Schematic diagrams of the possible climate regimes reached as function of the CO₂ atmospheric content (in bar) and the H₂O content available at the surface (in global equivalent layer (GEL), in meters). The top and bottom panels describe the case of synchronous and asynchronous spin states, respectively. The red stars indicate the parts of the diagram that have been probed in this work using GCM simulations. The stars that lie on top of the left y-axis correspond to the case of a dry surface and atmosphere while those on the right y-axis consider planets completely covered by water. The presence of a background gas such as N₂ could significantly modify the lower part of the diagram (pCO₂< 1 bar typically). It would favor the heat redistribution, which in turn could (1) prevent the CO₂ atmospheric collapse and (2) reduce the amount of ice possibly trapped in water ice glaciers.