= Solution
The <radiation pressure> at a photospheric <temperature> near $5800$ K is only about $0.3$ Pa. For an illustrative photospheric <gas> <density> $3\times10^{-4}\,\mathrm{kg\,m^{-3}}$ and <mean molecular weight> near $1.3$, the <ideal gas> <pressure> is about $10^4$ Pa. Thus <gas pressure> dominates those outer layers by many orders of magnitude. Both the <temperature> and <density> are needed: low <temperature> alone is not a complete comparison.
For homologous <stars>, hydrostatic and ideal-gas estimates give $T\sim\mu m_HGM/(k_BR)$ and $\rho\sim M/R^3$. Therefore
$$
\frac{P_{\rm rad}}{P_{\rm gas}}=\frac{a\mu m_HT^3}{3\rho k_B}
\propto\boxed{\mu^4M^2},
$$
with a structural coefficient independent of <mass> only under the homology assumption. As <mass> rises, radiation becomes increasingly important. A rough solar interior <normalization> of $10^{-3}$-$10^{-2}$ suggests equality after a <mass> increase by tens, while realistic radiation-dominated structure and composition shift the scale; <stars> of order $10^2M_\odot$ are a useful estimate for strong radiation support. The very small \i[photospheric] ratio must not be used as a universal <normalization> for their whole interiors.
Radiation also transfers outward <momentum>. Comparing radiative <acceleration> $\kappa L/(4\pi r^2c)$ with <gravity> gives the Eddington <luminosity>
$$
\boxed{L_{\rm Edd}=\frac{4\pi cGM}{\kappa}.}
$$
Near this scale, radiatively driven winds and envelope instabilities can remove matter or impede further accretion. <Opacity>, composition, <rotation>, <mass> loss and formation history affect the limiting stellar <mass>. The Eddington condition is a luminosity-to-mass constraint, not a unique composition-independent maximum stellar <mass>.
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