Tibor Török

Confined and ejective eruptions of kink-unstable flux ropes

The ideal helical kink instability of a force-free coronal magnetic flux rope, anchored in the photosphere, is studied as a model for solar eruptions. Using the flux rope model of Titov and D?moulin as the initial condition in MHD simulations, both the development of helical shape and the rise profile of a confined (or failed) filament eruption (on 2002 May 27) are reproduced in very good agreement with the observations. By modifying the model such that the magnetic field decreases more rapidly with height above the flux rope, a full (or ejective) eruption of the rope is obtained in very good agreement with the developing helical shape and the exponential-to-linear rise profile of a fast coronal mass ejection (CME) on 2001 May 15. This confirms that the helical kink instability of a twisted magnetic flux rope can be the mechanism of the initiation and the initial driver of solar eruptions. The agreement of the simulations with properties that are characteristic of many eruptions suggests that they are often triggered by the kink instability. The decrease of the overlying field with height is a main factor in deciding whether the instability leads to a confined event or to a CME.

Eruption of a Kink-unstable Filament in NOAA Active Region 10696

We present rapid-cadence Transition Region and Coronal Explorer (TRACE) observations that show evidence of a filament eruption from NOAA active region 10696, accompanied by an X2.5 flare, on 2004 November 10. The eruptive filament, which manifests as a fast coronal mass ejection some minutes later, rises as a kinking structure with an apparently exponential growth of height within TRACEs field of view. We compare the characteristics of this filament eruption with MHD numerical simulations of a kink-unstable magnetic flux rope, finding excellent qualitative agreement. We suggest that while tether weakening by breakout-like quadrupolar reconnection may be the release mechanism for the previously confined flux rope, the driver of the expansion is most likely the MHD helical kink instability.

A MODEL FOR MAGNETICALLY COUPLED SYMPATHETIC ERUPTIONS

Sympathetic eruptions on the Sun have been observed for several decades, but the mechanisms by which one eruption can trigger another remain poorly understood. We present a three-dimensional MHD simulation that suggests two possible magnetic trigger mechanisms for sympathetic eruptions. We consider a configuration that contains two coronal flux ropes located within a pseudo-streamer and one rope located next to it. A sequence of eruptions is initiated by triggering the eruption of the flux rope next to the streamer. The expansion of the rope leads to two consecutive reconnection events, each of which triggers the eruption of a flux rope by removing a sufficient amount of overlying flux. The simulation qualitatively reproduces important aspects of the global sympathetic event on 2010 August 1 and provides a scenario for the so-called twin filament eruptions. The suggested mechanisms are also applicable for sympathetic eruptions occurring in other magnetic configurations.

The Writhe of Helical Structures in the Solar Corona

Context. Helicity is a fundamental property of magnetic fields, conse rved in ideal MHD. In flux rope topology, it consists of twist and writhe helicity. Despite the common occurrence of helical structures in the solar atmosphere, little is known about how their shape relates to the writhe, which fraction of helicity is contain ed in writhe, and how much helicity is exchanged between twist and writhe when they erupt. Aims. Here we perform a quantitative investigation of these questions relevant for coronal flux ropes. Methods. The decomposition of the writhe of a curve into local and nonlocal components greatly facilitates its computation. We use it to study the relation between writhe and projected S shape of helical curves and to measure writhe and twist in numerical simulations of flux rope instabilities. The results are discussed with re gard to filament eruptions and coronal mass ejections (CMEs) . Results. (1) We demonstrate that the relation between writhe and projected S shape is not unique in principle, but that the ambiguity does not affect low-lying structures, thus supporting the established empirical rule which associates stable forward (reverse) S shaped structures low in the corona with positive (negative) helic ity. (2) Kink-unstable erupting flux ropes are found to trans form a far smaller fraction of their twist helicity into writhe helicity than o ften assumed. (3) Confined flux rope eruptions tend to show str onger writhe at low heights than ejective eruptions (CMEs). This argues against suggestions that the writhing facilitates the rise o f the rope through the overlying field. (4) Erupting filaments which are S shaped already before the eruption and keep the sign of their axis writhe (which is expected if field of one chirality dominates the source vol ume of the eruption), must reverse their S shape in the course of the rise. Implications for the occurrence of the helical kink instabi lity in such events are discussed. (5) The writhe of rising lo ops can easily be estimated from the angle of rotation about the direction of ascent, once the apex height exceeds the footpoint separation significantly. Conclusions. Writhe can straightforwardly be computed for numerical data and can often be estimated from observations. It is useful in interpreting S shaped coronal structures and in constrai ning models of eruptions.

Simulations of Emerging Magnetic Flux. I. The Formation of Stable Coronal Flux Ropes

We present results from three-dimensional visco-resistive magnetohydrodynamic simulations of the emergence of a convection zone magnetic flux tube into a solar atmosphere containing a pre-existing dipole coronal field, which is orientated to minimize reconnection with the emerging field. We observe that the emergence process is capable of producing a coronal flux rope by the transfer of twist from the convection zone, as found in previous simulations. We find that this flux rope is stable, with no evidence of a fast rise, and that its ultimate height in the corona is determined by the strength of the pre-existing dipole field. We also find that although the electric currents in the initial convection zone flux tube are almost perfectly neutralized, the resultant coronal flux rope carries a significant net current. These results suggest that flux tube emergence is capable of creating non-current-neutralized stable flux ropes in the corona, tethered by overlying potential fields, a magnetic configuration that is believed to be the source of coronal mass ejections.

Coronal Magnetic Reconnection Driven by CME Expansion—the 2011 June 7 Event

Coronal mass ejections (CMEs) erupt and expand in a magnetically structured solar corona. Various indirect observational pieces of evidence have shown that the magnetic field of CMEs reconnects with surrounding magnetic fields, forming, e.g., dimming regions distant from the CME source regions. Analyzing Solar Dynamics Observatory (SDO) observations of the eruption from AR 11226 on 2011 June 7, we present the first direct evidence of coronal magnetic reconnection between the fields of two adjacent active regions during a CME. The observations are presented jointly with a data-constrained numerical simulation, demonstrating the formation/intensification of current sheets along a hyperbolic flux tube at the interface between the CME and the neighboring AR 11227. Reconnection resulted in the formation of new magnetic connections between the erupting magnetic structure from AR 11226 and the neighboring active region AR 11227 about 200 Mm from the eruption site. The onset of reconnection first becomes apparent in the SDO/AIA images when filament plasma, originally contained within the erupting flux rope, is redirected toward remote areas in AR 11227, tracing the change of large-scale magnetic connectivity. The location of the coronal reconnection region becomes bright and directly observable at SDO/AIA wavelengths, owing to the presence of down-flowing cool, dense (1010 cm(-3)) filament plasma in its vicinity. The high-density plasma around the reconnection region is heated to coronal temperatures, presumably by slow-mode shocks and Coulomb collisions. These results provide the first direct observational evidence that CMEs reconnect with surrounding magnetic structures, leading to a large-scale reconfiguration of the coronal magnetic field.

2010 August 1-2 Sympathetic Eruptions. I. Magnetic Topology of the Source-surface Background Field

A sequence of apparently coupled eruptions was observed on 2010 August 1-2 by Solar Dynamics Observatory and STEREO. The eruptions were closely synchronized with one another, even though some of them occurred at widely separated locations. In an attempt to identify a plausible reason for such synchronization, we study the large-scale structure of the background magnetic configuration. The coronal field was computed from the photospheric magnetic field observed at the appropriate time period by using the potential field source-surface model. We investigate the resulting field structure by analyzing the so-called squashing factor calculated at the photospheric and source-surface boundaries, as well as at different coronal cross-sections. Using this information as a guide, we determine the underlying structural skeleton of the configuration, including separatrix and quasi-separatrix surfaces. Our analysis reveals, in particular, several pseudo-streamers in the regions where the eruptions occurred. Of special interest to us are the magnetic null points and separators associated with the pseudo-streamers. We propose that magnetic reconnection triggered along these separators by the first eruption likely played a key role in establishing the assumed link between the sequential eruptions. The present work substantiates our recent simplified magnetohydrodynamic model of sympathetic eruptions and provides a guide for further deeper study of these phenomena. Several important implications of our results for the S-web model of the slow solar wind are also addressed.

DISTRIBUTION OF ELECTRIC CURRENTS IN SOLAR ACTIVE REGIONS

There has been a long-standing debate on the question of whether or not electric currents in solar active regions are neutralized. That is, whether or not the main (or direct) coronal currents connecting the active region polarities are surrounded by shielding (or return) currents of equal total value and opposite direction. Both theory and observations are not yet fully conclusive regarding this question, and numerical simulations have, surprisingly, barely been used to address it. Here we quantify the evolution of electric currents during the formation of a bipolar active region by considering a three-dimensional magnetohydrodynamic simulation of the emergence of a sub-photospheric, current-neutralized magnetic flux rope into the solar atmosphere. We find that a strong deviation from current neutralization develops simultaneously with the onset of significant flux emergence into the corona, accompanied by the development of substantial magnetic shear along the active regions polarity inversion line. After the region has formed and flux emergence has ceased, the strong magnetic fields in the regions center are connected solely by direct currents, and the total direct current is several times larger than the total return current. These results suggest that active regions, the main sources of coronal mass ejections and flares, are born with substantial net currents, in agreement with recent observations. Furthermore, they support eruption models that employ pre-eruption magnetic fields containing such currents.

MAGNETOHYDRODYNAMIC SIMULATIONS OF INTERPLANETARY CORONAL MASS EJECTIONS

We describe a new MHD model for the propagation of interplanetary coronal mass ejections (ICMEs) in the solar wind. Accurately following the propagation of ICMEs is important for determining space weather conditions. Our model solves the MHD equations in spherical coordinates from a lower boundary above the critical point to Earth and beyond. On this spherical surface, we prescribe the magnetic field, velocity, density, and temperature calculated typically directly from a coronal MHD model as time-dependent boundary conditions. However, any model that can provide such quantities either in the inertial or rotating frame of the Sun is suitable. We present two validations of the technique employed in our new model and a more realistic simulation of the propagation of an ICME from the Sun to Earth.

Initiation of Coronal Mass Ejections by Sunspot Rotation

We study a filament eruption, two-ribbon flare, and coronal mass ejection (CME) that occurred in NOAA Active Region 10898 on 6 July 2006. The filament was located South of a strong sunspot that dominated the region. In the evolution leading up to the eruption, and for some time after it, a counter-clockwise rotation of the sunspot of about 30 degrees was observed. We suggest that the rotation triggered the eruption by progressively expanding the magnetic field above the filament. To test this scenario, we study the effect of twisting the initially potential field overlying a pre-existing flux-rope, using three-dimensional zero-β MHD simulations. We first consider a relatively simple and symmetric system, and then study a more complex and asymmetric magnetic configuration, whose photospheric-flux distribution and coronal structure are guided by the observations and a potential field extrapolation. In both cases, we find that the twisting leads to the expansion of the overlying field. As a consequence of the progressively reduced magnetic tension, the flux-rope quasi-statically adapts to the changed environmental field, rising slowly. Once the tension is sufficiently reduced, a distinct second phase of evolution occurs where the flux-rope enters an unstable regime characterised by a strong acceleration. Our simulations thus suggest a new mechanism for the triggering of eruptions in the vicinity of rotating sunspots.