The Hanle Effect as a Diagnostic of Magnetic Fields in Stellar Envelopes. I. Theoretical Results for Integrated Line Profiles

The Hanle e†ect concerns the modiÐcation of polarized resonance-line scattering by magnetic Ðelds ; thus, it can be used as a diagnostic of stellar magnetic Ðelds. The Hanle e†ect has been used to determine the Ðeld strength and distribution of magnetic structures present in prominences of the Sun. To investigate its potential use in stellar astronomy, the simpliÐed case of an optically thin axisymmetric ring illuminated by a stellar point source is considered. The results are then used to derive the polarization from polar plumes, equatorial disks, and spherical shells. The integrated line polarization is calculated for axisymmetric rings with a variety of magnetic Ðeld orientations, and in every case the polarization is proportional to sin2 i (where i is the viewing inclination), just as in the zero Ðeld case. It is also found that the Hanle e†ect can signiÐcantly alter the integrated line polarization. In some cases the position angle of the polarization in the line can be rotated by 90¡ relative to the zero Ðeld case. We consider the Hanle e†ect as a possible diagnostic of magnetic Ðelds in stellar winds with prominent ultraviolet and visible resonance lines. For these lines the diagnostic has sensitivity in the range of 1È1000 G. The Zeeman e†ect is not normally applicable for diagnosing magnetic Ðelds in stellar winds in the subkilogauss range ; thus, the Hanle e†ect should provide an especially useful new method of determining magnetic Ðelds in stars other than the Sun. Possibilities for measuring the Ðelds in early-type stars using ultraviolet observations is discussed. Subject headings : line : formation È polarization È stars : magnetic Ðelds È Sun: magnetic Ðelds È Sun: prominences