A Novel Poloidal-Toroidal Approach for Spherical Force-Free Field Reconstruction of Coronal Magnetic Fields

Understanding solar eruptive phenomena requires accurate information about the coronal magnetic field. However, due to current technological limitations, direct measurement of the coronal magnetic field in three dimensions remains nearly impossible. Consequently, it is often approximated as a force-free field (FFF) using vector magnetogram data, which provide the three components of the magnetic field on the two-dimensional photospheric surface as boundary conditions.

Previously, we introduced a novel method for reconstructing coronal magnetic fields based on the poloidal-toroidal (PT) representation, which led to the development of the NFPT (Nonvariational Force-Free Field Code in Poloidal-Toroidal Formulation) in Cartesian coordinates. However, this approach did not account for the spherical geometry of the Sun's surface.

In this study, we present an improved FFF code that operates in spherical coordinates, incorporating the PT representation. This approach facilitates straightforward implementation of photospheric boundary conditions, with vector magnetogram data used as input. In our code, the source-surface top boundary is set at 2.5 solar radii, where the source surface region is believed to exist. The new code has been validated against analytic models by Low and Lou (1990) and compared with other FFF codes. This spherical-coordinate-based code aims to improve the accuracy of magnetic field information in an equilibrium state, thereby bringing qualitative enhancements to the initial conditions for global heliospheric modeling.