[1] The 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 CO 2 and H 2 O released from the magma during its crystallization. In order to constrain the various cooling timescales of the system, we developed a 1-D parameterized convection model of a magma ocean coupled with a 1-D radiative-convective model of the atmosphere. We conducted a parametric study and described the influences of the initial volatile inventories, the initial depth of the magma ocean, and 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, 1.5, 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. Using a more accurate calculation of opacities, we show that Venus is much closer to this threshold distance than in previous models. So there are conditions such as no water ocean is formed on Venus. Moreover, for Mars and Earth, water ocean formation timescales 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. On the other hand, Venus could have remained in the magma ocean stage for most of its accretion.

On the basis of geological evidence, it is often stated that the early martian climate was warm enough for liquid water to flow on the surface thanks to the greenhouse effect of a thick atmosphere. We present 3D global climate simulations of the early martian climate performed assuming a faint young sun and a CO 2 atmosphere with surface pressure between 0.1 and 7 bars. The model includes a detailed representation of radiative transfer using revised CO 2 gas collision induced absorption properties, and a parameterisation of CO2 ice cloud microphysical and radiative properties. A wide range of possible climates is explored using various values of obliquities, orbital parameters, cloud microphysic parameters, atmospheric dust loading, and surface properties.Unlike on present-day Mars, for pressures higher than a fraction of a bar surface temperatures vary with altitude because of adiabatic cooling / warming of the atmosphere. In most simulations, CO 2 ice clouds cover a major part of the planet. Previous studies suggested that they could have warmed the planet thanks to their scattering greenhouse effect. However, even assuming parameters that maximize this effect, it does not exceed +15 K. Combined with the revised CO 2 spectroscopy and the impact of surface CO 2 ice on the planetary albedo, we find that a CO 2 atmosphere could not have raised the annual mean temperature above 0 • C anywhere on the planet. The collapse of the atmosphere into permanent CO 2 ice caps is predicted for pressures higher than 3 bar, or conversely at pressure lower than one bar if the obliquity is low enough. Summertime diurnal mean surface temperatures above 0 • C (a condition which could have allowed rivers and lakes to form) are predicted for obliquity larger than 40 • at high latitudes but not in locations where most valley networks or layered sedimentary units are observed. In the absence of other warming mechanisms, our climate model results are thus consistent with a cold early Mars scenario in which non climatic mechanisms must occur to explain the evidence for liquid water. In a companion paper by Wordsworth et al., we simulate the hydrological cycle on such a planet and discuss how this could have happened in more detail.

How the volatile content influences the primordial surface conditions of terrestrial planets and, thus, their future geodynamic evolution is an important question to answer. We simulate the secular convective cooling of a 1‐D magma ocean (MO) in interaction with its outgassed atmosphere. The heat transfer in the atmosphere is computed either using the grey approximation or using a k‐correlated method. We vary the initial CO2 and H2O contents (respectively from 0.1 × 10−2 to 14 × 10−2 wt % and from 0.03 to 1.4 times the Earth Ocean current mass) and the solar distance—from 0.63 to 1.30 AU. A first rapid cooling stage, where efficient MO cooling and degassing take place, producing the atmosphere, is followed by a second quasi steady state where the heat flux balance is dominated by the solar flux. The end of the rapid cooling stage (ERCS) is reached when the mantle heat flux becomes negligible compared to the absorbed solar flux. The resulting surface conditions at ERCS, including water ocean's formation, strongly depend both on the initial volatile content and solar distance D. For D > DC, the “critical distance,” the volatile content controls water condensation and a new scaling law is derived for the water condensation limit. Although today's Venus is located beyond DC due to its high albedo, its high CO2/H2O ratio prevents any water ocean formation. Depending on the formation time of its cloud cover and resulting albedo, only 0.3 Earth ocean mass might be sufficient to form a water ocean on early Venus.