The so-called regularized Biot-Savart laws (RBSLs, Titov et al., ApJL 2018) provide an efficient and flexible method for constructing pre-eruptive configurations (PECs) whose characteristics are constrained by remote-sensing observations. This method allows one to calculate the field of magnetic flux ropes (MFRs) of small diameters and an arbitrary axis shape. The field of the PEC is generally a superposition of (1) such an MFR field, (2) an ambient potential field determined, e.g., by the radial field component of an observed magnetogram, and (3) a so-called compensating potential field that counteracts perturbations of the radial field by the MFR at the boundary. The constructed PEC is then relaxed in a line-tied zero-beta MHD simulation toward a force-free equilibrium.
We have recently upgraded our method in two ways. First, we have reformulated the RBSLs so that the compensating field can be neglected if the distance between the MFR footprints is much less than the solar radius. Second, we have developed an optimization method to minimize unbalanced magnetic forces prior to the MHD relaxation of a modeled PEC. This minimization is obtained by optimizing the shape and axial current of the corresponding MFR with a modified Gauss-Newton method of least squares.
We apply the upgraded method to construct sigmoidal PECs for the 2009 February 13 CME event. The resulting PECs have a complex core magnetic structure, with the MFR nested within a sheared magnetic arcade. Both the MFR and the arcade are bounded in the central region of the PECs by current layers. Depending on the strength of the current in the pre-relaxed MFR, the core of the final PEC can also contain a vertical current layer, which is then embedded in the sheared arcade, underneath the MFR. Our structural analysis reveals building blocks that match the morphological features typically observed in bipolar PECs (e.g., Moore et al., ApJ 2001) very well. This suggests that the method will not only be beneficial as a tool for modeling solar eruptions, but also for scientific studies that require a detailed understanding of the magnetic structure of PECs.
*Research supported by NSF, NASA, and AFOSR