Faraday Rotation Distributions from Stellar Magnetism in Wind-Blown Bubbles

Faraday rotation is a valuable tool for detecting magnetic fields. Here the technique is considered in relation to wind-blow bubbles. In the context of spherical winds with azimuthal or split monopole stellar magnetic field geometries, we derive maps of the distribution of position angle (PA) rotation of linearly polarized radiation across projected bubbles. We show that the morphology of maps for split monopole fields are distinct from those produced by the toroidal field topology; however, the toroidal case is the one most likely to be detectable because of its slower decline in field strength with distance from the star. We also consider the important case of a bubble with a spherical sub-volume that is field-free to approximate crudely a "swept-up" wind interaction between a fast wind (or possibly a supernova ejecta shell) overtaking a slower magnetized wind from a prior state of stellar evolution. With an azimuthal field, the resultant PA map displays two arc-like features of opposite rotation measure, similar to observations of the supernova remnant G296.5+10.0. We illustrate how PA maps can be used to disentangle Faraday rotation contributions made by the interstellar medium versus the bubble. Although our models involve simplifying assumptions, their consideration leads to a number of general robust conclusions for use in the analysis of radio mapping datasets.