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The thermal evolution of magma oceans produced by collision with giant impactors late in accretion is  xpected to depend on the composition and structure of the atmosphere through the greenhouse effect of CO2 and H2O released from the magma during its crystallization. We developed a 1D parameterized convection model of a magma ocean coupled with a 1D radiative convective model of the atmosphere. We conducted a parametric study and described the influences of some important parameters such as the Sun-planet distance. Our results suggest that a steam atmosphere delays the end of the magma ocean phase by typically 1 Myr. Water vapor condenses to an ocean after 0.1 Myr, 1.5 Myr and 10 Myr for, respectively, Mars, Earth and Venus. This time would be virtually infinite for an Earth-sized planet located at less than 0.66 AU from the Sun. So there are conditions such as no water ocean is formed on Venus. Moreover, for Mars and Earth, water ocean formation time scales are shorter than typical time gaps between major impacts. This implies that successive water oceans may have developed during accretion, making easier the loss of their atmospheres by impact erosion

Thermal evolution of an early magma ocean in interaction with the atmosphere: conditions for the condensation of a water ocean