Influence of planetary rotation on metal-silicate mixing and equilibration in a magma ocean

At a late stage of its accretion, the Earth experienced high-energy planetary impacts. Following each collision, the metal core of the impactor sank into molten silicate magma oceans. The efficiency of chemical equilibration between these silicates and the metal core controlled the composition of the Earth interior and left a signature on geochemical and isotopic data. These data constrain the timing, pressure and temperature of Earth formation, but their interpretation strongly depends on the efficiency of metal-silicate mixing and equilibration. We investigate the role of planetary rotation on the dynamics of the sinking metal and on its chemical equilibration using laboratory experiments of particle clouds settling in a rotating fluid. Our clouds initially sink as spherical turbulent thermals, but after a critical depth, rotation becomes important and they transition to a vortical columnar flow aligned with the rotation axis. Applied to Earth formation, our results predict that rotation strongly affects the fall of metal in the magma ocean for impactors smaller than 459 km in radius on a proto-Earth that rotates twice faster than today. On a proto-Earth spinning 5 times faster than today, rotation is important for any impactor smaller than the Earth itself. In contrast with a thermal that grows in all directions, the vortical column grows vertically but keeps a constant horizontal extent. The slower dilution in vortical columns reduces chemical equilibration compared to previous estimates that neglect planetary rotation. We find that rotation significantly affects the degree of equilibration for highly siderophile elements with partition coefficients larger than ${10}^3$. In this case, for a planet spinning twice faster than today, the degree of equilibration decreases by up to a factor 2 compared to previous estimates that neglect the effect of rotation. Finally, the ultimate fate of iron drops is to be detrained from the vortical column as an iron rain, reconciling the traditional iron rain scenario with the model of turbulent thermal.