The <radiative diffusion in a star> equation gives the homology scaling
$$
L\propto\frac{R T_c^4}{\kappa\rho_c}.
$$
Using the central scalings from part (i) and the electron-scattering opacity $\kappa\propto1+X$ yields
$$
\boxed{L\propto\frac{\mu^4}{1+X}M^3}.
$$
The radius cancels because an electron-scattering opacity is independent of density and temperature.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 317 / 2 / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-317/2/ii/solution