New Hydrodynamic Solutions for Line-driven Winds of Hot Massive Stars Using the Lambert W-function

Hot massive stars present strong stellar winds that are driven by absorption, scattering and re\-emission of photons the ions atmosphere (\textit{line-driven winds}). A better comprehension this phenomenon, a more accurate calculation hydrodynamics radiative acceleration is required to reduce number free parameters in spectral fitting, determine wind such as mass-loss rates velocity profiles. We use non-LTE model-atmosphere code CMFGEN numerically solve transfer equation calculate $g_\text{rad}(r)$. Under assumption depends only on radial coordinate, we analytically motion means Lambert $W$-function. An iterative procedure between solution executed order obtain final self-consistent field no longer based any $\beta$-law. apply Lambert-procedure three O supergiant ($\zeta$-Puppis, HD~165763 $\alpha$-Cam) discuss Lambert-solutions for It found that, even without recalculation rate, allows consistent profiles when fitting using performed. Synthetic spectra calculated from our show significant differences compared initial $\beta$-law models. The results indicate importance profile its usage interpretation observed spectra.