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Register a new userA new equation of state for dense hydrogen-helium mixtures II: taking into account hydrogen-helium interactions
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Authors
Gilles Chabrier
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In a recent paper (Chabrier et al. 2019), we have derived a new equation of state (EOS) for dense hydrogen/helium mixtures which covers the temperature-density domain from solar-type stars to brown dwarfs and gaseous planets. This EOS is based on the so-called additive volume law and thus does not take into account the interactions between the hydrogen and helium species. In the present paper, we go beyond these calculations by taking into account H/He interactions, derived from quantum molecular dynamics simulations. These interactions, which eventually lead to H/He phase separation, become important at low temperature and high density, in the domain of brown dwarfs and giant planets. The tables of this new EOS are made publicly available.
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We present a new equation of state (EOS) for dense hydrogen/helium mixtures which covers a range of densities from $10^{-8}$ to $10^6$ g.cm$^{-3}$, pressures from $10^{-9}$ to $10^{13}$ GPa and temperatures from $10^{2}$ to $10^{8}$ K. The calculations combine the EOS of Saumon, Chabrier & vanHorn (1995) in the low density, low temperature molecular/atomic domain, the EOS of Chabrier & Potekhin (1998) in the high-density, high-temperature fully ionized domain, the limits of which differ for H and He, and ab initio quantum molecular dynamics (QMD) calculations in the intermediate density and temperature regime, characteristic of pressure dissociation and ionization. The EOS for the H/He mixture is based on the so-called additive volume law and thus does not take into account the interactions between the two species. A major improvement of the present calculations over existing ones is that we calculate the entropy over the entire density-temperature domain, a necessary quantity for stellar or planetary evolution calculations. The EOS results are compared with existing experimental data, namely Hugoniot shock experiments for pure H and He, and with first principle numerical simulations for both the single elements and the mixture. This new EOS covers a wide range of physical and astrophysical conditions, from jovian planets to solar-type stars, and recovers the existing relativistic EOS at very high densities, in the domains of white dwarfs and neutron stars.
Iglesias et al. (2002) showed that the Rayleigh scattering from helium atoms decreases by collective effects in the atmospheres of cool white dwarf stars. Their study is here extended to consider an accurate evaluation of the atomic polarizability and the density effects involved in the Rayleigh cross section over a wide density-temperature region. The dynamic dipole polarizability of helium atoms in the ground state is determinated with the oscillator-strength distribution approach. The spectral density of oscillator strength considered includes most significant single and doubly excited transitions to discrete and continuum energies. Static and dynamic polarizability results are confronted with experiments and other theoretical evaluations shown a very good agreement. In addition, the refractive index of helium is evaluated with the Lorentz-Lorenz equation and shows a satisfactory agreement with the most recent experiments. The effect of spatial correlation of atoms on the Rayleigh scattering is calculated with Monte Carlo simulations and effective energy potentials that represent the particle interactions, covering fluid densities between 0.005 and a few g/cm$^3$ and temperatures between $1000$ K and $15000$ K. We provide analytical fits from which the Rayleigh cross section of fluid helium can be easily calculated at wavelength $lambda>505.35$ AA. Collision-induced light scattering was estimated to be the dominant scattering process at densities greater than 1-2 g/cm$^3$ depending on the temperature.
We present new multi-band (UBVI) time-series data of helium burning variables in the Carina dwarf spheroidal galaxy. The current sample includes 92 RR Lyrae-six of them are new identifications-and 20 Anomalous Cepheids, one of which is new identification. The analysis of the Bailey diagram shows that the luminosity amplitude of the first overtone component in double-mode variables is located along the long-period tail of regular first overtone variables, while the fundamental component is located along the short-period tale of regular fundamental variables. This evidence further supports the transitional nature of these objects. Moreover, the distribution of Carina double-mode variables in the Petersen diagram (P_1/P_0 vs P_0) is similar to metal-poor globulars (M15, M68), to the dwarf spheroidal Draco and to the Galactic Halo. This suggests that the Carina old stellar population is metal-poor and affected by a small spread in metallicity. We use trigonometric parallaxes for five field RR Lyrae stars to provide an independent estimate of the Carina distance using the observed reddening free Period--Wesenheit [PW, (BV)] relation. Theory and observations indicate that this diagnostic is independent of metallicity. We found a true distance modulus of mu=20.01pm0.02 (standard error of the mean) pm0.05 (standard deviation) mag. We also provided independent estimates of the Carina true distance modulus using four predicted PW relations (BV, BI, VI, BVI) and we found: mu=(20.08pm0.007pm0.07) mag, mu=(20.06pm0.006pm0.06) mag, mu=(20.07pm0.008pm0.08) mag and mu=(20.06pm0.006pm0.06) mag. Finally, we identified more than 100 new SX Phoenicis stars that together with those already known in the literature (340) make Carina a fundamental laboratory to constrain the evolutionary and pulsation properties of these transitional variables.
Density Functional Theory (DFT) calculations show a weak interaction between hydrogen and helium in iron, in contrast to previous reports of a strong trapping of hydrogen at helium. The strong preference of He and H to occupy regions with low electronic density (such as vacancies) explains this discrepancy, with vacancy-He and vacancy-H binding forces concealing the repulsive interaction between He and H. Furthermore, Rate Theory simulations based on our DFT-calculated V$_n$He$_m$H$_p$ cluster energetics predict, as it is observed in some experiments, that synergetic effects could be expected between H and He in iron under irradiation.
We calculate the equation of state of dense hydrogen within the chemical picture. Fluid variational theory is generalized for a multi-component system of molecules, atoms, electrons, and protons. Chemical equilibrium is supposed for the reactions dissociation and ionization. We identify the region of thermodynamic instability which is related to the plasma phase transition. The reflectivity is calculated along the Hugoniot curve and compared with experimental results. The equation-of-state data is used to calculate the pressure and temperature profiles for the interior of Jupiter.
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