Abstract
Although usually considered as a technique for predicting electron states in dense plasmas, atom-in-jellium calculations can be used to predict the mean displacement of the ion from its equilibrium position in colder matter, as a function of compression and temperature. The Lindemann criterion of a critical displacement for melting can then be employed to predict the melt locus, normalizing for instance to the observed melt temperature or to more direct simulations such as molecular dynamics (MD). This approach reproduces the high pressure melting behavior of Al as calculated using the Lindemann model and thermal vibrations in the solid. Applied to Fe, we find that it reproduces the limited-range melt locus of a multiphase equation of state (EOS) and the results of ab initio MD simulations, and agrees less well with a Lindemann construction using an older EOS. The resulting melt locus lies significantly above the older melt locus for pressures above 1.5\,TPa, but is closer to recent ab initio MD results and extrapolations of an analytic fit to them. This study confirms the importance of core freezing in massive exoplanets, predicting that a slightly smaller range of exoplanets than previously assessed would be likely to exhibit dynamo generation of magnetic fields by convection in the liquid portion of the core.
Highlights
Thousands of exoplanets have been discovered [1], most around stars of different types than the sun and with orbits and mean mass density of a much wider variety than the planets of the solar system
This depends on the circumstances of each particular exoplanet, including its composition—influencing the specific Fe alloys in the core as well as the proportion of silicates to Fe—and history, which depends on the type of star it orbits and interactions with other exoplanets in the system, but the relevent material physics property is the melt curve of Fe
The procedure used here for calculating the melt curve is significantly different than previous approaches: rather than integrating an equation involving the ion-thermal Grüneisen parameter, the mean amplitude of vibrations used in computing the Debye frequency was used directly to determine the melt curve with no integration required and, no accumulation of error with increasing compression
Summary
Thousands of exoplanets have been discovered [1], most around stars of different types than the sun and with orbits and mean mass density of a much wider variety than the planets of the solar system. Recent QMD and path-integral Monte Carlo results have indicated that the simpler approach of calculating the electron states for a single atom in a spherical cavity within a uniform charge density of ions and electrons, representing the surrounding atoms, reproduces their more rigorous EOS for dense plasmas [28,29] This atom-in-jellium approach [30] was developed originally to predict the electron-thermal energy of matter at high temperatures and compressions [21] as an advance over the primitive electronic models neglecting any treatment of shell structure as in Thomas-Fermi and related approaches [31].
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