Energy Storage for Extreme Solar Eruptions

The energy source for major solar eruptions, such as flares and coronal mass ejections (CMEs), is  recognized to be the free magnetic energy (energy above the potential field state) stored in the solar magnetic field prior to eruption.  A key question for both predicting future eruptions and estimating their possible magnitude is, what is the bound to this energy?

The Aly-Sturrock theorem states that the energy of a fully force-free field cannot exceed the energy of the so-called open field. If the theorem holds, this places an upper limit on the amount of free energy that can be stored.  This is not a practical limit, as even the largest CMEs open only a portion of the coronal magnetic field.  The energy of a closely related field, the partially open field (POF), is believed to provide the corresponding limit for a localized region, such as an active region.  We have developed practical methods for estimating the POF energy (POFE). The estimates are based on potential-field like solves that can be computed rapidly.  We test our estimation methods by comparing them with the maximum energy storage achieved in MHD simulations of three solar eruptions:  July 14, 2000, October 1, 2011, and March 7, 2012.  We discuss the practicality of applying POFE estimates routinely to solar active regions. 

Research supported by NASA and NSF.