Date of Award

Fall 2001

Project Type


Program or Major


Degree Name

Doctor of Philosophy

First Advisor

T G Forbes


This thesis presents new theoretical models of solar eruptions which are derived from older models that involve a loss of equilibrium of the Sun's coronal magnetic field. These models consist of a magnetic flux rope nested within an arcade of magnetic loop. Prior to an eruption, the flux rope floats in the corona under a balance between magnetic compression and tension forces. When an eruption occurs, the magnetic compression exceeds the magnetic tension and causes the flux rope to be thrown outwards, away from the Sun. Three important factors which impact the occurrence and evolution of the eruptive processes are investigated. These factors are magnetic reconnection, new emerging flux, and the large scale curvature of the flux rope.

First, our new results confirm that in the absence of reconnection, magnetic tension in two-dimensional configuration is always strong enough to prevent escape of the flux rope to infinity after it erupts. However, only a relatively small reconnection rate is needed to allow the flux rope to escape to infinity. Specifically, for a coronal density model that decreases exponentially with height we find that average Alfven Mach number MA for the inflow into the reconnection site can be as small as M A = 0.005 and still be fast enough to give a plausible eruption. The best fit to observations is obtained by assuming an inflow rate on the order of MA ≈ 0.1.

Second, we have found that the emergence of new flux system in the vicinity of a preexisting flux rope can cause a loss of ideal-MHD equilibrium under certain circumstances. But the circumstances which lead to eruption are much richer and more complicated than commonly described in the existing literatures. Our model results suggest that the actual circumstances leading to an eruption are sensitive, not only to the polarity of the emerging region, but to several other parameters, such as its strength, distance, and area as well. The results also indicate that in general there is no simple, universal relation between the orientation of the emerging flux and the likelihood of an eruption.

Finally, our research shows that the large-scale curvature of a flux rope increases the magnetic compression and helps propel it outwards. We also find that the maximum total magnetic energy which can be stored in our model before equilibrium is lost is 1.53 times the energy of the potential field, which is consistent with the theoretical limit, 1.662, for the fully opened field predicted by Aly [1991] and Sturrock [1991].