= CNO homology with density-dependent inverse-cubic opacity
{c}
{title2=$L\propto\mu^7M^5,\quad R\propto\mu^{3/8}M^{5/8}$}
For gas-pressure-supported <stellar homology> with specific nuclear heating $\epsilon=\epsilon_0\rho T^{13}$ and <opacity> $\kappa=\kappa_0\rho T^{-3}$, the dimensionless radiative coefficient is proportional to $L\mu^{-7}M^{-5}$. The nuclear coefficient is proportional to $\mu^{13}M^{15}/(LR^{16})$. Holding both and the dimensionless profiles fixed gives the displayed scalings. The <Stefan–Boltzmann law> then gives $T_e\propto\mu^{25/16}M^{15/16}$ and $L\propto\mu^{-4/3}T_e^{16/3}$. The coefficients, pressure regime and composition assumptions must be held as specified; these relations are not universal laws for massive stars.
Back to article page
