= Constant-opacity gas-pressure stellar homology
{title2=$L\propto\mu^4M^3/\kappa$}
For homologous gas-pressure-supported stars, <hydrostatic equilibrium> gives $T_c\propto\mu M/R$ and $\rho_c\propto M/R^3$. <Radiative diffusion> gives $L\propto RT_c^4/(\kappa\rho_c)$, so the radius cancels and yields the displayed cubic mass scaling. Composition and opacity are held fixed. Strong radiation pressure alters this gas-pressure relation towards the <Eddington luminosity> scaling.
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