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Terrestrial planets covered globally with thick oceans (termed ocean planets)in the habitable zone were previously inferred to have extremely hot climatesin most cases. This is because ${\rm H_2O}$ high-pressure (HP) ice on theseafloor prevents chemical weathering and, thus, removal of atmospheric CO$_2$.Previous studies, however, ignored melting of the HP ice and horizontalvariation in heat flux from oceanic crusts. Here we examine whether high heatfluxes near the mid-ocean ridge melts the HP ice and thereby removesatmospheric ${\rm CO_2}$. We develop integrated climate models of an Earth-sizeocean planet with plate tectonics for different ocean masses, which include theeffects of HP ice melting, seafloor weathering, and the carbonate-silicategeochemical carbon cycle. We find that the heat flux near the mid-ocean ridgeis high enough to melt the ice, enabling seafloor weathering. In contrast tothe previous theoretical prediction, we show that climates of terrestrialplanets with massive oceans lapse into extremely cold ones (or snowball states)with CO$_2$-poor atmospheres. Such extremely cold climates are achieved mainlybecause the HP ice melting fixes seafloor temperature at the meltingtemperature, thereby keeping a high weathering flux regardless of surfacetemperature. We estimate that ocean planets with oceans several tens of theEarth's ocean mass no longer maintain temperate climates. These results suggestthat terrestrial planets with extremely cold climates exist even in thehabitable zone beyond the solar system, given the frequency of water-richplanets predicted by planet formation theories.

Runaway climate cooling of ocean planets in the habitable zone: a consequence of seafloor weathering enhanced by melting of high-pressure ice