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(lambda ) and expansion velocity v(lambda ) is excellent. Even with noise at the 15% level, the recovery for r(lambda ) remains reasonably robust, though the results for v(lambda ) are more strongly affected. Although more sophisticated techniques are required to infer v(lambda ) 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.