The Topology of Magnetic Reconnection in Solar Flares

xiABSTRACTIn order to better understand the location and evolution of magnetic reconnection, whichis thought to be the energy release mechanism in solar flares, I combine the analysis of hardX-ray (HXR) sources observed by RHESSI with a three-dimensional, quantitative magneticcharge topology (MCT) model.I first examine the evolution of reconnection by analyzing the relationship betweenobserved HXR footpoint motions and a topological feature called spine lines. With a highdegree of confidence, I find that the HXR footpoints sources moved along the spine lines.The standard two dimensional flare model cannot explain this relationship. Therefore, Ipresent a three dimensional model in which the movement of footpoints along spine linescan be understood.To better analyze the location of reconnection, I developed a more detailed methodfor representing photospheric magnetic fields in the MCT model. This new method canportray internal changes and rotations of photospheric magnetic flux regions, which wasnot possible with the original method.I then examine the location of reconnection by assuming a relationship between thebuild-up of energy in stressed coronal magnetic fields and the measurement of the changein separator flux per unit length. I find that the value of this quantity is larger on theseparators that connect the HXR footpoint sources than the value on the separators thatdo not. Therefore, I conclude that we are able to understand the location of HXR sourcesobserved in flares in terms of a physical and mathematical model of the topology of theactive region.In summary, based on the success of the MCT model in relating the motion of HXRsources to the evolution of magnetic reconnection on coronal separators, as well as mymathematical and physical model of energy storage at separators, I conclude the MCTmodel gives useful insight into the relationship between sites of HXR emission and thetopology of flare productive active regions.