Self-similar solution of fast magnetic reconnection: Semi-analytic study of inflow region

An evolutionary process of the fast magnetic reconnection in ``free space'' which is free from any influence of outer circumstance has been studied semi-analytically, and a self-similarly expanding solution has been obtained. The semi-analytic solution is consistent with the results of our numerical simulations performed in our previous paper (see Nitta et al. 2001). This semi-analytic study confirms the existence of self-similar growth. On the other hand, the numerical study by time dependent computer simulation clarifies the stability of the self-similar growth with respect to any MHD mode. These results confirm the stable self-similar evolution of the fast magnetic reconnection system.Comment: 15 pages, 7 figure

Fast magnetic reconnection in free space: self-similar evolution process

We present a new model for time evolution of fast magnetic reconnection in free space, which is characterized by self-similarity. Reconnection triggered by locally enhanced resistivity assumed at the center of the current sheet can self-similarly and unlimitedly evolve until external factors affect the evolution. The possibility and stability of this type of evolution are verified by numerical simulations in a very wide spatial dynamic range. Actual astrophysical reconnection in solar flares and geomagnetospheric substorms can be treated as an evolutionary process in free space, because the resultant scale is much larger than the initial scale. In spite of this fact, most of the previous numerical works focused on the evolutionary characters strongly affected by artificial boundary conditions on the simulation boundary. Our new model clarifies a realistic evolution for such cases. The characteristic structure around the diffusion region is quite similar to the Petschek model which is characterized by a pair of slow-mode shocks and the fast-mode rarefaction-dominated inflow. However, in the outer region, a vortex-like return flow driven by the fast-mode compression caused by the piston effect of the plasmoid takes place. The entire reconnection system expands self-similarly.Comment: 17 Pages, 17 Figure

Magnetic Reynolds number dependence of reconnection rate and flow structure of the self-similar evolution model of fast magnetic reconnection

This paper investigates Magnetic Reynolds number dependence of the ``self-similar evolution model'' (Nitta et al. 2001) of fast magnetic reconnection. I focused my attention on the flow structure inside and around the reconnection outflow, which is essential to determine the entire reconnection system (Nitta et al. 2002). The outflow is consist of several regions divided by discontinuities, e.g., shocks, and it can be treated by a shock-tube approximation (Nitta 2004). By solving the junction conditions (e.g., Rankine-Hugoniot condition), the structure of the reconnection outflow is obtained. Magnetic reconnection in most astrophysical problems is characterized by a huge dynamic range of its expansion ($sim 10^7$ for typical solar flares) in a free space which is free from any influence of external circumstances. Such evolution results in a spontaneous self-similar expansion which is controlled by two intrinsic parameters: the plasma-$beta$ and the magnetic Reynolds number. The plasma-$beta$ dependence had been investigated in our previous paper. This paper newly clarifies the relation between the reconnection rate and the inflow structure just outside the Petschek-like slow shock: As the magnetic Reynolds number increases, strongly converging inflow toward the Petschek-like slow shock forms, and it significantly reduces the reconnection rate.Comment: 16 pages. to appear in ApJ (2006 Jan. 20 issue

A Model for Patchy Reconnection in Three Dimensions

We show, theoretically and via MHD simulations, how a short burst of reconnection localized in three dimensions on a one-dimensional current sheet creates a pair of reconnected flux tubes. We focus on the post-reconnection evolution of these flux tubes, studying their velocities and shapes. We find that slow-mode shocks propagate along these reconnected flux tubes, releasing magnetic energy as in steady-state Petschek reconnection. The geometry of these three-dimensional shocks, however, differs dramatically from the classical two-dimensional geometry. They propagate along the flux tube legs in four isolated fronts, whereas in the two-dimensional Petschek model, they form a continuous, stationary pair of V-shaped fronts. We find that the cross sections of these reconnected flux tubes appear as teardrop shaped bundles of flux propagating away from the reconnection site. Based on this, we argue that the descending coronal voids seen by Yohkoh SXT, LASCO, and TRACE are reconnected flux tubes descending from a flare site in the high corona, for example after a coronal mass ejection. In this model, these flux tubes would then settle into equilibrium in the low corona, forming an arcade of post-flare coronal loops.Comment: 27 pages plus 16 figure

Fast Collisionless Reconnection Condition and Self-Organization of Solar Coronal Heating

I propose that solar coronal heating is a self-regulating process that keeps the coronal plasma roughly marginally collisionless. The self-regulating mechanism is based on the interplay of two effects. First, plasma density controls coronal energy release via the transition between the slow collisional Sweet-Parker regime and the fast collisionless reconnection regime. This transition takes place when the Sweet--Parker layer becomes thinner than the characteristic collisionless reconnection scale. I present a simple criterion for this transition in terms of the upstream plasma density (n_e), the reconnecting (B_0) and guide (B_z) magnetic field components, and the global length (L) of the reconnection layer: L < 6.10^9 cm [n_e/(10^{10}/cm^3)]^(-3) (B_0/30G)^4 (B_0/B_z)^2. Next, coronal energy release by reconnection raises the ambient plasma density via chromospheric evaporation and this, in turn, temporarily inhibits subsequent reconnection involving the newly-reconnected loops. Over time, however, radiative cooling gradually lowers the density again below the critical value and fast reconnection again becomes possible. As a result, the density is highly inhomogeneous and intermittent but, statistically, does not deviate strongly from the critical value which is comparable with the observed coronal density. Thus, in the long run, the coronal heating process can be represented by repeating cycles that consist of fast reconnection events (i.e., nanoflares), followed by rapid evaporation episodes, followed by relatively long periods (1-hour) during which magnetic stresses build up and simultaneously the plasma cools down and precipitates.Comment: 17 pages, no figures; accepted to the Astrophysical Journal; replaced to match the accepted versio

Magnetic Reconnection Triggered by the Parker Instability in the Galaxy: Two-Dimensional Numerical Magnetohydrodynamic Simulations and Application to the Origin of X-Ray Gas in the Galactic Halo

We propose the Galactic flare model for the origin of the X-ray gas in the Galactic halo. For this purpose, we examine the magnetic reconnection triggered by Parker instability (magnetic buoyancy instability), by performing the two-dimensional resistive numerical magnetohydrodynamic simulations. As a result of numerical simulations, the system evolves as following phases: Parker instability occurs in the Galactic disk. In the nonlinear phase of Parker instability, the magnetic loop inflates from the Galactic disk into the Galactic halo, and collides with the anti-parallel magnetic field, so that the current sheets are created in the Galactic halo. The tearing instability occurs, and creates the plasmoids (magnetic islands). Just after the plasmoid ejection, further current-sheet thinning occurs in the sheet, and the anomalous resistivity sets in. Petschek reconnection starts, and heats the gas quickly in the Galactic halo. It also creates the slow and fast shock regions in the Galactic halo. The magnetic field ($B\sim 3 \mu$G), for example, can heat the gas ($n\sim 10^{-3}$ cm$^{-3}$) to temperature of $\sim 10^6$ K via the reconnection in the Galactic halo. The gas is accelerated to Alfv\'en velocity ($\sim 300$ km s$^{-1}$). Such high velocity jets are the evidence of the Galactic flare model we present in this paper, if the Doppler shift of the bipolar jet is detected in the Galactic halo. Full size figures are available at http://www.kwasan.kyoto-u.ac.jp/~tanuma/study/ApJ2002/ApJ2002.htmlComment: 13 pages, 12 figures, uses emulateapj.sty, accepted by Ap

Plasmoid-Induced-Reconnection and Fractal Reconnection

As a key to undertanding the basic mechanism for fast reconnection in solar flares, plasmoid-induced-reconnection and fractal reconnection are proposed and examined. We first briefly summarize recent solar observations that give us hints on the role of plasmoid (flux rope) ejections in flare energy release. We then discuss the plasmoid-induced-reconnection model, which is an extention of the classical two-ribbon-flare model which we refer to as the CSHKP model. An essential ingredient of the new model is the formation and ejection of a plasmoid which play an essential role in the storage of magnetic energy (by inhibiting reconnection) and the induction of a strong inflow into reconnection region. Using a simple analytical model, we show that the plasmoid ejection and acceleration are closely coupled with the reconnection process, leading to a nonlinear instability for the whole dynamics that determines the macroscopic reconnection rate uniquely. Next we show that the current sheet tends to have a fractal structure via the following process path: tearing, sheet thinning, Sweet- Parker sheet, secondary tearing, further sheet thinning... These processes occur repeatedly at smaller scales until a microscopic plasma scale (either the ion Larmor radius or the ion inertial length) is reached where anomalous resistivity or collisionless reconnection can occur. The current sheet eventually has a fractal structure with many plasmoids (magnetic islands) of different sizes. When these plasmoids are ejected out of the current sheets, fast reconnection occurs at various different scales in a highly time dependent manner. Finally, a scenario is presented for fast reconnection in the solar corona on the basis of above plasmoid-induced-reconnection in a fractal current sheet.Comment: 9 pages, 11 figures, with using eps.sty; Earth, Planets and Space in press; ps-file is also available at http://stesun8.stelab.nagoya-u.ac.jp/~tanuma/study/shibata2001

Self-Consistent MHD Modeling of a Coronal Mass Ejection, Coronal Dimming, and a Giant Cusp-Shaped Arcade Formation

We performed magnetohydrodynamic simulation of coronal mass ejections (CMEs) and associated giant arcade formations, and the results suggested new interpretations of observations of CMEs. We performed two cases of the simulation: with and without heat conduction. Comparing between the results of the two cases, we found that reconnection rate in the conductive case is a little higher than that in the adiabatic case and the temperature of the loop top is consistent with the theoretical value predicted by the Yokoyama-Shibata scaling law. The dynamical properties such as velocity and magnetic fields are similar in the two cases, whereas thermal properties such as temperature and density are very different.In both cases, slow shocks associated with magnetic reconnectionpropagate from the reconnection region along the magnetic field lines around the flux rope, and the shock fronts form spiral patterns. Just outside the slow shocks, the plasma density decreased a great deal. The soft X-ray images synthesized from the numerical results are compared with the soft X-ray images of a giant arcade observed with the Soft X-ray Telescope aboard {\it Yohkoh}, it is confirmed that the effect of heat conduction is significant for the detailed comparison between simulation and observation. The comparison between synthesized and observed soft X-ray images provides new interpretations of various features associated with CMEs and giant arcades.Comment: 39 pages, 18 figures. Accepted for publication in the Astrophysical Journal. The PDF file with high resplution figures can be downloaded from http://www.kwasan.kyoto-u.ac.jp/~shiota/study/ApJ62426.preprint.pdf

Morphology and density of post-CME current sheets

Eruption of a coronal mass ejection (CME) drags and "opens" the coronal magnetic field, presumably leading to the formation of a large-scale current sheet and the field relaxation by magnetic reconnection. We analyze physical characteristics of ray-like coronal features formed in the aftermath of CMEs, to check if the interpretation of this phenomenon in terms of reconnecting current sheet is consistent with the observations. The study is focused on measurements of the ray width, density excess, and coronal velocity field as a function of the radial distance. The morphology of rays indicates that they occur as a consequence of Petschek-like reconnection in the large scale current sheet formed in the wake of CME. The hypothesis is supported by the flow pattern, often showing outflows along the ray, and sometimes also inflows into the ray. The inferred inflow velocities range from 3 to 30 km s$^{-1}$, consistent with the narrow opening-angle of rays, adding up to a few degrees. The density of rays is an order of magnitude larger than in the ambient corona. The density-excess measurements are compared with the results of the analytical model in which the Petschek-like reconnection geometry is applied to the vertical current sheet, taking into account the decrease of the external coronal density and magnetic field with height. The model results are consistent with the observations, revealing that the main cause of the density excess in rays is a transport of the dense plasma from lower to larger heights by the reconnection outflow

Two-Dimensional MHD Numerical Simulations of Magnetic Reconnection Triggered by A Supernova Shock in Interstellar Medium, Generation of X-Ray Gas in Galaxy

We examine the magnetic reconnection triggered by a supernova (or a point explosion) in interstellar medium, by performing two-dimensional resistive magnetohydrodynamic (MHD) numerical simulations with high spatial resolution. We found that the magnetic reconnection starts long after a supernova shock (fast-mode MHD shock) passes a current sheet. The current sheet evolves as follows: (i) Tearing-mode instability is excited by the supernova shock, and the current sheet becomes thin in its nonlinear stage. (ii) The current-sheet thinning is saturated when the current-sheet thickness becomes comparable to that of Sweet-Parker current sheet. After that, Sweet-Parker type reconnection starts, and the current-sheet length increases. (iii) ``Secondary tearing-mode instability'' occurs in the thin Sweet-Parker current sheet. (iv) As a result, further current-sheet thinning occurs and anomalous resistivity sets in, because gas density decreases in the current sheet. Petschek type reconnection starts and heats interstellar gas. Magnetic energy is released quickly while magnetic islands are moving in the current sheet during Petschek type reconnection. The released magnetic energy is determined by the interstellar magnetic field strength, not energy of initial explosion nor distance to explosion. We suggest that magnetic reconnection is a possible mechanism to generate X-ray gas in Galaxy.Comment: 17 pages using emulateapj.sty, 24 figures (4colors), submitted to ApJ, mpeg simulations and psfiles are available at http://stesun8.stelab.nagoya-u.ac.jp/~tanuma/apj2000/apj2000.htm