Thermal flux escaping the top of a pure water atmosphere for a range of surface temperatures. The run-away greenhouse effect manifests itself as a plateau in the outgoing flux: there is no stable thermal equilibrium when the external or internal heating is higher than this critical flux F_crit. We mark the Goldblatt et al. (2013) result of a full frequency-dependent radiative transfer 1D model (F_crit = 282W m⁻²) and the Leconte et al. (2013) result of a 3D climate model (F_crit = 375 W m⁻²) with dotted lines. The grey opacity parametrization of Matsui & Abe (1986a), with κ₀ = 0.01 m² kg⁻¹ and linear pressure dependence (full red line), results in a too high critical flux value. We find a better match when adopting a two orders of magnitude higher opacity, κ₀ = 1.0 m² kg⁻¹.