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Rotation can markedly impact the interpretation of spectral diagnostics from hot stars with winds. Using a newly developed formal solution code, and a semianalytic model for the effects of rotation on the wind structure, we investigate the effects of rotation on the observed spectrum. Nonphotospheric lines formed in extended, optically thick atmospheres do not show just the simple classical Doppler line broadening. In such cases the traditional method of convolving the line profile with a rotation profile is insufficient. To handle these situations, we start with a sophisticated one-dimensional model of a stellar atmosphere and use a two-dimensional observer's-frame code to calculate the observed effect on line profiles under various assumptions about the two-dimensional velocity field and density distribution. Because it should generally be a small effect, rotational distortion of the stellar surface is currently ignored. Gravity darkening is also not handled at this time. Importantly, the code handles arbitrary line profiles and line blends, and lines formed at any depth in the stellar photosphere or wind. We apply the code to models that were used to investigate the Small Magellanic Cloud O7 Iaf+ supergiant AV 83. We find that the distortions in the velocity field caused by rotation can have a significant influence on the profile shape, while modifications to the density structure primarily influence the line strength. These affect the quality of the spectroscopic fits to the data, and consequently, the derived velocity field and other stellar parameters might be significantly biased for rapidly rotating stars with extended winds. The code will made available with CMFGEN and can be used to examine the influence of rotation on spectroscopic fitting and derived stellar parameters.

We present a new formulation of the short characteristic method for solving the transfer equation in axially symmetric systems. The radiation field is solved for on a grid in r and the spherical polar angle β, with radiation coordinates chosen to take into account the spherical nature of the underlying source. Such a coordinate system is advantageous because it takes into account the inherent discontinuities and symmetries due to the forward-peaking nature of the radiation field. An important consequence of this is that the determination of the boundary condition for the intensity along a short characteristic does not involve an interpolation across a discontinuity. A parabolic approximation for the source function provides the best combination of accuracy, stability, and speed. Systematic errors introduced by using a weighted trapezoidal rule for quadrature in the radiation coordinate μ were overcome by using a monotonic cubic polynomial to approximate integrands. The code has been successfully used to solve the polarized transfer equation and employs both an approximate operator iteration and Ng acceleration to improve convergence. Comparison with an accurate long characteristic code shows that a tremendous saving in computation time can be realized with a minimal loss of accuracy.