Magnetic free energies of breakout coronal mass ejections

A critical issue in understanding and eventually predicting coronal mass ejections (CMEs) is determining the magnetic free energy that can drive the explosive eruption. We present calculations of this free energy for the breakout CME model, which postulates that the preeruption magnetic topology is a multipolar field with a null point in the corona. Using analytical and numerical methods, we determine the free energies for two broad families of photospheric flux distributions, parameterized by the radius of the coronal null and the degree to which flux is concentrated near the poles and equator. The available CME energy attains a broad maximum for distributions whose potential null resides between about 1.25 and 1.75 solar radii, and falls off toward zero as the null approaches the surface or moves out to infinity. These results may explain the wide range of energies observed for CMEs and their associated flares. We find that concentrating the surface flux to narrower latitude bands near the poles and equator, on the other hand, has little effect on the available energy. Our mathematical approach currently is restricted to spherically axisymmetric systems. Its generalization to fully three-dimensional fields might provide the foundation of a first-principles forecasting technique for solar eruptions.