Planetary Ices and the Linear Mixing Approximation

M. Bethkenhagen, E. R. Meyer, S. Hamel, N. Nettelmann, M. French, L. Scheibe, C. Ticknor, L. A. Collins, J. D. Kress, J. J. Fortney, R. Redmer

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60 Scopus citations

Abstract

The validity of the widely used linear mixing approximation (LMA) for the equations of state (EOSs) of planetary ices is investigated at pressure-temperature conditions typical for the interiors of Uranus and Neptune. The basis of this study is ab initio data ranging up to 1000 GPa and 20,000 K, calculated via density functional theory molecular dynamics simulations. In particular, we determine a new EOS for methane and EOS data for the 1:1 binary mixtures of methane, ammonia, and water, as well as their 2:1:4 ternary mixture. Additionally, the selfdiffusion coefficients in the ternary mixture are calculated along three different Uranus interior profiles and compared to the values of the pure compounds. We find that deviations of the LMA from the results of the real mixture are generally small; for the thermal EOSs they amount to 4% or less. The diffusion coefficients in the mixture agree with those of the pure compounds within 20% or better. Finally, a new adiabatic model of Uranus with an inner layer of almost pure ices is developed. The model is consistent with the gravity field data and results in a rather cold interior (Tcore ∼ 4000 K).

Original languageEnglish
Article number67
JournalAstrophysical Journal
Volume848
Issue number1
DOIs
StatePublished - Oct 10 2017
Externally publishedYes

Funding

M.B., N.N., M.F., and R.R. gratefully acknowledge support from the Deutsche Forschungsgemeinschaft within the SFB 652, the SPP 1488, and the FOR 2440. Computing power was provided by the ITMZ of the University of Rostock as well as by the North-German Supercomputing Alliance (HLRN). E.R.M., C.T., J.D.K., and L.A.C. gratefully acknowledge support from the Advanced Simulation and Computing Program (ASC), science campaigns 1 and 4, and LANL, which is operated by LANS, LLC for the NNSA of the U.S. DOE under Contract No. DE-AC52-06NA25396. S.H. and M. B. acknowledge support by the U.S. Department of Energy at the Lawrence Livermore National Laboratory under contract No. DE-AC52-07NA27344 and the LDRD 16-ERD-011.

Keywords

  • diffusion
  • equation of state
  • planets and satellites: composition
  • planets and satellites: individual (Uranus, Neptune)
  • planets and satellites: interiors

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