Equation of state of iron under core conditions of large rocky exoplanets



The recent discovery of thousands of planets outside our Solar System raises fundamental questions about the variety of planetary types and their corresponding interior structures and dynamics. To better understand these objects, there is a strong need to constrain material properties at the extreme pressures found within planetary interiors1,2. Here we used high-powered lasers at the National Ignition Facility to ramp compress iron over nanosecond timescales to 1.4 TPa (14 million atmospheres)—a pressure four times higher than for previous static compression data. A Lagrangian sound-speed analysis was used to determine pressure, density and sound speed along a continuous isentropic compression path. Our peak pressures are comparable to those predicted at the centre of a terrestrial-type exoplanet of three to four Earth masses3, representing the first absolute equation of state measurements for iron at such conditions. These results provide an experiment-based mass–radius relationship for a hypothetical pure iron planet that can be used to evaluate plausible compositional space for large, rocky exoplanets.

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Fig. 1: Free-surface velocity measurements from a dynamically compressed multi-thickness Fe sample.
Fig. 2: Isentropic Pρ path of Fe to 3.7 Earth-mass planet core conditions.
Fig. 3: Sound velocity and Grüneisen parameter as a function of density for iron.
Fig. 4: Mass–radius relationships for homogeneous-composition planets.

Change history

  • 24 April 2018

    In the version of this Letter originally published, in the Acknowledgements, the surname of M. Herrmann was misspelt as ‘Hermann’. This has now been corrected.


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We thank the laser and target fabrication staff of the NIF, G. Wisoff, M. Herrmann and B. Goldstein. Beam time was granted through the Science Use of NIF programme. This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under contract number DE-AC52-07NA27344, with additional support from the Department of Energy, University of California and Miller Institute for Basic Research in Science. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.

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R.F.S., D.E.F., D.G.B. and J.H.E. designed, executed and analysed the data from the ramp compression experiments. P.M.C. helped with the analysis of the VISAR data. S.J.A. and A.F.P. performed hydrocode modelling to help determine the systematic uncertainties in the measurement. T.S.D., J.K.W. and D.C.S. performed the comparisons of experimental data with EOS models and theory. R.G.K and G.W.C. helped interpret the data.

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Correspondence to Raymond F. Smith.

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Supplementary Figures 1–7, Supplementary Table 1.

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Smith, R.F., Fratanduono, D.E., Braun, D.G. et al. Equation of state of iron under core conditions of large rocky exoplanets. Nat Astron 2, 452–458 (2018). https://doi.org/10.1038/s41550-018-0437-9

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