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