Scattering line polarization in rotating, optically thick disks

Context. To interpret observations of astrophysical disks, it is essential to understand the formation process of the emitted light. If the disk is optically thick, scattering dominated and permeated by a Keplerian velocity field, non-local thermodynamic equilibrium (NLTE) radiative transfer modeling must be done to compute the emergent spectrum from a given disk model. Aims. We investigate NLTE polarized line formation in different simple disk models and aim to demonstrate the importance of both radiative transfer effects and scattering, as well as the effects of velocity fields. Methods. We self-consistently solve the coupled equations of radiative transfer and statistical equilibrium for a two-level atom model by means of Jacobi iteration. We use the short characteristics method of formal solution in two-dimensional axisymmetric media and compute scattering polarization, that is Q/I and U/I line profiles, using the reduced intensity formalism. We account for the presence of Keplerian velocity fields by casting the radiative transfer equation in the observer's frame. Results. Relatively simple (homogeneous and isothermal) disk models show complex intensity profiles that owe their shape to the interplay of multidimensional NLTE radiative transfer and the presence of rotation. The degree of scattering polarization is significantly influenced not only by the inclination of the disk with respect to observer, but also by the optical thickness of the disk and the presence of rotation. Stokes U/I shows double-lobed profiles with amplitude that increases with the disk rotation. Conclusions. Our results suggest that the line profiles, especially the polarized ones, emerging from gaseous disks differ significantly from the profiles predicted by simple approximations. Even in the case of the simple two-level atom model, we obtain line profiles that are diverse in shape, but typically symmetric in Stokes Q and antisymmetric in Stokes U. A clear indicator of disk rotation is the presence of Stokes U, which might prove to be a useful diagnostic tool. We also demonstrate that, for moderate rotational velocities, an approximate treatment can be used, where NLTE radiative transfer is done in the velocity field-free approximation, and Doppler shift is applied in the process of spatial integration over the whole emitting surface.