Thermal evolution of an early magma ocean in interaction with the atmosphere

Thermal evolution of magma oceans produced by collision with giant impactors late in accretion is expected 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. In order to constrain the various cooling timescales of the system, we developed a 1D parameterized convection model of the thermal evolution of a magma ocean coupled with a 1D radiative-convective model of a primitive atmosphere. We conducted a parametric study and depicted the influence of various parameters such as the initial volatile inventories, the initial depth of the magma ocean or the radiogenic heat production rate on the cooling sequence. Our results show that the presence of a convective-radiative steam atmosphere has a strong influence on the duration of the magma ocean phase varying from a few thousand years without atmosphere to typically 1 Myr when a steam atmosphere is present. The time required for the formation of a water ocean is respectively 0.1 Myr, 1.5 Myr and 10 Myr for Mars, Earth and Venus. This time would be virtually infinite for an Earth-sized planet located closer than 0.66 AU from the Sun. Because for Mars and Earth, these times are definitely shorter than the average time between major impacts, successive water oceans could have developed on Earth and Mars during accretion, making easier the loss of their atmospheres by impact erosion. On the contrary, Venus could have remained in the magma ocean stage for most of its accretion.