Authors: Abhinav G. Iyer (The University of Sydney), Michael S. Wheatland (The University of Sydney)

Solar flares and coronal mass ejections (CMEs) are energetic events on the Sun that produce intense radiation, accelerated particles, and launch material into space. Flares and CMEs are generally understood to be caused by the loss of stability of the coronal magnetic field and the subsequent release of energy stored in coronal electric currents. To explain the changes in energy associated with flares and CMEs, it is necessary to understand the origin of the coronal magnetic field. In practice, the coronal magnetic field in a volume of interest is decomposed into a potential (current-free) field, matching the normal component of the field at the boundary, and a field that closes within the volume, with zero normal component at the boundary. However, both the potential and the closed fields are produced by currents inside and outside the volume, which entangles the contribution of each source to the magnetic field.

Here, following Schuck and Linton (2024), we use the Helmholtz decomposition, together with the Biot-Savart law, to attribute the coronal magnetic field in a given volume to internal and external current sources. We also partition the total magnetic energy based on the current source. The energy of the potential field can be decomposed into boundary surface integral terms alone, allowing us to use observed magnetic field maps to study the evolution of the potential field energy. By tracking the evolution of the potential field energy, and the separate contributions from the internal and external currents, we gain insight into how the origin of the flux threading the boundary changes during energetic events. We apply these methods to SDO/HMI SHARP vector magnetograms of active region AR 12673, and a sequence of non-linear force-free field (NLFFF) models of AR 11158.