The Zeeman effect in the Sobolev approximation: applications to spherical stellar winds

Modern spectropolarimeters are capable of detecting subkilogauss field strengths using the Zeeman effect in line profiles from the static photosphere, but supersonic Doppler broadening makes it more difficult to detect the Zeeman effect in the wind lines of hot stars. Nevertheless, the recent advances in observational capability motivate an assessment of the potential for detecting the magnetic fields threading such winds. We incorporate the weak-field longitudinal Zeeman effect in the Sobolev approximation to yield integral expressions for the flux of circularly polarized emission. To illustrate the results, two specific wind flows are considered: (i) spherical constant expansion with   v ( r ) = v _∞  and (ii) homologous expansion with   v ( r ) ∝ r   . Axial and split monopole magnetic fields are used to schematically illustrate the polarized profiles. For constant expansion, optically thin lines yield the well-known 'flat-topped' total intensity emission profiles and an antisymmetric circularly polarized profile. For homologous expansion, we include occultation and wind absorption to provide a more realistic observational comparison. Occultation severely reduces the circularly polarized flux in the redshifted component, and in the blueshifted component, the polarization is reduced by partially offsetting emission and absorption contributions. We find that for a surface field of approximately 100 G, the largest polarizations result for thin but strong recombination emission lines. Peak polarizations are approximately 0.05 per cent, which presents a substantial although not inconceivable sensitivity challenge for modern instrumentation.