Free-energy model for fluid helium at high density

Abstract

We present a semi-analytical free-energy model aimed at characterizing the thermodynamic properties of dense fluid helium, from the low-density atomic phase to the high-density fully ionized regime. The model is based on a free-energy minimization method and includes various different contributions representative of the correlations between atomic and ionic species and electrons. This model allows the computation of the thermodynamic properties of dense helium over an extended range of density and temperature and leads to the computation of the phase diagram of dense fluid helium, with its various temperature and pressure ionization contours. One of the predictions of the model is that pressure ionization occurs abruptly at ρ ∼ > 10 g cm −3 , i.e. P ∼ > 20 Mbar, from atomic helium He to fully ionized helium He 2+ , or at least to a strongly ionized state, without He + stage, except at high enough temperature for temperature ionization to become dominant. These predictions and this phase diagram provide a guide for future dynamical experiments or numerical first-principle calculations aimed at studying the properties of helium at very high density, in particular its metallization. Indeed, the characterization of the helium phase diagram bears important consequences for the thermodynamic, magnetic and transport properties of cool and dense astrophysical objects, among which the solar and the numerous recently discovered extrasolar giant planets.

Fluid helium at conditions of giant planetary interiors

“…The value of ␥ decreases upon compression up to the density of 13 g cm Ϫ3 and then begins to increase at higher densities. In comparison, a plasma model (22) and the He equation of state from the SESAME tables (23) predict large oscillations in the value of ␥ associated with pressure-induced ionization transitions; these oscillations are not found in our study. In the plasma or ''chemical'' picture (22) the fluid is viewed as a collection of electrons, atoms, and singly and doubly charged ions with internal energy levels that are assumed to be unperturbed by interactions with surrounding particles.…”

“…The influence of temperature on the electronic structure is also illustrated by the carrier concentration, which increases with increasing pressure and increasing temperature, primarily due to closing of the energy gap. We predict that experimental measurements along the 15-fold precompressed Hugoniot will be particularly revealing: requiring an initial (precompressed) pressure of 1 Mbar at ambient temperature, this Hugoniot includes pressure-temperature conditions at which our results differ significantly from those of the plasma model (22), and the nonmetal-to-metal transition should be experimentally detectable via optical absorption and reflectance measurements.…”

“…The magnetic diffusivity ϭ 1/ 0 , where is the electrical conductivity and 0 the magnetic permeability, controls the free-decay time of the magnetic field; it also controls the power of the field and its form, whether it be dipolar or multipolar, via the dimensionless magnetic Ekman number E ϭ /⍀D 2 and magnetic Reynolds number Rm ϭ u/ D, where ⍀ is the rotation rate, D is depth of (41)]. Dotted line shows the difference in density at 20,000 K between our calculations and the plasma model (22). Comparison with LAPW calculations show that PAW is accurate to at least 300 Mbar, whereas at 1 Gbar, PAW overestimates the pressure by 10%.…”

First-Principles Studies of the Metallization and the Equation of State of Solid Helium

“…Metallic solid helium is expected to be present in the outer layers of white dwarfs (WD) [3]. After the initial star has exhausted all its nuclear fuel, it sheds its outer layer and leaves behind a dense carbon-oxygen core of the size of the earth that is surrounded by an envelope of pure helium, hydrogen, or a mixture.…”

“…Most WD models rely on semi-analytical descriptions in the chemical picture [3] where one treats helium as a collection of stable atoms, ions, and free electrons interacting via approximate pair potentials. While such approaches work well at low density, they cannot describe the complex interactions in a very dense system, and a more fundamental description is required instead.…”