= Sonic-point obstruction at the Eddington luminosity
For an optically thick diffusion-controlled wind, put $\beta=P_{\rm gas}/(P_{\rm gas}+P_{\rm rad})$. Diffusion gives $(\log T)'=-g\Gamma\beta/[4a_g^2(1-\beta)]$. At $\Gamma=1$, the numerator of the <gas and radiation pressure stellar wind equation> is $2a_g^2/r+g\beta/[4(1-\beta)]>0$ for finite-temperature gas and $0<\beta<1$. A subsonic branch then decelerates and cannot pass a regular <sonic point>. This statement is specific to subsonically launched winds in this transport model, not to every supersonic solution or every form of stellar-wind driving.
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