The Zeeman Effect in the Sobolev Approximation II: Split Monopole Fields and the "Heartbeat" Stokes V Profile

We calculate the circularly polarized Stokes V profile for emission lines, formed in hot-star winds threaded with a weak radial magnetic field. For simplicity, the field is treated as a split monopole under the assumptions that it has been radially combed by the wind, and rotation is not playing a central role. Invoking the weak-field approximation, we find that the V profile has a characteristic ``heartbeat’’ shape exhibiting multiple sign inversions, which might be mistaken for noise in the absence of theoretical guidance. We also conclude that there is a tendency for the V profile to integrate to zero on each side of the line separately.