Gas-pressure branch of a mixed-pressure alpha disk ($\bar{\nu }\propto r{\Sigma }^{2/3}$)

For small positive radiation-to-gas ratio, constant opacity, fixed alpha and molecular constants, eliminate $\lambda$ between $\lambda \propto H\Omega \Sigma$ and $\lambda \Sigma \propto H^7{\Omega }^6$. This gives $H^6\propto {\Sigma }^2{\Omega }^{-5}$ and $\bar{\nu }\propto {\Sigma }^{2/3}{\Omega }^{-2/3}$. Keplerian rotation supplies the displayed radial power. Since $\bar{\nu }\Sigma \propto {\Sigma }^{5/3}$, its derivative with respect to surface density is positive and local viscous perturbations diffuse rather than amplify.