Abstract In this thesis solar active longitudes of X-ray flares and sunspots are studied. The fact that solar activity does not occur uniformly at all heliographic longitudes was noticed by Carrington as early as in 1843. The longitude ranges where solar activity occurs preferentially are called active longitudes. Active longitudes have been found in various manifestations of solar activity, such as sunspots, flares, radio emission bursts, surface and heliospheric magnetic fields, and coronal emissions. However, the active longitudes found when using different rigidly rotating reference frames differ significantly from each other. One reason is that the whole Sun does not rotate rigidly but differentially at different layers and different latitudes. The other reason is that the rotation of the Sun also varies with time. Earlier studies used a dynamic rotation frame for the differential rotation of the Sun and found two persistent active longitudes of sunspots in 1878-1996. However, the migration of active longitudes with respect to the Carrington rotation was treated there rather coarsely. We improved the accuracy of migration to less than one hour. Accordingly, not only the rotation parameters for each class of solar flares and sunspots are found to agree well with each other, but also the non-axisymmetry of flares and sunspots is systematically increased. We also studied the long-term variation of solar surface rotation. Using the improved analysis, the spatial distribution of sunspots in 1876-2008 is analyzed. The statistical evidence for different rotation in the northern and southern hemispheres is greatly improved by the revised treatment. Moreover, we have given consistent evidence for the periodicity of about one century in the north-south difference.

In this dissertation we consider the dynamics of the solar interior, with particular focus on angular momentum balance and magnetic field confinement within the tachocline. In Part I we review current knowledge of the Sun's rotation. We summarise the main mechanisms by which angular momentum is transported within the Sun, and discuss the difficulties in reconciling the observed uniform rotation of the radiative interior with purely hydrodynamical theories. Following Gough & McIntyre (1998) we conclude that a global-scale interior magnetic field provides the most plausible explanation for the observed uniform rotation, provided that it is confined within the tachocline. We discuss potential mechanisms for magnetic field confinement, assuming that the field has a roughly axial-dipolar structure. In particular, we argue that the field is confined, in high latitudes, by a laminar downwelling flow driven by turbulence in the tachocline and convection zone above. In Part II we describe how the magnetic confinement picture is affected by the presence of compositional stratification in the 'helium settling layer' below the convection zone. We use scaling arguments to estimate the rate at which the settling layer forms, and verify our predictions with a simple numerical model. We discuss the implications for lithium depletion in the convection zone. In Part III we present numerical results showing how the Sun's interior magnetic field can be confined, in the polar regions, while maintaining uniform rotation within the radiative envelope. These results come from solving the full, nonlinear equations numerically. We also show how these results can be understood in terms of a reduced, analytical model that is asymptotically valid in the parameter regime of relevance to the solar tachocline. In Part IV we discuss how our high-latitude model can be extended to a global model of magnetic confinement within the tachocline.

Observations show that Coronal Mass Ejections (CMEs) are associated with twisted magnetic flux configurations. Conventionally, CMEs are modeled by shearing and twisting the footpoints of a certain distribution of magnetic flux at the solar surface and letting it evolve at the surface. Of course, the surface velocities and magnetic field patterns should ultimately be obtained from realistic simulations of the solar convection zone where the field is generated by dynamo action. Therefore, a unified treatment of the convection zone and the CMEs is needed. Numerical simulations of turbulent dynamos show that the amplification of magnetic fields can be catastrophically quenched at magnetic Reynolds numbers typical of the interior of the Sun. A strong flux of magnetic helicity leaving the dynamo domain can alleviate this quenching. In this sense, a realistic (magnetic) boundary condition is an important ingredient of a successful solar dynamo model. Using a two-layer model developed in this thesis, we combine a dynamo-active region with a magnetically inert but highly conducting upper layer which models the solar corona. In four steps we improve this setup from a forced to a convectively driven dynamo and from an isothermal to a polytropic stratified corona. The simulations show magnetic fields that emerge at the surface of the dynamo region and are ejected into the coronal part of the domain. Their morphological form allows us to associate these events with CMEs. Magnetic helicity is found to change sign in the corona to become consistent with recent helicity measurements in the solar wind. Our convection-driven dynamo model with a coronal envelope has a solar-like differential rotation with radial (spoke-like) contours of constant rotation rate, together with a solar-like meridional circulation and a near-surface shear layer. The spoke-like rotation profile is due to latitudinal entropy gradient which violates the Taylor--Proudman balance through the baroclinic term. We find mean magnetic fields that migrate equatorward in models both with and without the coronal layer. One remarkable result is that the dynamo action benefits substantially from the presence of a corona becoming stronger and more realistic. The two-layer model represents a new approach to describe the generation of coronal mass ejections in a self-consistent manner. On the other hand, it has important implications for solar dynamo models as it admits many magnetic features observed in the Sun. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 5: Manuscript; Paper 6: Manuscript.</p>