= Solution
If radiation dominates the <central pressure>, equate $P_c\sim GM_*^2/R_*^4$ to $aT_c^4/3$. This gives
$$
\boxed{R_*\sim\left(\frac{3G}{a}\right)^{1/4}\frac{M_*^{1/2}}{T_c}.}
$$
At roughly fixed burning <temperature>, the corresponding mass-radius scaling is $R_*\propto M_*^{1/2}$, rather than the gas-pressure estimate $R_*\propto M_*$. <Radiation pressure> alone does not determine a unique <radius> at a specified <mass>: a thermal or nuclear-burning condition is still needed to specify $T_c$. The relation is a homology estimate, not a universal exact law for all massive <stars>.
Back to article page
