= Polytropic stellar wind
{title2=$\dot M=4\pi r^2\rho u$}
A steady spherical <polytropic flow> escaping a point-mass potential conserves the outward <mass loss rate> and the <Bernoulli function> $C=u^2/2+c_s^2/(\gamma-1)-GM/r$. For positive terminal speed, a finite-radius smooth <sonic point> requires $C>0$ and $1<\gamma<5/3$. Its sound speed obeys $c_{s,c}^2=2C(\gamma-1)/(5-3\gamma)$, and evaluating the conserved flux there selects the transonic <mass loss rate>. Other parameter limits need separate treatment.
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