Catastrophic Behavior Of Coronal Flux Rope In Multipole Magnetic Fields

Coronal mass ejections (CMEs) belong to large-scale solar active phenomena. They cause strong disturbances of the Earth's space environment, and serve as a main source of disastrous space weather. The observational and theoretical study of CMEs has been as an important subject in the fields of solar physics and solar-terrestrial space physics. Although the study has been carried out for several decades, the origin of CMEs is still not fully understood because of the difficulty in observing them directly. In this thesis, we study the origin of CMEs and propose some possible triggering mechanisms for CMEs.After a brief review of observational features and current research status of CMEs, we summarize the theoretical models of CMEs, especially the coronal flux rope catastrophe model closely related to this thesis. Then we describe our main results in the study of coronal flux rope catastrophe. In terms of a 2.5-dimensional MHD model in spherical geometry, we investigate the equilibrium properties and catastrophic behaviors of the coronal flux rope system in different background magnetic fields with complicated topology.First, we study the catastrophic behavior of the coronal flux rope system in an octapole background magnetic field that contains three magnetic arcades: a partly open one in the center across the equator and two fully closed in the flank, and a magnetic flux rope inside the central arcade. The initial state is in equilibrium and the flux rope is attached to the solar surface. With respect to an increase of either the annular flux or the axial flux of the rope, the flux rope system exhibits a catastrophic behavior: the rope erupts upward and escapes to infinity as either of the two fluxes exceeds a certain critical value. Under the force-free field regime, we calculate the catastrophic energy threshold of the system. We find that the threshold depends on the magnetic fluxes of the flux rope and the extent to which the central arcade is open, though the catastrophic energy threshold is larger than that of the corresponding partly open field in all cases. For a given open flux of the central arcade, the energy threshold increases with increasing annual flux or decreasing axial flux of the flux rope. Moreover, for given annular and axial fluxes of the flux rope, the more open the central arcade is, the lower of the threshold will be. These results differ from those for the bipolar background field case, in which the catastrophic energy threshold is almost independent of the magnetic fluxes of the flux rope and the extent to which the background field is open. The reason for such a difference is briefly discussed.Secondly, we study the catastrophic behavior of multiple coronal flux rope system. The background magnetic field is an octapole force-free field containing three bipolar fields, and the central bipolar component is partly opened. A flux rope is introduced within each bipolar field. Starting from this state, we increase either the annular or the axial flux of a certain flux rope to examine the catastrophic behavior of the system in two regimes, the ideal MHD regime and the resistive MHD regime. It is shown that when the annular flux or the axial flux of the rope of interest exceeds a certain critical value, the rope breaks away from the base and escapes to infinity, leaving a current sheet below. The destiny of the remainder flux ropes relies on whether magnetic reconnection takes place across the newly formed current sheet. In the ideal MHD regime, i.e., in the absence of reconnection, these ropes remain to be attached to the solar surface in equilibrium, whereas in the resistive MHD regime they also erupt upward. During this process, magnetic reconnection plays a crucial role: it changes the topology of the background field outside the attached flux rope in such a way that the constraint on these ropes is substantially relaxed and the corresponding catastrophic energy threshold is reduced accordingly, leading to a catastrophic eruption of these ropes. The catastrophic behavior of multiple coronal flux rope system demonstrates that the interaction between several independent magnetic flux systems in different active regions provides a possible mechanism for sympathetic events occurring on the sun.Finally, we study the catastrophic behavior of coronal flux rope system caused by photospheric flux emergence somewhere on the photosphere in or- der to reexamine the relationship between photospheric magnetic flux emergence and solar explosive phenomena such as CMEs. In this study, we fix the magnetic fluxes of the flux rope, introduce a photospheric flux emergence to change the background field, and examine how the flux rope system responds to the flux emergence. The initial magnetic field is taken to be a force-free field, consisting of an isolated flux rope attached to the base and a bipolar background field surrounding it. A flux emergence is then introduced somewhere on the photosphere, and it causes a variation of the topology of the background field and a formation of a current sheet at the interface between the newly emerging and preexisting fluxes. It is shown that as the total emerging flux increases, the flux rope system exhibits a catastrophic behavior in some cases, and the relevant controlling factors include the location and field orientation of the newly emerging arcade and whether magnetic reconnection takes place across the newly formed current sheet. For the situation that the emergence region lies away from the equator, we divide it into two categories according to the orientation of the emerging flux. For the case that the emerging flux and the background flux are the same in orientation, the flux rope erupts upward and a catastrophe takes place provided that the emerging flux exceeds a certain critical value irrespective as to whether magnetic reconnection occurs across the newly formed current sheet. The role of the reconnection across the newly formed current sheet is just to reduce the critical value of the emerging flux mentioned above. On the contrary, if the emerging flux and the background flux are opposite in orientation, the flux rope always sticks to the photosphere, and no catastrophe occurs. If the center of the emergence region is located at the equator, the existence of magnetic reconnection across the current sheet formed between the emerging flux and the background flux does play an important role in the catastrophic behavior of the system. In the absence of magnetic reconnection, catastrophe exists for the system irrespective the orientation of the emerging flux. Nevertheless, it becomes easier for a catastrophe to be triggered if the orientation of the emerging flux is opposite to that of the background flux. In the presence of magnetic reconnection, only when the orientation of the emerging flux is opposite can a catastrophe be present, and moreover, in comparison with the case without magnetic reconnection, the triggering of the catastrophe of the system becomes easier. The conclusions in the presence of magnetic reconnection described above are superficially similar to those reached by previous studies in regard to the relationship between photospheric new flux emergence and coronal flux rope eruption. However, we have reached these conclusions based on the viewpoint of MHD catastrophe. In this context, the role of the flux emergence in the flux rope eruption is not a driver but a trigger. "Slow" photospheric flux emergence changes the topology of the background field gradually so as to affect the catastrophic behavior of the whole system. In appropriate cases, the flux emergence causes the state of the system to near and eventually to reach its catastrophic point, leading to the occurrence of a catastrophe and an abrupt "fast" eruption of the flux rope.