Bernhard Kliem

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.

Ideal kink instability of a magnetic loop equilibrium

The force-free coronal loop model by Titov & Demoulin (1999) is found to be unstable with respect to the ideal kink mode, which suggests this instability as a mechanism for the initiation of flares. The long-wavelength ( m= 1) mode grows for average twists � > 3.5� (at a loop aspect ratio of≈ 5). The threshold of instability increases with increasing major loop radius, primarily because the aspect ratio then also increa ses. Numerically obtained equilibria at subcritical twist are very close to the approximate analytical equilibrium; they do not show indications of sigmoidal shape. The growth of kink perturbations is eventually slowed down by the surrounding potential field , which varies only slowly with radius in the model. With this field a global eruption is not obtained in the ideal MHD limit. Kink perturbations with a rising loop apex lead to the formation of a vertical current sheet below the apex, which does not occur in the cylindrical approximation.

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.

Formation of current sheets and sigmoidal structure by the kink instability of a magnetic loop

We study dynamical consequences of the kink instability of a twisted coronal flux rope, using the force-free coronal loop model by Titov & Demoulin (1999) as the initial condition in ideal-MHD simulations. When a critical value of the twist is exceeded, the long-wavelength (m=1) kink mode develops. Analogous to the well-known cylindrical approximation, a helical current sheet is then formed at the interface with the surrounding medium. In contrast to the cylindrical case, upward-kinking loops form a second, vertical current sheet below the loop apex at the position of the hyperbolic flux tube (generalized X line) in the model. The current density is steepened in both sheets and eventually exceeds the current density in the loop (although the kink perturbation starts to saturate in our simulations without leading to a global eruption). The projection of the field lines that pass through the vertical current sheet shows an S shape whose sense agrees with the typical sense of transient sigmoidal ( forward or reverse S-shaped) structures that brighten in soft X rays prior to coronal eruptions. The upward-kinked loop has the opposite S shape, leading to the conclusion that such sigmoids do not generally show the erupting loops themselves but indicate the formation of the vertical current sheet below them that is the central element of the standard flare model.

OBSERVATIONS AND MODELING OF THE EARLY ACCELERATION PHASE OF ERUPTING FILAMENTS INVOLVED IN CORONAL MASS EJECTIONS

We examine the early phases of two near-limb filament destabilizations involved in coronal mass ejections (CMEs) on 2005 June 16 and July 27, using high-resolution, high-cadence observations made with the Transition Region and Coronal Explorer (TRACE), complemented by coronagraphic observations by the Mauna Loa Solar Observatory (MLSO) and the Solar and Heliospheric Observatory (SOHO). The filaments heights above the solar limb in their rapid-acceleration phases are best characterized by a height dependence h(t) ∝ tm with m near, or slightly above, 3 for both events. Such profiles are incompatible with published results for breakout, MHD-instability, and catastrophe models. We show numerical simulations of the torus instability that approximate this height evolution in case a substantial initial velocity perturbation is applied to the developing instability. We argue that the sensitivity of magnetic instabilities to initial and boundary conditions requires higher fidelity modeling of all proposed mechanisms if observations of rise profiles are to be used to differentiate between them. The observations show no significant delays between the motions of the filament and of overlying loops: the filaments seem to move as part of the overall coronal field until several minutes after the onset of the rapid-acceleration phase.

Photospheric flux cancellation and associated flux rope formation and eruption

Aims. We study an evolving bipolar active region that exhibits flux cancellation at the internal polarity inversion line, the formation of a soft X-ray sigmoid along the inversion line and a coronal mass ejection. The aim is to investigate the quantity of flux cancellation that is involved in flux rope formation in the time period leading up to the eruption.Methods. The active region is studied using its extreme ultraviolet and soft X-ray emissions as it evolves from a sheared arcade to flux rope configuration. The evolution of the photospheric magnetic field is described and used to estimate how much flux is reconnected into the flux rope.Results. About one third of the active region flux cancels at the internal polarity inversion line in the 2.5 days leading up to the eruption. In this period, the coronal structure evolves from a weakly to a highly sheared arcade and then to a sigmoid that crosses the inversion line in the inverse direction. These properties suggest that a flux rope has formed prior to the eruption. The amount of cancellation implies that up to 60% of the active region flux could be in the body of the flux rope. We point out that only part of the cancellation contributes to the flux in the rope if the arcade is only weakly sheared, as in the first part of the evolution. This reduces the estimated flux in the rope to similar to 30% or less of the active region flux. We suggest that the remaining discrepancy between our estimate and the limiting value of similar to 10% of the active region flux, obtained previously by the flux rope insertion method, results from the incomplete coherence of the flux rope, due to nonuniform cancellation along the polarity inversion line. A hot linear feature is observed in the active region which rises as part of the eruption and then likely traces out the field lines close to the axis of the flux rope. The flux cancellation and changing magnetic connections at one end of this feature suggest that the flux rope reaches coherence by reconnection immediately before and early in the impulsive phase of the associated flare. The sigmoid is destroyed in the eruption but reforms quickly, with the amount of cancellation involved being much smaller than in the course of its original formation.

Wavelet Analysis of Solar Flare Hard X-Rays

We apply a multiresolution analysis to hard X-ray (HXR) time profiles f(t) of solar flares. This method is based on a wavelet transform (with triangle-shaped wavelets), which yields a dynamic decomposition of the power at different timescales T, the scalogram P(T, t). For stationary processes, time-averaged power coefficients, the scalegram S(T), can be calculated. We develop an algorithm to transform these (multiresolution) scalegrams S(T) into a standard distribution function of physical timescales, N(T). We analyze 647 solar flares observed with the Compton Gamma Ray Observatory (CGRO), recorded at energies ≥25 keV with a time resolution of 64 ms over 4 minutes in each flare. The main findings of our wavelet analysis are: 1. In strong flares, the shortest detected timescales are found in the range Tmin ≈ 0.1-0.7 s. These minimum timescales are found to correlate with the flare loop size r (measured from Yohkoh images in 46 flares), according to the relation Tmin(r) ≈ 0.5(r/109 cm) s. Moreover, these minimum timescales are subject to a cutoff, Tmin(ne) TDefl(ne), which corresponds to the electron collisional deflection time at the loss-cone site of the flare loops (inferred from energy-dependent time delays in CGRO data). 2. In smoothly varying flares, the shortest detected timescales are found in the range Tmin ≈ 0.5-5 s. Because these smoothly varying flares exhibit also large trap delays, the lack of detected fine structure is likely to be caused by the convolution with trapping times. 3. In weak flares, the shortest detected timescales cover a large range, Tmin ≈ 0.5-50 s, mostly affected by Poisson noise. 4. The scalegrams S(T) show a power-law behavior with slopes of βmax ≈ 1.5-3.2 (for strong flares) over the timescale range of [Tmin, Tpeak]. Dominant peaks in the timescale distribution N(T) are found in the range Tpeak ≈ 0.5-102 s, often coinciding with the upper cutoff of N(T). These observational results indicate that the fastest significant HXR time structures detected with wavelets (in strong flares) are related to physical parameters of propagation and collision processes. If the minimum timescale Tmin is associated with an Alfvenic crossing time through elementary acceleration cells, we obtain sizes of racc ≈ 75-750 km, which have a scale-invariant ratio racc/r ≈ 0.03 to flare loops and are consistent with cell sizes inferred from the frequency bandwidth of decimetric millisecond spikes.

FLUX ROPE FORMATION PRECEDING CORONAL MASS EJECTION ONSET

We analyze the evolution of a sigmoidal (S-shaped) active region toward eruption, which includes a coronal mass ejection (CME) but leaves part of the filament in place. The X-ray sigmoid is found to trace out three different magnetic topologies in succession: a highly sheared arcade of coronal loops in its long-lived phase, a bald-patch separatrix surface (BPSS) in the hours before the CME, and the first flare loops in its major transient intensity enhancement. The coronal evolution is driven by photospheric changes which involve the convergence and cancellation of flux elements under the sigmoid and filament. The data yield unambiguous evidence for the existence of a BPSS, and hence a flux rope, in the corona prior to the onset of the CME.

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.

Toward understanding the early stages of an impulsively accelerated coronal mass ejection - SECCHI observations

Context. The expanding magnetic flux in coronal mass ejections (CMEs) often forms a cavity. Studies of CME cavities have so far been limited to the pre-event configuration to evolved CMEs at great heights, and to two-dimensional imaging data. Aims. Quantitative analysis of three-dimensional cavity evolution at CME onset can reveal information that is relevant to the genesis of the eruption. Methods. A spherical model was simultaneously fit to Solar Terrestrial Relations Observatory (STEREO) Extreme Ultraviolet Imager (EUVI) and Inner Coronagraph (COR1) data of an impulsively accelerated CME on 25 March 2008, which displays a well-defined extreme ultraviolet (EUV) and white-light cavity of nearly circular shape already at low heights h ≈ 0.2R� . The center height h(t) and radial expansion r(t) of the cavity were obtained in the whole height range of the main acceleration. We interpret them as the axis height and as a quantity proportional to the minor radius of a flux rope. Results. The three-dimensional expansion of the CME exhibits two phases in the course of its main upward acceleration. From the first h and r data points, taken shortly after the onset of the main acceleration, the erupting flux shows an overexpansion compared to its rise, as expressed by the decrease in the aspect ratio from κ = h/r ≈ 3t oκ ≈ (1.5–2). This phase is approximately coincident with the impulsive rise in the acceleration and is followed by a phase of very gradual change in the aspect ratio (a nearly self-similar expansion) toward κ ∼ 2. 5a th ∼ 10R� . The initial overexpansion of the CME cavity can be caused by flux conservation around a rising flux rope of decreasing axial current and by the addition of flux to a growing, or by even newly formed, flux rope by magnetic reconnection. Further analysis will be required to decide which of these contributions is dominant. The data also suggest that the horizontal component of the impulsive cavity expansion (parallel to the solar surface) triggers the associated EUV wave, which subsequently detaches from the CME volume.