M2: Determination of the entropy in the protolunar disk

Master M2 internship

The origin of the Moon is one of the oldest problems studied in Earth Sciences. The most widely accepted model today is that of a Giant Impact. According to this model an impactor, named Theia, hit the proto-Earth. Large-scale hydrodynamic simulations show that within hours after the impact a large protolunar disk formed. From this initial state, the disk cooled and condensed to finally form the Earth and Moon couple. This was a complex process that followed a quasi-entropic trajectory. Hence the most important parameter that we need to know to model the formation of our planet and our Moon is the entropy that could have been stored in the protolunar disk after the impact. But this is also one of the least known quantities.

In this internship, we will calculate the amount of entropy that can be stored in the protolunar disk as a result of such a giant impact. During an impact, the pressure and temperature of a material evolve along a Hugoniot equation of state. The position along the Hugoniot is determined by the parameters of the impact, of the target, and of the impactor. We model the composition of the proto-Earth and of Theia with pyrolytic composition, as an approximant for the bulk silicate Earth. We choose a couple representative points along the Hugoniot (shock) equation of state of pyrolite.

Then we use a combination of ab initio molecular dynamics simulations and thermodynamic integration to obtain the free energy and the entropy of that pyrolytic fluid at the conditions attained during the impact. Thus we characterize the state of the protolunar disk in the aftermath of the giant impact. We compare the values of the entropy with the entropy of the critical point. We estimate the amounts of vapor and liquid that can be produced in the disk upon cooling, from which we can put constraints on the evolution of the protolunar disk all the way until its condensation in the stage of magma ocean.

We will run the simulations on the supercomputers of the TGCC supercomputing center of the CEA. The internship is supported by the ERC IMPACT project. For further information don’t hesitate to contact Razvan Caracas in IPGP at caracas@ipgp.fr. For application follow the instructions from the IPGP internship pages: http://www.ipgp.fr/fr/stage-etudiants

Ref: https://www.sciencedirect.com/science/article/abs/pii/S0012821X20304076

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