Magnetic Flux Cancellation and Coronal Magnetic Energy

I investigate the processes at work in the cancellation of normal magnetic flux in solar magnetograms and study the relationships between cancellation and the budget of free magnetic energy in the coronal magnetic field that can power solar flares and CMEs. After defining cancellation mathematically, I derive equations that quantify the evolution of free magnetic energy in response to arbitrary plasma flows on the boundary, including flows consistent with cancellation.While cancellation can reduce the magnetic energy in both the actual coronal field and the potential field matching the same normal field boundary condition, cancellation can, in the process, increase the difference between the two; i.e., cancellation can increase the free magnetic energy in the corona. By making simple assumptions based upon typical observed field configurations in filament channels, I show that cancellation tends to add free energy to these fields. Finally, I discuss the implications of this fact, as well as wider applications of the free energy flux formalism developed here. I also briefly address related issues, including the relationship of cancellation to Taylor’s hypothesis. Subject headinggs: MHD — Sun: activity — Sun: coronal mass ejections (CMEs) — Sun: flares — Sun: magnetic fields