Comparison of Vector Magnetograms from the Solenoidal and Irrotational Components of the Magnetic Field

According to the Helmholtz Theorem, the solar magnetic field can be defined in terms of an irrotational and a solenoidal component. We will discuss the partitioning of the field into these components as a means of attributing elements of the magnetic field to its vorticity and divergence. We will then d iscuss the advantages of th is decomposition as applied to SDO/HMI vector magnetograms. Helmholtz Decomposition •According to the Helmholtz Theorem, a vector field can be written as a sum of an irrotational (curl-free) and s o l e n o i d a l ( d i v e r g e n c e f r e e ) component. •On a finite domain, there is also a harmonic component that is both divergence and curl free.