Magma ocean crystallization model coupling fluid mechanics and thermo-chemistry: application to the lunar magma ocean.

Understanding the dynamics of magma ocean crystallisation during planetary cooling can elucidate the initial mantle structure and subsequent evolution of early planetary bodies. However, most studies on magma ocean crystallisation focus on either the thermo-chemistry (e.g., Johnson et al. 2021) or the fluid dynamics of a cooling magma ocean (e.g., Maurice et al. 2017). This precludes investigations into coupled thermo-mechanical processes, such as the effect of convection and phase segregation on chemical differentiation. However, coupled models are challenging to implement due to their numerical complexity and limited experimental constraints on magma ocean crystallisation for model calibration.

We develop a two-phase, 6-component model in a 2D rectangular domain based on a multi-phase, multi-component reactive transport model framework (Keller & Suckale, 2019). Magma ocean convection is modelled using Stokes equations while crystal settling is calculated using a form of hindered Stokes law. The fluid mechanics model is coupled with a thermo-chemical model of evolving temperature, phase proportions, and phase compositions to form a reactive transport model, following Keller & Katz (2016). We apply this model to the lunar magma ocean (LMO) by describing the melt and crystal compositions with 6 pseudo-components (approximating forsterite-fayalite, orthopyroxene-clinopyroxene and anorthite-albite mineral systems). To calibrate the melting temperature and composition of each component, we fit data from fractional crystallisation experiments for a Taylor Whole Moon composition (Schmidt & Krättli 2022) using a transitional Markov Chain Monte Carlo method.

The 6-component melting model calibrated to experimental data is successfully implemented in the reactive transport model. First results indicate the importance of crystal settling speed and magma convection speed on convective mixing, magma ocean stratification, and crystal cumulate formation. The small size of the Moon and its relatively well-constrained magma ocean history, make the LMO an excellent case study to apply the model. However, with the aid of new experimental data for larger and chemically different planets, such as Mars, this model can provide more general insight into the early evolution of terrestrial bodies.

REFERENCES: Maurice et al. (2017) doi:10.1002/2016JE005250, Johnson et al. (2021) doi: 10.1016/j.epsl.2020.116721,  Keller & Suckale (2019) doi:10.1093/gji/ggz287, Keller & Katz (2016)  doi: 10.1093/petrology/egw030,  Schmidt & Krättli (2022) doi:10.1029/2022JE007187