Quadratic albedo feedback saddle-node ($F_{\mathrm{crit}}=A^2/(4B)$)

A perturbation energy balance $\dot{T}\propto F-AT+B{T}^2$ with positive $A,B$ has a stable lower-temperature root and an unstable upper root for $F<A^2/(4B)$. They merge at $T=A/(2B)$; equality is marginal. Extrapolation of this local model is not an empirical runaway threshold for a real planet.