Magnetogram-matching Biot–Savart Law and Decomposition of Vector Magnetograms
В. С. Титов, Cooper Downs, Tibor Török, Jon A. Linker, Michael Prazak, Jiong Qiu · The Astrophysical Journal · 2025
Abstract We generalize a magnetogram-matching Biot–Savart law (BSl) from planar to spherical geometry. For a given coronal current density J , this law determines the magnetic field B ˜ whose radial component vanishes at the surface. The superposition of B ˜ with a potential field defined by a given surface radial field, B r , provides the entire configuration where B r remains unchanged by the currents. Using this approach, we (1) upgrade our regularized BSls for constructing coronal magnetic flux ropes (MFRs) and (2) propose a new method for decomposing a measured photospheric magnetic field as B = B pot + B T + B S ˜ , where the potential, B pot, toroidal, B T , and poloidal, B S ˜ , fields are determined by B r , J r , and the surface divergence of B – B pot, respectively, all derived from magnetic data. Our B T is identical to the one in the alternative Gaussian decomposition by P. W. Schuck et al., while B pot and B S ˜ are different from their poloidal fields B P , which are potential in the infinitesimal proximity to the upper and lower side of the surface, respectively. In contrast, our B S ˜