Atom-in-jellium equations of state and melt curves in the white dwarf regime

TL;DR

This study develops comprehensive equations of state and melt curves for elements relevant to white dwarf stars using atom-in-jellium calculations, revealing insights into their thermodynamic behavior across a wide density and energy range.

Contribution

It introduces the widest range of self-consistent electronic shell structure calculations for white dwarf elements and applies a generalized Lindemann criterion to estimate melt curves.

Findings

Elements of the same atomic weight to atomic number ratio asymptote to the same T=0 isotherm.

The melt curve model reproduces previous thermodynamic studies for the one component plasma.

For some elements, the melt model provides a reliable estimate of the melt curve across various conditions.

Abstract

Atom-in-jellium calculations of the electron states, and perturbative calculations of the Einstein frequency, were used to construct equations of state (EOS) from around $10^{-5}$ to $10^7$g/cm$^3$ and $10^{-4}$ to $10^{6}$eV for elements relevant to white dwarf (WD) stars. This is the widest range reported for self-consistent electronic shell structure calculations. Elements of the same ratio of atomic weight to atomic number were predicted to asymptote to the same $T=0$ isotherm, suggesting that, contrary to recent studies of the crystallization of WDs, the amount of gravitational energy that could be released by separation of oxygen and carbon is small. A generalized Lindemann criterion based on the amplitude of the ion-thermal oscillations calculated using atom-in-jellium theory, previously used to extrapolate melt curves for metals, was found to reproduce previous thermodynamic studies of the melt curve of the one component plasma with a choice of vibration amplitude consistent with low pressure results. For elements for which low pressure melting satisfies the same amplitude criterion, such as Al, this melt model thus gives a likely estimate of the melt curve over the full range of normal electronic matter; for the other elements, it provides a useful constraint on the melt locus.