 Kramers homology with a variable nuclear exponent

For a chemically uniform, gas-pressure-supported stellar homology with Kramers' opacity law and specific heating $ϵ={ϵ}_0\rho T^{\nu }$, radiative diffusion in a star gives $L\propto {\kappa }_0^{-1}{\mu }^{15/2}{M}^{11/2}{R}^{-1/2}$. Nuclear heating gives $L\propto {ϵ}_0{\mu }^{\nu }{M}^{\nu +2}{R}^{-\nu -3}$. Equating them yields $R^{\nu +5/2}\propto {ϵ}_0{\kappa }_0{\mu }^{\nu -15/2}{M}^{\nu -7/2}$. 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.