Critical decay index for eruptions of ‘short’ filaments

ABSTRACT Model of a partial current-carrying torus loop anchored to the photosphere is analysed. Conditions of the catastrophic loss of equilibrium are considered and corresponding value of the critical decay index of external magnetic field is found. Taking into account line-tying conditions leads to non-monotonous dependence of the critical decay index on the height of the apex and length of the flux rope (its endpoints separation). For relatively short flux ropes, the critical decay index is significantly lower than unity, which is in contrast to widespread models with the typical critical decay index above unity. The steep decrease of the critical index with height at low heights is due to the sharp increase of the curvature of the flux-rope axis that transforms from a nearly straight line to a crescent.

How does the magnetosphere go to sleep?

<p>Energy and circulation in the Earth’s magnetosphere and ionosphere are largely determined by conditions in the solar wind and interplanetary magnetic field. When the driving from the solar wind is turned off (to a minimum), we expect the activity to die down but exactly how this happens is not known.  Utilizing global MHD modelling, we have addressed the questions of what constitutes the quietest state for the magnetosphere and how it is approached following a northward turning in the IMF that minimizes the driving. We observed an exponential decay with a decay time of about 1 hr in several integrated parameters related to different aspects of magnetospheric activity, including the total field-aligned current into and out of the ionosphere.  The time rate of change for the cessation of activity was also measured in total field aligned current estimates from the AMPERE project, adding observational support to this finding.  Events of distinct northward turnings of the interplanetary magnetic field were identified, with prolonged periods of stable southward driving conditions followed by northward interplanetary magnetic field conditions. A well-defined exponential decay could be identified in the total hemispheric field-aligned current following the northward turning with a generic decay constant of 0.9, corresponding to an e-folding time of 1.1 hr. A possible physical explanation for the exponential decay follows from considering what needs to happen for the convection in the magnetosphere to slow down, or stop, namely the unwinding of the field-aligned current carrying flux tubes in the coupled magnetosphere-ionosphere system. A statistical analysis of the ensemble of events also reveals both a seasonal and a day/night variation in the decay parameter, with faster decay observed in the winter than in the summer hemisphere and on the nightside than on the dayside. These results can be understood in terms of stronger/weaker line tying of the ionospheric foot points of magnetospheric field lines for higher/lower conductivity.  Additional global modeling results with varying conductance scenarios for the ionosphere confirm this interpretation.   </p>

Drifting of the line-tied footpoints of CME flux-ropes

Context. Bridging the gap between heliospheric and solar observations of eruptions requires the mapping of interplanetary coronal mass ejection (CME) footpoints down to the Sun’s surface. But this not straightforward. Improving the understanding of the spatio-temporal evolutions of eruptive flares requires a comprehensive standard model. But the current model is only two-dimensional and cannot address the question of interplanetary CME footpoints. Aims. Existing 3D extensions to the standard model show that flux-rope footpoints are surrounded by curved-shaped quasi-separatrix layer (QSL) footprints that can be related with hook-shaped flare-ribbons. We build upon this finding and further address the joint questions of their time-evolution, and of the formation of flare loops at the ends of the flaring polarity inversion line (PIL) of the erupting bipole, which are both relevant for flare understanding in general and for interplanetary CME studies in particular. Methods. We calculated QSLs and relevant field lines in an MHD simulation of a torus-unstable flux-rope. The evolving QSL footprints are used to define the outer edge of the flux rope at different times, and to identify and characterize new 3D reconnection geometries and sequences that occur above the ends of the flaring PIL. We also analyzed flare-ribbons as observed in the extreme ultraviolet by SDO/AIA and IRIS during two X-class flares. Results. The flux-rope footpoints are drifting during the eruption, which is unexpected due to line-tying. This drifting is due to a series of coronal reconnections that erode the flux rope on one side and enlarge it on the other side. Other changes in the flux-rope footpoint-area are due to multiple reconnections of individual field lines whose topology can evolve sequentially from arcade to flux rope and finally to flare loop. These are associated with deformations and displacements of QSL footprints, which resemble those of the studied flare ribbons. Conclusions. Our model predicts continuous deformations and a drifting of interplanetary CME flux-rope footpoints whose areas are surrounded by equally evolving hooked-shaped flare-ribbons, as well as the formation of flare loops at the ends of flaring PILs which originate from the flux-rope itself, both of which being due to purely three-dimensional reconnection geometries. The observed evolution of flare-ribbons in two events supports the model, but more observations are required to test all its predictions.