Inference of steady stellar wind v ( r ) laws from optically thin emission lines III . Inversion of total line intensity distributions

The variation with wavelength for a sequence of total intensities of stellar wind lines is considered as a basis for deriving the wind velocity law v(r). In particular, we focus on the case where the continuum formation in the wind is dominated by the free-free opacity so that the inner radius increases with wavelength, as is realized in some massive winds like those of the Wolf-Rayet stars. The line emission in the wind occurs exterior to the continuum photosphere, hence lines observed at different wavelengths probe different regions of the wind acceleration. A major consequence of these physical conditions is the opportunity to infer v(r), even if non-monotonic. Numerical examples are given to test the method, in which smooth and non-smooth monotonic v(r), non-monotonic v(r), and the effects of noise are addressed. In the absence of noise, the inversion of the simulated data for radius r(λ) and expansion velocity v(λ) is excellent. Even with noise at the 15% level, the recovery for r(λ) remains reasonably robust, though the results for v(λ) are more strongly affected. Although more sophisticated techniques are required to infer v(λ) from noisy data, the simpler considerations presented here provide a basic theoretical framework for applying the inversion and indicate the potential of the method for deriving the wind flow structure.