Numerical simulations of the production of extinct short‐lived nuclides by magnetic flaring in the early solar system

Abstract Using the X‐ray flare observations of low‐mass protostars, we developed numerical simulations of thermal processing and irradiation of protoCAIs in the magnetic reconnection ring within the X‐wind formulation. Observed X‐ray flare luminosities have been used to model various simulation flare characteristics. Several approximations have been made regarding the thermal evolution that involve condensation, evaporation, and coagulation of protoCAIs. Ensembles of refractory cores with ferromagnesian mantles were evolved for irradiation production of the short‐lived nuclides ⁷Be, ¹⁰Be, ⁴¹Ca, ³⁶Cl, ²⁶Al, and ⁵³Mn. Three distinct grain‐size distributions of protoCAIs with refractory cores in the ranges of 32μ m‐20 mm, 125 μ m‐16 mm, and 500 μ m‐13 mm were thermally evolved for irradiation. The latter two size distributions were found to result in the accumulation of protoCAIs in the reconnection ring during an X‐wind cycle, and hence can account for the total inventory of ²⁶Al in the early solar system. The canonical value of ?5 × 10^‐5 for ²⁶Al/²⁷ Al can be inferred from the impulsive flare simulations by a suitable choice of simulation parameters. However, in most of the remaining simulations, the irradiation of protoCAIs by superflare(s) with Lx > 10³² ergs s^‐1 subsequent to their thermal processing in the reconnection ring would be required to explain the experimental abundances of the short‐lived nuclides. These superflares have never been reliably observed in young stellar objects. If they are real, they would be extremely rare. The paucity of these superflares could impose stringent constraints on the validity of the X‐wind irradiation scenario as the source of the short‐lived nuclides.     

Numerical Study for the Bursty Nature of Spontaneous Fast Reconnection

In this paper, spontaneous fast reconnection in a neutral current sheet, which is initially perturbed by a localized resistivity, is studied by the newly developed Space-Time Conservation Element and Solution Element (CESE) method. After the initial perturbation is switched off, an anomalous resistivity is allowed to occur if a threshold of the local electron-ion drift velocity is exceeded. For a given threshold value, the amount of the reconnected magnetic flux introduced by the initial perturbation is very crucial for the onset of the anomalous resistivity. The numerical results indicate that fast reconnection can develop self-consistently with slow shocks extending between the diffusion region and a large-scale plasmoid-like structure, which is pushed forward by the reconnection outflow. A Petschek-like configuration is then built up, but it can not be sustained as a quasi-steady state. In fact, during the reconnection evolution, the diffusion region undergoes an elongation process so that after the dynamic process is nonlinearly saturated secondary tearing is subject to occur at the center of the system. This leads to enhanced and time-dependent reconnection. The reconnection evolution is further studied in various physical situations, also confirming the bursty nature of the spontaneous fast reconnection mechanism.     

Reconnection in the Solar Corona: Role of the Kelvin–Helmholtz Instability

We consider the stability of current sheets where a normal component of the field is present. It is well known that reconnection in such systems progresses orders of magnitude too slow to explain observations, even when full kinetic models are used. We consider here a new possible mechanism for fast reconnection in such systems. We consider the effect of the possible presence of velocity shear that can drive the Kelvin–Helmholtz instability (KHI). The effect of the KHI is shown to convert shear flow into compression flow that drives reconnection. Three scaling effects can be discerned in the simulations. First, the reconnection rate is directly controlled by the driving mechanism which is provided by the KHI. The result of this new mechanism is that fast reconnection can be achieved even in absence of anomalous resistivity. Second, the effect of varying the initial sheared flow along the main magnetic field direction enhances the reconnection process. Finally, the reconnection rate is insensitive to the value of resistivity.     

Cancelling magnetic feature and filament activation

We report in this paper the analysis of the evolution of a magnetic fragment observed in NOAA 9445 on 5 May, 2001. This magnetic fragment emerged laterally to a filament which later split into two parts. The bifurcation site coincided with the magnetic fragment location and the part of the filament which split was later destabilized and a flare occurred. The magnetic flux variations in the magnetic fragment and in the surrounding area were analyzed and, considering their trends and other observational signatures (Hα brightenings and associated plasma motions), we could infer that it was a cancelling magnetic feature (CMF).We determined some geometrical and physical parameters of the CMF (area, magnetic flux variation, cancellation speed and flux cancellation rate) using high resolution magnetograms taken by BBSO. We compared the observed parameters of the CMF with the parameters of low‐lying reconnection current sheets given in the model proposed by Litvinenko (1999) and found good agreement between observed and theoretical values. Therefore, we conclude that a low‐lying magnetic reconnection process might be the cause of the filament activation. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Transition-Region Explosive Events: Reconnection Modulated by p-Mode Waves

Transition-region explosive events (TREEs) have long been proposed as a consequence of magnetic reconnection. However, several critical issues have not been well addressed, such as the location of the reconnection site, their unusually short lifetime (about one minute), and the recently discovered repetitive behaviour with a period of three to five minutes. In this paper, we perform MHD numerical simulations of magnetic reconnection, where the effect of five-minute solar p-mode oscillations is examined. UV emission lines are synthesised on the basis of numerical results in order to compare with observations directly. It is found that several typical and puzzling features of the TREEs with impulsive bursty behaviour can only be explained if there exist p-mode oscillations and the reconnection site is located in the upper chromosphere at a height range of around 1900 km < h < 2150 km above the solar surface. Furthermore, the lack of proper motions of the high-velocity ejection may be due to a rapid change of temperature along the reconnection ejecta.     

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.     

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.     

Reconnection sites in Jupiter’s magnetotail and relation to Jovian auroras

The Galileo spacecraft explored Jupiter’s magnetotail in a low-inclination orbit, where it detected the signatures of tail reconnection. In this paper, we examine and classify the tail reconnection signatures into four types: dipolarizations, strong northward B_θ excursions, tailward-moving plasmoids and planetward-moving plasmoids. The distribution of these four types of events is used to infer the most probable location of the Jovian tail reconnection site to be near 0200 LT at a planetocentric distance of 80 Jovian radii. Dipolarizations are mainly observed planetward of this point, and strong northward B_θ excursions and plasmoids are found mostly tailward. The observations also suggest that the Jovian tail reconnection starts at a point (neutral point), a localized region in the tail, instead of along an extended azimuthal line (X-line). Using the updated Khurana’s Jupiter’s magnetospheric model, which includes the external field and the effects of the swept-back configuration of tail field lines, we map the signatures of Jovian tail reconnection into the Jupiter’s ionosphere. We confirm that the dawn auroral storms or the polar dawn spots observed by the Hubble Space Telescope (HST) are located close to the extrapolated footpoints of tail dipolarizations and could be the auroral signatures of tail reconnection.     

太阳光球层磁重联的直接证据

本文首次给出了发生在太阳光球磁重联的一个直接的观测证据。 这一磁重联的观测特征是:(1)重联发生在一新浮现磁通量区的一极与极性相反的老磁通量之间;(2)重联前中性线附近磁剪切明显;(3)被重联两极为一对消磁结构,重联发生在稳定的磁通量损失数小时之后;(4)一个级别为C2.9的亚耀斑发生在重联之前。该耀斑以重联区为中心,双带离重联位置2～3万公里,直到耀斑极大相后14分钟,重联仍未发生;(5)重联后,磁对消速率呈增大趋势。     

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     

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.     

Steady magnetic reconnection in three dimensions

The concepts of magnetic reconnection that have been developed in two dimensions need to be generalised to three-dimensional configurations. Reconnection may be defined to occur when there is an electric field (E) parallel to field lines (known as potential singular lines) which are potential reconnection locations and near which the field has an X-type topology in a plane normal to that field line. In general there is a continuum of neighbouring potential singular lines, and which one supports reconnection depends on the imposed flow or electric field. For steady reconnection the nearby flow and electric field are severely constrained in the ideal region by the condition that E = 0 there. Potential singular lines may occur in twisted prominence fields or in the complex magnetic configuration above sources of mixed polarity of an active region or a supergranulation cell. When reconnection occurs there is dynamic MHD behaviour with current concentration and strong plasma jetting along the singular line and the singular surfaces which map onto them.     

Reconnection driven by an erupting filament in the May 14, 1981 flare

We present observations of the flare of May 14, 1981, which can be classified as a three-ribbon flare. After a detailed analysis in metric, decimetric, microwave, optical, and X-ray ranges we propose that the event was caused by a reconnection process driven by erupting filament. The energy was liberated in the current sheet above the filament in the region between the erupting flux and the overlying field. It is shown that plasma microinstabilities develop as the plasma enters the current sheet. The observations indicate that during the precursor phase a certain low-frequency turbulence, such as ion-accoustic turbulence had to be present.The reconnection rate was growing due to the increasing tension of the stretched overlying field. It is shown that the reconnection proceeded in the Sonnerup-Petschek regime during the precursor, and changed to the pile-up regime in the fast reconnection phase, when the maximal lateral expansion (50 km s^–1) of the H ribbons was observed. The proposed process of reconnection driven by an erupting filament can be applied to three- and four-ribbon flares.     

The structure of the magnetopause

The solar wind is a magnetized flowing plasma that intersects the Earth's magnetosphere at a velocity much greater than that of the compressional fast mode wave that is required to deflect that flow. A bow shock forms that alters the properties of the plasma and slows the flow, enabling continued evolution of the properties of the flow on route to its intersection with the magnetopause. Thus the plasma conditions at the magnetopause can be quite unlike those in the solar wind. The boundary between this “magnetosheath” plasma and the magnetospheric plasma is many gyroradii thick and is surrounded by several boundary layers. A very important process occurring at the magnetopause is reconnection whereby there is a topological change in magnetic flux lines so that field lines can connect the solar wind plasma to the terrestrial plasma, enabling the two to mix. This connection has important consequences for momentum transfer from the solar wind to the magnetosphere. The initiation of reconnection appears to be at locations where the magnetic fields on either side of the magnetopause are antiparallel. This condition is equivalent to there being no guide field in the reconnection region, so at the reconnection point there is truly a magnetic neutral or null point. Lastly reconnection can be spatially and temporally varying, causing the region of the magnetopause to be quite dynamic.     

Solar coronal heating by magnetic cancellation – III. Thermodynamics

We present two-dimensional numerical magnetohydrodynamics simulations of a coronal X-ray bright point (XBP) caused by a cancelling magnetic feature (CMF). Cancellation is driven by converging motions of two magnetic bipolar sources. These sources are initially disconnected from each other so that both, the CMF and the associated reconnection/heating event (i.e. the XBP), are modelled in a self-consistent way. In the initial state, there is no X-point but two separatrices are present. Hence, the reconnection/heating and the cancellation phases have not yet started. Our numerical experiments end shortly after the converging magnetic bipole has fully cancelled. By this time, reconnection in the inner domain has ceased and occurs only at the base. Solving the energy equation with various heating and cooling terms included, and considering different bottom boundary conditions, reveals that the unrealistically high temperatures produced by Ohmic heating are reduced to more moderate temperatures of 1.5–2 MK consistent with observations of XBPs, if thermal conduction is included and density and temperature are fixed at the base.     

Spontaneous magnetic reconnection

The present review concerns the relevance of collisionless reconnection in the astrophysical context. Emphasis is put on recent developments in theory obtained from collisionless numerical simulations in two and three dimensions. It is stressed that magnetic reconnection is a universal process of particular importance under collisionless conditions, when both collisional and anomalous dissipation are irrelevant. While collisional (resistive) reconnection is a slow, diffusive process, collisionless reconnection is spontaneous. On any astrophysical time scale, it is explosive. It sets on when electric current widths become comparable to the leptonic inertial length in the so-called lepton (electron/positron) “diffusion region”, where leptons de-magnetise. Here, the magnetic field contacts its oppositely directed partner and annihilates. Spontaneous reconnection breaks the original magnetic symmetry, violently releases the stored free energy of the electric current, and causes plasma heating and particle acceleration. Ultimately, the released energy is provided by mechanical motion of either the two colliding magnetised plasmas that generate the current sheet or the internal turbulence cascading down to lepton-scale current filaments. Spontaneous reconnection in such extended current sheets that separate two colliding plasmas results in the generation of many reconnection sites (tearing modes) distributed over the current surface, each consisting of lepton exhausts and jets which are separated by plasmoids. Volume-filling factors of reconnection sites are estimated to be as large as \({<}10^{-5}\) per current sheet. Lepton currents inside exhausts may be strong enough to excite Buneman and, for large thermal pressure anisotropy, also Weibel instabilities. They bifurcate and break off into many small-scale current filaments and magnetic flux ropes exhibiting turbulent magnetic power spectra of very flat power-law shape \(W_b\propto k^{-\alpha }\) in wavenumber k with power becoming as low as \(\alpha \approx 2\). Spontaneous reconnection generates small-scale turbulence. Imposed external turbulence tends to temporarily increase the reconnection rate. Reconnecting ultra-relativistic current sheets decay into large numbers of magnetic flux ropes composed of chains of plasmoids and lepton exhausts. They form highly structured current surfaces, “current carpets”. By including synchrotron radiation losses, one favours tearing-mode reconnection over the drift-kink deformation of the current sheet. Lepton acceleration occurs in the reconnection-electric field in multiple encounters with the exhausts and plasmoids. This is a Fermi-like process. It results in power-law tails on the lepton energy distribution. This effect becomes pronounced in ultra-relativistic reconnection where it yields extremely hard lepton power-law energy spectra approaching \(F(\gamma )\propto \gamma ^{-1}\), with \(\gamma \) the lepton energy. The synchrotron radiation limit becomes substantially exceeded. Relativistic reconnection is a probable generator of current and magnetic turbulence, and a mechanism that produces high-energy radiation. It is also identified as the ultimate dissipation mechanism of the mechanical energy in collisionless magnetohydrodynamic turbulent cascades via lepton-inertial-scale turbulent current filaments. In this case, the volume-filling factor is large. Magnetic turbulence causes strong plasma heating of the entire turbulent volume and violent acceleration via spontaneous lepton-scale reconnection. This may lead to high-energy particle populations filling the whole volume. In this case, it causes non-thermal radiation spectra that span the entire interval from radio waves to gamma rays.     

Flux-Rope Twist in Eruptive Flares and CMEs: Due to Zipper and Main-Phase Reconnection

The nature of three-dimensional reconnection when a twisted flux tube erupts during an eruptive flare or coronal mass ejection is considered. The reconnection has two phases: first of all, 3D “zipper reconnection” propagates along the initial coronal arcade, parallel to the polarity inversion line (PIL); then subsequent quasi-2D “main-phase reconnection” in the low corona around a flux rope during its eruption produces coronal loops and chromospheric ribbons that propagate away from the PIL in a direction normal to it. One scenario starts with a sheared arcade: the zipper reconnection creates a twisted flux rope of roughly one turn (\(2\pi \) radians of twist), and then main-phase reconnection builds up the bulk of the erupting flux rope with a relatively uniform twist of a few turns. A second scenario starts with a pre-existing flux rope under the arcade. Here the zipper phase can create a core with many turns that depend on the ratio of the magnetic fluxes in the newly formed flare ribbons and the new flux rope. Main phase reconnection then adds a layer of roughly uniform twist to the twisted central core. Both phases and scenarios are modeled in a simple way that assumes the initial magnetic flux is fragmented along the PIL. The model uses conservation of magnetic helicity and flux, together with equipartition of magnetic helicity, to deduce the twist of the erupting flux rope in terms the geometry of the initial configuration. Interplanetary observations show some flux ropes have a fairly uniform twist, which could be produced when the zipper phase and any pre-existing flux rope possess small or moderate twist (up to one or two turns). Other interplanetary flux ropes have highly twisted cores (up to five turns), which could be produced when there is a pre-existing flux rope and an active zipper phase that creates substantial extra twist.     

Evidence of Magnetic Reconnection in Solar Flares and a Unified Model of Flares

The solar X-ray observing satellite Yohkoh has discovered various new dynamic features in solar flares and corona, e.g., cusp-shaped flare loops, above-the-loop-top hard X-ray sources, X-ray plasmoid ejections from impulsive flares, transient brightenings (spatially resolved microflares), X-ray jets, large scale arcade formation associated with filament eruption or coronal mass ejections, and so on. It has soon become clear that many of these features are closely related to magnetic reconnection. We can now say that Yohkoh established (at least phenomenologically) the magnetic reconnection model of flares. In this paper, we review various evidence of magnetic reconnection in solar flares and corona, and present unified model of flares on the basis of these new Yohkoh observations. This revised version was published online in July 2006 with corrections to the Cover Date.