International audienceSeveral episodes of complete melting have probably occurred during the first stages of the Earth's evolution. We have developed a numerical model to monitor the thermal and melt fraction evolutions of a cooling and crystallizing magma ocean from an initially fully molten mantle. For this purpose, we numerically solve the heat equation in 1D spherical geometry, accounting for turbulent heat transfer, and integrating recent and strong experimental constraints from mineral physics. We have explored different initial magma ocean viscosities, compositions, thermal boundary layer thicknesses and initial core temperatures.We show that the cooling of a thick terrestrial magma ocean is a fast process, with the entire mantle becoming significantly more viscous within 20 kyr. Due to the slope difference between the adiabats and the melting curves, the solidification of the molten mantle occurs from the bottom up. In the meantime, a crust forms due to the high surface radiative heat flow, the last drop of fully molten silicate is restricted to the upper mantle. Among the studied parameters, the magma ocean lifetime is primarily governed by its viscosity. Depending on the thermal boundary layer thickness at the core–mantle boundary, the thermal coupling between the core and magma ocean can either insulate the core during the magma ocean solidification and favor a hot core or drain the heat out of the core simultaneously with the cooling of the magma ocean. Reasonable thickness for the thermal boundary layer, however, suggests rapid core cooling until the core–mantle boundary temperature results in a sluggish lowermost mantle. Once the crystallization of the lowermost mantle becomes significant, the efficiency of the core heat loss decreases. Since a hotter liquidus favors crystallization at hotter temperatures, a hotter deep mantle liquidus favors heat retention within the core. In the context of an initially fully molten mantle, it is difficult to envision the formation of a basal magma ocean or to prevent a major heat depletion of the core. As a consequence, an Earth's geodynamo sustained only by core cooling during 4 Gyr seems unlikely and other sources of motion need to be invoked

6The thermal evolution of planets during their accretionary growth is strongly 7 influenced by impact heating. The temperature increase following a collision 8 takes place mostly below the impact location in a volume a few times larger 9 than that of the impactor. Impact heating depends essentially on the radius of 10 the impacted planet. When this radius exceeds ∼ 1000 km, the metal phase 11 melts and forms a shallow and dense pool that penetrates the deep mantle 12 as a diapir. To study the evolution of a metal diapir we propose a model 13 of thermo-chemical readjustment that we compare to numerical simulations in 14 axisymmetric spherical geometry and with variable viscosity. We show that the 15 metallic phase sinks with a velocity of order of a Stokes velocity. The thermal 16 energy released by the segregation of metal is smaller but comparable to the 17 thermal energy buried during the impact. However as the latter is distributed 18 in a large undifferentiated volume and the former potentially liberated into a 19 much smaller volume (the diapir and its close surroundings) a significant heating 20 of the metal can occur raising its temperature excess by at most a factor 2 or 3. 21When the viscosity of the hot differentiated material decreases, the proportion 22 of thermal energy transferred to the undifferentiated material increases and a 23 protocore is formed at a temperature close to that of the impact zone. 24 3 planets, a local differentiation may occur between heavy metal and light silicates 54 in the heated anomaly (Tonks and Melosh, 1992). Hence, a thermo-chemical 55 readjustment follows, associated with the sinking of the metallic component 56 toward the center of the impacted protoplanet ( Fig. 1). 57For large planets, gravitational energy release due to core formation can 58 induce melting of the whole planet (Stevenson, 1989; Ricard et al., 2009). This 59 subsequent melting depends on the mechanisms of the metal descent (Samuel 60 and Tackley, 2008; Golabek et al., 2008). The aim of this study is to determine 61 the thermal evolution of metal during descent and the thermal state of the core. 62First, we propose analytical and numerical isoviscous models of segregation 63 of a purely spherical iron diapir. As the viscosity contrast between molten metal 64 and undifferentiated cold material can reach several orders of magnitude, we 65 then focus on more realistic models of segregation of metal after a large impact 66 with temperature dependent rheologies. We show that the size of impactors and 67 viscosities involved largely determine the inner thermal state of a young planet. 68 2. Thermo-chemical state after large impact 69 2.1. Thermal state 70 After a meteoritical impact, heating is localized in a spherical region called 71 the isobaric core just beneath the impact site. The radius of the isobaric core 72 R ic is comparable to the radius of the impactor R imp and depends on en-73 ergy conversion during the shock. With a minimal set of assumptions, we get 74 R ic = 3 1/3 R imp following Senshu et...