THE EFFECTS OF GRAVITY DARKENING ON THE ULTRAVIOLET CONTINUUM POLARIZATION PRODUCED BY CIRCUMSTELLAR DISKS

We investigate the effects of gravity darkening on the UV continuum polarization produced by an axisymmetric disk that surrounds a rapidly rotating star. Although the model; is a single scattering approximation, we do include the effects of attenuation (electron scattering plus hydrogen bound-free absorption) by the disk, using an approach similar to that of Sobolev (1963). Because of the gravity darkening of the star and the attenuation within the disk, the radiation field is not axially symmetric about the radius vector. This implies that the polarization source functions are no longer provided by the finite disk depolarization factors of Cassinelli, Nordsieck, & Murison (1987), which are functions of the intensity moments in a spherically symmetric atmosphere. We reformulate the polarization source functions using generalized intensity moment tensors (J, H-i, K-ij) that are valid for an arbitrary radiation field and envelope geometry. We find that the polarization source functions are simplest when using intensity moments in the observer's reference frame. On the other hand, the intensity moments are most easily evaluated in the stellar reference frame. Using the rotation transformation properties of the generalized intensity moments, we relate the observer's moments to those evaluated in the stellar reference frame. Our procedure for determining the polarization source functions thus merely involves choosing a set of Euler angles for the coordinate rotations, and then evaluating the associated rotation matrix. The geometrical complications of polarization transfer are thus reduced to obtaining a coordinate rotation matrix. Using this method, we calculate the polarization produced by a circumstellar disk. Because the scattered radiation, which is dominated by light from the stellar equator, has a lower effective temperature than the direct radiation from the star, the polarization shortward of the Wien peak is smaller than previously expected. This UV depolarization is largest for rapid rotators, later spectral types, and envelope geometries that have a small density ratio between the equator and pole. We find that for a thin dense disk, the amount of UV depolarization is inadequate to explain the observed UV polarization of Be stars. Thus their UV depolarization is most likely a result of metal line blanketing by the envelope. For envelopes that are only moderately flattened, there is significant polarization cancellation by the polar material, owing to the polar brightening of the star, but the shape is incorrect to explain the UV observations of Be stars. In some instances gravity darkening causes the polar cancellation to be large enough that the position angle flips by 90 degrees. Thus gravity darkening provides a new method for causing a wavelength-dependent position angle flip for a disk geometry, which is a possible polarization diagnostic for distinguishing thin dense disks from moderately flattened envelopes.