Data-analyse en wiskundige modellering van de initiatie van coronalemassa-ejecties

摘要

It is widely accepted that solar flares and CoronalMass Ejections (CMEs) are magnetically dominated phenomena. Among the various energy sources, only the magnetic one can account for the energy requirements of such violent phenomena. It is also generally accepted that the magnetic energy necessary to drive a solar eruption should be stored in the electric currents, that lead to a non-potentialmagnetic field configuration. However, how this energy is built up into the corona and under which conditions it is suddenly released at a later stage, is not clear yet. Therefore, to better understand the dynamics of these solar eruptions, joined observational and theoretical research efforts are required. In this PhD project, we combined data analysis of solar images with advanced mathematical modeling in order to improve our understanding of such violent phenomena that are the major drivers of the space weather.Starting from the results obtained by van der Holst et al. (2007), we investigated the response of the solar corona when different driving mechanismsare applied as time-dependent boundary conditions. We performed axisymmetric numerical Magnetohydrodynamics (MHD) simulations using the Versatile Advection Code (VAC) (T´oth 1996) on the VIC cluster of the KU Leuven. The initial condition consists out of a helmet streamer embeddedin a bi-modal solar wind. To obtain a magnetic field configuration thatresembles the breakout model (Antiochos et al. 1999), at the solar surface, symmetrically with respect the solar equator, we added an extra magnetic field with an orientation that is anti-parallel with respect to the orientation of the overlying field. In order to build up magnetic freeenergy into the system, we applied both magnetic shearing motions alongthe polarity inversion line and magnetic flux emergence from below the photosphere. Since the initial steady state, the numerical grid, the numerical method and all the boundary conditions, except for the azimuthal component of the vector potential and of the velocity, are the same for both types of driving, this allowed us to objectively compare the two driving mechanisms. We found that the overall evolution of the system is very similar when the two driving mechanisms are applied. As a consequence of the applied boundary conditions, the magnetic pressure insidethe central arcade increases and the arcade starts to expand, eventually compressing the X-point and forming a current sheet. At a certain moment magnetic reconnection sets in, transferring flux from the overlying field toward the side arcades eventually detaching the helmet streamer and resulting in a slow blowout CME. We found that when shearing motions are present also flare reconnection at the flanks of the central arcade is observed, while this is absent when flux emergence is at work. We alsofound that the injection of magnetic helicity is not a condicio sine qua non for the eruption to occur. However, when helicity is injected intothe system a threshold has been found. This seems to confirm the hypothesis that magnetic helicity may be a lower boundary for the magnetic free energy: helicity injection results in an increase of the magnetic freeenergy, eventually leading to a non-equilibrium process. These results pointed out the relevance of the role that the global magnetic field and the solar wind play in the CME initiation and propagation. In Chap. 4, following the combined observational and theoretical approach that has been the driver of these four years of research, we investigated the dynamics of the 2009 September 21 event. This slow CME, associated with a prominence eruption, underwent a strong latitudinal deflection during its propagation within the first four solar radii. We used stereoscopic images provided by the twin NASA Solar TErrestrial RElations Observatory (STEREO) spacecraft in order to reconstruct the three-dimensional trajectory of the CME bothwith the ExtremeUltraViolet Imager (EUVI) and COR1 coronagraph. The prominence left the Sun at a projected latitude of 37◦ S and entered the COR1 field-of-view (FOV) ata projected latitude of about 25◦ S, where it underwent a furtherdeflection toward the heliospheric current sheet (HCS), eventually reaching it. During its further propagation the CME longitude did not change more than 10◦, propagating almost along a meridional plane.In order to reproduce the observed dynamics, we performed an axisymmetric MHD simulation, starting from a magnetic field configuration that closely resembled the PFSS extrapolation for 2009 September 19.We applied localized shearing motions that mimicked the observed ones and introduced an amount of magnetic helicity comparable to the one measured for the active region (AR). As a consequence of the magnetic pressure imbalance due to the interchange reconnection that occurred in the null point inside the pseudostreamer, during its outward propagation, the CME was rapidly deflected toward the equator. The simulation reasonably well reproduced the observed dynamic s eventually fitting the observed height-time and latitude-time evolution of the observed CME. We also increased the strength of the global magnetic field and as a result the CME deflection toward the solar equator was more abrupt. We concluded that during solar minima, even CMEs originating from high latitudes can be easily deflected toward the HCS, eventually resulting in geo-effective events. How rapidly they are deflected depends on the strength of both the overlying magnetic field and the flux rope magnetic flux.Chapter 5was devoted to an observational analysis of the magnetic helicity flux in ARs that gave rise to either halo CMEs or failed eruptions. We analyzed ten ARs that gave rise to twelve halo CMEs and we measured the helicity injection rates, the helicity accumulations and the magnetic fluxes in order to investigate whether a relation between magnetic helicity fluxand CME initiation could be identified. We found that no unique behavior was observed. The major magnetic helicity injection has been observed during flux emergence events, however, for at least two cases the helicity injection was the consequence of photospheric shearing motions. In fact, no flux emergence/cancellation has been observed for those ARs. We also found that impulsive CMEs seem to not follow the hemispheric helicity rule, while this is the case for gradual CMEs. However, our sample wasvery limited and further investigation is needed to firmly validate this hypothesis. For a significant amount of ARs an abrupt change in the helicity injection rate was correlated with the CMEs occurence. We argued that this helicity injection could be the consequence of the magnetic torque imbalance between the coronal and the sub-photospheric part of the flux tube. In order to further investigate this phenomenon, we analyzed a failed eruption. From the Transition Region and Coronal Explorer (TRACE) images we inferred the helicity variation during the event and we compared it with the helicity injection measured from theMichelson Doppler Imager (MDI) magnetograms. We found that the helicity injection was of the opposite sign with respect to the model prediction. However, if the AR as a whole is considered and if we assume that during reconnection events helicity is transferred from one flux system to the other, the helicity injection predicted by the model is consistent with our measurements. Next, we investigated the role of shearing motions in the2010 April 3 filament eruption that resulted in the first geo-effectiveCME of solar cycle 24. We observed persistent shearing flows parallel to the polarity inversion line, that resulted in the reduction of the inclination between the axial field of the filament and the overlying field, eventually reducing the efficiency of the reconnection between these two field distributions. However, the filament underwent an eruption. We calculated the index for the torus instability and we found that at the moment of the eruption the system was torus unstable. Therefore, we concluded that the observed shearing motions may have resulted in the increase of the axial flux of the filament and as a consequence in the increase of its magnetic pressure. This increase in the magnetic pressure lifted up the flux rope slowly, eventually bringing its axis to a height where the condition for the torus instability is satisfied, resulting in thefilament eruption.The last chapter of the present thesis has been devoted to the development of a three-dimensional, data-inspired, non-zero plasma-beta MHD model for the initiation of CMEs. We presented a method to reconstruct the magnetic field starting from a solar magnetogram and under the assumption of force-free equilibrium. We superposed thesolution to an hydrostatic equilibrium and used the MPI-AMRVAC code (Keppens et al. 2012) to advance the MHD equations in time. We applied the method to the AR NOAA 9415 that during its transit across the solar diskgave rise to several CMEs and flares. Magnetic free energy has been introduced into the system by applying vortex motions along iso-contours ofthe vertical magnetic field distribution. The resulting magnetic configuration had the same chirality as the AR 9415. We then applied convergence motions toward the polarity inversion line that resembled the motionsobserved for the AR. As a result of the magnetic reconnection between the highly sheared magnetic field lines a flux rope is formed. While the reconnection continues more and more flux is transferred to the flux rope, eventually increasing the magnetic pressure inside it and driving theeruption. The obtained CME has a velocity of about 550 km/s and presents a typical three-part structure. We also found that even though the CMEpropagates in a medium where the plasma-beta is larger than one, due to the higher magnetic field, the plasma-beta is ∼ 0.1 withinthe flux rope. This transition of the plasma- is often observed in magnetic clouds.Concluding, the present thesis summarizes our efforts to develop a bilateral, observational and numerical, approach to uncover the physics that governs the dynamics of CMEs. The final goal of this challenging as well as fascinating research path will eventually allowus to provide valuable and reliable space weather forecasts.