= Kramers homology with a variable nuclear exponent
{c}
{title2=$R\propto M^{(\nu-7/2)/(\nu+5/2)}$}
For a chemically uniform, gas-pressure-supported <stellar homology> with <Kramers' opacity law> and specific heating $\epsilon=\epsilon_0\rho T^\nu$, <radiative diffusion in a star> gives $L\propto\kappa_0^{-1}\mu^{15/2}M^{11/2}R^{-1/2}$. Nuclear heating gives $L\propto\epsilon_0\mu^\nu M^{\nu+2}R^{-\nu-3}$. Equating them yields $R^{\nu+5/2}\propto\epsilon_0\kappa_0\mu^{\nu-15/2}M^{\nu-7/2}$. Thus $\nu=7/2$ gives a mass-independent radius, whereas $\nu=23/2$ gives $R\propto M^{4/7}$ and $L\propto M^{73/14}$. The coefficients and dimensionless profiles must be fixed; this is an idealized radiative model rather than a universal stellar law.
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