Four-phase modelling of metal-silicate differentiation in planetesimals

Collisions of planetesimals with pre-differentiated cores aided in the formation of the cores in the terrestrial planets in our Solar System. The differentiation of the interior of planetesimals from a primitive chondritic composition to differentiated metallic core and silicate mantle is therefore an important step in the development of the early Solar System, setting the initial conditions for collisional planetary growth. However, meteoritic evidence of the differentiation stage of planetesimals are rare and challenging to interpret. Therefore, mathematical models are necessary to constrain the timescales and elucidate the physics behind metal-silicate segregation in planetesimals. We present progress towards a new numerical model which models the thermo-chemical and fluid-mechanical evolution of silicate-metal planetesimals. The model is comprised of four material phases: solid and liquid silicates, and solid and liquid Fe-FeS metal. Hence, the model quantifies the different segregation rates of metal alloys at various stages of planetary melting. The thermo-chemical evolution quantifies the melting and chemical fractionation of the materials using two separate phase diagrams for the silicate and iron systems respectively and calibrated based on enstatite chondrite meteorites as the starting primitive material. The fluid mechanics represents conditions where the silicate liquid phase dominates and captures the settling of solid particles and immiscible liquid metal droplets by hindered Stokes settling. Our model will simulate core formation under a range of initial planetesimal compositions, nebular compositions, and planetesimal sizes. We also intend to implement compatible element partitioning into our model, in particular Hf-W isotope partitioning, to compare our model results with the meteoritic record. Results from our model will allow more robust estimations of the timescales for planetesimal core formation.