Instabilities in line-driven stellar winds. IV - Linear perturbations in three dimensions

Nonradial wave propagation in line-driven stellar winds is analyzed including both finite disk effects and the line-drag effect of scattered line radiation. Within the local (WKB) analysis the results apply to wavelengths both longer and shorter than the Sobolev length. The finite disk causes short-wavelength waves with lateral velocity polarization to be unstable in the idealized case of pure absorption; however, the growth rates are smaller than for radially polarized waves, and the instability is damped by a relatively small amount of scattering. Hence, in realistic stellar winds, where the driving is primarily by scattering lines, perturbations with an arbitrary mixture of lateral and radial polarizations at the wind base should quickly become nearly radially polarized farther out in the wind. The implications of these results are discussed, both for interpretation of observational signatures of wind structure and for theoretical calculations aimed at modeling the nonlinear evolution of wind instabilities.