A numerical simulation of magnetic reconnection and radiative cooling in line-tied current sheets

We have used the radiative MHD equations for an optically thin plasma to carry out a numerical experiment related to the formation of post-flare loops. The numerical experiment starts with a current sheet that is in mechanical and thermal equilibrium, but which is unstable to both tearing-mode and thermal-condensation instabilities. The current sheet is line-tied at one end to a photospheric-like boundary and evolves asymmetrically. The effects of thermal conduction, resistivity variation, and gravity are ignored. In general, we find that reconnection in the nonlinear stage of the tearing-mode instability can strongly affect the onset of condensations unless the radiative cooling time scale is much smaller than the tearing-mode time scale. When the ambient plasma is less than 0.2, the reconnection enters a regime where the outflow from the reconnection region is supermagnetosonic with respect to the fast-mode wave speed. In the supermagnetosonic regime the most rapidly condensing regions occur downstream of a fast-mode shock that forms where the outflow impinges on closed loops attached to the photospheric-like boundary. A similar shock-induced condensation might occur during the formation of post-flare loops.     

Neutral line motion due to reconnection in two-ribbon solar flares and magnetospheric substorms

Two kinematic models of line-tied reconnection are considered which describe the motion of a magnetic neutral line (NL) during the main phase of a two-ribbon solar flare and during the recovery phase of a magnetospheric substorm in the geomagnetic tail. The models are kinematic in that they use only the magnetic induction equation, which suffices to determine the position and velocity of the NL as functions of time if the rate of reconnection is prescribed. The solar flare model shows that the observed large decrease in the rate at which “post”-flare loops rise upward from the photosphere during the main phase does not require a corresponding decrease in the rate of reconnection. Instead it is found that a constant rate of reconnection can account for the motion of the loops for almost the entire period during which they are observed. By contrast, application of the same procedures to the recovery phase of the magnetospheric substorm in the tail predicts a slightly increasing speed of NL motion if the rate of reconnection is constant. Furthermore, it is found that the motion of the NL relative to the ambient medium may account for much of the observed asymmetry in the magnetic field in the plasma sheet during recovery. Due to this motion, the plasma sheet thickness may be up to 4 times smaller and the normal magnetic field component up to 2 times weaker in the region tailward of the NL than in the corresponding region earthward of the NL.     

On the magnetic reconnection of electric currents in solar flares

The role of the electric currents distributed over the volume of an active region on the Sun is considered from the standpoint of solar flare physics. We suggest including the electric currents in a topological model of the magnetic field in an active region. Typical values of the mutual inductance and the interaction energy of the coronal electric currents flowing along magnetic loops have been estimated for the M7/1N flare on April 27, 2006. We show that if these currents actually make a significant contribution to the flare energetics, then they must manifest themselves in the photosphericmagnetic fields. Depending on their orientation, the distributed currents can both help and hinder reconnection in the current layer at the separator during the flare. Asymmetric reconnection of the currents is accompanied by their interruption and an inductive change in energy. The reconnection of currents in flares differs significantly from the ordinary coalescence instability of magnetic islands in current layers. Highly accurate measurements of the magnetic fields in active regions are needed for a quantitative analysis of the role of distributed currents in solar flares.     

The Observational Evidence on the Loop–Loop Interaction in a Flare–CME Event on April 15, 1998

The evolution of the soft X-ray and EUV coronal loops related to the April 15, 1998 solar flare–CME event is studied with multiwavelength observations including hard X-rays (BATSE), microwaves (NoRP, CNAO) and magnetograms (SOHO/MDI), as well as images from Yohkoh/SXT and SOHO/EIT at 195 Å. It is shown that: (1) two soft X-ray and EUV loops rose, crossed and turned bright, (2) near one footpoint of these loops, the background magnetic field decreased, (3) there were similar quasi periodic oscillations in the time profiles of hard X-ray and microwave emissions, which characterized the loop–loop coalescence instability, (4) after the loop–loop reconnection, two new loops formed, the small one stayed at the original place, and the large one ejected out as part of the constructed prominence cloud. Based upon these observations, we argue that the decrease of the background magnetic field near these loops caused them to rise and approach each other, and in turn, the fast loop–loop coalescence instability took place and triggered the flare and the CME.     

Long term evolution of the magnetized Kelvin Helmholtz instability with resistivity

MHD simulation study is performed to investigate magnetic reconnection induced by the Kelvin Helmholtz instability in the parallel configuration of the uniform magnetic field geometry as well as the sheared field geometry. Highly distorted magnetic field lines due to Kelvin Helmholtz instability become reconnected and flattened so that they resume the straight field line structure in the final stage. When the initial magnetic field is sheared, magnetic islands formed as a result of magnetic reconnection are transported toward the weak field region but they soon disappear since these islands are of small scales and suffer strong diffusions. Morphological change in the long term evolution is most dramatic in the small range of magnetic field intensity in both the uniform field case and the sheared field case, which is not too strong to stabilize vortex growing early on or too weak to have negligible effect on the instability. Energy conversion and the momentum transport are also most effective in this small range.     

3-D MHD simulation of plasmoid formation during coalescence of two current loops

We consider two force-free current loops, as proposed by Gold and Hoyle (1960), as the initial current loops, to investigate two types of the magnetic reconnection process, the partial and complete reconnections during coalescence of these loops, by using a 3-D resistive MHD code. It is shown that two plasmoids can be produced on both sides of the coalescence area by both types of the magnetic reconnection process during coalescence of two current loops. It is also shown that strong fast magnetosonic waves can be induced in the partial reconnection case of two-current-loop collision. When two current loops collide locally at two points, four plasmoids can be produced and two of these plasmoids merge into one.     

CME's,filament eruptions,and sheared low-lying magnetic loops in multipolar magnetic configuration

The finite element method was used to solve a partial differential equation (magnetostatic equation) for multipolar magnetic regions. It is found that the height of magnetic field lines above the magnetic neutral line of a central strong bipolar magnetic field decreases as the field lines' footpoints approach the neutral line and also with increased magnetic shear. Both the electric current density and plasma pressure in the sheared low-lying loops are high. We suggest that the sheared low-lying loops may store the energies of large coronal mass ejections (CMEs) and filament eruptions. In addition, it is found that a lower pressure area exists above the low-lying loops and that it is similar in morphology to a coronal cavity. Above the lower pressure area there is a higher pressure area, which may be the source of CMEs. In this area magnetic shear leads to magnetic reconnection, which may be the cause of high coronal temperature.     

Shocks produced by impulsively driven reconnection

Shock waves produced by impulsively driven reconnection may be important during flares or during the emergence of magnetic flux from the photosphere into the corona. Here we investigate such shock waves by carrying out numerical experiments using two-dimensional magneto-hydrodynamics. The results of the numerical experiments imply that there are three different categories of shocks associated with impulsively driven reconnection: (1) fast-mode, blast waves which rapidly propagate away from the reconnection site; (2) slow-mode, Petschek shocks which are attached to the reconnection site; and (3) fast-mode, termination shocks which terminate the plasma jets flowing out from the reconnection site. Fast-mode blast waves are a common feature of many flare models, but the Petschek shocks and jet termination shocks are specific to reconnection models. These two different types of reconnection shocks might contribute to chromospheric ablation and energetic particle acceleration in flares.     

Model for flare loops,fast motions,and opening of magnetic field in the corona

A model is presented for the penetration into the corona of a new magnetic field of a developing bipolar region and for its interaction with an old large-scale coronal field. An important feature of the model is a reconnection of the old and new fields inside the current sheet arising along the zero line of the total magnetic field calculated in the potential approximation. The magnetic reconnection and accumulation of plasma inside the current sheet can explain the appearance of dense coronal loops and the energy source at their tops. The plasma together with the magnetic lines is flowed into the sheet from both its sides. This fact explains the appearance of coronal cavities above the loops. If the large-scale field gradually decreases with the height, the loop motion is slowed down. The account of the dipolar structure of the magnetic field at large heights explains the possibility of a rapid break of the new field through the corona and the appearance of transients and open field regions - the coronal holes. In this case a fast rising current sheet can be a source of accelerated particles and of type II radio burst, instead of the shock wave considered usually.     

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.     

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.     

Magnetospheric substorm models: Comparison with neutral sheet magnetic field observations

Four models for geomagnetic substorms, a quiet tail model, and models incorporating structural effects of the tail are examined for consistency with magnetic-field data during satellite crossings of the tail neutral sheet/plasma sheet. For this data the tearing mode instability model is always consistent, and inward moving distant neutral line is sometimes consistent, quasi-steady reconnection with slow shock and intermediate wave structure and locally quiet tail rarely consistent, and an outward propagating rarefaction wave is never consistent with the magnetic observations. In several cases structural effects of the tail are consistent with key features of the magnetic signatures.     

Erratum to: The Maunder Minimum and the Sun as the Possible Source of Particles Creating Increased Abundance of the <Superscript>14</Superscript>C Carbon Isotope

Solar flares take place in regions of strong magnetic fields and are generally accepted to be the result of a resistive instability leading to magnetic reconnection. When new flux emerges into a pre-existing active region it can act as a flare and coronal mass ejection trigger. In this study we observed active region 10955 after the emergence of small-scale additional flux at the magnetic inversion line. We found that flaring began when additional positive flux levels exceeded 1.38×10²⁰ Mx (maxwell), approximately 7 h after the initial flux emergence. We focussed on the pre-flare activity of one B-class flare that occurred on the following day. The earliest indication of activity was a rise in the non-thermal velocity one hour before the flare. 40 min before flaring began, brightenings and pre-flare flows were observed along two loop systems in the corona, involving the new flux and the pre-existing active region loops. We discuss the possibility that reconnection between the new flux and pre-existing loops before the flare drives the flows by either generating slow mode magnetoacoustic waves or a pressure gradient between the newly reconnected loops. The subsequent B-class flare originated from fast reconnection of the same loop systems as the pre-flare flows.     

One-photon and two-photon annihilation lines in gamma-bursts,I

This paper and subsequent Paper II are an investigation of the annihilation line formation in gamma-ray bursts based on the assumption of positron production in a strong magnetic field (because of one-photon absorption of hard gamma-quanta radiated in the neutron star hot polar spot). We discuss a two-photon annihilation line in this paper. It is shown that if the star magnetic field is greater than 3×10¹² G, the relative flux in the line depends solely on the hardness of the continuum and is, as a rule, less than or about 10–20% of the total flux. This is consistent with the spectral data recorded by ‘Venera-11’ and ‘Venera-12’ space probes. The annihilation region formation above the hot polar spot is discussed, and positron density and annihilation region dimensions are estimated.     

Tearing instability in the pulsar magnetosphere

Equations governing the coupling of the scalar and vector potentials for a resistive electron-positron plasma in a strong magnetic field are derived. It is shown that in the presence of magnetic shear, a tearing instability may occur. The latter can lead to magnetic field line reconnection and the formation of magnetic islands which could affect the dynamics of the pulsar magnetosphere.     

Numerical study of line-tied magnetic reconnection

A two-dimensional configuration, analogous to that at the start of the main phase in two-ribbon flares, is modelled numerically by self-consistently solving the time-dependent MHD equations. The initial state consists of a vertical current sheet with an external plasma beta value of 0.1 and a magnetic Reynolds number of 10^–3. Although the model does not yet include gravity or a full energy equation, many of the principal dynamical features of the main phase in a flare are present. In particular, the numerical results confirm the earlier prediction of the kinematic Kopp-Pneuman (1976) model that a neutral line forms at the base of the corona and rises upwards as open, extended field lines close back down to form loops (i.e., post-flare loops). By the end of the computation a state of nonlinear reconnection containing slow shocks has developed, and the velocity of the plasma flowing into the neutral line region is approximately 0.06 times the corresponding inflow Alfvén velocity - a value consistent with the steady-state nonlinear reconnection theory of Soward and Priest (1977). The speed at which the neutral line rises in the numerical simulation varies from an initial value of 0.02 to a final value of - 0.12 times the inflow Alfvén speed.     

Mass upflows in ‘post’-flare loops

A self-consistent numerical model of a reconnecting magnetic field configuration similar to that occurring during the main-phase of two-ribbon flares is used to estimate the upflow caused by the fast-mode expansion of the magnetic field moving into the reconnection region. Such an expansion creates a field-aligned pressure gradient which accelerates plasma upward from the chromospheric base of magnetic field lines in the region external to the loops. The numerical results imply that the amount of mass sucked up in this way is even smaller than was previously estimated by Kopp and Pneuman who used a kinematic model. Therefore, some indirect mechanism (such as evaporation), which would probably derive its motive power from the thermal energy generated by the reconnection, is required to explain the large mass upflows inferred from observations.     

Anomalous deformation of the Earth's bow shock in the lunar wake: Joint measurement by Chang’E-1 and SELENE

Because the solar wind (SW) flow is usually super-sonic, a fast-mode bow shock (BS) is formed in front of the Earth's magnetosphere, and the Moon crosses the BS at both dusk and dawn flanks. On the other hand, behind of the Moon along the SW flow forms a tenuous region called lunar wake, where the flow can be sub-Alfvénic (and thus sub-sonic) because of its low-density status. Here we report, with joint measurement by Chang’E-1 and SELENE, that the Earth's BS surface is drastically deformed in the lunar wake. Despite the quasi-perpendicular shock configuration encountered at dusk flank under the Parker-spiral magnetic field, no clear shock surface can be found in the lunar wake, while instead gradual transition of the magnetic field from the upstream to downstream value was observed for a several-minute interval. This finding suggests that the ‘magnetic ramp’ is highly broadened in the wake where a fast-mode shock is no longer maintained due to the highly reduced density. On the other hand, observations at the 100 km altitude on the dayside show that the fast-mode shock is maintained even when the width of the downstream region is smaller than a typical scale length of a perpendicular shock. Our results suggest that the Moon is not so large to eliminate the BS at 100 km altitude on the dayside, while the magnetic field associated with the shock structure is drastically affected in the lunar wake.     

太阳耀斑磁重联的数值模拟

数值模拟了太阳耀斑中二维磁重联过程。结果表明,当重联Ｘ 点比较高时,演化过程能再现双带耀斑中耀斑环的运动等主要特征;当重联Ｘ 点比较低时,可解释致密耀斑的观测特征。结果还表明,耀斑环上升和重联点上升之间没有直接的联系。     

Evidence for interchange reconnection between a coronal hole and an adjacent emerging flux region

Coronal holes are regions of dominantly monopolar magnetic field on the Sun where the field is considered to be ‘open’ towards interplanetary space. Magnetic bipoles emerging in proximity to a coronal hole boundary naturally interact with this surrounding open magnetic field. In the case of oppositely aligned polarities between the active region and the coronal hole, we expect interchange reconnection to take place, driven by the coronal expansion of the emerging bipole as well as occasional eruptive events. Using SOHO/EIT and SOHO/MDI data, we present observational evidence of such interchange reconnection by studying AR 10869 which emerged close to a coronal hole. We find closed loops forming between the active region and the coronal hole leading to the retreat of the hole. At the same time, on the far side of the active region, we see dimming of the corona which we interpret as a signature of field line ‘opening’ there, as a consequence of a topological displacement of the ‘open’ field lines of the coronal hole. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)