Inference of steady stellar wind v(r) laws from optically thin emission lines II. Occultation effects and the determination of intrinsic stellar properties

This paper extends previous work on the inversion of line profiles to obtain wind velocity laws to a case that includes the occultation of light from the far side of the star. The velocity law v(r) is assumed to be from a wind that is steady and spherically symmetric. The wind is also assumed to be optically thin in the emission line profile. Themajor result here is the derivation of an analytic inversion formula. The effects of stellar occultation are shown to produce a significant change in the analysis from paper I, and by accounting for the occultation, the red-shifted emission of P Cygni profiles can be used to obtain v(r). Using simulated line profiles as generated from a radiation transport code to test the procedure, the inversion technique based on optically thin lines successfully recovers v(r) distributions for weak LTE Hα profiles from hot star winds. Even in the case of NLTE Hα lines, the technique is seen to reproduce the model velocity distribution quite well. Our inversion technique thus remains robust outside the scope of our assumptions, owing primarily to an empirical approach for applying the method. An important aspect of our empirical approach is the possibility of estimating intrinsic stellar and wind properties, such as the mass-loss rate Ṁ , photospheric radius R, and the stellar distance D. As an example, photospheric stellar radii are derived from the model profiles and found to be in good agreement with the input values, with typical errors of about 5%. Even in the NLTE case, the photospheric radii are underestimated by only 10–20%.