Solution
= Solution
Equate the <accretion luminosity> to the surface luminosity:
$$
\frac{GM\dot M}{R}\propto R^2T_{\rm eff}^4.
$$
Using $R\propto M^3T_{\rm eff}^{-24}$ from part i gives
$$
M^8\propto\dot M T_{\rm eff}^{68}.
$$
Substitution into $L\propto M^6T_{\rm eff}^{-44}$ yields the accreting <Hayashi track>
$$
\boxed{L\propto\dot M^{3/4}T_{\rm eff}^{7}}.
$$