Constraints for the presence of a liquid surface ocean. Each marker shows the outcome of a simulation for a given imposed albedo (the equivalent effective flux is shown on the top axis) and atmospheric surface pressure. Blue dots show cases where a liquid surface ocean is stable. Red crosses show cases where a steam atmosphere forms. The top panel shows the results of traditional models in which convection inhibition is disregarded, and the bottom panel shows results with convection inhibition. The dashed (solid) line roughly depicts the limit to the stability of an ocean in the case without (with) inhibition. One can see that the inhibition limits the stability of oceans to higher albedos, i.e., less irradiated planets.