Three Dimensional Magnetic Field In The Solar Atmosphere And Associated Activities

The solar atmosphere is constituted of highly magnetized plasma. Magnetic fields play a key role in understanding various active phenomena in the solar atmosphere, such as flares, filaments and prominences, and coronal mass ejections. Various nonlin-ear force-free field extrapolation methods developed in the past years and vector mag-netic fields obtained by sophisticated spectro-polarimeters provide a totally new view on the solar magnetic fields and associated activities and phenomena. In this thesis, we perform a detailed study on the solar active regions and active phenomena via obser-vations and force-free field modelling. First, we discuss the polarization observation and the validity of magnetic field inversion codes. Then, we analyze in detail the three dimensional magnetic field structure of active regions and filaments. We systemati-cally discuss the observation of polarization profiles, the Stokes inversion of magnetic fields, the analysis of vector magnetic fields in the photosphere, and extrapolations of magnetic fields to upper layers. Based on these, we further analyze the mechanisms of solar flares, filaments/prominences, and coronal mass ejections, and the relationships between them. Finally, we obtain the new results as follows.Using the two inversion codes (UNNOFIT and MELANIE) based on the Milne-Eddington solar atmospheric model, we build and compare vector magnetic maps obtained by two spectro-polarimeters, of which one is the ground-based Telescope Heliographique pour l'Etude du Magnetisme et des Instabilites Solaires/Multi-Raies (THEMIS/MTR) and the other is Solar Optical Telescope/Spectro-Polarimeter (SOT/SP) on board Hinode. To this end, we adopt the observation of a facular region within the active region NOAA 10996 on 2008 May 23, and find consistent results concerning the field strength, azimuth, and inclination distributions. Because SOT/SP is free from the seeing effect and has better spatial resolution, we are able to resolve small magnetic polarities with sizes of 1" to 2", and we can detect strong horizontal magnetic fields, which converge or diverge in negative or positive facular polarities. These findings support models which suggest the existence of small vertical flux tube bundles in faculae. A new method is proposed to get the relative formation heights of the multi-lines observed by MTR assuming the validity of a flux tube model for the faculae. We found that the FeⅠ6302.5 A line is formed higher than the FeⅠ5250.2 A line.We study the three-dimensional magnetic field configuration of the two-ribbon flare in the active region NOAA 10930 on 2006 December 13, using the optimization method for nonlinear force-free field (NLFFF) extrapolation and the photospheric vector mag-netic field with high spatial resolution obtained by Hinode SOT/SP. The magnetic topol-ogy can be described as a highly sheared core field and a quasi-potential envelope field of magnetic arcades. The core field clearly shows some dips supposed to sustain a fila-ment. Free energy release in the flare, calculated by subtracting the energy contained in the NLFFF and the corresponding potential field, is 2.4×1031 ergs, which is about 2% of the energy in the potential field before the flare. We also calculate the shear angles, defined as the angles between the NLFFF and potential fields, and find that they be-come larger at some particular sites in the lower atmosphere after the flare, while they become significantly smaller in most places implying that the whole configuration gets closer to the potential field. The CaⅡH line images obtained with the Broadband Filter Imager (BFI) of the SOT and the 1600 A images with the Transition Region and Coro-nal Explorer(TRACE) show that the pre-flare heating occurs mainly in the core field. These results provide evidence in support of the tether-cutting model of solar flares. In addition, we study the correlation heights, which indicate the formation height of Extreme Ultraviolet (EUV) lines in the active region using observations from the EUV Imaging Spectrometer (EIS) on board Hinode. After solving the line blending problem between the HeⅡ256.32 A and SiⅩ256.37 A lines by the double Gaussian curve fitting, we find that the transition region lies higher in a strong magnetic area. In a pre-flare heating area, there possibly exist multi-thermal loops as implied by comparing the Doppler velocity and the magnetic field on the solar disk.We compute the three-dimensional magnetic field of the active region NOAA 10767 in order to study the magnetic configuration of active region filaments. The NLFFF model is adopted to compute the magnetic field above the photosphere, where the vector magnetic field was observed by THEMIS/MTR on 2005 May 27. We propose a new method to remove the 180°ambiguity of the transverse field. We then analyze the implications of the preprocessing of the data by minimizing the total force and torque in the observed vector fields. This provides a consistent bottom boundary condition for the NLFFF model. Then, using the optimization method to compute the coronal field, we find a magnetic flux rope along the polarity inversion line. The magnetic flux rope aligns well with part of an Ha filament, while the total distribution of the magnetic dips coincides with the whole Ha filament. This implies that the magnetic field structure in one section of the filament is a flux rope, while the other is a sheared arcade. The arcade induced a left-bearing filament in the magnetic field of negative helicity, which is opposite to the chirality of barbs that a flux rope, having a magnetic field of the same helicity sign, would induce. The field strength in the center of the flux rope is about 700 Gauss. An M1.1 flare occurred in the same active region. TRACE observations of the flux rope or filament eruption show a strong writhing motion of the erupting structure, suggesting that the flux rope converted some of its twist into writhe during the eruption. After calculating the twist of the pre-eruptive flux rope, we find that it is in very good agreement with thresholds of the helical kink instability found in numerical simulations. We conclude that the activation and rise of the flux rope were triggered and initially driven by the kink instability. We also estimate the height distribution of the decay index of the external magnetic field before the eruption with a potential field. The decay indices stay below the threshold for the "torus instability" for a significant height range above the erupting flux rope. This provides a possible explanation for the confinement of the eruption, hence for the absence of a CME.With three-dimensional magnetic fields, we further study the magnetic topology and helicity injection associated with different solar activities. First, we find that magnetic null points have a close relationship with coronal bright points. The linear structure of a null point is described by the spine and fan. Magnetic reconnection in the spine and fan produces coronal bright points. Second, since magnetic null points are not necessarily present in all regions, we study the quasi-separatrix layer (QSL) associated with the M1.1 flare on 2005 May 27, and find that the ultraviolet flare ribbon of the flare coincides well with the intersection between the QSL and the photosphere, while hard X-ray (HXR) sources at the peak of the flare seem to coincide with the foot-points of the erupting helical structures, which indicates a high possibility that HXR sources can be produced efficiently in the flux rope. Finally, the relationship between the evolution of the twist of a flux rope and the helicity injection is studied. They have a positive relationship with each other. Helicity injection by both horizontal motions, such as twisting and shearing, and vertical motions, such as flux emergence, could increase the twist and cause an eruption of a flux rope, which leads to the formation of CMEs.