Isentropic compression of hydrogen: Probing conditions deep in planetary interiors

Abstract

We perform ab initio calculations for the equation of state of dense liquid hydrogen and deuterium using quantum molecular dynamics simulations based on finite-temperature density functional theory. This extensive data set allows us to determine specific density-temperature-pressure tracks such as the cold curve, precompressed and principal Hugoniot curves, and isentropes which are essential for the analysis and interpretation of highpressure experiments. In this study we focus on conditions probed by recent quasi-isentropic shock compression experiments that have reached a so-far unprecedented 108-fold compression of gaseous deuterium. As these states of matter are relevant for the deep interior of Jupiter-like exoplanets we simultaneously give predictions for their isentropes.

Frontiers and Challenges in Warm Dense Matter

“…The orange curve is almost identical with the principal Hugoniot starting at 20 K and 0.0855 g/cm 3 for which we show data (diamonds) [111]. Solid and broken lines are DFT-MD results [120] circles [117] and diamonds [111]) and Hugoniot curves for precompressed states of deuterium (blue and green circles [117]) are shown as well as a point representing a 108-fold compression of gaseous deuterium [119]. The DFT-MD Hugoniot curves for different initial conditions fixed by the experiment are derived from our ab initio EOS data [120] which coincide with another ab initio data set [84].…”

“…4.1 with a given EOS. We calculate the compression paths of deuterium starting from an initial temperature of 283 K and a density of 0.04 g/cm 3 [119] using our DFT-MD data [120]. For the measured compression ratio we expect a final pressure of 13 Mbar at 1,500 K, significantly lower than the predicted 18 Mbar at 3,500 K as derived from a semi-empirical EOS used in the hydrocode.…”

“…Solid and broken lines are DFT-MD results [120] circles [117] and diamonds [111]) and Hugoniot curves for precompressed states of deuterium (blue and green circles [117]) are shown as well as a point representing a 108-fold compression of gaseous deuterium [119]. The DFT-MD Hugoniot curves for different initial conditions fixed by the experiment are derived from our ab initio EOS data [120] which coincide with another ab initio data set [84]. Both reproduce the experimental pressures very well while they underestimate the temperature onset of dissociation slightly [117].…”

Comparing Jupiter interior structure models to Juno gravity measurements and the role of a dilute core

“…For comparison, we consider models using the ab initio equations of state of hydrogen and helium calculated by Becker et al [] (REOS3) with the procedure for estimating the entropy described by Miguel et al []. Finally, we also consider models using the SCvH EOS through the entire pressure range of the planet.…”

“…Significant progress has been made in understanding hydrogen-helium mixtures at planetary conditions [Saumon et al, 1995;Saumon and Guillot, 2004;Vorberger et al, 2007;Militzer et al, 2008;Fortney and Nettelmann, 2010;Nettelmann et al, 2012;Militzer, 2013;Becker et al, 2013;Militzer et al, 2016], but interior model predictions are still sensitive to the hydrogen-helium equation of state used Miguel et al, 2016]. In section 2.1 we describe the derivation of barotropes from a hydrogen-helium equation of state based on ab initio materials simulations [Militzer, 2013;Hubbard and Militzer, 2016], make comparisons to other equations of states, and consider simple perturbations to better understand their effect on the models.…”