of magnetic reconnection associated with conical slow shocks, assuming that the shock surfaces are two identical cones with circular cross sections symmetrical about the ±x-axis. In the inflow region upstream of the shocks, two oppositely directed magnetic fields are separated by a current sheet. The model treats the current sheet as a tangential discontinuity and treats shocks and tangential discontinuity as surfaces of zero thickness. The dynamical structure of the global magnetic field in the continuous regions is studied using compressible, non-resistive MHD equations. In the inflow region, nonplanar magnetic field lines first move toward the current sheet. Near the sheet, the middle sections of the field lines become highly flattened, almost parallel to the sheet. Eventually, then oppositely directed field lines merge across the tangential discontinuity between the two shocks, and the magnetic lines are reconnected at the intersection of the shock and the tangential discontinuity. Reconnected magnetic lines are carried away at high speeds by the MHD flow in the outflow region, downstream of the shocks.     

Turbulence Diffusion and Energy Spectrum Analysis of Large-scale Current Sheets in Flares

Magnetic reconnection (MR) is one of the most important physical processes for many dynamical phenomena in the universe. Magnetohydrodynamical (MHD) simulation is an effective way to study the MR process and the physical pictures related to the MR. With different parameter setups, we investigate the influences of the Magnetic Reynolds number and spatial resolution on the reconnection rate, numerical dissipation, and energy spectrum distribution in the MHD simulation. We have found that the magnetic Reynolds number $R_m$ has definite impact on the reconnection rate and energy spectrum distribution. The characteristic time for entering into the non-linear phase will be earlier as the Reynolds number increases. When it comes to the tearing phase, the reconnection rate will increase rapidly. On the other hand, the magnetic Reynolds number affects significantly the Kolmogorov microscopic scale $l_{\mathit{ko}}$, which becomes smaller as $R_m$ increases. An extra dissipation is defined as the combined effect of the numerical diffusion and turbulence dissipation. It is shown that the extra dissipation is dominated by the numerical diffusion before the tearing mode instability takes place. After the instability develops, the extra dissipation rises vastly, which indicates that turbulence caused by the instability can enhance the diffusion obviously. Furthermore, the energy spectrum analysis indicates that $l_{\mathit{ko}}$ of the large-scale current sheet may appear at a macroscopic MHD scale very possibly.