We calculate the circularly polarized Stokes V(λ) 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(λ) 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(λ) profile to integrate to zero on each side of the line separately. The overall scale of V(λ)/I(λ) is set by the ratio of the field strength to the flow speed, B/v, characteristic of the line-forming region, and is of the order of 0.1% for a wind magnetic field B ≅ 100G at depths where the wind speed is v ≅ 100 km s−1.
Gayley, K.; and Ignace, Richard. 2010. The Zeeman Effect in the Sobolev Approximation II. Radial Split Monopole Fields and the ‘Heartbeat’ Stokes V Profile.. The Astrophysical Journal. Vol.708 https://doi.org/10.1088/0004-637X/708/1/615 ISSN: 0004-637X