Mass-radius relationships for exoplanets

For planets other than Earth, interpretation of the composition and structure depends largely on comparing the mass and radius with the composition expected given their distance from the parent star. The composition implies a mass-radius relation which relies heavily on equations of state calculated from electronic structure theory and measured experimentally on Earth. We lay out a method for deriving and testing equations of state, and deduce mass-radius and mass-pressure relations for key materials whose equation of state is reasonably well established, and for differentiated Fe/rock. We find that variations in the equation of state, such as may arise when extrapolating from low pressure data, can have significant effects on predicted mass- radius relations, and on planetary pressure profiles. The relations are compared with the observed masses and radii of planets and exoplanets. Kepler-10b is apparently 'Earth- like,' likely with a proportionately larger core than Earth's, nominally 2/3 of the mass of the planet. CoRoT-7b is consistent with a rocky mantle over an Fe-based core which is likely to be proportionately smaller than Earth's. GJ 1214b lies between the mass-radius curves for H2O and CH4, suggesting an 'icy' composition with a relatively large core or a relatively large proportion of H2O. CoRoT-2b is less dense than the hydrogen relation, which could be explained by an anomalously high degree of heating or by higher than assumed atmospheric opacity. HAT-P-2b is slightly denser than the mass-radius relation for hydrogen, suggesting the presence of a significant amount of matter of higher atomic number. CoRoT-3b lies close to the hydrogen relation. The pressure at the center of Kepler-10b is 1.5+1.2-1.0 TPa. The central pressure in CoRoT-7b is probably close to 0.8TPa, though may be up to 2TPa.Comment: Added more recent exoplanets. Tidied text and references. Added extra "rock" compositions. Responded to referee comment

Viscosity coefficient of dense fluid hydrogen

Evaluations of the viscosity of the dense hydrogen are presented in a region whese dissociation plays a major role. The viscosity is computed by a classical molecular dynamics model where the fraction of dissociated hydrogen is a priori given by the Ross model. A universal fit is given, based on scaling laws of inverse power potential

Theoretical and experimental refraction index of shock compressed and pre-compressed water in the megabar pressure range

The refraction index of water at megabar pressures was calculated ab initio with the quantum molecular dynamics (QMD) package ABINIT using the projector augmented (PAW) formalism. Calculations were compared to experimental results obtained by laser-driven shocks on water in standard conditions and on water samples statically precompressed at ${\approx}10\ \text{kBar}$ . The refraction index was measured in transparent and opaque states of water using a VISAR diagnostics. We also modelled the data using an extended Lorentz-Drude model. At high compressions, a strong increase of the refraction index is observed both in experimental results and in the theoretical calculations, which is an indication of water approaching band gap closure

Molecular dynamics simulations of shock compressed heterogeneous materials. II. The graphite/diamond transition case for astrophysics applications

We present a series of molecular dynamics simulations of the shock compression of copper matrices containing a single graphite inclusion: these model systems can be related to some specific carbon-rich rocks which, after a meteoritic impact, are found to contain small fractions of nanodiamonds embedded in graphite in the vicinity of high impedance minerals. We show that the graphite to diamond transformation occurs readily for nanometer-sized graphite inclusions, via a shock accumulation process, provided the pressure threshold of the bulk graphite/diamond transition is overcome, independently of the shape or size of the inclusion. Although high diamond yields (similar to 80%) are found after a few picoseconds in all cases, the transition is non-isotropic and depends substantially on the relative orientation of the graphite stack with respect to the shock propagation, leading to distinct nucleation processes and size-distributions of the diamond grains. A substantial regraphitization process occurs upon release and only inclusions with favorable orientations likely lead to the preservation of a fraction of this diamond phase. These results agree qualitatively well with the recent experimental observations of meteoritic impact samples. (C) 2015 AIP Publishing LLC