3D Reconstruction of a Rotating Erupting Prominence

A bright prominence associated with a coronal mass ejection (CME) was seen erupting from the Sun on 9 April 2008. This prominence was tracked by both the Solar Terrestrial Relations Observatory (STEREO) EUVI and COR1 telescopes, and was seen to rotate about the line of sight as it erupted; therefore, the event has been nicknamed the "Cartwheel CME." The threads of the prominence in the core of the CME quite clearly indicate the structure of a weakly to moderately twisted flux rope throughout the field of view, up to heliocentric heights of 4 solar radii. Although the STEREO separation was 48 degrees, it was possible to match some sharp features in the later part of the eruption as seen in the 304 {\AA} line in EUVI and in the H\alpha-sensitive bandpass of COR1 by both STEREO Ahead and Behind. These features could then be traced out in three-dimensional space, and reprojected into a view in which the eruption is directed towards the observer. The reconstructed view shows that the alignment of the prominence to the vertical axis rotates as it rises up to a leading-edge height of \approx 2.5 solar radii, and then remains approximately constant. The alignment at 2.5 solar radii differs by about 115 degrees from the original filament orientation inferred from H{\alpha} and EUV data, and the height profile of the rotation, obtained here for the first time, shows that two thirds of the total rotation is reached within \approx 0.5 solar radii above the photosphere. These features are well reproduced by numerical simulations of an unstable moderately twisted flux rope embedded in external flux with a relatively strong shear field component.Comment: published in Solar Physics (Online First

Reconnection of a kinking flux rope triggering the ejection of a microwave and hard X-ray source. II. Numerical Modeling

Numerical simulations of the helical ($m\!=\!1$) kink instability of an arched, line-tied flux rope demonstrate that the helical deformation enforces reconnection between the legs of the rope if modes with two helical turns are dominant as a result of high initial twist in the range $\Phi\gtrsim6\pi$. Such reconnection is complex, involving also the ambient field. In addition to breaking up the original rope, it can form a new, low-lying, less twisted flux rope. The new flux rope is pushed downward by the reconnection outflow, which typically forces it to break as well by reconnecting with the ambient field. The top part of the original rope, largely rooted in the sources of the ambient flux after the break-up, can fully erupt or be halted at low heights, producing a "failed eruption." The helical current sheet associated with the instability is squeezed between the approaching legs, temporarily forming a double current sheet. The leg-leg reconnection proceeds at a high rate, producing sufficiently strong electric fields that it would be able to accelerate particles. It may also form plasmoids, or plasmoid-like structures, which trap energetic particles and propagate out of the reconnection region up to the top of the erupting flux rope along the helical current sheet. The kinking of a highly twisted flux rope involving leg-leg reconnection can explain key features of an eruptive but partially occulted solar flare on 18 April 2001, which ejected a relatively compact hard X-ray and microwave source and was associated with a fast coronal mass ejection.Comment: Solar Physics, in pres

The origin of net electric currents in solar active regions

There is a recurring question in solar physics about whether or not electric currents are neutralized in active regions (ARs). This question was recently revisited using three-dimensional (3D) magnetohydrodynamic (MHD) numerical simulations of magnetic flux emergence into the solar atmosphere. Such simulations showed that flux emergence can generate a substantial net current in ARs. Another source of AR currents are photospheric horizontal flows. Our aim is to determine the conditions for the occurrence of net vs. neutralized currents with this second mechanism. Using 3D MHD simulations, we systematically impose line-tied, quasi-static, photospheric twisting and shearing motions to a bipolar potential magnetic field. We find that such flows: (1) produce both {\it direct} and {\it return} currents, (2) induce very weak compression currents - not observed in 2.5D - in the ambient field present in the close vicinity of the current-carrying field, and (3) can generate force-free magnetic fields with a net current. We demonstrate that neutralized currents are in general produced only in the absence of magnetic shear at the photospheric polarity inversion line - a special condition rarely observed. We conclude that, as magnetic flux emergence, photospheric flows can build up net currents in the solar atmosphere, in agreement with recent observations. These results thus provide support for eruption models based on pre-eruption magnetic fields possessing a net coronal current.Comment: 14 pages and 11 figures (Accepted in The Astrophysical Journal

Catastrophe versus instability for the eruption of a toroidal solar magnetic flux rope

The onset of a solar eruption is formulated here as either a magnetic catastrophe or as an instability. Both start with the same equation of force balance governing the underlying equilibria. Using a toroidal flux rope in an external bipolar or quadrupolar field as a model for the current-carrying flux, we demonstrate the occurrence of a fold catastrophe by loss of equilibrium for several representative evolutionary sequences in the stable domain of parameter space. We verify that this catastrophe and the torus instability occur at the same point; they are thus equivalent descriptions for the onset condition of solar eruptions.Comment: V2: update to conform to the published article; new choice for internal inductance of torus; updated Fig. 2; new Figs. 3, 5, and

Ideal kink instability of a magnetic loop equilibrium

The force-free coronal loop model by Titov & D\'emoulin (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 \Phi\ga3.5\pi (at a loop aspect ratio of $\approx$ 5). The threshold of instability increases with increasing major loop radius, primarily because the aspect ratio then also increases. 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.Comment: Astron. Astrophys. Lett., accepte

Initiation and Early Kinematic Evolution of Solar Eruptions

We investigate the initiation and early evolution of 12 solar eruptions, including six active region hot channel and six quiescent filament eruptions, which were well observed by the \textsl{Solar Dynamics Observatory}, as well as by the \textsl{Solar TErrestrial RElations Observatory} for the latter. The sample includes one failed eruption and 11 coronal mass ejections, with velocities ranging from 493 to 2140~km~s$^{-1}$. A detailed analysis of the eruption kinematics yields the following main results. (1) The early evolution of all events consists of a slow-rise phase followed by a main-acceleration phase, the height-time profiles of which differ markedly and can be best fit, respectively, by a linear and an exponential function. This indicates that different physical processes dominate in these phases, which is at variance with models that involve a single process. (2) The kinematic evolution of the eruptions tends to be synchronized with the flare light curve in both phases. The synchronization is often but not always close. A delayed onset of the impulsive flare phase is found in the majority of the filament eruptions (5 out of 6). This delay, and its trend to be larger for slower eruptions, favor ideal MHD instability models. (3) The average decay index at the onset heights of the main acceleration is close to the threshold of the torus instability for both groups of events (although based on a tentative coronal field model for the hot channels), suggesting that this instability initiates and possibly drives the main acceleration.Comment: Accepted for publication in ApJ; 24 pages, 12 figures, 3 table

Testing non-linear force-free coronal magnetic field extrapolations with the Titov-Demoulin equilibrium

CONTEXT: As the coronal magnetic field can usually not be measured directly, it has to be extrapolated from photospheric measurements into the corona. AIMS: We test the quality of a non-linear force-free coronal magnetic field extrapolation code with the help of a known analytical solution. METHODS: The non-linear force-free equations are numerically solved with the help of an optimization principle. The method minimizes an integral over the force-free and solenoidal condition. As boundary condition we use either the magnetic field components on all six sides of the computational box in Case I or only on the bottom boundary in Case II. We check the quality of the reconstruction by computing how well force-freeness and divergence-freeness are fulfilled and by comparing the numerical solution with the analytical solution. The comparison is done with magnetic field line plots and several quantitative measures, like the vector correlation, Cauchy Schwarz, normalized vector error, mean vector error and magnetic energy. RESULTS: For Case I the reconstructed magnetic field shows good agreement with the original magnetic field topology, whereas in Case II there are considerable deviations from the exact solution. This is corroborated by the quantitative measures, which are significantly better for Case I. CONCLUSIONS: Despite the strong nonlinearity of the considered force-free equilibrium, the optimization method of extrapolation is able to reconstruct it; however, the quality of reconstruction depends significantly on the consistency of the input data, which is given only if the known solution is provided also at the lateral and top boundaries, and on the presence or absence of flux concentrations near the boundaries of the magnetogram.Comment: 6 pages, 2 figures, Research Not

Testing magnetofrictional extrapolation with the Titov-D\'emoulin model of solar active regions

We examine the nonlinear magnetofrictional extrapolation scheme using the solar active region model by Titov and D\'emoulin as test field. This model consists of an arched, line-tied current channel held in force-free equilibrium by the potential field of a bipolar flux distribution in the bottom boundary. A modified version, having a parabolic current density profile, is employed here. We find that the equilibrium is reconstructed with very high accuracy in a representative range of parameter space, using only the vector field in the bottom boundary as input. Structural features formed in the interface between the flux rope and the surrounding arcade-"hyperbolic flux tube" and "bald patch separatrix surface"-are reliably reproduced, as are the flux rope twist and the energy and helicity of the configuration. This demonstrates that force-free fields containing these basic structural elements of solar active regions can be obtained by extrapolation. The influence of the chosen initial condition on the accuracy of reconstruction is also addressed, confirming that the initial field that best matches the external potential field of the model quite naturally leads to the best reconstruction. Extrapolating the magnetogram of a Titov-D\'emoulin equilibrium in the unstable range of parameter space yields a sequence of two opposing evolutionary phases which clearly indicate the unstable nature of the configuration: a partial buildup of the flux rope with rising free energy is followed by destruction of the rope, losing most of the free energy.Comment: 14 pages, 10 figure

A Parametric Study of Erupting Flux Rope Rotation. Modeling the "Cartwheel CME" on 9 April 2008

The rotation of erupting filaments in the solar corona is addressed through a parametric simulation study of unstable, rotating flux ropes in bipolar force-free initial equilibrium. The Lorentz force due to the external shear field component and the relaxation of tension in the twisted field are the major contributors to the rotation in this model, while reconnection with the ambient field is of minor importance. Both major mechanisms writhe the flux rope axis, converting part of the initial twist helicity, and produce rotation profiles which, to a large part, are very similar in a range of shear-twist combinations. A difference lies in the tendency of twist-driven rotation to saturate at lower heights than shear-driven rotation. For parameters characteristic of the source regions of erupting filaments and coronal mass ejections, the shear field is found to be the dominant origin of rotations in the corona and to be required if the rotation reaches angles of order 90 degrees and higher; it dominates even if the twist exceeds the threshold of the helical kink instability. The contributions by shear and twist to the total rotation can be disentangled in the analysis of observations if the rotation and rise profiles are simultaneously compared with model calculations. The resulting twist estimate allows one to judge whether the helical kink instability occurred. This is demonstrated for the erupting prominence in the "Cartwheel CME" on 9 April 2008, which has shown a rotation of \approx 115 degrees up to a height of 1.5 R_sun above the photosphere. Out of a range of initial equilibria which include strongly kink-unstable (twist Phi=5pi), weakly kink-unstable (Phi=3.5pi), and kink-stable (Phi=2.5pi) configurations, only the evolution of the weakly kink-unstable flux rope matches the observations in their entirety.Comment: Solar Physics, submitte