= Radiative-envelope convection matching
{title2=$\nabla_{\mathrm{rad}}(T_b)=\nabla_{\mathrm{ad}}$}
For $P=C(T^b+K)^{1/p}$ with $p=n+1$ and $b=4+n+m$, the logarithmic radiative <temperature> gradient is $(p/b)(1+K/T^b)$. At a marginal boundary with an efficient ideal-gas <convective envelope>, the <Schwarzschild criterion> equates it to $(\gamma-1)/\gamma$. Hence $K=T_b^b[(b/p)(\gamma-1)/\gamma-1]$. The notation $K=T_0^b$ with real positive $T_0$ requires a nonnegative bracket. Vanishing $p$ or $b$ needs the corresponding logarithmic integration instead of this power form.
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