Early-type Wolf-Rayet ( WR ) stellar models harbour 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 semi-analytical estimates and WR models from both MESA and ( 46 ) ; four conclusions are present .
First , early-type WR stars do not harbour inflated envelopes since they have either strong winds or insufficient luminosities .
Second , the condition for an opacity bump to harbour a sonic point is expressible as a minimum mass loss rate , \dot { M } _ { sp } ( L _ { * } ) .
In agreement with ( 45 ) and ( 21 ) , the majority of galactic early-type WR stars can harbour sonic points at the iron opacity bump .
However , about half of those in the Large Magellanic Cloud can not 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 } \mathrm { M } _ { \odot } 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 } \simeq 145 in the wind ; a value consistent with studies by ( 17 ) and ( 40 ) .