The Wolf-Rayet Stellar Response To The Iron Opacity Bump: Envelope Inflation, Winds, and Microturbulence

Early-type Wolf-Rayet(WR) stellar models harbor a super-Eddington layer in their outer envelopes due to a prominent iron opacity bump. In the past few decades, one-dimensional hydrostatic and time-steady hydrodynamic models have suggested a variety of WR responses to a super-Eddington force including envelope inflation and optically thick winds. In this paper, I study these responses using semianalytical estimates and WR models from both MESA and Ro & Matzner; four conclusions are present. First, early-type WR stars do not harbor inflated envelopes because they have either strong winds or insufficient luminosities. Second, the condition for an opacity bump to harbor a sonic point is expressible as a minimum mass-loss rate, $\dot{M}_{\rm sp}(L_*)$. In agreement with Grassitelli et al. and Ro, the majority of galactic early-type WR stars can harbor sonic points at the iron opacity bump. However, about half of those in the Large Magellanic Cloud cannot given typical wind parameters. Third, WR winds driven by the iron opacity bump must have mass-loss rates that exceed a global minimum of $10^{-5.8}-10^{-6}M_\odot\,{\rm yr}^{-1}$. Lastly, the observed early-type WR distribution follows a simple mass-loss relation derived here if the radiation-to-gas pressure ratio is approximately $p_r/p_g \sim 145$ in the wind; a value consistent with studies by Grafener et al. and Nakauchi & Saio.