 Composition shift of a convective pre-main-sequence track

For convective contraction with power-law opacity $\kappa \propto \rho T^4$ at fixed stellar mass and opacity normalization, $T_e\propto {\mu }^{1/2}{R}^{1/8}$ and $L\propto {\mu }^2{R}^{5/2}$. Eliminating $R$ gives $L\propto {\mu }^{-8}{T}_e^{20}$. Thus a larger mean molecular weight moves the track to larger effective temperature at a given luminosity, with $T_e{|}_L\propto {\mu }^{2/5}$. Contraction decreases both temperature and luminosity for this particular opacity exponent.