Wolf-Rayet Mass-Loss Limits Due to Frequency Redistribution
  The hypothesis that CAK-type line driving is responsible for the large observed Wolf-Rayet (W-R) mass-loss rates has been called into question in recent theoretical studies. The purpose of this paper is to reconsider the plausibility of line driving of W-R winds within the standard approach using the Sobolev approximation while advancing the conceptual understanding of this topic. Due to the multiple scattering required in this context, of particular importance is the role of photon frequency redistribution into spectral gaps, which in the extreme limit yields the statistical Sobolev-Rosseland (SSR) mean approximation. Interesting limits to constrain are the extremes of no frequency redistribution, wherein the small radii and corresponding high W-R surface temperature induces up to twice the mass-loss rate relative to cooler stars, and the SSR limit, whereby the reduced efficiency of the driving drops the mass flux by as much as an order of magnitude whenever there exist significant gaps in the spectral line distribution. To see how this efficiency drop might be sufficiently avoided to permit high W-R mass loss, we explore the suggestion that ionization stratification may serve to fill the gaps globally over the wind. We find that global ionization changes can only fill the gaps sufficiently to cause about a 25% increase in the mass-loss rate over the local SSR limit. Higher temperatures and more ionization states (especially of iron) may be needed to achieve optically thick W-R winds, unless strong clumping corrections eliminate the need for such winds. 
Andrew J. Onifer (Los Alamos National Lab.) and Kenneth G. Gayley   (Univ. of Iowa)